# 10. Silicon photonics enhanced with functional oxides: new opportunities

S Abel and J Fompeyrine

IBM Research GmbH, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland

**Status.** Photonics is the backbone for high-speed internet across the world. In recent years, the need for bandwidth in servers drove the development towards a tighter integration of electro-optical systems. Silicon photonics is becoming the leading baseline technology for integrated optics, as CMOS was for integrated microelectronics. The key advantages of silicon photonics are low fabrication costs and reduced circuits' footprint, enabled by the large contrast in refractive index between SiO$_2$ and Si. Alike CMOS, one can envision new materials as critical add-ons to the future of silicon photonics. Such materials will either enhance device performances, or enable functionalities that do not exist in silicon. For long range data communication, LiNbO$_3$ modulators are the standard technology, albeit provided as discrete components. They demonstrate that functional oxide materials are already today crucial in photonics. Besides numerous properties that are appealing for real-world applications in the electrical domain, many oxides have also interesting optical characteristics. Their refractive indices can be altered by applying an electric, magnetic, thermal or mechanical strain field, as summarized in figure 16. This figure illustrates also that modulation, switching or optical isolation are essential functions when transceiving data between or on chip. In the following sections we present a short review of the state of the art for silicon photonics enhanced by functional oxides highlighting that optical properties in oxides can be mapped to specific functionalities in integrated optics.

**Current and future challenges.** As of today, most of the challenges are related to the growth of materials with the appropriate optical properties, and to the methods required to integrate such materials with the silicon photonics baseline technology. For most of the properties highlighted in figure 16, the relevant optical characteristics are often tightly related to structural features. The Pockels effect describes for example the change of refractive index $\Delta n$ for a material upon application of an electric field $E$, $\Delta n(E) \propto r \times E$. The Pockels coefficient 'r' vanishes for centro-symmetric crystals, and this effect is therefore only non-zero in materials whose crystalline structure is non-centrosymmetric, such as LiNbO$_3$ or BaTiO$_3$. Giant thermo-optic effects are also present in oxides that exhibit metal to insulator transition as a function of temperature. A large change in the real and imaginary part of the refractive index can be observed when the transition is crossed, such as in VO$_2$ [145]. The transition is here directly correlated to a structural transition to a rutile phase, and can also be strongly impacted by lattice distortions [146], hence by the mechanical strain field in the films. Finally, magneto-optic effects can be exploited in materials with a strong Verdet constant, provided the crystal structure does not favor mixed valences that could translate in high optical losses. Growing

thin films with the required structural and optical properties is therefore a challenging task, and an intense research is focusing on controlling intrinsic materials features. VO$_2$ can for example be grown within a wide oxidation range, and its thermo-optical properties are dominated by the oxidation state, as well as by the dopants [147]. With the advent of new generic techniques to grow epitaxial perovskites on silicon, high quality BaTiO$_3$ films can be grown on silicon and exhibit a strong Pockels effect [148]. In this case the epitaxial strain has a strong impact on the direction of the ferroelectric polarization, and the optical device design must take into account the microstructure [149]. For the integration of functional oxides with silicon photonics, two methods are explored, each having its specific challenges. First, direct growth on silicon can first be employed, using standard deposition methods. Besides the structural characteristics described previously, the films must also result in very low optical propagation losses when processed in waveguides. Recent reports have pointed out that propagation losses in BaTiO$_3$ grown on silicon can be substantially reduced [150], with values of a few dB/cm within reach. Direct wafer bonding is however another promising approach, as it enables to optimize the oxide layer independently from integration aspects—including for its optical losses. This method has been successfully used to integrate LiNbO$_3$ thin films onto silicon photonics circuits [151], as well as for magneto-optical devices based on garnets [152].

**Advances in science and technology to meet challenges.** Once integrated in silicon, devices can be fabricated that exploit the oxide properties in silicon photonics devices. In the recent years, the potential of this approach has been demonstrated in various device types, as illustrated in figure 17. The phase transition of VO$_2$ has been utilized in ultra-compact optical switches such as ring resonators with a diameter of 3 µm [153]. Broadband absorption switches have been demonstrated as well for 0.5 µm length, using the variation of the complex part of the refractive index in VO$_2$. Such VO$_2$/Si hybrid photonic devices are typically designed as standard silicon photonic structures that are locally covered with a thin VO$_2$ layer. The interaction length is then restricted to a few µm, so that the insertion losses of the devices remain low, e.g. <2 dB. Recently, the demonstration of an electrically induced metal-to-insulator transition has been reported [154], opening the path to fully integrated electro-optical switches using VO$_2$. Switching and modulation in active BaTiO$_3$ devices has been also recently reported. Passive and active ring resonators and Mach–Zehnder modulators with a bandwidth of up to 5 GHz and 0.8 GHz, respectively, have been demonstrated [155, 156]. Remarkably, the corresponding effective Pockels coefficient in the BaTiO$_3$ layer is almost an order of magnitude higher than in LiNbO$_3$ modulators. Besides applications for high-speed switches, optical devices might also exploit the Pockels effect in very efficient, low-speed tuning elements which are necessary in highly scaled, resonant silicon photonic circuits. In [155] the resonance of a BaTiO$_3$-based race track resonator could for example be tuned with only 4 µW nm$^{-1}$. One of the current challenges in this field is to disentangle the contribution of physical effects intermixed with the Pockels
# 10. Silicon photonics enhanced with functional oxides: new opportunities

S Abel and J Fompeyrine

IBM Research GmbH, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland

**Status.** Photonics is the backbone for high-speed internet across the world. In recent years, the need for bandwidth in servers drove the development towards a tighter integration of electro-optical systems. Silicon photonics is becoming the leading baseline technology for integrated optics, as CMOS was for integrated microelectronics. The key advantages of silicon photonics are low fabrication costs and reduced circuits' footprint, enabled by the large contrast in refractive index between SiO$_2$ and Si. Alike CMOS, one can envision new materials as critical add-ons to the future of silicon photonics. Such materials will either enhance device performances, or enable functionalities that do not exist in silicon. For long range data communication, LiNbO$_3$ modulators are the standard technology, albeit provided as discrete components. They demonstrate that functional oxide materials are already today crucial in photonics. Besides numerous properties that are appealing for real-world applications in the electrical domain, many oxides have also interesting optical characteristics. Their refractive indices can be altered by applying an electric, magnetic, thermal or mechanical strain field, as summarized in figure 16. This figure illustrates also that modulation, switching or optical isolation are essential functions when transceiving data between or on chip. In the following sections we present a short review of the state of the art for silicon photonics enhanced by functional oxides highlighting that optical properties in oxides can be mapped to specific functionalities in integrated optics.

**Current and future challenges.** As of today, most of the challenges are related to the growth of materials with the appropriate optical properties, and to the methods required to integrate such materials with the silicon photonics baseline technology. For most of the properties highlighted in figure 16, the relevant optical characteristics are often tightly related to structural features. The Pockels effect describes for example the change of refractive index $\Delta n$ for a material upon application of an electric field $E$, $\Delta n(E) \propto r \times E$. The Pockels coefficient 'r' vanishes for centro-symmetric crystals, and this effect is therefore only non-zero in materials whose crystalline structure is non-centrosymmetric, such as LiNbO$_3$ or BaTiO$_3$. Giant thermo-optic effects are also present in oxides that exhibit metal to insulator transition as a function of temperature. A large change in the real and imaginary part of the refractive index can be observed when the transition is crossed, such as in VO$_2$ [145]. The transition is here directly correlated to a structural transition to a rutile phase, and can also be strongly impacted by lattice distortions [146], hence by the mechanical strain field in the films. Finally, magneto-optic effects can be exploited in materials with a strong Verdet constant, provided the crystal structure does not favor mixed valences that could translate in high optical losses. Growing

thin films with the required structural and optical properties is therefore a challenging task, and an intense research is focusing on controlling intrinsic materials features. VO$_2$ can for example be grown within a wide oxidation range, and its thermo-optical properties are dominated by the oxidation state, as well as by the dopants [147]. With the advent of new generic techniques to grow epitaxial perovskites on silicon, high quality BaTiO$_3$ films can be grown on silicon and exhibit a strong Pockels effect [148]. In this case the epitaxial strain has a strong impact on the direction of the ferroelectric polarization, and the optical device design must take into account the microstructure [149]. For the integration of functional oxides with silicon photonics, two methods are explored, each having its specific challenges. First, direct growth on silicon can first be employed, using standard deposition methods. Besides the structural characteristics described previously, the films must also result in very low optical propagation losses when processed in waveguides. Recent reports have pointed out that propagation losses in BaTiO$_3$ grown on silicon can be substantially reduced [150], with values of a few dB/cm within reach. Direct wafer bonding is however another promising approach, as it enables to optimize the oxide layer independently from integration aspects—including for its optical losses. This method has been successfully used to integrate LiNbO$_3$ thin films onto silicon photonics circuits [151], as well as for magneto-optical devices based on garnets [152].

**Advances in science and technology to meet challenges.** Once integrated in silicon, devices can be fabricated that exploit the oxide properties in silicon photonics devices. In the recent years, the potential of this approach has been demonstrated in various device types, as illustrated in figure 17. The phase transition of VO$_2$ has been utilized in ultra-compact optical switches such as ring resonators with a diameter of 3 µm [153]. Broadband absorption switches have been demonstrated as well for 0.5 µm length, using the variation of the complex part of the refractive index in VO$_2$. Such VO$_2$/Si hybrid photonic devices are typically designed as standard silicon photonic structures that are locally covered with a thin VO$_2$ layer. The interaction length is then restricted to a few µm, so that the insertion losses of the devices remain low, e.g. <2 dB. Recently, the demonstration of an electrically induced metal-to-insulator transition has been reported [154], opening the path to fully integrated electro-optical switches using VO$_2$. Switching and modulation in active BaTiO$_3$ devices has been also recently reported. Passive and active ring resonators and Mach–Zehnder modulators with a bandwidth of up to 5 GHz and 0.8 GHz, respectively, have been demonstrated [155, 156]. Remarkably, the corresponding effective Pockels coefficient in the BaTiO$_3$ layer is almost an order of magnitude higher than in LiNbO$_3$ modulators. Besides applications for high-speed switches, optical devices might also exploit the Pockels effect in very efficient, low-speed tuning elements which are necessary in highly scaled, resonant silicon photonic circuits. In [155] the resonance of a BaTiO$_3$-based race track resonator could for example be tuned with only 4 µW nm$^{-1}$. One of the current challenges in this field is to disentangle the contribution of physical effects intermixed with the Pockels
<figure><img src="image_21.png" /><figcaption>**Figure 16.** (Left) Optical properties present in functional oxides that can potentially be exploited in the (upper right) optical data transmission chain implemented in (lower right) integrated photonics.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Figure 17.** Summary of device demonstration for (a) BaTiO₃-based low-power tuning device, (b) BaTiO₃-based high speed modulator (adapted from [156] with permission of OSA, The Optical Society), VO₂-based electro-optic switch (adapted from [154] with permission of OSA, The Optical Society), YIG-based optical isolator (adapted from [152] with permission of NPG).</figcaption></figure>

effect, which is necessary to ultimately boost the bandwidth of the devices to 40 GHz and higher. Finally, integrated devices exploiting non-reciprocal light transmission have been also demonstrated [152]. Direct growth as well as wafer bonding on silicon waveguides have been achieved, mainly using garnets based on yttrium and iron. Although the figure of merit are moderate and quite strongly impacted by high propagation losses, this device demonstration nicely illustrates how the

introduction of oxide-based materials enable functionalities that are complex to implement in silicon only.

*Concluding remarks.* Together with the advent of integrated silicon photonics, the need to expand CMOS technology beyond its limit helped new deposition and integration techniques to emerge. This is in particular true for the science and technology of functional oxides: seminal works have been
<figure><img src="image_22.png" /><figcaption>**Figure 16.** (Left) Optical properties present in functional oxides that can potentially be exploited in the (upper right) optical data transmission chain implemented in (lower right) integrated photonics.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>**Figure 17.** Summary of device demonstration for (a) BaTiO₃-based low-power tuning device, (b) BaTiO₃-based high speed modulator (adapted from [156] with permission of OSA, The Optical Society), VO₂-based electro-optic switch (adapted from [154] with permission of OSA, The Optical Society), YIG-based optical isolator (adapted from [152] with permission of NPG).</figcaption></figure>

effect, which is necessary to ultimately boost the bandwidth of the devices to 40 GHz and higher. Finally, integrated devices exploiting non-reciprocal light transmission have been also demonstrated [152]. Direct growth as well as wafer bonding on silicon waveguides have been achieved, mainly using garnets based on yttrium and iron. Although the figure of merit are moderate and quite strongly impacted by high propagation losses, this device demonstration nicely illustrates how the

introduction of oxide-based materials enable functionalities that are complex to implement in silicon only.

**Concluding remarks.** Together with the advent of integrated silicon photonics, the need to expand CMOS technology beyond its limit helped new deposition and integration techniques to emerge. This is in particular true for the science and technology of functional oxides: seminal works have been
reported in the last years, where the unique optical properties
of such materials are exploited in devices co-integrated within
a silicon photonic platform. The primary field of applications
remains centered on data communications. Nevertheless,

having a technology like silicon photonics cross-fertilized
with novel materials concepts, new research directions might
arise in applications as different as quantum photonics, brain-
inspired computing, or high-performance integrated sensors.
reported in the last years, where the unique optical properties
of such materials are exploited in devices co-integrated within
a silicon photonic platform. The primary field of applications
remains centered on data communications. Nevertheless,

having a technology like silicon photonics cross-fertilized
with novel materials concepts, new research directions might
arise in applications as different as quantum photonics, brain-
inspired computing, or high-performance integrated sensors.
# 11. New oxide microcavities applications: from polariton lasers to fundamental physics at room-temperature

J Zuniga-Perez

CRHEA-CNRS, Rue Bernard Gregory, Sophia-Antipolis,
06560 Valbonne, France

**Status.** If an emitter is embedded within an optical cavity and their interaction strength becomes larger than the interaction strength of the emitter and cavity modes with their respective environments, then the emitter-cavity system will enter the strong-coupling regime. The system can be no longer described in terms of independent emitter and cavity photon states, but rather in terms of mixed states: microcavity polaritons (polaritons, in the following). The recent interest in these quasi-particles arises from the combination of a particular energy dispersion, with a minimum at $k_{parallel} = 0$, and the bosonic character of polaritons, which behave as bosons as far as excitons do so (i.e. below the Mott density). These two properties allowed the observation of Bose-Einstein condensation in a solid-state system, and the fabrication of a new type of lasers in which the gain mechanism is no longer stimulated photon emission but polariton scattering stimulated by final state occupancy. Interestingly, the operation temperature of these polariton lasers is limited by the temperature stability of the excitons. In this context, ZnO appears very appealing due to its 60 meV exciton binding energy, which assures exciton stability, and small Bohr radius <2 nm, which assures exciton bosonic behaviour up to large particle densities.

In recent years, the development of ZnO-based microcavities has enabled polariton lasing in planar microcavities, first at low temperature [157] and then at room-temperature [158], as well as the observation of polariton parametric scattering at room-temperature in ZnO microwires [159] (see figure 18). Furthermore, the large exciton-cavity photon interaction strength in some ZnO microcavities, characterized by Rabi energies in excess of 200 meV, has allowed to explore new types of condensates with excitonic fractions attaining 97% [160, 161], which are in general not accessible in other materials systems.

**Current and future challenges.** In spite of the recent realizations [158, 160], including the first hints for weak-lasing within a condensate of interacting bosons [161], ZnO is mostly considered as a material for applied polaritonics rather than for fundamental physics. There are probably two main reasons for this:

1. The polariton condensate ‘checklist’ has not been yet fully provided for the ZnO system: (i) extended spatial coherence—i.e. $g^1(r)$—has been scarcely measured [160]; (ii) two-threshold behavior has never been reported; (iii) other footprints, such as the spontaneous spin symmetry breaking, have not been reported either. While there are already sufficient facts proving the polariton nature of the observed nonlinear emission [157–161], the

<figure><img src="image_23.png" /><figcaption>**Figure 18.** Scanning electron microscopy images of the two typical ZnO-based microcavities: planar, on the left, and microwire-based, on the right.</figcaption></figure>

aforementioned measurements in one and the same ZnO microcavity would close any further debate.

2. The fabrication of planar ZnO microcavities is much more complex and less controlled than that of GaAs-based microcavities, mainly due to the lack of ideal Bragg reflectors [157, 158, 162]. One might consider this argument equally valid for fundamental and for applied physics; however, the room-temperature operation argument is strong enough to prevail when devices are considered.

A most attractive option would be to combine fundamental and applied physics in existing ZnO microcavities. Indeed, many of these cavities, especially microwires, are multimode; therein, exciton resonances are coupled to several cavity modes, resulting in a ladder of polariton branches [158–161]. These cavities are, as illustrated in figure 19, perfect candidates for achieving parametric processes at room-temperature [159, 163] (e.g. for generation of entangled photons).

To exploit these parametric processes it would be necessary to develop adapted spectroscopic techniques, which are common at telecommunication wavelengths but rare in the UV, as well as to improve microcavity fabrication. These advances should be accompanied by the possibility of polariton condensates (and polariton) manipulation, not only optically but also electrically, which would open definitively the doors for practical polariton-based ZnO devices [164].

**Advances in science and technology to meet challenges.** In order to manipulate polaritons and polariton condensates, these should live as long as possible. Even if the last generation of planar ZnO microcavities display quality factors well above 1000 [158, 162], enabling to achieve polariton lasing at room-temperature, larger quality factors and more homogeneous photonic landscapes are necessary to ease polariton manipulation. If we refer to the more mature GaAs system, this means employing homoepitaxial ZnO-based distributed Bragg reflectors [165] with a large number of pairs (typically larger than 30), due to a reduced refractive index contrast; alternatively, new techniques for cavity report onto dielectric mirrors [158] would be extremely challenging but very rich in
# 11. New oxide microcavities applications: from polariton lasers to fundamental physics at room-temperature

J Zuniga-Perez

CRHEA-CNRS, Rue Bernard Gregory, Sophia-Antipolis,
06560 Valbonne, France

**Status.** If an emitter is embedded within an optical cavity and their interaction strength becomes larger than the inter-action strength of the emitter and cavity modes with their respective environments, then the emitter-cavity system will enter the strong-coupling regime. The system can be no longer described in terms of independent emitter and cav-ity photon states, but rather in terms of mixed states: micro-cavity polaritons (polaritons, in the following). The recent interest in these quasi-particles arises from the combina-tion of a particular energy dispersion, with a minimum at $k_{parallel} = 0$, and the bosonic character of polaritons, which behave as bosons as far as excitons do so (i.e. below the Mott density). These two properties allowed the observation of Bose-Einstein condensation in a solid-state system, and the fabrication of a new type of lasers in which the gain mech-anism is no longer stimulated photon emission but polariton scattering stimulated by final state occupancy. Interestingly, the operation temperature of these polariton lasers is limited by the temperature stability of the excitons. In this context, ZnO appears very appealing due to its 60 meV exciton bind-ing energy, which assures exciton stability, and small Bohr radius <2 nm, which assures exciton bosonic behaviour up to large particle densities.

In recent years, the development of ZnO-based microcavities has enabled polariton lasing in planar microcavities, first at low temperature [157] and then at room-temperature [158], as well as the observation of polariton parametric scattering at room-temperature in ZnO microwires [159] (see figure 18). Furthermore, the large exciton-cavity photon interaction strength in some ZnO microcavities, characterized by Rabi energies in excess of 200 meV, has allowed to explore new types of condensates with excitonic fractions attaining 97% [160, 161], which are in general not accessible in other materials systems.

**Current and future challenges.** In spite of the recent real-izations [158, 160], including the first hints for weak-lasing within a condensate of interacting bosons [161], ZnO is mostly considered as a material for applied polaritonics rather than for fundamental physics. There are probably two main reasons for this:

1. The polariton condensate ‘checklist’ has not been yet fully provided for the ZnO system: (i) extended spatial coherence—i.e. $g^1(r)$—has been scarcely measured [160]; (ii) two-threshold behavior has never been reported; (iii) other footprints, such as the spontaneous spin symmetry breaking, have not been reported either. While there are already sufficient facts proving the polariton nature of the observed nonlinear emission [157–161], the

<figure><img src="image_24.png" /><figcaption>**Figure 18.** Scanning electron microscopy images of the two typical ZnO-based microcavities: planar, on the left, and microwire-based, on the right.</figcaption></figure>

aforementioned measurements in one and the same ZnO microcavity would close any further debate.

2. The fabrication of planar ZnO microcavities is much more complex and less controlled than that of GaAs-based microcavities, mainly due to the lack of ideal Bragg reflec-tors [157, 158, 162]. One might consider this argument equally valid for fundamental and for applied physics; however, the room-temperature operation argument is strong enough to prevail when devices are considered.

A most attractive option would be to combine fundamen-tal and applied physics in existing ZnO microcavities. Indeed, many of these cavities, especially microwires, are multimode; therein, exciton resonances are coupled to several cavity modes, resulting in a ladder of polariton branches [158–161]. These cavities are, as illustrated in figure 19, perfect candi-dates for achieving parametric processes at room-temperature [159, 163] (e.g. for generation of entangled photons).

To exploit these parametric processes it would be necessary to develop adapted spectroscopic techniques, which are com-mon at telecommunication wavelengths but rare in the UV, as well as to improve microcavity fabrication. These advances should be accompanied by the possibility of polariton con-densates (and polariton) manipulation, not only optically but also electrically, which would open definitively the doors for practical polariton-based ZnO devices [164].

**Advances in science and technology to meet challenges.** In order to manipulate polaritons and polariton condensates, these should live as long as possible. Even if the last genera-tion of planar ZnO microcavities display quality factors well above 1000 [158, 162], enabling to achieve polariton lasing at room-temperature, larger quality factors and more homo-geneous photonic landscapes are necessary to ease polariton manipulation. If we refer to the more mature GaAs system, this means employing homoepitaxial ZnO-based distributed Bragg reflectors [165] with a large number of pairs (typically larger than 30), due to a reduced refractive index contrast; alternatively, new techniques for cavity report onto dielectric mirrors [158] would be extremely challenging but very rich in
<figure><img src="image_24.png" /><figcaption>**Figure 19.** (a) Emission intensity below threshold measured at room-temperature along the thickness gradient in a fully-hybrid planar ZnO microcavity showing 4 lower polariton branches (the cavity thickness changes from $3\lambda/2$ to $3\lambda$). $\lambda$ is the wavelength corresponding to the excitonic resonance, shown as solid line. (b) Fourier-space photoluminescence mapping of a ZnO microwire cavity under four different pumping powers. Reproduced with permission from [159], copyright 2012 by the American Physical Society.</figcaption></figure>

terms of future possibilities, since the fabrication of the active region and of the mirror would become completely decoupled.

Direct electrical injection of ZnO polariton lasers is for the moment unrealistic because of the difficulties in achieving reliable and large enough *p*-type doping. In this sense, any progress in developing *p*-type oxides compatible with ZnO, in particular with a suitable band alignment, would be a real breakthrough that would have an enormous impact. On the other hand, electrical manipulation of polaritons does not need such *p*-type material: in this case, the technological difficulty lies in the fabrication of electrical contacts sufficiently

close to the microcavity active region without degrading its properties (neither the excitonic nor the photonic).

***Concluding remarks.*** The access to an unprecedented range of polaritons (from photonic to very massive ones) combined with room-temperature operation promise new discoveries and applications in ZnO-based polaritonics. Besides, new types of ZnO cavities increasing the richness of the topic can be already envisaged, either by extending the wavelength spectrum addressed by ZnO cavities [166] or by exploiting its piezoelectric character, which leads naturally to the field of cavity optomechanics.
<figure><img src="image_25.png" /><figcaption>**Figure 19.** (a) Emission intensity below threshold measured at room-temperature along the thickness gradient in a fully-hybrid planar ZnO microcavity showing 4 lower polariton branches (the cavity thickness changes from $3\lambda/2$ to $3\lambda$). $\lambda$ is the wavelength corresponding to the excitonic resonance, shown as solid line. (b) Fourier-space photoluminescence mapping of a ZnO microwire cavity under four different pumping powers. Reproduced with permission from [159], copyright 2012 by the American Physical Society.</figcaption></figure>

terms of future possibilities, since the fabrication of the active region and of the mirror would become completely decoupled.

Direct electrical injection of ZnO polariton lasers is for the moment unrealistic because of the difficulties in achieving reliable and large enough *p*-type doping. In this sense, any progress in developing *p*-type oxides compatible with ZnO, in particular with a suitable band alignment, would be a real breakthrough that would have an enormous impact. On the other hand, electrical manipulation of polaritons does not need such *p*-type material: in this case, the technological difficulty lies in the fabrication of electrical contacts sufficiently

close to the microcavity active region without degrading its properties (neither the excitonic nor the photonic).

***Concluding remarks.*** The access to an unprecedented range of polaritons (from photonic to very massive ones) combined with room-temperature operation promise new discoveries and applications in ZnO-based polaritonics. Besides, new types of ZnO cavities increasing the richness of the topic can be already envisaged, either by extending the wavelength spectrum addressed by ZnO cavities [166] or by exploiting its piezoelectric character, which leads naturally to the field of cavity optomechanics.
## 12. Multiferroic bismuth ferrite

R Ramesh

Departments of Materials Science & Engineering and Physics,
University of California, Berkeley, CA 94720, USA

**Status.** Complex oxides present a broad range of interesting functionalities, such as high temperature superconductivity, colossal magnetoresistance, (anti-) ferromagnetic, (anti-) ferroelectric, piezoelectric and more recently multiferroic properties. $BiFeO_3$ (BFO) is the only room temperature multiferroic (antiferromagnetic and ferroelectric) so far, which has attracted great interest and extensive investigation in the past decade. It has a rhombohedral unit cell, built with two distorted perovskite cells connected along a pseudocubic [111] direction [167, 168]. It is also a G-type antiferromagnet with Neél temperature of ~673 K [100] and a symmetry-allowed, small canted moment due to the Dzyaloshinskii–Moriya interaction [169]. The hybridization between the two 6s electrons in Bi [170] with surrounding oxygen ions leads to a large displacement of the Bi cations relative to the oxygen octahedral along the [111] direction with a Curie temperature of 1103 K and the spontaneous ferroelectric polarization of about 90 $\mu$C cm$^{-2}$ [171].

The synthesis of high quality epitaxial thin films through a variety of techniques (pulsed laser deposition (or laser MBE), sputtering, MBE, CVD) has already been well-established [172]. In thin films, both 71° and 109° domain walls are observed. Figure 20 shows the magneto-transport behavior of 109° domain walls, an atomic resolution image of which is shown in figure 20(a). Conducting atomic force microscopy (AFM) based measurements, figure 20(b), show that the walls are less resistive, (compared to the domain itself) typically by 2–3 orders of magnitude [173]. Macroscopic magnetotransport studies, Figures 20(c) and (d) show the existence of a large magnetoresistance when the transport direction and magnetic field direction coincide along the wall plane. Low temperature magnetotransport data, figure 20(d), shows a positive temperature coefficient, i.e. it decreases with decreasing temperature. It would be fascinating to study the possible emergence of metallic behavior at the domain walls, a grand challenge for the field of complex oxides [174]. Large compressive epitaxial constraint induces a phase transition to a super-tetragonal phase. Partial relaxation of the epitaxial constraint by increasing the film thickness leads to the formation of a mixed phase nanostructure which exhibits the coexistence of both the *R*- and *T*-phases. The highly distorted *R*-phase in this ensemble, shows a significantly enhanced ferromagnetism. These observations raise several questions: (i) first, what is the magnetic state of the strained *R*-phase?

Given that spin-orbit coupling is the source of the canted moment in the bulk of BFO, can this enhanced moment be explained based on the strain and confinement imposed on the *R*-phase? What is the state of the Dzyaloshinski–Moriya vector in such a strained system? Are there other pathways to enhance the canted moment arising from D–M interactions, perhaps through engineering the crystal symmetry of $BiFeO_3$? If yes, does this also present a pathway to switch the magnetic state with the application of a magnetic field?

Electric field control of ferromagnetism is the most exciting development, figure 21. Element specific x-ray spectromicroscopy, magnetotransport and scanning electron microscopy polarization analysis has demonstrated the direct coupling between the canted moment in a domain and the moment in the CoFe ferromagnet [175, 176]. Figure 21: The coupling between a CoFe layer (FM) and the BFO can be probed using a standard spin valve like structure, shown schematically in (A); the corresponding schematic of the exchange coupling at the CoFe–BFO interface is shown in (B). Figure 21(C) illustrates the essence of the coupling studies. In red is the ferroelectric hysteresis, while the blue data is the resistance modulation of the spin valve with an electric field. For comparison, the magnetic field dependent modulation of the spin valve resistance is shown in (D). There are ample opportunities to improve on this. First, switching from a spin valve to a tunnel junction will yield at least an order of magnitude improvement of the resistance modulation. It would be extremely valuable to study approaches to grow out-of-plane magnetized ferromagnets and tunnel junctions on the BFO.

**Current and future challenges.** The field of multiferroics and magnetoelectrics is poised for some exciting times in the next 5–10 years. While a significant amount of fundamental understanding has been gained, it is now time for these scientific discoveries to be translated into the first stage of technological applications. Indeed, this could be said of the entire field of oxide electronics, where the science has always been well ahead of the technological implementations. If a room temperature multiferroic with a spontaneous magnetic moment (canted or otherwise) that is an order of magnitude higher than that in BFO, then this would be a game changer. There is quite a bit of worldwide effort focused on this. In the meantime, a focused effort on using exchange or strain coupled heterostructures may be the most available pathway to demonstrate devices. Perhaps the biggest focus area has to be low power electronics, since this is the most important advantage of going to electric fields compared to magnetic fields. At a higher level, it is important to explore new device concepts as well as new product markets that take advantage of the coupling between electricity and magnetism.
## 12. Multiferroic bismuth ferrite

R Ramesh

Departments of Materials Science & Engineering and Physics,
University of California, Berkeley, CA 94720, USA

**Status.** Complex oxides present a broad range of interesting functionalities, such as high temperature superconductivity, colossal magnetoresistance, (anti-) ferromagnetic, (anti-) ferroelectric, piezoelectric and more recently multiferroic properties. $BiFeO_3$ (BFO) is the only room temperature multiferroic (antiferromagnetic and ferroelectric) so far, which has attracted great interest and extensive investigation in the past decade. It has a rhombohedral unit cell, built with two distorted perovskite cells connected along a pseudocubic [111] direction [167, 168]. It is also a G-type antiferromagnet with Neél temperature of ~673 K [100] and a symmetry-allowed, small canted moment due to the Dzyaloshinskii–Moriya interaction [169]. The hybridization between the two 6s electrons in Bi [170] with surrounding oxygen ions leads to a large displacement of the Bi cations relative to the oxygen octahedral along the [111] direction with a Curie temperature of 1103 K and the spontaneous ferroelectric polarization of about 90 $\mu$C cm$^{-2}$ [171].

The synthesis of high quality epitaxial thin films through a variety of techniques (pulsed laser deposition (or laser MBE), sputtering, MBE, CVD) has already been well-established [172]. In thin films, both 71° and 109° domain walls are observed. Figure 20 shows the magneto-transport behavior of 109° domain walls, an atomic resolution image of which is shown in figure 20(a). Conducting atomic force microscopy (AFM) based measurements, figure 20(b), show that the walls are less resistive, (compared to the domain itself) typically by 2–3 orders of magnitude [173]. Macroscopic magnetotransport studies, Figures 20(c) and (d) show the existence of a large magnetoresistance when the transport direction and magnetic field direction coincide along the wall plane. Low temperature magnetotransport data, figure 20(d), shows a positive temperature coefficient, i.e. it decreases with decreasing temperature. It would be fascinating to study the possible emergence of metallic behavior at the domain walls, a grand challenge for the field of complex oxides [174]. Large compressive epitaxial constraint induces a phase transition to a super-tetragonal phase. Partial relaxation of the epitaxial constraint by increasing the film thickness leads to the formation of a mixed phase nanostructure which exhibits the coexistence of both the *R*- and *T*-phases. The highly distorted *R*-phase in this ensemble, shows a significantly enhanced ferromagnetism. These observations raise several questions: (i) first, what is the magnetic state of the strained *R*-phase?

Given that spin-orbit coupling is the source of the canted moment in the bulk of BFO, can this enhanced moment be explained based on the strain and confinement imposed on the *R*-phase? What is the state of the Dzyaloshinski–Moriya vector in such a strained system? Are there other pathways to enhance the canted moment arising from D–M interactions, perhaps through engineering the crystal symmetry of $BiFeO_3$? If yes, does this also present a pathway to switch the magnetic state with the application of a magnetic field?

Electric field control of ferromagnetism is the most exciting development, figure 21. Element specific x-ray spectromicroscopy, magnetotransport and scanning electron microscopy polarization analysis has demonstrated the direct coupling between the canted moment in a domain and the moment in the CoFe ferromagnet [175, 176]. Figure 21: The coupling between a CoFe layer (FM) and the BFO can be probed using a standard spin valve like structure, shown schematically in (A); the corresponding schematic of the exchange coupling at the CoFe–BFO interface is shown in (B). Figure 21(C) illustrates the essence of the coupling studies. In red is the ferroelectric hysteresis, while the blue data is the resistance modulation of the spin valve with an electric field. For comparison, the magnetic field dependent modulation of the spin valve resistance is shown in (D). There are ample opportunities to improve on this. First, switching from a spin valve to a tunnel junction will yield at least an order of magnitude improvement of the resistance modulation. It would be extremely valuable to study approaches to grow out-of-plane magnetized ferromagnets and tunnel junctions on the BFO.

**Current and future challenges.** The field of multiferroics and magnetoelectrics is poised for some exciting times in the next 5–10 years. While a significant amount of fundamental understanding has been gained, it is now time for these scientific discoveries to be translated into the first stage of technological applications. Indeed, this could be said of the entire field of oxide electronics, where the science has always been well ahead of the technological implementations. If a room temperature multiferroic with a spontaneous magnetic moment (canted or otherwise) that is an order of magnitude higher than that in BFO, then this would be a game changer. There is quite a bit of worldwide effort focused on this. In the meantime, a focused effort on using exchange or strain coupled heterostructures may be the most available pathway to demonstrate devices. Perhaps the biggest focus area has to be low power electronics, since this is the most important advantage of going to electric fields compared to magnetic fields. At a higher level, it is important to explore new device concepts as well as new product markets that take advantage of the coupling between electricity and magnetism.
<figure><img src="image_25.png" /><figcaption>**Figure 20.** (a) An atomic resolution TEM image of the 109° domain wall; (b) conducting AFM image of transport through such domain walls; (c) macroscopic magnetotransport data through an array of 109° walls showing the significant MR for transport and *H* parallel to the wall while transport and/or *H* normal to the wall shows very little MR; (d) temperature dependence of the resistance and MR behavior.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>**Figure 21.** (A) A schematic of the spin valve test structure on BFO; (B) a schematic of the exchange coupling at the CoFe–BFO interface; (C) ferroelectric hysteresis (red) and MR hysteresis (blue) of the spin valve; (D) the corresponding *R*–*H* plot of the spin valve.</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>**Figure 20.** (a) An atomic resolution TEM image of the 109° domain wall; (b) conducting AFM image of transport through such domain walls; (c) macroscopic magnetotransport data through an array of 109° walls showing the significant MR for transport and *H* parallel to the wall while transport and/or *H* normal to the wall shows very little MR; (d) temperature dependence of the resistance and MR behavior.</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>**Figure 21.** (A) A schematic of the spin valve test structure on BFO; (B) a schematic of the exchange coupling at the CoFe–BFO interface; (C) ferroelectric hysteresis (red) and MR hysteresis (blue) of the spin valve; (D) the corresponding *R*–*H* plot of the spin valve.</figcaption></figure>
# 13. Novel functionalities at oxide (multi)ferroic domain walls

Nicola A Spaldin

Materials Theory, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland

There has been tremendous interest recently in interfaces between insulating oxides with different electrical polarizations, in which electrostatic stability requires screening of the so-called polar discontinuity by either free or bound charge. The resulting accumulation of carriers in a narrow almost 2D region has been associated with a range of phenomena, including electrical conductivity, magnetism and even superconductivity (for a review see [177]). In most cases, such interfaces are engineered using layer-by-layer growth of two different materials, and the location of the screening layer is therefore fixed statically within the material. Particularly exciting, and to date less well studied, are polar discontinuities generated at ferroelectric domain walls through head-to-head or tail-to-tail components of the ferroelectric polarization. In this case, all of the physics of a static discontinuous polar interface is captured, with the additional desirable feature that the position of a ferroelectric domain wall can be changed using an applied electric field. Here we review the progress in this area to date, mention some other novel functionalities at ferroic and multiferroic domain walls, and discuss likely future directions.

**Status.** The first observation of room temperature electrical conductivity in a ferroelectric domain wall occurred in thin films of the prototypical multiferroic, $BiFeO_3$ [178]. The original data is reproduced in figure 22. Ferroelectric domains were written and imaged using piezoforce microscopy (PFM), and local conductivity was measured using high-resolution conductive atomic force microscopy (c-AFM). Conductivity was observed at 180° and 109° domain walls and associated with an electrostatic potential step accompanied by a change in band gap across the wall; subsequently the 71° domain walls were also shown to be conducting [179]. Clever patterning of domain walls of various orientations in $BiFeO_3$ using scanning probe microscopy techniques later proved that the accumulation of carriers is indeed governed by the magnitude of the polar discontinuity at the wall, and demonstrated that this polar discontinuity can be tuned dynamically [180].

A particularly interesting development was the report of conductivity at the ferroelectric domain walls in the multiferroic hexagonal manganites [181]. Here the improper nature of the ferroelectricity leads naturally to a domain structure with coexisting neutral, head-to-head and tail-to-tail walls. The authors showed that the electrical conductance in hexagonal $ErMnO_3$ varies continuously with the domain wall orientation, with the tail-to-tail walls, which are screened by the accumulation of positive charge, having the highest conductivity in this p-type material.

While the phenomenon of electrically conducting ferroelectric domain walls was at first believed to be a property of multiferroics, it was soon after demonstrated in the conventional ferroelectrics lead zirconium titanate (PZT) [182] and $BaTiO_3$ [183]. In the PZT case, the walls were nominally neutral with no polar discontinuity, although high-resolution transmission electron microscopy indicated many small steps which would require local screening. In the $BaTiO_3$ example, head-to-head and tail-to-tail walls were created by so-called frustrated poling, and stabilized by the combined availability of free carriers and coupled ferroelastic clamping.

Additional evidence of the importance of the interaction between ferroelectric domain walls, defects and clamping was provided by an intriguing study of the relationship between domain walls and conductivity in strained multiferroic strontium manganite, $SrMnO_3$ [184]. First, the theoretically predicted ferroelectric polarization in tensile-strained films of $SrMnO_3$ was confirmed using second harmonic generation (SHG). Electrostatic force microscopy then revealed an unexpected behavior: The ferroelectric domains were found to form discrete chargeable nanodomains with distinct conductances (figure 23). A model was proposed in which oxygen vacancies, which are stabilized by the tensile strain, accumulate at the domain walls and create a potential barrier to charge transport between the domains.

While the focus of this short road map is on electrical conductivity at ferroelectric domain walls, we mention that other intriguing properties have been reported at the domain walls in various ferroic systems, including a net magnetism at the ferroelectric domain walls in otherwise antiferromagnetic multiferroic $BiFeO_3$ and (my personal favourite) the occurrence of BCS superconductivity at the ferroelastic twin boundaries in Na-doped $WO_3$ [174]. (For a review of other functionalities see [177].) While simple model explanations exist—the superconductivity is likely due to the higher concentration of carriers compared with the bulk sample, and the net magnetism is likely related to changes in structure and bonding at the interface—the details of these and related phenomena remain to be fully understood.

**Current and future challenges, and advances required to meet them.** Much remains to be understood mechanistically regarding the nature and origin of electrical conductivity at multiferroic domain walls. Here a combination of first-principles and phenomenological theories with a wide range of detailed and careful characterization tools addressing different time- and length-scales will be required for progress. In particular, the interplay between the detailed atomic structure of the walls, the screening of associated internal electric fields with minority or majority free carriers and/or bound charge, and the role of ionic point defects still remain to be elucidated. None of these properties can be measured straightforwardly, with characterization of point defects such as oxygen vacancies being particularly challenging. Electronic structure
# 13. Novel functionalities at oxide (multi)ferroic domain walls

Nicola A Spaldin

Materials Theory, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland

There has been tremendous interest recently in interfaces between insulating oxides with different electrical polarizations, in which electrostatic stability requires screening of the so-called polar discontinuity by either free or bound charge. The resulting accumulation of carriers in a narrow almost 2D region has been associated with a range of phenomena, including electrical conductivity, magnetism and even superconductivity (for a review see [177]). In most cases, such interfaces are engineered using layer-by-layer growth of two different materials, and the location of the screening layer is therefore fixed statically within the material. Particularly exciting, and to date less well studied, are polar discontinuities generated at ferroelectric domain walls through head-to-head or tail-to-tail components of the ferroelectric polarization. In this case, all of the physics of a static discontinuous polar interface is captured, with the additional desirable feature that the position of a ferroelectric domain wall can be changed using an applied electric field. Here we review the progress in this area to date, mention some other novel functionalities at ferroic and multiferroic domain walls, and discuss likely future directions.

**Status.** The first observation of room temperature electrical conductivity in a ferroelectric domain wall occurred in thin films of the prototypical multiferroic, $BiFeO_3$ [178]. The original data is reproduced in figure 22. Ferroelectric domains were written and imaged using piezoforce microscopy (PFM), and local conductivity was measured using high-resolution conductive atomic force microscopy (c-AFM). Conductivity was observed at 180° and 109° domain walls and associated with an electrostatic potential step accompanied by a change in band gap across the wall; subsequently the 71° domain walls were also shown to be conducting [179]. Clever patterning of domain walls of various orientations in $BiFeO_3$ using scanning probe microscopy techniques later proved that the accumulation of carriers is indeed governed by the magnitude of the polar discontinuity at the wall, and demonstrated that this polar discontinuity can be tuned dynamically [180].

A particularly interesting development was the report of conductivity at the ferroelectric domain walls in the multiferroic hexagonal manganites [181]. Here the improper nature of the ferroelectricity leads naturally to a domain structure with coexisting neutral, head-to-head and tail-to-tail walls. The authors showed that the electrical conductance in hexagonal $ErMnO_3$ varies continuously with the domain wall orientation, with the tail-to-tail walls, which are screened by the accumulation of positive charge, having the highest conductivity in this p-type material.

While the phenomenon of electrically conducting ferroelectric domain walls was at first believed to be a property of multiferroics, it was soon after demonstrated in the conventional ferroelectrics lead zirconium titanate (PZT) [182] and $BaTiO_3$ [183]. In the PZT case, the walls were nominally neutral with no polar discontinuity, although high-resolution transmission electron microscopy indicated many small steps which would require local screening. In the $BaTiO_3$ example, head-to-head and tail-to-tail walls were created by so-called frustrated poling, and stabilized by the combined availability of free carriers and coupled ferroelastic clamping.

Additional evidence of the importance of the interaction between ferroelectric domain walls, defects and clamping was provided by an intriguing study of the relationship between domain walls and conductivity in strained multiferroic strontium manganite, $SrMnO_3$ [184]. First, the theoretically predicted ferroelectric polarization in tensile-strained films of $SrMnO_3$ was confirmed using second harmonic generation (SHG). Electrostatic force microscopy then revealed an unexpected behavior: The ferroelectric domains were found to form discrete chargeable nanodomains with distinct conductances (figure 23). A model was proposed in which oxygen vacancies, which are stabilized by the tensile strain, accumulate at the domain walls and create a potential barrier to charge transport between the domains.

While the focus of this short road map is on electrical conductivity at ferroelectric domain walls, we mention that other intriguing properties have been reported at the domain walls in various ferroic systems, including a net magnetism at the ferroelectric domain walls in otherwise antiferromagnetic multiferroic $BiFeO_3$ and (my personal favourite) the occurrence of BCS superconductivity at the ferroelastic twin boundaries in Na-doped $WO_3$ [174]. (For a review of other functionalities see [177].) While simple model explanations exist—the superconductivity is likely due to the higher concentration of carriers compared with the bulk sample, and the net magnetism is likely related to changes in structure and bonding at the interface—the details of these and related phenomena remain to be fully understood.

**Current and future challenges, and advances required to meet them.** Much remains to be understood mechanistically regarding the nature and origin of electrical conductivity at multiferroic domain walls. Here a combination of first-principles and phenomenological theories with a wide range of detailed and careful characterization tools addressing different time- and length-scales will be required for progress. In particular, the interplay between the detailed atomic structure of the walls, the screening of associated internal electric fields with minority or majority free carriers and/or bound charge, and the role of ionic point defects still remain to be elucidated. None of these properties can be measured straightforwardly, with characterization of point defects such as oxygen vacancies being particularly challenging. Electronic structure
<figure><img src="image_27.png" /><figcaption>**Figure 22.** First observation of conducting ferroelectric domain walls in a multiferroic material. Left: out-of-plane piezoforce microscopy image of a written domain pattern in a monodomain BiFeO₃ film, showing up (U) and down (D) components of ferroelectric polarization. Right: corresponding conducting atomic force microscopy image showing conduction at the domain walls. The scale bar is in picoamperes. From [178], reproduced with permission.</figcaption></figure>

calculations for domain walls are also not routine due to both the computational demands of the large supercells required to model realistic domain wall spacings and defect profiles, and the state-of-the art methods required to appropriately incorporate physically meaningful electrostatic boundary conditions. The material chemistries and crystal structures that have been explored to date remain rather limited, and doubtless new behaviours, as well as clarifications of existing ones, will be achieved when a broader chemical and structural palette is explored. Regarding potential for devices, while it is hard to be predictive, such sub-nanometre sized, electrically tunable, conducting entities are certainly seductive. For consideration for practical applications there are two outstanding challenges: An increased current density at the walls—perhaps even demonstration of a metal–insulator transition—should be achieved, as well as a route to controlled manipulation of their position.

*Concluding remarks.* Novel and emergent properties at ferroelectric and multiferroic domain walls offer arguably one of the most interesting new research directions in the field of complex oxides and will undoubtedly continue to be actively pursued in the next years. While a direct route to applications is not yet entirely clear, the technological potential is huge, and provides an additional driver for progress, in addition to the desire to understand the intriguing fundamental physics.

<figure><img src="image_28.png" /><figcaption>**Figure 23.** Normalized conductance of a multiferroic SrMnO₃ film measured using electrostatic force microscopy. The degree of brightness indicates the conductance of each stripe-like ferroelectric domain. The scale bar is 0.5 µm. From [184], reproduced with permission.</figcaption></figure>
<figure><img src="image_28.png" /><figcaption>**Figure 22.** First observation of conducting ferroelectric domain walls in a multiferroic material. Left: out-of-plane piezoforce microscopy image of a written domain pattern in a monodomain BiFeO₃ film, showing up (U) and down (D) components of ferroelectric polarization. Right: corresponding conducting atomic force microscopy image showing conduction at the domain walls. The scale bar is in picoamperes. From [178], reproduced with permission.</figcaption></figure>

calculations for domain walls are also not routine due to both the computational demands of the large supercells required to model realistic domain wall spacings and defect profiles, and the state-of-the art methods required to appropriately incorporate physically meaningful electrostatic boundary conditions. The material chemistries and crystal structures that have been explored to date remain rather limited, and doubtless new behaviours, as well as clarifications of existing ones, will be achieved when a broader chemical and structural palette is explored. Regarding potential for devices, while it is hard to be predictive, such sub-nanometre sized, electrically tunable, conducting entities are certainly seductive. For consideration for practical applications there are two outstanding challenges: An increased current density at the walls—perhaps even demonstration of a metal–insulator transition—should be achieved, as well as a route to controlled manipulation of their position.

*Concluding remarks.* Novel and emergent properties at ferroelectric and multiferroic domain walls offer arguably one of the most interesting new research directions in the field of complex oxides and will undoubtedly continue to be actively pursued in the next years. While a direct route to applications is not yet entirely clear, the technological potential is huge, and provides an additional driver for progress, in addition to the desire to understand the intriguing fundamental physics.

<figure><img src="image_29.png" /><figcaption>**Figure 23.** Normalized conductance of a multiferroic SrMnO₃ film measured using electrostatic force microscopy. The degree of brightness indicates the conductance of each stripe-like ferroelectric domain. The scale bar is 0.5 µm. From [184], reproduced with permission.</figcaption></figure>
# 14. Switchable 2D electron gas at the multiferroic interfaces

Sergey Ostanin, Vladislav Borisov and Ingrid Mertig

Institute of Physics, Martin Luther University Halle-
Wittenberg, Von-Seckendorff-Platz 1, 06099 Halle, Germany

**Status.** Surprisingly, a 2D electron gas (2DEG) can appear at the interface between robustly insulating oxides. This fascinating phenomenon, which was first observed [73, 185, 186] in LaAlO₃/SrTiO₃ (LAO/STO), is attributed usually to its LaO/TiO₂-terminated (001) perovskite interface. To explain the emerged 2DEG the researches, assuming mostly that the interface is perfect and stepless, invoke the arguments related to the issue of polar catastrophe. Since LAO (001) represents alternately charged planes [LaO]⁺ and [AlO₂]⁻, each interfacial La transfers ½ electron into the next and formally neutral TiO₂-layer of STO. Therefore, the oxidation state of interfacial Ti decreases. This scenario for the Ti³.⁵⁺ valence state and corresponding d-orbital reconstruction, which results in 2DEG at the LaO/TiO₂ interface, was modeled [187] from first principles. However, all epitaxially grown oxide heterostructures contain intrinsic imperfections, such as oxygen vacancies and substitutional intermixing of cations across the interface. Each type of these interfacial defects causes additional charged carriers, namely, electrons for oxygen vacancies and holes for the Sr substitutes [188, 189]. Thus, both of these defect-based mechanisms contribute to the 2DEG effect as well but mediate it differently. For instance, the Sr/La intermixing >30% completely destroys the 2DEG. There is a family of composite perovskites for which the LaO/TiO₂ termination is formed unavoidably. In particular, 2DEG can appear between STO (001) and LaFeO₃ (LFO). Recently, Li et al [190] have reported that the crystalline and partially amorphous ABO₃/STO (A = La, Pr, Nd and B = Al, Ga) interfaces become conducting for ABO₃ thicker than 4 unit cells (u.c.). High crystallinity of the interface is crucial for the polar catastrophe mechanism of 2DEG. After oxygen annealing (when the O redox mechanism is removed) the interfaces prepared at 500 °C and below become insulating while samples prepared at 515 °C and above are conducting [190]. In the context of the underlying 2DEG mechanisms and their interplay, the *ab initio* calculation show that, with increasing amount of interfacial defects for each of the Sr substitutes and O vacancies, these two mechanisms act oppositely.

**Current and future challenges.** Presently, the focus of discussions around the 2DEG shifts gradually toward its functionality and switchability. Here, the so-called multiferroic TiO₂-based interfaces seem very promising. When the STO component of the composite system is replaced by a robust ferroelectric (FE), such as BaTiO₃ (BTO), this may create an extra functionality due to its switchable polarization. Indeed, the LAO/BTO heterostructure was fabricated already [191]. On the other hand, when LAO is replaced by a magnetically ordered perovskite, this allows to change the magnetization, *M*, of magnetic side by the BTO polarization reversal. The

change of *M* is crudely estimated using the coercive field *E*<sub>c</sub> [192]: Δ*M* ~ *α**E*<sub>c</sub>, where *α* is the magnetoelectric coupling coefficient. Meanwhile, among all magnetically ordered cubic perovskites ABO<sub>3</sub>, the overwhelming majority are antiferromagnetic (AFM) and insulating. Some of them are in a good lattice match with FEs and, therefore, the AFM/FE oxide interfaces can be grown epitaxially. For instance, LFO/PbTiO<sub>3</sub> is a good candidate for externally tuned 2DEG. It should be noted that manipulation with the FE polarization along [001] is not trivial. Robustly switchable epitaxial FEs are thicker than 5 u.c. and since they grow in complete unit cells, their surface termination and interfacial composition are correlated. Hence, the target TiO<sub>2</sub>-terminated interface of FE means that the other termination or surface is AO-terminated. Until now, it is not clear whether the depolarization field coming from the surface affects the ferroelectrically driven 2DEG. Regarding the AFM side, its thickness-dependent scenario of the 2DEG as well as the role of its interfacial defects need a careful study. A critical limitation for the gap width in AFMs, compared to that of the wide gap FEs, is an open question so far.

**Advances in science and technology to meet challenges.** The density functional theory suggests that the 2DEG emerged at the multiferroic interface may occur with no defects and, moreover, without La species. This has been anticipated [193] from first principles by combining BTO and the *G*-type AFM insulator, SrTcO₃ (STcO), which possesses the orthorhombically distorted perovskite structure and whose lattice mismatch with BTO (001) is <1%. Since the experimental gap of STcO is not available, this value was modeled between 0.5 eV and 3 eV, using the Hubbard parametrization. Two types of terminations of BTO/STcO, i.e. BaO/TcO₂ and TiO₂/SrO as shown in figure 24, were simulated using superlattice geometry and a supercell with vacuum, which both mimic differently the electrostatic boundary conditions. The interatomic force minimization results in the ionic displacements near the interfaces, which change locally the FE and magnetic properties so that the system screens off the chemical potential mismatch between the two materials.

Using the site-projected density of states (DOS), calculated for each atomic layer of BTO/STcO, one can disclose [193] how the valence- and conduction-band edges vary toward the interface and how the electron (hole) carriers appear in the gap, within few interfacial u.c., as shown in figure 24. Then, by integrating the DOS tails occurring in the gap, the induced charges, their electron (hole) character and spin polarization were evaluated. For each termination, the character of the 2DEG carriers changes from electrons to holes upon the polarization reversal. This conclusive theoretical result weakly depends on the optionally used electrostatic boundary conditions, the film thickness and degree of electronic correlations. The 2DEG effect, which is controlled by the FE state of BTO, is anticipated for the defect-free and atomically sharp interfaces of BTO/STcO.

**Concluding remarks.** Multiferroic interfaces between the FE and AFM insulating perovskites, as the contemporary theory suggests, may form such 2DEG, for which the charge character
# 14. Switchable 2D electron gas at the multiferroic interfaces

Sergey Ostanin, Vladislav Borisov and Ingrid Mertig

Institute of Physics, Martin Luther University Halle-
Wittenberg, Von-Seckendorff-Platz 1, 06099 Halle, Germany

**Status.** Surprisingly, a 2D electron gas (2DEG) can appear at the interface between robustly insulating oxides. This fascinating phenomenon, which was first observed [73, 185, 186] in LaAlO₃/SrTiO₃ (LAO/STO), is attributed usually to its LaO/TiO₂-terminated (001) perovskite interface. To explain the emerged 2DEG the researches, assuming mostly that the interface is perfect and stepless, invoke the arguments related to the issue of polar catastrophe. Since LAO (001) represents alternately charged planes [LaO]⁺ and [AlO₂]⁻, each interfacial La transfers ½ electron into the next and formally neutral TiO₂-layer of STO. Therefore, the oxidation state of interfacial Ti decreases. This scenario for the Ti³.₅⁺ valence state and corresponding d-orbital reconstruction, which results in 2DEG at the LaO/TiO₂ interface, was modeled [187] from first principles. However, all epitaxially grown oxide heterostructures contain intrinsic imperfections, such as oxygen vacancies and substitutional intermixing of cations across the interface. Each type of these interfacial defects causes additional charged carriers, namely, electrons for oxygen vacancies and holes for the Sr substitutes [188, 189]. Thus, both of these defect-based mechanisms contribute to the 2DEG effect as well but mediate it differently. For instance, the Sr/La intermixing >30% completely destroys the 2DEG. There is a family of composite perovskites for which the LaO/TiO₂ termination is formed unavoidably. In particular, 2DEG can appear between STO (001) and LaFeO₃ (LFO). Recently, Li et al [190] have reported that the crystalline and partially amorphous ABO₃/STO (A = La, Pr, Nd and B = Al, Ga) interfaces become conducting for ABO₃ thicker than 4 unit cells (u.c.). High crystallinity of the interface is crucial for the polar catastrophe mechanism of 2DEG. After oxygen annealing (when the O redox mechanism is removed) the interfaces prepared at 500 °C and below become insulating while samples prepared at 515 °C and above are conducting [190]. In the context of the underlying 2DEG mechanisms and their interplay, the *ab initio* calculation show that, with increasing amount of interfacial defects for each of the Sr substitutes and O vacancies, these two mechanisms act oppositely.

**Current and future challenges.** Presently, the focus of discussions around the 2DEG shifts gradually toward its functionality and switchability. Here, the so-called multiferroic TiO₂-based interfaces seem very promising. When the STO component of the composite system is replaced by a robust ferroelectric (FE), such as BaTiO₃ (BTO), this may create an extra functionality due to its switchable polarization. Indeed, the LAO/BTO heterostructure was fabricated already [191]. On the other hand, when LAO is replaced by a magnetically ordered perovskite, this allows to change the magnetization, *M*, of magnetic side by the BTO polarization reversal. The

change of *M* is crudely estimated using the coercive field *E*<sub>c</sub> [192]: Δ*M* ~ *α*(*E*<sub>c</sub>*, where *α* is the magnetoelectric coupling coefficient. Meanwhile, among all magnetically ordered cubic perovskites ABO<sub>3</sub>, the overwhelming majority are antiferromagnetic (AFM) and insulating. Some of them are in a good lattice match with FEs and, therefore, the AFM/FE oxide interfaces can be grown epitaxially. For instance, LFO/PbTiO<sub>3</sub> is a good candidate for externally tuned 2DEG. It should be noted that manipulation with the FE polarization along [001] is not trivial. Robustly switchable epitaxial FEs are thicker than 5 u.c. and since they grow in complete unit cells, their surface termination and interfacial composition are correlated. Hence, the target TiO<sub>2</sub>-terminated interface of FE means that the other termination or surface is AO-terminated. Until now, it is not clear whether the depolarization field coming from the surface affects the ferroelectrically driven 2DEG. Regarding the AFM side, its thickness-dependent scenario of the 2DEG as well as the role of its interfacial defects need a careful study. A critical limitation for the gap width in AFMs, compared to that of the wide gap FEs, is an open question so far.

**Advances in science and technology to meet challenges.** The density functional theory suggests that the 2DEG emerged at the multiferroic interface may occur with no defects and, moreover, without La species. This has been anticipated [193] from first principles by combining BTO and the *G*-type AFM insulator, SrTcO₃ (STcO), which possesses the orthorhombically distorted perovskite structure and whose lattice mismatch with BTO (001) is <1%. Since the experimental gap of STcO is not available, this value was modeled between 0.5 eV and 3 eV, using the Hubbard parametrization. Two types of terminations of BTO/STcO, i.e. BaO/TcO₂ and TiO₂/SrO as shown in figure 24, were simulated using superlattice geometry and a supercell with vacuum, which both mimic differently the electrostatic boundary conditions. The interatomic force minimization results in the ionic displacements near the interfaces, which change locally the FE and magnetic properties so that the system screens off the chemical potential mismatch between the two materials.

Using the site-projected density of states (DOS), calculated for each atomic layer of BTO/STcO, one can disclose [193] how the valence- and conduction-band edges vary toward the interface and how the electron (hole) carriers appear in the gap, within few interfacial u.c., as shown in figure 24. Then, by integrating the DOS tails occurring in the gap, the induced charges, their electron (hole) character and spin polarization were evaluated. For each termination, the character of the 2DEG carriers changes from electrons to holes upon the polarization reversal. This conclusive theoretical result weakly depends on the optionally used electrostatic boundary conditions, the film thickness and degree of electronic correlations. The 2DEG effect, which is controlled by the FE state of BTO, is anticipated for the defect-free and atomically sharp interfaces of BTO/STcO.

**Concluding remarks.** Multiferroic interfaces between the FE and AFM insulating perovskites, as the contemporary theory suggests, may form such 2DEG, for which the charge character
<figure><img src="image_29.png" /><figcaption>**Figure 24.** The layer-resolved energy positions of the valence and conduction bands, calculated for each termination of BTO/STcO and for dually polar BTO. The hole (electron) charge carriers induced in the band gap are shown by red (blue) shaded area.</figcaption></figure>

of ferroelectrically induced carriers changes from the p- to n-type by the polarization reversal. The effect should robustly appear at the perfect interface even if the defect-based mechanisms of 2DEG, originated due to the interfacial cation mixing, oxygen vacancies and interstitial species, were excluded from consideration. The dominant mechanism of ferroelectrically driven 2DEG is the electron/hole transfer that goes so that charged carriers are accumulated near the interface, within a few layers. When BTO is forced to be paraelectric the effect disappears. This suggests another scenario of a thermally driven 2DEG, which can be switched on and off. Thus, the FE/AFM

interfaces offer extremely promising applications. Until now, the theory is not able (i) to suggest the voltage needed for the FE switch of 2DEG and also (ii) to claim which polarization state of BTO is initially formed under the non-equilibrium growth conditions. Nevertheless, these findings could stimulate further studies, which include the effect of spin-orbit coupling in non-centrosymmetric composite oxides.

**Acknowledgement.** This work was supported by Sonderforschungsbereich SFB 762, ‘Functionality of Oxide Interfaces’.
<figure><img src="image_30.png" /><figcaption>**Figure 24.** The layer-resolved energy positions of the valence and conduction bands, calculated for each termination of BTO/STcO and for dually polar BTO. The hole (electron) charge carriers induced in the band gap are shown by red (blue) shaded area.</figcaption></figure>

of ferroelectrically induced carriers changes from the p- to n-type by the polarization reversal. The effect should robustly appear at the perfect interface even if the defect-based mechanisms of 2DEG, originated due to the interfacial cation mixing, oxygen vacancies and interstitial species, were excluded from consideration. The dominant mechanism of ferroelectrically driven 2DEG is the electron/hole transfer that goes so that charged carriers are accumulated near the interface, within a few layers. When BTO is forced to be paraelectric the effect disappears. This suggests another scenario of a thermally driven 2DEG, which can be switched on and off. Thus, the FE/AFM

interfaces offer extremely promising applications. Until now, the theory is not able (i) to suggest the voltage needed for the FE switch of 2DEG and also (ii) to claim which polarization state of BTO is initially formed under the non-equilibrium growth conditions. Nevertheless, these findings could stimulate further studies, which include the effect of spin-orbit coupling in non-centrosymmetric composite oxides.

**Acknowledgement.** This work was supported by Sonderforschungsbereich SFB 762, ‘Functionality of Oxide Interfaces’.
# 15. Magnetoelectric coupling in multiferroic epitaxial thin film composites

Vera Lazenka¹, Michael Lorenz²

¹ KU Leuven, Leuven, Belgium

² Universität Leipzig, Leipzig, Germany

**Status.** Recent progress in materials science and technology and the hope for realization of novel device functionalities has renewed research interest in multiferroic and magnetoelectric materials [194, 195]. In particular, complex oxide heterostructures offer the possibility to realize next generation electronics, such as novel data storage devices [195]. Magnetoelectric multiferroic composites consisting of several closely coupled phases show advantages compared to single-phase magnetoelectrics in terms of value of magnetoelectric coefficient, control of its temperature dependence, and design of tailored materials for applications [194–198]. Important for applications is the strength of magnetoelectric coupling. The linear and nonlinear coupling coefficients in single phase magnetoelectrics are usually low [194]. However, indirect coupling due to strain effects, i.e. inclusion of piezomagnetism and magnetostiction, or piezoelectricity and electrostriction, can be orders of magnitude higher in two-phase composite materials [194]. Because not only the elastic coupling at the interface, but also exchange-bias effects, or modulation of the charge carrier concentrations can mediate the indirect magnetoelectric coupling, its distinct identification in multiphase composites is a matter of current research [195].

Among the possible composite geometries of the coupled phases, the multilayer structure, i.e. a so called 2-2 composite consisting of pairs of 2D stacked layers, is expected to be far superior to bulk composites. This is because out-of-plane leakage currents in the low-resistive ferromagnetic phase are considerably reduced, and because piezoelectric thin layers can be easily and almost homogeneously poled electrically [196]. Both effects may enhance the magnetoelectric coupling in superlattice composites by orders of magnitude. Vaz pointed out, that magnetoelectric coupling in composites is interfacial in origin, and that the three different, above mentioned mediation types elastic strain, charge, and exchange bias provide different characteristic responses and functionalities [197].

Among the many possible combinations of ferroelectric, ferromagnetic, or multiferroic materials in composites, the BiFeO₃–BaTiO₃ solid solution is mentioned as ‘highly exciting towards the realization of a room temperature single phase multiferroic magnetoelectric material’, as pointed out by Priya et al in [198](p 103 ff). In order to further illustrate the current status of magnetoelectric composites with special emphasis on epitaxial BaTiO₃–BiFeO₃ superlattices, we show in the following recent examples how to correlate the magnetoelectric voltage coefficient α<sub>ME</sub> with microstructural features and the magnetic spin structure. Figure 25 shows the temperature-dependent α<sub>ME</sub> of two epitaxial BaTiO₃–BiFeO₃ thin film superlattices, and illustrates the chemical and structural homogeneity of the well ordered high-α<sub>ME</sub> sample grown at 0.25 mbar with atomically smooth, coherent interfaces [199–201]. (The linear)

magnetoelectric voltage coefficient α<sub>ME</sub> was determined using an inductive AC-method by α<sub>ME</sub> = dV/(tdH), where V is the voltage induced by the exciting AC magnetic field H, and t is the thickness of the sample, see [199–201] and references therein. Up to now, the highest magnetoelectric voltage coefficient of 49 V cm<sup>-1</sup> Oe<sup>-1</sup> at 300 K and 1 kHz has been reached in a multiferroic (BaTiO₃–BiFeO₃) × 15 superlattice with total thickness of 208 nm, which is correlated to atomically coherent interfaces, see figure 25 and [201].

Similarly high α<sub>ME</sub> of 43 V cm<sup>-1</sup> Oe<sup>-1</sup> at 300 K was obtained in a series of chemically homogenous 67% BaTiO₃–33% BiFeO₃ composite films [202]. In comparison, a ceramic BiFeO₃ bulk sample showed only α<sub>ME</sub> = 7.1 mV cm<sup>-1</sup> Oe<sup>-1</sup>, and a slightly higher value of 9.15 mV cm<sup>-1</sup> Oe<sup>-1</sup> was achieved in a Bi<sub>0.8</sub>Gd<sub>0.2</sub>FeO₃ bulk sample. Epitaxial single-phase BiFeO₃ films show α<sub>ME</sub> = 2–4 V cm<sup>-1</sup> Oe<sup>-1</sup>. At the same time, the BaTiO₃–CoFe₂O₄ nanocomposite system, consisting of CoFe₂O₄ nanowires in a BaTiO₃ matrix, showed a α<sub>ME</sub> around 80 mV cm<sup>-1</sup> Oe<sup>-1</sup>, in agreement with values published by Ramesh et al, see [202]. As a proof of the reliability of the used magnetoelectric measurement setup, the α<sub>ME</sub> coefficient measured across a non-magnetoelectric Fe (5 nm)–LiNbO₃ (100 µm) heterostructure amounted only 0.05 mV cm<sup>-1</sup> Oe<sup>-1</sup>.

**Current and future challenges.** Not well understood are the different temperature and DC magnetic field dependences of the magnetoelectric voltage coefficients of BaTiO₃–BiFeO₃ superlattices and homogeneous composite films, see figures 25 and 26, and [199–202]. In a first attempt, we were able to correlate the α<sub>ME</sub> values of the superlattices with density of oxygen vacancies and antiphase octahedral rotations [199]. Interestingly, interface-engineered oxygen octahedral coupling was recently used to manipulate the magnetic and electronic anisotropy in manganite heterostructures, see [276]. Moreover, the magnetic spin structure was found to affect the characteristics of α<sub>ME</sub> in an external magnetic field [200]. Detailed investigation of the microscopic strain in multiferroic superlattices requires high-resolution TEM investigations, as shown in [201]. In the homogeneous BaTiO₃–BiFeO₃ composite films, the magnetoelectric coupling seems to be correlated to an oxygen vacancy superstructure [202]. The temperature dependence of α<sub>ME</sub> of the homogeneous composite films is opposite to that of the superlattices, so that strain-mediated coupling alone cannot explain its origin [202]. Probably, charge-mediated magnetoelectric coupling may be important additionally [202, 203].

**Advances in science and technology to meet challenges.** In addition to the above mentioned microstructural methods, nuclear forward scattering of synchrotron radiation is an ideal approach to access the local magnetic spin structure on the nanoscale. The measured scattering spectra for a BiFeO₃ thin film and a (BaTiO₃–BiFeO₃) × 15 multilayer together with the fits are presented in figure 26(a). The fits show a spin reorientation in the highly strained BiFeO₃ layers within the multilayer compared to the single film, see insets of
## 15. Magnetoelectric coupling in multiferroic epitaxial thin film composites

Vera Lazenka¹, Michael Lorenz²

¹ KU Leuven, Leuven, Belgium

² Universität Leipzig, Leipzig, Germany

**Status.** Recent progress in materials science and technology and the hope for realization of novel device functionalities has renewed research interest in multiferroic and magnetoelectric materials [194, 195]. In particular, complex oxide heterostructures offer the possibility to realize next generation electronics, such as novel data storage devices [195]. Magnetoelectric multiferroic composites consisting of several closely coupled phases show advantages compared to single-phase magnetoelectrics in terms of value of magnetoelectric coefficient, control of its temperature dependence, and design of tailored materials for applications [194–198]. Important for applications is the strength of magnetoelectric coupling. The linear and nonlinear coupling coefficients in single phase magnetoelectrics are usually low [194]. However, indirect coupling due to strain effects, i.e. inclusion of piezomagnetism and magnetostiction, or piezoelectricity and electrostriction, can be orders of magnitude higher in two-phase composite materials [194]. Because not only the elastic coupling at the interface, but also exchange-bias effects, or modulation of the charge carrier concentrations can mediate the indirect magnetoelectric coupling, its distinct identification in multiphase composites is a matter of current research [195].

Among the possible composite geometries of the coupled phases, the multilayer structure, i.e. a so called 2-2 composite consisting of pairs of 2D stacked layers, is expected to be far superior to bulk composites. This is because out-of-plane leakage currents in the low-resistive ferromagnetic phase are considerably reduced, and because piezoelectric thin layers can be easily and almost homogeneously poled electrically [196]. Both effects may enhance the magnetoelectric coupling in superlattice composites by orders of magnitude. Vaz pointed out, that magnetoelectric coupling in composites is interfacial in origin, and that the three different, above mentioned mediation types elastic strain, charge, and exchange bias provide different characteristic responses and functionalities [197].

Among the many possible combinations of ferroelectric, ferromagnetic, or multiferroic materials in composites, the BiFeO₃–BaTiO₃ solid solution is mentioned as ‘highly exciting towards the realization of a room temperature single phase multiferroic magnetoelectric material’, as pointed out by Priya *et al* in [198](p 103 ff). In order to further illustrate the current status of magnetoelectric composites with special emphasis on epitaxial BaTiO₃–BiFeO₃ superlattices, we show in the following recent examples how to correlate the magnetoelectric voltage coefficient α<sub>ME</sub> with microstructural features and the magnetic spin structure. Figure 25 shows the temperature-dependent α<sub>ME</sub> of two epitaxial BaTiO₃–BiFeO₃ thin film superlattices, and illustrates the chemical and structural homogeneity of the well ordered high-α<sub>ME</sub> sample grown at 0.25 mbar with atomically smooth, coherent interfaces [199–201]. (The linear)

magnetoelectric voltage coefficient α<sub>ME</sub> was determined using an inductive AC-method by α<sub>ME</sub> = dV/(tdH), where V is the voltage induced by the exciting AC magnetic field H, and t is the thickness of the sample, see [199–201] and references therein. Up to now, the highest magnetoelectric voltage coefficient of 49 V cm<sup>-1</sup> Oe<sup>-1</sup> at 300 K and 1 kHz has been reached in a multiferroic (BaTiO₃–BiFeO₃) × 15 superlattice with total thickness of 208 nm, which is correlated to atomically coherent interfaces, see figure 25 and [201].

Similarly high α<sub>ME</sub> of 43 V cm<sup>-1</sup> Oe<sup>-1</sup> at 300 K was obtained in a series of chemically homogenous 67% BaTiO<sub>3</sub>–33% BiFeO<sub>3</sub> composite films [202]. In comparison, a ceramic BiFeO<sub>3</sub> bulk sample showed only α<sub>ME</sub> = 7.1 mV cm<sup>-1</sup> Oe<sup>-1</sup>, and a slightly higher value of 9.15 mV cm<sup>-1</sup> Oe<sup>-1</sup> was achieved in a Bi<sub>0.8</sub>Gd<sub>0.2</sub>FeO<sub>3</sub> bulk sample. Epitaxial single-phase BiFeO<sub>3</sub> films show α<sub>ME</sub> = 2–4 V cm<sup>-1</sup> Oe<sup>-1</sup>. At the same time, the BaTiO<sub>3</sub>–CoFe<sub>2</sub>O<sub>4</sub> nanocomposite system, consisting of CoFe<sub>2</sub>O<sub>4</sub> nanowires in a BaTiO<sub>3</sub> matrix, showed a α<sub>ME</sub> around 80 mV cm<sup>-1</sup> Oe<sup>-1</sup>, in agreement with values published by Ramesh *et al*, see [202]. As a proof of the reliability of the used magnetoelectric measurement setup, the α<sub>ME</sub> coefficient measured across a non-magnetoelectric Fe (5 nm)–LiNbO<sub>3</sub> (100 µm) heterostructure amounted only 0.05 mV cm<sup>-1</sup> Oe<sup>-1</sup>.

**Current and future challenges.** Not well understood are the different temperature and DC magnetic field dependences of the magnetoelectric voltage coefficients of BaTiO₃–BiFeO₃ superlattices and homogeneous composite films, see figures 25 and 26, and [199–202]. In a first attempt, we were able to correlate the α<sub>ME</sub> values of the superlattices with density of oxygen vacancies and antiphase octahedral rotations [199]. Interestingly, interface-engineered oxygen octahedral coupling was recently used to manipulate the magnetic and electronic anisotropy in manganite heterostructures, see [276]. Moreover, the magnetic spin structure was found to affect the characteristics of α<sub>ME</sub> in an external magnetic field [200]. Detailed investigation of the microscopic strain in multiferroic superlattices requires high-resolution TEM investigations, as shown in [201]. In the homogeneous BaTiO₃–BiFeO₃ composite films, the magnetoelectric coupling seems to be correlated to an oxygen vacancy superstructure [202]. The temperature dependence of α<sub>ME</sub> of the homogeneous composite films is opposite to that of the superlattices, so that strain-mediated coupling alone cannot explain its origin [202]. Probably, charge-mediated magnetoelectric coupling may be important additionally [202, 203].

**Advances in science and technology to meet challenges.** In addition to the above mentioned microstructural methods, nuclear forward scattering of synchrotron radiation is an ideal approach to access the local magnetic spin structure on the nanoscale. The measured scattering spectra for a BiFeO₃ thin film and a (BaTiO₃–BiFeO₃) × 15 multilayer together with the fits are presented in figure 26(a). The fits show a spin reorientation in the highly strained BiFeO₃ layers within the multilayer compared to the single film, see insets of
<figure><img src="image_30.png" /><figcaption>**Figure 25.** (a) Temperature dependent magnetoelectric (ME) voltage coefficient of two (BaTiO₃–BiFeO₃) × 15 superlattices grown at the indicated oxygen partial pressures with pulsed laser deposition on SrTiO₃ (001). (b) HAADF and EDXS maps of Ba, O and Bi of a typical (BaTiO₃–BiFeO₃) × 15 superlattice grown at 0.25 mbar with state-of-the-art magnetoelectric coefficient. Note that the SrTiO₃ substrate is on top in the images in (b). The Ti and Fe maps (not shown) are similar to that of Ba and Bi, respectively. The scale bar is 60 nm. (c) HR-TEM image of the superlattice from (b), demonstrating the coherent and strain-free growth of the layers near the surface of the high-α<sub>ME</sub> superlattice. Images adopted with permission from [201].</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>**Figure 26.** (a) Nuclear forward scattering time spectra of a BiFeO₃ thin film and a (BaTiO₃/BiFeO₃) × 15 multilayer. The spectra were recorded at room temperature and zero external magnetic field. The solid lines are the model fits of the spectra. The insets in (a) are schematic representations of the fitting model for the thin film and the multilayer. *m̄* is the magnetic moment of the BiFeO₃ layer(s) and *k̄* is the wave vector along the photon beam. Figures reprinted from [200] with the permission on AIP Publishing. (b) Magnetoelectric (ME) coefficient as a function of DC bias magnetic field at 300 K for the BiFeO₃–BaTiO₃ multilayers with the indicated number of double layers from 2 to 20. The inset in (b) is α<sub>ME</sub> of a single phase BiFeO₃ thin film for comparison. It shows different characteristics.</figcaption></figure>

figure 26(a) [200]. We correlate the enhanced magnetic and magnetoelectric properties observed in the multilayers with the suppression of the spiral spin magnetic structure which is due to high epitaxial strain in the multilayer and interfacial interaction between ferroelectric BaTiO₃ and multiferroic BiFeO₃ [200]. In our latest work we show the tunability of the magnetization and of magnetoelectric coefficient in the multilayered BaTiO₃–BiFeO₃ system by varying the number of interfaces. A nearly perpendicularly magnetized multilayer with 20 layer pairs was fabricated that shows the highest value of magnetoelectric coefficient in this series of superlattices, see figure 26(b).

**Concluding remarks.** With the knowledge about magnetoelectric coupling mechanisms and the correlation to the particular microstructure and magnetic spin structure a design of novel artificial thin film composites will be possible. Tailored coupling parameters could meet the requirements for future applications in magnetoelectric sensors and memories [198, 203].

**Acknowledgements.** We acknowledge financial support of the Deutsche Forschungsgemeinschaft (DFG) within SFB 762 ‘Functionality of Oxide Interfaces’, and of the Fund for Scientific Research—Flandern (FWO) and the KU Leuven Concerted Action (GOA 14/007).
<figure><img src="image_31.png" /><figcaption>**Figure 25.** (a) Temperature dependent magnetoelectric (ME) voltage coefficient of two (BaTiO₃–BiFeO₃) × 15 superlattices grown at the indicated oxygen partial pressures with pulsed laser deposition on SrTiO₃ (001). (b) HAADF and EDXS maps of Ba, O and Bi of a typical (BaTiO₃–BiFeO₃) × 15 superlattice grown at 0.25 mbar with state-of-the-art magnetoelectric coefficient. Note that the SrTiO₃ substrate is on top in the images in (b). The Ti and Fe maps (not shown) are similar to that of Ba and Bi, respectively. The scale bar is 60 nm. (c) HR-TEM image of the superlattice from (b), demonstrating the coherent and strain-free growth of the layers near the surface of the high-α<sub>ME</sub> superlattice. Images adopted with permission from [201].</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>**Figure 26.** (a) Nuclear forward scattering time spectra of a BiFeO₃ thin film and a (BaTiO₃/BiFeO₃) × 15 multilayer. The spectra were recorded at room temperature and zero external magnetic field. The solid lines are the model fits of the spectra. The insets in (a) are schematic representations of the fitting model for the thin film and the multilayer. *m̄* is the magnetic moment of the BiFeO₃ layer(s) and *k̄* is the wave vector along the photon beam. Figures reprinted from [200] with the permission on AIP Publishing. (b) Magnetoelectric (ME) coefficient as a function of DC bias magnetic field at 300 K for the BiFeO₃–BaTiO₃ multilayers with the indicated number of double layers from 2 to 20. The inset in (b) is α<sub>ME</sub> of a single phase BiFeO₃ thin film for comparison. It shows different characteristics.</figcaption></figure>

figure 26(a) [200]. We correlate the enhanced magnetic and magnetoelectric properties observed in the multilayers with the suppression of the spiral spin magnetic structure which is due to high epitaxial strain in the multilayer and interfacial interaction between ferroelectric BaTiO₃ and multiferroic BiFeO₃ [200]. In our latest work we show the tunability of the magnetization and of magnetoelectric coefficient in the multilayered BaTiO₃–BiFeO₃ system by varying the number of interfaces. A nearly perpendicularly magnetized multilayer with 20 layer pairs was fabricated that shows the highest value of magnetoelectric coefficient in this series of superlattices, see figure 26(b).

**Concluding remarks.** With the knowledge about magnetoelectric coupling mechanisms and the correlation to the particular microstructure and magnetic spin structure a design of novel artificial thin film composites will be possible. Tailored coupling parameters could meet the requirements for future applications in magnetoelectric sensors and memories [198, 203].

**Acknowledgements.** We acknowledge financial support of the Deutsche Forschungsgemeinschaft (DFG) within SFB 762 ‘Functionality of Oxide Interfaces’, and of the Fund for Scientific Research—Flandern (FWO) and the KU Leuven Concerted Action (GOA 14/007).
# 16. Self-assembled multiferroic nanocomposites

G Srinivasan

Physics Department, Oakland University, Rochester, MI 48309, USA

**Status.** Multiferroic materials that exhibit two or more of the primary ferroic properties (ferromagnetism, ferroelectricity, ferroelasticity) have been of interests in recent years. A composite made of a ferromagnetic and ferroelectric phases is an engineered multiferroic in which coupling between the ferroic phases could occur through a variety of mechanisms including transfer of strain, charge, or spin torque at the interface. Our focus here is on strain mediated magneto-electric (ME) coupling in the composites and is defined as induced polarization in an applied magnetic field (direct ME effect) or an induced magnetization (or anisotropy field) in an electric field (converse ME effect) [204, 205]. Strong ME coupling was reported in oxide composites with ferrimagnetic spinel and hexagonal ferrites or ferromagnetic manganites and ferroelectrics such as barium titanate (BTO), lead zirconate titanate (PZT), and lead magnesium niobate-lead titanate. Efforts so far on the multiferroic composites have focused on the nature of ME coupling at low-frequencies and at mechanical resonance modes and applications such as magnetic sensors, tunable inductors and capacitors, dual electric and magnetic-field tunable signal processing devices such as resonators, filters, and phase shifters for use at 1–110 GHz, in energy harvesting, solar cells, and random access memories [204, 205].

**Current and future challenges.** The strength of strain mediated ME interactions is expected to be strong in nanocomposites due to a surface-to-volume ratio that is a factor of $10^3$ to $10^6$ higher than for thin film composites in which substrate clamping weakens the ME coupling. Such clamping can be easily overcome in nanopillars in a host matrix, core-shell fibers and core-shell particles [206–209]. Synthesis of nanopillars of ferrites in BTO, PZT or $BiFeO_3$ matrix was reported by several techniques including pulsed laser deposition [209]. Ferrite-ferroelectric core–shells nanotubes were synthesized on porous anodized aluminum oxide (AAO) or membrane templates by a combined sol–gel and electrochemical deposition technique [204, 205]. The use of electrospinning was reported for core-shell fiber synthesis [207]. The technique utilizes electrical forces to produce fibers of diameters in the range 100 to 1000 nm (figures 27(a) and (b)). Synthesis of core–shell particles of ferrite and BTO or PZT by techniques including surfactant-assisted thermal method and by hydrothermal annealing process were reported. In recent studies particles of BTO and spinel ferrite were functionalized by attaching complementary coupling groups and a core-shell particulate composite (figures 27(c) and (d)) was formed by covalent bonds between the two particles with the addition of a coupling agent [208, 209].

Although nm-scale multiferroic oxide composites with core–shell structures have been synthesized and characterized in recent years [207–209], further assembly of nanomaterials

to well-ordered mm-size superstructures is of importance for applications in useful technologies [212]. Traditional lithography techniques are not viable for fabricating mm-size structures with nm-periodicity [211, 212]. Assuming an assembly rate of $10^3$ s$^{-1}$, for example, would require 16 min for a $10^3 \times 10^3$ 2D planar array of unit blocks and nearly 300 h for a $10^3 \times 10^3 \times 10^3$ array. Chemical and DNA/RNA assisted self-assembly and external stimuli such as magnetic and electric fields for instantaneous assembly are of interest in this regard [208–210]. Modeling efforts on such self-assembly techniques and theory of ME coupling in assembled superstructures are lacking at present. It is necessary to consider the electric and magnetic dipole-dipole interactions in modeling the assemblies and for theory of low-frequency ME effects and coupling at individual and collective resonance modes of the composites. Similarly for modeling ME coupling at ferromagnetic and magneto-acoustic resonances one has to develop theory of magnetic modes in assemblies [204].

**Advances in science and technology to meet challenges.** Focused efforts are essential on assembly of the nanomaterial into superstructures with strong ME coupling at low-frequencies and at resonance modes. Recent studies on chemical-, DNA-assisted, and magnetic and electric field-directed assembly techniques are noteworthy in this regard. (i) Chemical assembly: core–shell nanoparticles of NFO and BTO were assembled by attaching complementary chemical groups, azide and alkyne, to the particles and then assembling them by Cu(I)-assisted click-reaction [207]. Studies by SEM and scanning microwave microscopy (SMM) at 1–26 GHz showed the core-shell structures with well-defined interfaces (figure 27). Evidence for strong ME coupling was observed through magnetic field induced polarization and magnetodielectric effects. (ii) DNA-assisted assembly: a ‘click’ methodology was used to covalently attach alkyne functionalized oligomeric DNA (ODN) to azide-functionalized nanoparticles and fibers. The ODN groups allowed for specific reversible DNA-DNA hybridization for the formation of core-shell particles, PZT fiber coated with ferrite particles, and bundles of core–shell nanowires [213]. Figures 28(a) and (b) show SEM and SMM images of DNA-assembled NFO–BTO core–shell particles. Although employment of DNA as a linker has been reported for nanoparticle assembly, essentially no work has been reported using RNA [207, 210]. Like DNA, RNA can base-pair with complementary RNA (or DNA) with the additional ability of base-pairing with complementary sequences on the same strand. It is expected that RNA will have slightly weaker binding characteristics than DNA thus allowing for lower melting temperatures used in restructuring morphologies. The ability to custom synthesize DNA and RNA with 100 or greater nucleotides, provides us with a wide range of possibilities for controlling the interaction strength and specificity between nanoparticles, leading to superior control in generating macrostructures.

Building blocks of core-shell particles and coaxial fibers could be assembled in uniform or nonuniform magnetic fields *H* and in DC or AC electric fields *E* ([207, 213] and references
# 16. Self-assembled multiferroic nanocomposites

G Srinivasan

Physics Department, Oakland University, Rochester, MI 48309, USA

**Status.** Multiferroic materials that exhibit two or more of the primary ferroic properties (ferromagnetism, ferroelectricity, ferroelasticity) have been of interests in recent years. A composite made of a ferromagnetic and ferroelectric phases is an engineered multiferroic in which coupling between the ferroic phases could occur through a variety of mechanisms including transfer of strain, charge, or spin torque at the interface. Our focus here is on strain mediated magneto-electric (ME) coupling in the composites and is defined as induced polarization in an applied magnetic field (direct ME effect) or an induced magnetization (or anisotropy field) in an electric field (converse ME effect) [204, 205]. Strong ME coupling was reported in oxide composites with ferrimagnetic spinel and hexagonal ferrites or ferromagnetic manganites and ferroelectrics such as barium titanate (BTO), lead zirconate titanate (PZT), and lead magnesium niobate-lead titanate. Efforts so far on the multiferroic composites have focused on the nature of ME coupling at low-frequencies and at mechanical resonance modes and applications such as magnetic sensors, tunable inductors and capacitors, dual electric and magnetic-field tunable signal processing devices such as resonators, filters, and phase shifters for use at 1–110 GHz, in energy harvesting, solar cells, and random access memories [204, 205].

**Current and future challenges.** The strength of strain mediated ME interactions is expected to be strong in nanocomposites due to a surface-to-volume ratio that is a factor of $10^3$ to $10^6$ higher than for thin film composites in which substrate clamping weakens the ME coupling. Such clamping can be easily overcome in nanopillars in a host matrix, core-shell fibers and core-shell particles [206–209]. Synthesis of nanopillars of ferrites in BTO, PZT or $BiFeO_3$ matrix was reported by several techniques including pulsed laser deposition [209]. Ferrite-ferroelectric core–shells nanotubes were synthesized on porous anodized aluminum oxide (AAO) or membrane templates by a combined sol–gel and electrochemical deposition technique [204, 205]. The use of electrospinning was reported for core-shell fiber synthesis [207]. The technique utilizes electrical forces to produce fibers of diameters in the range 100 to 1000 nm (figures 27(a) and (b)). Synthesis of core–shell particles of ferrite and BTO or PZT by techniques including surfactant-assisted thermal method and by hydrothermal annealing process were reported. In recent studies particles of BTO and spinel ferrite were functionalized by attaching complementary coupling groups and a core-shell particulate composite (figures 27(c) and (d)) was formed by covalent bonds between the two particles with the addition of a coupling agent [208, 209].

Although nm-scale multiferroic oxide composites with core–shell structures have been synthesized and characterized in recent years [207–209], further assembly of nanomaterials

to well-ordered mm-size superstructures is of importance for applications in useful technologies [212]. Traditional lithography techniques are not viable for fabricating mm-size structures with nm-periodicity [211, 212]. Assuming an assembly rate of $10^3$ s$^{-1}$, for example, would require 16 min for a $10^3 \times 10^3$ 2D planar array of unit blocks and nearly 300 h for a $10^3 \times 10^3 \times 10^3$ array. Chemical and DNA/RNA assisted self-assembly and external stimuli such as magnetic and electric fields for instantaneous assembly are of interest in this regard [208–210]. Modeling efforts on such self-assembly techniques and theory of ME coupling in assembled superstructures are lacking at present. It is necessary to consider the electric and magnetic dipole-dipole interactions in modeling the assemblies and for theory of low-frequency ME effects and coupling at individual and collective resonance modes of the composites. Similarly for modeling ME coupling at ferromagnetic and magneto-acoustic resonances one has to develop theory of magnetic modes in assemblies [204].

**Advances in science and technology to meet challenges.** Focused efforts are essential on assembly of the nanomaterial into superstructures with strong ME coupling at low-frequencies and at resonance modes. Recent studies on chemical-, DNA-assisted, and magnetic and electric field-directed assembly techniques are noteworthy in this regard. (i) Chemical assembly: core–shell nanoparticles of NFO and BTO were assembled by attaching complementary chemical groups, azide and alkyne, to the particles and then assembling them by Cu(I)-assisted click-reaction [207]. Studies by SEM and scanning microwave microscopy (SMM) at 1–26 GHz showed the core-shell structures with well-defined interfaces (figure 27). Evidence for strong ME coupling was observed through magnetic field induced polarization and magnetodielectric effects. (ii) DNA-assisted assembly: a ‘click’ methodology was used to covalently attach alkyne functionalized oligomeric DNA (ODN) to azide-functionalized nanoparticles and fibers. The ODN groups allowed for specific reversible DNA-DNA hybridization for the formation of core-shell particles, PZT fiber coated with ferrite particles, and bundles of core–shell nanowires [213]. Figures 28(a) and (b) show SEM and SMM images of DNA-assembled NFO–BTO core–shell particles. Although employment of DNA as a linker has been reported for nanoparticle assembly, essentially no work has been reported using RNA [207, 210]. Like DNA, RNA can base-pair with complementary RNA (or DNA) with the additional ability of base-pairing with complementary sequences on the same strand. It is expected that RNA will have slightly weaker binding characteristics than DNA thus allowing for lower melting temperatures used in restructuring morphologies. The ability to custom synthesize DNA and RNA with 100 or greater nucleotides, provides us with a wide range of possibilities for controlling the interaction strength and specificity between nanoparticles, leading to superior control in generating macrostructures.

Building blocks of core-shell particles and coaxial fibers could be assembled in uniform or nonuniform magnetic fields *H* and in DC or AC electric fields *E* ([207, 213] and references
<figure><img src="image_32.png" /><figcaption>**Figure 27.** (a) AFM topography and (b) scanning microwave microscopy (SMM) phase images for fibers of nickel ferrite (NFO) core and PZT shell made by electrospinning. (c) SEM and SMM images for a particle with NFO core and BTO shell synthesized by chemical assembly. (d) SMM capacitance image for NFO core-BTO shell particle.</figcaption></figure>

<figure><img src="image_33.png" /><figcaption>**Figure 28.** (a) SEM and (b) SMM images for DNA-assembled NFO shell-BTO core particle. (c) and (d) SEM images for superstructures of NFO-BTO core-shell particles assembled in a uniform and rotating magnetic fields, respectively.</figcaption></figure>

therein). Models predict the assembly to result in a variety of superstructures, such as rings, chains, bundles, and arrays due to magnetic dipole moment and electric polarization associated with the nanostructures. In the case of *H*-directed assembly one could apply either a uniform field or a field gradient [214]. Under a uniform field *H* (at angles other than 0 or 180°) a magnetic moment will be subjected to a torque that aligns the moment along *H*. A field gradient, however, exerts an attractive force on the moment associated with a particle or fiber and moves and aligns them in the regions of high field strengths. As the assembly proceeds, magnetic dipole moment of fibers will create a nonuniform field and exerts a force on neighboring nanostructures leading to local variation in the assembly symmetry. For modeling *H*-driven assembly, it is necessary consider the influence of magnetic moment, size and shape of the nanostructures.

The assembly of a nanomaterial in an AC electric field is due to dielectrophoresis, i.e. motion of a high aspect ratio nanoparticle due to induced polarization in *E*. The techniques has been successfully used for alignment and assembly of conducting, semiconducting and nonconducting nanowires and particles [215]. Although the assembly is usually done in an

AC field with the speed of assembly and resulting configuration are dependent on the strength and frequency of the AC field, dielectrophoresis was reported in DC fields as well. In some studies a combined AC and DC electric fields and AC *E*-field and static *H*-field were used for orienting nanostructures and for their assembly. The superstructures could also be assembled in crossed *E* and *H*-fields that offers enhanced flexibility in types of assembled structure.

**Concluding remarks.** Composite multiferroics are of fundamental and technological importance. The strain mediated coupling is expected to be much stronger in nanocomposites than in thin film structures. It is however necessary to assemble superstructures of such nanomaterials for basic studies on ME coupling and for a variety of applications. Several viable paths for instantaneous assembly of the nanocomposites have been discussed here. We anticipate new phenomena, theory and novel applications to emerge from this research.

**Acknowledgement.** GS is supported by grants from the Army Research office, the National Science Foundation and DARPA.
<figure><img src="image_33.png" /><figcaption>**Figure 27.** (a) AFM topography and (b) scanning microwave microscopy (SMM) phase images for fibers of nickel ferrite (NFO) core and PZT shell made by electrospinning. (c) SEM and SMM images for a particle with NFO core and BTO shell synthesized by chemical assembly. (d) SMM capacitance image for NFO core-BTO shell particle.</figcaption></figure>

<figure><img src="image_34.png" /><figcaption>**Figure 28.** (a) SEM and (b) SMM images for DNA-assembled NFO shell-BTO core particle. (c) and (d) SEM images for superstructures of NFO-BTO core-shell particles assembled in a uniform and rotating magnetic fields, respectively.</figcaption></figure>

therein). Models predict the assembly to result in a variety of superstructures, such as rings, chains, bundles, and arrays due to magnetic dipole moment and electric polarization associated with the nanostructures. In the case of *H*-directed assembly one could apply either a uniform field or a field gradient [214]. Under a uniform field *H* (at angles other than 0 or 180°) a magnetic moment will be subjected to a torque that aligns the moment along *H*. A field gradient, however, exerts an attractive force on the moment associated with a particle or fiber and moves and aligns them in the regions of high field strengths. As the assembly proceeds, magnetic dipole moment of fibers will create a nonuniform field and exerts a force on neighboring nanostructures leading to local variation in the assembly symmetry. For modeling *H*-driven assembly, it is necessary consider the influence of magnetic moment, size and shape of the nanostructures.

The assembly of a nanomaterial in an AC electric field is due to dielectrophoresis, i.e. motion of a high aspect ratio nanoparticle due to induced polarization in *E*. The techniques has been successfully used for alignment and assembly of conducting, semiconducting and nonconducting nanowires and particles [215]. Although the assembly is usually done in an

AC field with the speed of assembly and resulting configuration are dependent on the strength and frequency of the AC field, dielectrophoresis was reported in DC fields as well. In some studies a combined AC and DC electric fields and AC *E*-field and static *H*-field were used for orienting nanostructures and for their assembly. The superstructures could also be assembled in crossed *E* and *H*-fields that offers enhanced flexibility in types of assembled structure.

**Concluding remarks.** Composite multiferroics are of fundamental and technological importance. The strain mediated coupling is expected to be much stronger in nanocomposites than in thin film structures. It is however necessary to assemble superstructures of such nanomaterials for basic studies on ME coupling and for a variety of applications. Several viable paths for instantaneous assembly of the nanocomposites have been discussed here. We anticipate new phenomena, theory and novel applications to emerge from this research.

**Acknowledgement.** GS is supported by grants from the Army Research office, the National Science Foundation and DARPA.
# 17. Combinatorial substrate epitaxy: a novel approach of epitaxy for oxide films

Wilfrid Prelier

Laboratoire CRISMAT, ENSICAEN, CNRS UMR 6508, 6 Boulevard Maréchal Juin, 14050 Caen, France

**Status.** Transition-metal oxides attract attention because of their fascinating properties, including superconductivity, magnetism, ferroelectricity or insulator-to-metal transitions. There has been a growing activity in the development of thin film transition metal oxides because of their relevance to device applications, because properties can be modified owing to thin film strains, especially epitaxial coherency strains. As a consequence, metastable polymorphs/phase arrangements with novel physical properties have been fabricated as thin films. Reducing the thickness of the layer down to a few unit cells is also interesting since novel properties can emerge at the interfaces between two oxides. Below, we will analyze necessary developments in the area of epitaxy of oxide films, and introduce the novel approach called combinatorial substrate epitaxy (CSE) [216–217].

**Current and future challenges.** The main approach to design metastable compositions in the transition-metal oxides films and generate novel electronic properties is the use of strain engineering where little changes can drastically modify the electronic properties [218]. It is, for example, possible to tune the critical temperature in ferroelectric or superconducting films [219, 220]. In that case, the substrate choice is of utmost importance in designing and preparing high-quality films. Typical single-crystal substrates are $SrTiO_3$, $LaAlO_3$ or $NdGaO_3$ but $DyScO_3$ have also been used. In spite of the large number of observations and promise of epitaxial oxide thin films, prior investigations have nevertheless largely focused on films on low-index commercially available single-crystal substrates (typically 001, 110 or 111). However, their cost and availability limit detailed investigations to a narrow region of special interfaces/orientations. As an example the growth, kinetics and understanding of anisotropic functional properties (i.e. polarization, magnetization, resistivity, etc), which are dependent on the orientation of the film with respect to the surface is extremely difficult to analyze. Also, growing a film on a single-crystal is a one at a time serial process. Nevertheless, the conventional approach is well optimized for making devices, and works well. To expand the study, one required the development of radically new approach such as the combinatorial substrate epitaxy (CSE), which was recently developed at Carnegie Mellon University, USA [216, 217]. We believe it is an exciting area, which can be used to for the development of oxide electronics.

**Advances in science and technology to meet challenges.** Rather than depositing on commercial single crystals, a new strategy used well-characterized polycrystalline samples where each grain of the substrate can be viewed as a single crystal of a particular orientation. Thus, there are thousands of substrates in any given film deposition. If one can prepare a ceramic, the surface can be simply polished, and used as

substrate. The orientation and structural quality of the substrate and film grains are investigated locally (and mapped) using electron backscattering diffraction (EBSD). The physical property of the films can also be mapped using local probes, such as scanning probe and near-field microscopy methods.

This combined approach, was applied to heterostructures of conducting $La_{0.7}Sr_{0.3}MnO_3$ and multiferroic $BiFeO_3$ films grown, using pulsed laser deposition, on polished polycrystalline $LaAlO_3$ ceramic substrates, fabricated using spark plasma sintering. This system is interesting since $BiFeO_3$ thin films have been widely studied on low-index orientations, such as (100), (110), and (111), of single crystal perovskites [221]. Typical images (see figure 29) indicate that the film epitaxy is dominated by local substrate-driven growth events that are consistent with each perovskite layer adopting a cube-on-cube epitaxial orientation relationship, for nearly all grain orientations of the substrate. The epitaxial $BiFeO_3$ heterostructure was also investigated using piezoforce microscopy (PFM), in a similar fashion to $BiFeO_3$ films grown on single crystals. Figure 30 shows the topography, out-of-plane PFM and in-plane PFM images, respectively, after the local application of a positive 12V bias in the central region that includes several grains and grain boundaries. A clear polarization reversal (comparing the central region to the outer regions) is observed in the OP image, as the PFM contrast is reversed. The observed change in the out-of-plane contrast with a specific voltage polarity (inducing up to downward OP switching only in our configuration) further validates the interpretation of the direction of the OP polarization component. This demonstrates that the ferroelectric properties of $BiFeO_3$ are maintained for these many orientations in the heterostructure on the $LaAlO_3$ substrate. The local epitaxial growth of pulsed laser deposited $Ca_2MnO_4$ films on polycrystalline spark plasma sintered $Sr_2TiO_4$ substrates was also investigated to determine phase formation and preferred epitaxial orientation relationships for isostructural Ruddlesden-Popper heteroepitaxy [222, 223].

These results demonstrate the potential of CSE in the design and growth of a wide range of complex functional oxides. They also open new directions for materials scientist and condensed matter physicists that could impact several areas. When CSE is coupled with scanning property measurements, high-throughput correlations can be generated between functional properties, film-substrate pairs, and crystal orientation, providing a library of physical property observations and expanding our understanding of engineering function into transition metal oxides. From the potential applications, it is further expected that this method could become a general rapid, convenient approach, for the search of metastable oxide films with a relatively low-cost fabrication, and this is probably one of the major topic to be explored. This will definitively speed the discovery of unexpected properties in oxide thin films.

**Concluding remarks.** These examples demonstrated that structure-property relationships can be investigated for complex oxide heterostructures using the combinatorial substrate epitaxy approach, a high-throughput method for investigating the local epitaxy and properties of films deposited on polycrystalline substrates. Generally, efforts need to be intensified
# 17. Combinatorial substrate epitaxy: a novel approach of epitaxy for oxide films

Wilfrid Prelier

Laboratoire CRISMAT, ENSICAEN, CNRS UMR 6508, 6 Boulevard Maréchal Juin, 14050 Caen, France

**Status.** Transition-metal oxides attract attention because of their fascinating properties, including superconductivity, magnetism, ferroelectricity or insulator-to-metal transitions. There has been a growing activity in the development of thin film transition metal oxides because of their relevance to device applications, because properties can be modified owing to thin film strains, especially epitaxial coherency strains. As a consequence, metastable polymorphs/phase arrangements with novel physical properties have been fabricated as thin films. Reducing the thickness of the layer down to a few unit cells is also interesting since novel properties can emerge at the interfaces between two oxides. Below, we will analyze necessary developments in the area of epitaxy of oxide films, and introduce the novel approach called combinatorial substrate epitaxy (CSE) [216–217].

**Current and future challenges.** The main approach to design metastable compositions in the transition-metal oxides films and generate novel electronic properties is the use of strain engineering where little changes can drastically modify the electronic properties [218]. It is, for example, possible to tune the critical temperature in ferroelectric or superconducting films [219, 220]. In that case, the substrate choice is of utmost importance in designing and preparing high-quality films. Typical single-crystal substrates are $SrTiO_3$, $LaAlO_3$ or $NdGaO_3$ but $DyScO_3$ have also been used. In spite of the large number of observations and promise of epitaxial oxide thin films, prior investigations have nevertheless largely focused on films on low-index commercially available single-crystal substrates (typically 001, 110 or 111). However, their cost and availability limit detailed investigations to a narrow region of special interfaces/orientations. As an example the growth, kinetics and understanding of anisotropic functional properties (i.e. polarization, magnetization, resistivity, etc), which are dependent on the orientation of the film with respect to the surface is extremely difficult to analyze. Also, growing a film on a single-crystal is a one at a time serial process. Nevertheless, the conventional approach is well optimized for making devices, and works well. To expand the study, one required the development of radically new approach such as the combinatorial substrate epitaxy (CSE), which was recently developed at Carnegie Mellon University, USA [216, 217]. We believe it is an exciting area, which can be used to for the development of oxide electronics.

**Advances in science and technology to meet challenges.** Rather than depositing on commercial single crystals, a new strategy used well-characterized polycrystalline samples where each grain of the substrate can be viewed as a single crystal of a particular orientation. Thus, there are thousands of substrates in any given film deposition. If one can prepare a ceramic, the surface can be simply polished, and used as

substrate. The orientation and structural quality of the substrate and film grains are investigated locally (and mapped) using electron backscattering diffraction (EBSD). The physical property of the films can also be mapped using local probes, such as scanning probe and near-field microscopy methods.

This combined approach, was applied to heterostructures of conducting $La_{0.7}Sr_{0.3}MnO_3$ and multiferroic $BiFeO_3$ films grown, using pulsed laser deposition, on polished polycrystalline $LaAlO_3$ ceramic substrates, fabricated using spark plasma sintering. This system is interesting since $BiFeO_3$ thin films have been widely studied on low-index orientations, such as (100), (110), and (111), of single crystal perovskites [221]. Typical images (see figure 29) indicate that the film epitaxy is dominated by local substrate-driven growth events that are consistent with each perovskite layer adopting a cube-on-cube epitaxial orientation relationship, for nearly all grain orientations of the substrate. The epitaxial $BiFeO_3$ heterostructure was also investigated using piezoforce microscopy (PFM), in a similar fashion to $BiFeO_3$ films grown on single crystals. Figure 30 shows the topography, out-of-plane PFM and in-plane PFM images, respectively, after the local application of a positive 12V bias in the central region that includes several grains and grain boundaries. A clear polarization reversal (comparing the central region to the outer regions) is observed in the OP image, as the PFM contrast is reversed. The observed change in the out-of-plane contrast with a specific voltage polarity (inducing up to downward OP switching only in our configuration) further validates the interpretation of the direction of the OP polarization component. This demonstrates that the ferroelectric properties of $BiFeO_3$ are maintained for these many orientations in the heterostructure on the $LaAlO_3$ substrate. The local epitaxial growth of pulsed laser deposited $Ca_2MnO_4$ films on polycrystalline spark plasma sintered $Sr_2TiO_4$ substrates was also investigated to determine phase formation and preferred epitaxial orientation relationships for isostructural Ruddlesden-Popper heteroepitaxy [222, 223].

These results demonstrate the potential of CSE in the design and growth of a wide range of complex functional oxides. They also open new directions for materials scientist and condensed matter physicists that could impact several areas. When CSE is coupled with scanning property measurements, high-throughput correlations can be generated between functional properties, film-substrate pairs, and crystal orientation, providing a library of physical property observations and expanding our understanding of engineering function into transition metal oxides. From the potential applications, it is further expected that this method could become a general rapid, convenient approach, for the search of metastable oxide films with a relatively low-cost fabrication, and this is probably one of the major topic to be explored. This will definitively speed the discovery of unexpected properties in oxide thin films.

**Concluding remarks.** These examples demonstrated that structure-property relationships can be investigated for complex oxide heterostructures using the combinatorial substrate epitaxy approach, a high-throughput method for investigating the local epitaxy and properties of films deposited on polycrystalline substrates. Generally, efforts need to be intensified
<figure><img src="image_34.png" /><figcaption>**Figure 29.** Inverse pole figure (orientation) maps of (a) the LaAlO₃ substrate, (b) the BiFeO₃ film, and their corresponding colour code (c). The white boxes indicate grains in the same region, confirming the film follows a 'grain-over-grain' growth. Adapted from [221], with the permission of AIP Publishing.</figcaption></figure>

<figure><img src="image_35.png" /><figcaption>**Figure 30.** Polling measurements of BiFeO₃ films across triple junctions ((a)–(c)) and grain boundaries ((d)–(f)). (a) PFM Topography, (b) out-of-plane, (c) in-plane, (d) PFM topography, (e) out-of-plane, and (f) in-plane. PFM contrasts were recorded after local application of a +12V bias showing a 180° switching event. The images confirm the film grown on ceramic has similar properties as those grown on single-crystals. Adapted from [221], with the permission of AIP Publishing.</figcaption></figure>

to rapidly prepare metastable phases in the form of thin films, and CSE is one of the potential approach to be used.

*Acknowledgement.* Partial support of the Conseil Régional Basse-Normandie (Programe Asie) is acknowledged.
<figure><img src="image_35.png" /><figcaption>**Figure 29.** Inverse pole figure (orientation) maps of (a) the LaAlO₃ substrate, (b) the BiFeO₃ film, and their corresponding colour code (c). The white boxes indicate grains in the same region, confirming the film follows a 'grain-over-grain' growth. Adapted from [221], with the permission of AIP Publishing.</figcaption></figure>

<figure><img src="image_36.png" /><figcaption>**Figure 30.** Polling measurements of BiFeO₃ films across triple junctions ((a)–(c)) and grain boundaries ((d)–(f)). (a) PFM Topography, (b) out-of-plane, (c) in-plane, (d) PFM topography, (e) out-of-plane, and (f) in-plane. PFM contrasts were recorded after local application of a +12V bias showing a 180° switching event. The images confirm the film grown on ceramic has similar properties as those grown on single-crystals. Adapted from [221], with the permission of AIP Publishing.</figcaption></figure>

to rapidly prepare metastable phases in the form of thin films, and CSE is one of the potential approach to be used.

**Acknowledgement.** Partial support of the Conseil Régional Basse-Normandie (Programe Asie) is acknowledged.
# 18. Topological oxide electronics

Masaki Uchida and Masashi Kawasaki

University of Tokyo

**Status.** In the past, oxide materials have been complementarily used in conventional semiconductor technologies and devices. In particular, polycrystalline or amorphous oxide thin films with a large band gap have been widely adopted as gate insulators, capacitors, or transparent conductors. In recent decades, on the other hand, a number of unprecedented functionalities such as high temperature superconductivity, colloidal magnetoresistance and electroresistance, and multiferroics have been discovered and attracted burgeoning attention for unique electronics applications as well as emerging new physics only realized in oxide materials. These properties and functionalities essentially originate from strong electron correlation in charge, spin, and orbital degrees of freedom. Technical advances in epitaxial film growth have opened the door to utilize the functional oxide thin films and also to explore atomically controlled oxide interfaces showing further emergent phenomena. Interface superconductivity and ferromagnetism are their examples demonstrating great potential of oxide heterostructures [224].

In the field of condensed matter physics, more recently, there is a growing awareness of other important degree of freedom, topology. Topology is the term used to describe or classify properties maintained for a continuous deformation in a given space. A topological state is thus intrinsically stable against perturbations favoring other different states, producing novel functionalities suited for storing and processing information as a state variable. Typical topological systems and their materials are summarized in figure 31. One example is a topological insulator, where the bulk bands have non-trivial topology in momentum space, giving rise to a symmetry protected conductive surface state [225]. This surface state is directly confirmed such as in bismuth selenides and bismuth tellurides, showing promise for dissipationless electronic devices. A more complicated state, connecting two sides of the surface state through the bulk, is also observed in transition-metal arsenides, called a topological semimetal. Quantum Hall systems represented by high-mobility GaAs heterostructure are another example of the topological phase, leading the research of edge states from the early period. The other example of topological systems is a magnetic skyrmion, where the spin textures have non-trivial topology in real space, giving rise to a topologically protected macroscopic spin object [226]. Typically, spins in two dimensions increasingly twist towards the center and show a vortex-like arrangement, as directly observed in chiral metals such as manganese silicides and germanides and a chiral insulator. The skyrmion behaves as a quasiparticle in a magnet, attracting rising attention as a stable information carrier.

The topological states are more generally characterized by topological numbers, which are respectively defined as integral of some spatial variances in the given space, and

correspondent properties such as edge current or fictitious field robustly emerge in the unit of quantum conductance ($e^2/h$) or flux ($h/e$). On the other hand, detailed performances of these topological properties, which are strongly dependent on fundamental parameters including electron correlation, spin-orbit interaction, and magnetic exchange interactions, as well as band gap and carrier concentration, require further improvement for their future applications. Oxide materials having the wide-ranging physical parameters are highly desirable for this purpose, and actually, several candidates in oxide films, interfaces, and superlattices are just beginning to be reported, as explained one by one in the following.

**Current and future challenges.** Several perovskite and pyrochlore oxides with heavy elements such as iridium and bismuth or their superlattices have been theoretically suggested to exhibit novel topological insulator or semimetal phases, which originate from interplay of strong spin-orbit interaction and electron correlation [227]. For example, the discovery of a large gap topological insulator will lead to effective use of the dissipationless surface conduction at room temperature. As illustrated in figure 32, in addition, control of the topological phase domains and the correspondent dissipationless conduction is one of the significant goals for developing future low power consumption devices. Magnetic topological semimetals as expected in pyrochlore iridates $R_2Ir_2O_7$, as well as magnetic topological insulators, are candidate systems for achieving magnetic control of the topological domains and conduction [228].

Regarding quantum Hall systems, most efforts have focused on the even-denominator fractional quantum Hall state observed in the GaAs system. Its ground state has been extensively examined in the context of a non-abelian state, where quasiparticles obey non-abelian braiding statistics and their exchange operation is expected to be applied in topological quantum computation [229]. Clean oxide 2D electron systems can be alternative candidates for further advancing this research. In particular, $ZnO/(Mg,Zn)O$ heterointerface, where the even-denominator state has been confirmed besides the GaAs heterostructure [230], is promising due to its higher controllability of the ratio between Zeeman and Landau splitting energies. Determination of the non-abelian state, such as by demonstrating $e/4$ charge and full spin polarization, will pave the way for application to the quantum computation.

Magnetic skyrmions have much potential for application in future nonvolatile memory device, which has advantages such as high memory density and low driving current, compared to the magnetic bubble and racetrack memories [231]. While skyrmion crystals have been observed both in metals and insulators, the discovery in magnetic semiconductors is one of the important challenges for controlling skyrmion states through the carrier doping. Among many magnetic oxides, for example, ferromagnetic semiconductor EuO is one of the leading candidates, because topological Hall effect resulting from the fictitious magnetic field has been confirmed in its film form [232]. For creating small
# 18. Topological oxide electronics

Masaki Uchida and Masashi Kawasaki

University of Tokyo

**Status.** In the past, oxide materials have been complementarily used in conventional semiconductor technologies and devices. In particular, polycrystalline or amorphous oxide thin films with a large band gap have been widely adopted as gate insulators, capacitors, or transparent conductors. In recent decades, on the other hand, a number of unprecedented functionalities such as high temperature superconductivity, colloidal magnetoresistance and electroresistance, and multiferroics have been discovered and attracted burgeoning attention for unique electronics applications as well as emerging new physics only realized in oxide materials. These properties and functionalities essentially originate from strong electron correlation in charge, spin, and orbital degrees of freedom. Technical advances in epitaxial film growth have opened the door to utilize the functional oxide thin films and also to explore atomically controlled oxide interfaces showing further emergent phenomena. Interface superconductivity and ferromagnetism are their examples demonstrating great potential of oxide heterostructures [224].

In the field of condensed matter physics, more recently, there is a growing awareness of other important degree of freedom, topology. Topology is the term used to describe or classify properties maintained for a continuous deformation in a given space. A topological state is thus intrinsically stable against perturbations favoring other different states, producing novel functionalities suited for storing and processing information as a state variable. Typical topological systems and their materials are summarized in figure 31. One example is a topological insulator, where the bulk bands have non-trivial topology in momentum space, giving rise to a symmetry protected conductive surface state [225]. This surface state is directly confirmed such as in bismuth selenides and bismuth tellurides, showing promise for dissipationless electronic devices. A more complicated state, connecting two sides of the surface state through the bulk, is also observed in transition-metal arsenides, called a topological semimetal. Quantum Hall systems represented by high-mobility GaAs heterostructure are another example of the topological phase, leading the research of edge states from the early period. The other example of topological systems is a magnetic skyrmion, where the spin textures have non-trivial topology in real space, giving rise to a topologically protected macroscopic spin object [226]. Typically, spins in two dimensions increasingly twist towards the center and show a vortex-like arrangement, as directly observed in chiral metals such as manganese silicides and germanides and a chiral insulator. The skyrmion behaves as a quasiparticle in a magnet, attracting rising attention as a stable information carrier.

The topological states are more generally characterized by topological numbers, which are respectively defined as integral of some spatial variances in the given space, and

correspondent properties such as edge current or fictitious field robustly emerge in the unit of quantum conductance ($e^2/h$) or flux ($h/e$). On the other hand, detailed performances of these topological properties, which are strongly dependent on fundamental parameters including electron correlation, spin-orbit interaction, and magnetic exchange interactions, as well as band gap and carrier concentration, require further improvement for their future applications. Oxide materials having the wide-ranging physical parameters are highly desirable for this purpose, and actually, several candidates in oxide films, interfaces, and superlattices are just beginning to be reported, as explained one by one in the following.

**Current and future challenges.** Several perovskite and pyrochlore oxides with heavy elements such as iridium and bismuth or their superlattices have been theoretically suggested to exhibit novel topological insulator or semimetal phases, which originate from interplay of strong spin-orbit interaction and electron correlation [227]. For example, the discovery of a large gap topological insulator will lead to effective use of the dissipationless surface conduction at room temperature. As illustrated in figure 32, in addition, control of the topological phase domains and the correspondent dissipationless conduction is one of the significant goals for developing future low power consumption devices. Magnetic topological semimetals as expected in pyrochlore iridates $R_2Ir_2O_7$, as well as magnetic topological insulators, are candidate systems for achieving magnetic control of the topological domains and conduction [228].

Regarding quantum Hall systems, most efforts have focused on the even-denominator fractional quantum Hall state observed in the GaAs system. Its ground state has been extensively examined in the context of a non-abelian state, where quasiparticles obey non-abelian braiding statistics and their exchange operation is expected to be applied in topological quantum computation [229]. Clean oxide 2D electron systems can be alternative candidates for further advancing this research. In particular, $ZnO/(Mg,Zn)O$ heterointerface, where the even-denominator state has been confirmed besides the GaAs heterostructure [230], is promising due to its higher controllability of the ratio between Zeeman and Landau splitting energies. Determination of the non-abelian state, such as by demonstrating $e/4$ charge and full spin polarization, will pave the way for application to the quantum computation.

Magnetic skyrmions have much potential for application in future nonvolatile memory device, which has advantages such as high memory density and low driving current, compared to the magnetic bubble and racetrack memories [231]. While skyrmion crystals have been observed both in metals and insulators, the discovery in magnetic semiconductors is one of the important challenges for controlling skyrmion states through the carrier doping. Among many magnetic oxides, for example, ferromagnetic semiconductor EuO is one of the leading candidates, because topological Hall effect resulting from the fictitious magnetic field has been confirmed in its film form [232]. For creating small
<figure><img src="image_36.png" /><figcaption>**Figure 31.** Typical topological materials and their candidates in oxide films.</figcaption></figure>

<figure><img src="image_37.png" /><figcaption>**Figure 32.** Concepts of topological electronics devices.</figcaption></figure>

skyrmions for high memory density, it is necessary to modulate magnetic exchange interactions in materials, especially, the Dzyaloshinskii–Moriya interaction, which favors a cating of the two neighboring spins. Magnetic oxide heterostructures with tunable magnetic interactions at the interface are a highly promising system for realizing size-controlled skyrmion states, as atomic-scale skyrmions have been already demonstrated in metal heterostructures [233].

***Advances in science and technology to meet challenges.*** For directly confirming the topological surface state in candidate films or superlattices, *in situ* characterization integrating film growth and angle-resolved photoemission spectroscopy is remarkably helpful. Microscopy techniques for visualizing topological phase domains and/or the correspondent surface conduction are also needed to be developed for strongly promoting this research field. Regarding quantum Hall systems, advances in oxide molecular beam epitaxy technique will enable us to create new high-mobility 2D electron systems. Development of process techniques is also important

for identifying the ground state such as by mesoscopic measurements. For demonstrating basic operations in skyrmion memory, an experiment combining transport measurement and direct observation using magnetic force microscopy or transmission electron microscopy is of key importance. Direct observation of interface skyrmion states is also technologically significant.

***Concluding remarks.*** Manipulation of topological properties in materials by external stimuli will trigger revolutionary changes in the present framework of electronics. The above described concepts are just a few examples that are expected to be realized in the typical topological systems—topological phases, quantum Hall systems, and skyrmion states. Once such basic operations of topological properties are demonstrated in oxide materials, it holds great promise for developing next generation innovative devices contributing low power consumption, quantum information, and magnetic memory technologies. The beginning of topological oxide electronics is envisaged on this frontier field.
<figure><img src="image_37.png" /><figcaption>**Figure 31.** Typical topological materials and their candidates in oxide films.</figcaption></figure>

<figure><img src="image_38.png" /><figcaption>**Figure 32.** Concepts of topological electronics devices.</figcaption></figure>

skyrmions for high memory density, it is necessary to modulate magnetic exchange interactions in materials, especially, the Dzyaloshinskii–Moriya interaction, which favors a cating of the two neighboring spins. Magnetic oxide heterostructures with tunable magnetic interactions at the interface are a highly promising system for realizing size-controlled skyrmion states, as atomic-scale skyrmions have been already demonstrated in metal heterostructures [233].

***Advances in science and technology to meet challenges.*** For directly confirming the topological surface state in candidate films or superlattices, *in situ* characterization integrating film growth and angle-resolved photoemission spectroscopy is remarkably helpful. Microscopy techniques for visualizing topological phase domains and/or the correspondent surface conduction are also needed to be developed for strongly promoting this research field. Regarding quantum Hall systems, advances in oxide molecular beam epitaxy technique will enable us to create new high-mobility 2D electron systems. Development of process techniques is also important

for identifying the ground state such as by mesoscopic measurements. For demonstrating basic operations in skyrmion memory, an experiment combining transport measurement and direct observation using magnetic force microscopy or transmission electron microscopy is of key importance. Direct observation of interface skyrmion states is also technologically significant.

***Concluding remarks.*** Manipulation of topological properties in materials by external stimuli will trigger revolutionary changes in the present framework of electronics. The above described concepts are just a few examples that are expected to be realized in the typical topological systems—topological phases, quantum Hall systems, and skyrmion states. Once such basic operations of topological properties are demonstrated in oxide materials, it holds great promise for developing next generation innovative devices contributing low power consumption, quantum information, and magnetic memory technologies. The beginning of topological oxide electronics is envisaged on this frontier field.
# 19. Control of orbital reconstruction, metal-to-insulator transitions and topologically nontrivial phases at oxide interfaces

Rossitza Pentcheva

Theoretical Physics, Department of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen, Lotharstrasse 1, 47057 Duisburg, Germany

**Status.** Technological demands driven by the fundamental limits of miniaturization of electronics devices call for the development of materials with tailored functionality that have the potential to substitute e.g. conventional semiconductors. Transition metal oxides (TMO) emerge as a promising class of such materials. Already in the bulk they exhibit a rich range of fascinating properties such as magnetism, superconductivity and ferroelectricity as a result of the interplay of charge, spin, orbital and lattice degrees of freedom [234]. Moreover, at their interfaces novel electronic phases can be stabilized that are not available in the parent compounds. This opens new avenues to design nanoscale materials with enhanced and new functionality. The past few years have witnessed an unprecedented activity in the field of oxide interfaces [186]. It is of paramount importance to achieve a fundamental understanding of the emergent physics at oxide interfaces. To this end, material-specific density functional calculations (DFT) can bring invaluable insight to identify and explore systematically the parameters that control this complex behaviour. In the following we will discuss the role of symmetry breaking, strain, exerted by the substrate, polar discontinuities, confinement, as well as variation in crystallographic orientation (see figure 33) in designing novel electronic ground states.

**Current and future challenges.** The ramifications of a polar discontinuity are evident in the case of the LaAlO₃/SrTiO₃ (001) interface. The AO/BO₂ stacking in the perovskite structure ABO₃ along the (001) direction leads to alternating positively and negatively charged layers in LaAlO₃ (LAO) and formally neutral layers SrTiO₃ (STO) and consequently an excess of 0.5 e at the TiO₂/LaO interface (see figure 33). SrTiO₃ quantum wells confined within LaAlO₃ with symmetric n-type interfaces are experimentally more challenging to realize than the commonly investigated thin LaAlO₃ films on SrTiO₃ (001), but bear analogies to the recently investigated GdTiO₃/SrTiO₃ superlattices [177]. DFT + U results predict that in the thinnest quantum wells (N = 2) the electrostatic doping results in a charge and orbitally ordered state (alternating $d_{xz}$, $d_{yz}$ at $Ti^{3+}$) sites accompanied by strong octahedral tilts and rotations that are not observed in bulk STO (figure 34(a)) [235].

Novel effectively 2D behavior can be achieved even without a valence discontinuity. An example are heterostructures containing the paramagnetic metal LaNiO₃ and the band insulator LaAlO₃. Although the initially proposed control of orbital polarization by strain [236] could only partially be realized [237], intriguing electronic behavior was detected in this system: confinement of a single LaNiO₃ layer leads to an opening of a gap under tensile strain (using e.g. SrTiO₃ as a substrate) [238].

This metal-to-insulator transition (MIT) is driven by the interplay of quantum confinement, electronic correlations and strain and emerges from a disproportionation of Ni into two inequivalent sites with different magnetic moments but similar total charges (figure 34(b)) [238], similar to the mechanism identified in bulk nickelates [239, 240]. Upon increasing the thickness of the LaNiO₃ layer the system quickly undergoes a dimensional crossover to a metallic state [241, 242]. In particular, the modification of bond angles and octahedral tilts under tensile strain effectively controls the bandwidth, triggering the MIT.

**Advances in science and technology to meet challenges.** Currently, the interest is shifting from the much studied (001) oriented perovskite systems to the (111)-crystallographic orientation. In the [111] direction the stacking changes to AO₃ and B layers (see figure 33), where each B layer forms a triangular lattice. In contrast to the (001) oriented superlattices, where the orbital polarization is limited due to the inherent covalency of the in-plane Ni–O bond, a strong control of orbital polarization can be achieved in (111)-oriented (LaNiO₃)₁/(LaAlO₃)₁ [243] or (NdNiO₃)₂/(LaAlO₃)₂ [244] superlattices. The spatial decoupling of the NiO₆ octahedra either through layering (figure 34(c)) [243] or antiferromagnetic order [244] suppresses the covalency and enables orbital polarization. The strong influence of the crystallographic orientation coupled with the inherent high frustration in the (111)-oriented superlattices makes these systems very promising to host exotic electronic phases. Recently, the stabilization of a polar metallic state in NdNiO₃ grown on LaAlO₃(111) was reported, that is not accessible in the (001) orientation [245].

A new research area aims at designing topological states in oxide superlattices with (111) crystallographic orientation [246]. A bilayer in this configuration comprises a combination of two triangular lattices and forms a buckled honeycomb lattice which is known to host nontrivial behavior. This combined with the correlated, multi-orbital nature of transition metal ions leads the emergence of a Dirac-point Fermi surface in SrTiO₃ and LaXO₃ bilayers (X = Mn, Co, Ni) sandwiched between LaAlO₃ as a spacer (see figures 34(d) and (e)). These states are interaction-driven (i.e. arise for a non-zero Hubbard U) and are protected by symmetry [243, 244, 247, 248]. Sublattice symmetry breaking of different origin leads to a Mott insulating gap. An interesting case emerges for LaMnO₃ where a topological transition takes place from a Chern insulator with a sizeable band gap of ~150 meV to Jahn-Teller distorted trivial Mott insulator [248].

**Concluding remarks.** The results achieved so far point to a series of parameters that can be used to tune the properties of oxide surfaces and interfaces in order to realize novel charge, magnetic and orbitally ordered states and enable control of functionality for applications in electronics and spintronics devices, as well as in energy conversion. Some major challenges for the future are the improvement in the theoretical description of strongly correlated systems e.g. by using hybrid functionals or dynamical mean-field theory, and, furthermore, the mastering of growth of highly polar surface orientations as the (111)-orientation, which has recently been demonstrated for nickelate superlattices (e.g. [244, 245]). Systems with this
# 19. Control of orbital reconstruction, metal-to-insulator transitions and topologically nontrivial phases at oxide interfaces

Rossitza Pentcheva

Theoretical Physics, Department of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen, Lotharstrasse 1, 47057 Duisburg, Germany

**Status.** Technological demands driven by the fundamental limits of miniaturization of electronics devices call for the development of materials with tailored functionality that have the potential to substitute e.g. conventional semiconductors. Transition metal oxides (TMO) emerge as a promising class of such materials. Already in the bulk they exhibit a rich range of fascinating properties such as magnetism, superconductivity and ferroelectricity as a result of the interplay of charge, spin, orbital and lattice degrees of freedom [234]. Moreover, at their interfaces novel electronic phases can be stabilized that are not available in the parent compounds. This opens new avenues to design nanoscale materials with enhanced and new functionality. The past few years have witnessed an unprecedented activity in the field of oxide interfaces [186]. It is of paramount importance to achieve a fundamental understanding of the emergent physics at oxide interfaces. To this end, material-specific density functional calculations (DFT) can bring invaluable insight to identify and explore systematically the parameters that control this complex behaviour. In the following we will discuss the role of symmetry breaking, strain, exerted by the substrate, polar discontinuities, confinement, as well as variation in crystallographic orientation (see figure 33) in designing novel electronic ground states.

**Current and future challenges.** The ramifications of a polar discontinuity are evident in the case of the LaAlO₃/SrTiO₃ (001) interface. The AO/BO₂ stacking in the perovskite structure ABO₃ along the (001) direction leads to alternating positively and negatively charged layers in LaAlO₃ (LAO) and formally neutral layers SrTiO₃ (STO) and consequently an excess of 0.5 e at the TiO₂/LaO interface (see figure 33). SrTiO₃ quantum wells confined within LaAlO₃ with symmetric n-type interfaces are experimentally more challenging to realize than the commonly investigated thin LaAlO₃ films on SrTiO₃ (001), but bear analogies to the recently investigated GdTiO₃/SrTiO₃ superlattices [177]. DFT + U results predict that in the thinnest quantum wells (N = 2) the electrostatic doping results in a charge and orbitally ordered state (alternating $d_{xz}$, $d_{yz}$ at $Ti^{3+}$) sites accompanied by strong octahedral tilts and rotations that are not observed in bulk STO (figure 34(a)) [235].

Novel effectively 2D behavior can be achieved even without a valence discontinuity. An example are heterostructures containing the paramagnetic metal LaNiO₃ and the band insulator LaAlO₃. Although the initially proposed control of orbital polarization by strain [236] could only partially be realized [237], intriguing electronic behavior was detected in this system: confinement of a single LaNiO₃ layer leads to an opening of a gap under tensile strain (using e.g. SrTiO₃ as a substrate) [238].

This metal-to-insulator transition (MIT) is driven by the interplay of quantum confinement, electronic correlations and strain and emerges from a disproportionation of Ni into two inequivalent sites with different magnetic moments but similar total charges (figure 34(b)) [238], similar to the mechanism identified in bulk nickelates [239, 240]. Upon increasing the thickness of the LaNiO₃ layer the system quickly undergoes a dimensional crossover to a metallic state [241, 242]. In particular, the modification of bond angles and octahedral tilts under tensile strain effectively controls the bandwidth, triggering the MIT.

**Advances in science and technology to meet challenges.** Currently, the interest is shifting from the much studied (001) oriented perovskite systems to the (111)-crystallographic orientation. In the [111] direction the stacking changes to AO₃ and B layers (see figure 33), where each B layer forms a triangular lattice. In contrast to the (001) oriented superlattices, where the orbital polarization is limited due to the inherent covalency of the in-plane Ni–O bond, a strong control of orbital polarization can be achieved in (111)-oriented (LaNiO₃)₁/(LaAlO₃)₁ [243] or (NdNiO₃)₂/(LaAlO₃)₂ [244] superlattices. The spatial decoupling of the NiO₆ octahedra either through layering (figure 34(c)) [243] or antiferromagnetic order [244] suppresses the covalency and enables orbital polarization. The strong influence of the crystallographic orientation coupled with the inherent high frustration in the (111)-oriented superlattices makes these systems very promising to host exotic electronic phases. Recently, the stabilization of a polar metallic state in NdNiO₃ grown on LaAlO₃(111) was reported, that is not accessible in the (001) orientation [245].

A new research area aims at designing topological states in oxide superlattices with (111) crystallographic orientation [246]. A bilayer in this configuration comprises a combination of two triangular lattices and forms a buckled honeycomb lattice which is known to host nontrivial behavior. This combined with the correlated, multi-orbital nature of transition metal ions leads the emergence of a Dirac-point Fermi surface in SrTiO₃ and LaXO₃ bilayers ($X = Mn, Co, Ni$) sandwiched between LaAlO₃ as a spacer (see figures 34(d) and (e)). These states are interaction-driven (i.e. arise for a non-zero Hubbard U) and are protected by symmetry [243, 244, 247, 248]. Sublattice symmetry breaking of different origin leads to a Mott insulating gap. An interesting case emerges for LaMnO₃ where a topological transition takes place from a Chern insulator with a sizeable band gap of ~150 meV to Jahn-Teller distorted trivial Mott insulator [248].

**Concluding remarks.** The results achieved so far point to a series of parameters that can be used to tune the properties of oxide surfaces and interfaces in order to realize novel charge, magnetic and orbitally ordered states and enable control of functionality for applications in electronics and spintronics devices, as well as in energy conversion. Some major challenges for the future are the improvement in the theoretical description of strongly correlated systems e.g. by using hybrid functionals or dynamical mean-field theory, and, furthermore, the mastering of growth of highly polar surface orientations as the (111)-orientation, which has recently been demonstrated for nickelate superlattices (e.g. [244, 245]). Systems with this
<figure><img src="image_38.png" /><figcaption>**Figure 33.** Side views of perovskite heterostructures along the (001) and (111) crystallographic directions along with parameters controlling the behaviour at oxide interfaces: symmetry breaking, strain, polar discontinuities, finite size effects, etc.</figcaption></figure>

<figure><img src="image_39.png" /><figcaption>**Figure 34.** Mechanisms of electronic and orbital reconstruction at oxide interfaces obtained from DFT+U calculations: a) charge and orbital order at a polar (LaAlO₃)₄/SrTiO₃)₂(001) superlattice with a very narrow STO QW (N = 2) [235]; b) Band gap opening in (LaAlO₃)₄/LaNiO₃)₁(001) under tensile strain due to Ni-site disproportionation [238]. In contrast, a strong control of orbital reconstruction is possible in the double perovskite La₂NiAlO₆ c) which corresponds to a (LaAlO₃)₄/LaNiO₃)₁(111) superlattice [243]. A Dirac-point Fermi surface in d) (LaAlO₃)₄/SrTiO₃)₂(111) [245] and e) (LaAlO₃)₄/LaNiO₃)₂(111) [243] is unstable with respect to symmetry lowering that opens a gap.</figcaption></figure>

crystallographic orientation promise an even richer spectrum of possibilities concerning orbital reconstructions and topologically nontrivial states.

**Acknowledgments.** Research supported by the German Science Foundation within SFB/TRR 80 'From electronic correlations to functionality'.
<figure><img src="image_39.png" /><figcaption>**Figure 33.** Side views of perovskite heterostructures along the (001) and (111) crystallographic directions along with parameters controlling the behaviour at oxide interfaces: symmetry breaking, strain, polar discontinuities, finite size effects, etc.</figcaption></figure>

<figure><img src="image_40.png" /><figcaption>**Figure 34.** Mechanisms of electronic and orbital reconstruction at oxide interfaces obtained from DFT+U calculations: a) charge and orbital order at a polar (LaAlO₃)₄/SrTiO₃)₂(001) superlattice with a very narrow STO QW (N = 2) [235]; b) Band gap opening in (LaAlO₃)₁/LaNiO₃)₁(001) under tensile strain due to Ni-site disproportionation [238]. In contrast, a strong control of orbital reconstruction is possible in the double perovskite La₂NiAlO₆ c) which corresponds to a (LaAlO₃)₄/LaNiO₃)₂(111) superlattice [243]. A Dirac-point Fermi surface in d) (LaAlO₃)₄/SrTiO₃)₂(111) [245] and e) (LaAlO₃)₄/LaNiO₃)₂(111) [243] is unstable with respect to symmetry lowering that opens a gap.</figcaption></figure>

crystallographic orientation promise an even richer spectrum of possibilities concerning orbital reconstructions and topologically nontrivial states.

**Acknowledgments.** Research supported by the German Science Foundation within SFB/TRR 80 'From electronic correlations to functionality'.
## 20. Kitaev exchange in hexagonal iridates and rhodates

Philipp Gegenwart

Experimentalphysik VI, Center for Electronic Correlations and Magnetism, Augsburg University, 86159 Augsburg, Germany

**Status.** The honeycomb Kitaev model [249] describes a novel spin interaction which couples a spin with its three neighbors in a special way: each of the three different bonds realizes an Ising like coupling of one spin component, e.g. $S_x$, $S_y$, or $S_z$, respectively. Consequently along an ‘x-bond’ the x-components of the spins are coupled and respectively the two other bonds couple the two other spin components. This leads to a strong exchange frustration between the spins, as these cannot simultaneously align with all neighbours preferring distinct quantization axes. The exchange frustration prohibits even for ferromagnetic coupling a finite-temperature ordering and leads to a highly correlated, but strongly fluctuating low-temperature regime called quantum spin liquid (QSL). Kitaev’s model requires a three-fold coordinated structure. It has attracted much attention, because it hosts a QSL with Majorana fermion excitations that could potentially be relevant for topological quantum computation [249]. An experimental realization is thus highly desired. However a bonding directional coupling of varying spin components in matter is generally quite unnatural and thus difficult to engineer.

In a seminal work, Jackeli and Khaliullin have predicted Kitaev exchange to arise in a certain class of ‘spin-orbit’ Mott insulating transition-metal (TM) oxides [250]. Figure 35(a), shows the d electron levels for heavy TM atoms in octahedral oxygen environment, as relevant e.g. for iridates with 5 electrons in the 5d shell. Here, the six $t_{2g}$ levels are split by spin-orbit coupling (which amounts to ~0.4 eV for iridates) in four $J_{eff} = 3/2$ and two $J_{eff} = 1/2$ states, the former being filled, the latter being half filled [251]. The resulting $J_{eff} = 1/2$ pseudospin has a wave function with orbital and spin contributions and one complex component. For the case of a 90° TM–O–TM bonding angle, as illustrated in figure 35(b), there appears a destructive interference between two different hopping processes. This leads to a bond-directional Ising type magnetic exchange (figure 35(c)) where only the $J_{eff} = 1/2$ components perpendicular to the plane formed by the two TM atoms and its O connections are coupled, like in a ‘quantum compass’ [251]. In $Na_2IrO_3$, edge-shared $IrO_6$ octahedra are connected as displayed in figure 35(d), leading to a honeycomb configuration with three different bonds that couple x, y, and z-components of the $J_{eff} = 1/2$ pseudospins, respectively, as required for the Kitaev exchange.

**Current and future challenges.** $Na_2IrO_3$ crystallizes in a layered C2/m structure with alternating stacks of Na-hexagonal layers and $IrO_6$ honeycomb layers filled by another Na-atom [252]. Its electronic and magnetic properties indicate a Mott insulating state with a gap of order 0.35 eV and spin-orbit coupled $J_{eff} = 1/2$ moments. However, instead of displaying the desired Kitaev QSL ground state the material shows a

zigzag antiferromagnetic ordering below $T_N = 15$ K. While the observed spin-orbital entanglement of fluctuations above $T_N$ directly points to the dominance of the Kitaev interaction [253], small admixture of additional interactions, which are allowed by crystal structure symmetry in $Na_2IrO_3$, prevent the formation of the QSL. These are in particular next-neighbour Heisenberg and off-diagonal anisotropic exchange interactions as well as various further neighbour couplings [254]. The isoelectronic $Li_2IrO_3$ crystallizes in three different structures illustrated in figure 36. Honeycomb $\alpha$-$Li_2IrO_3$ has so far only been synthesized in polycrystalline form [255]. Compared to $Na_2IrO_3$ it has compressed lattice parameters and a reduced gap ~0.16 eV. The Curie Weiss temperature of ~33 K is significantly smaller than for $Na_2IrO_3$ (~116 K). An incommensurate magnetic ordering appears at 15 K whose exact structure is yet unknown. Isostructural honeycomb $Li_2RhO_3$ with $Rh^{4+}$ is another most promising candidate material for Kitaev exchange [254]. Polycrystals did not show long-range ordering, but this needs to be confirmed on high-quality single crystals. $\alpha$-$RuCl_3$ is another honeycomb material with spin-orbit $J_{eff} = 1/2$ moments [256]. Advantageous compared to honeycomb iridates and rhodates, the $RuCl_6$ octahedra in this material are likely closer to cubic symmetry because of only very weak van der Waals forces between the honeycomb layers. This is ideal for undisturbed Kitaev physics.

**Advances in science and technology to meet challenges.** Crystal quality is a very important aspect for the characterization of candidate materials such as $\alpha$-$Li_2IrO_3$ or isostructural $Li_2RhO_3$. Clean single crystals are required in order to determine the magnetic ground state and the dynamical properties related to the Kitaev interaction. Furthermore, it is promising to search for new materials with other than planar honeycomb structures. The three-fold coordination needed for Kitaev physics can also be realized in 3D structures. Figure 36 shows different synthesized variants of $Li_2IrO_3$ which realize ‘hyper’- and ‘stripy’-honeycomb configurations [257]. Unfortunately, $\beta$- and $\gamma$-$Li_2IrO_3$ both display long-range magnetic ordering at 38 K, though the configuration of the spins within the ground state could only be explained by a highly dominating Kitaev exchange. In order to achieve a Kitaev QSL, fine tuning of structural properties by chemical composition, hydrostatic or uniaxial pressure is required. Respectively for thin films epitaxial strain can be used.

In addition to the search for new candidate materials, it is promising to investigate signatures of Kitaev physics in dynamical properties. Recent Raman scattering on $\alpha$-$RuCl_3$ has shown a broad continuum below 100 K which cannot be explained by conventional two-magnon scattering and is compatible with theoretical expectations for fractionalized Majorana excitations in Kitaev materials [258]. Further dynamical investigations e.g. by inelastic neutron scattering, magnetic resonant x-ray scattering and ultrafast optical spectroscopy are following this direction.

**Concluding remarks.** Driven by the discovery of topological insulators and motivated by the theoretical proposal of various
## 20. Kitaev exchange in hexagonal iridates and rhodates

Philipp Gegenwart

Experimentalphysik VI, Center for Electronic Correlations and Magnetism, Augsburg University, 86159 Augsburg, Germany

**Status.** The honeycomb Kitaev model [249] describes a novel spin interaction which couples a spin with its three neighbors in a special way: each of the three different bonds realizes an Ising like coupling of one spin component, e.g. $S_x$, $S_y$, or $S_z$, respectively. Consequently along an ‘x-bond’ the x-components of the spins are coupled and respectively the two other bonds couple the two other spin components. This leads to a strong exchange frustration between the spins, as these cannot simultaneously align with all neighbours preferring distinct quantization axes. The exchange frustration prohibits even for ferromagnetic coupling a finite-temperature ordering and leads to a highly correlated, but strongly fluctuating low-temperature regime called quantum spin liquid (QSL). Kitaev’s model requires a three-fold coordinated structure. It has attracted much attention, because it hosts a QSL with Majorana fermion excitations that could potentially be relevant for topological quantum computation [249]. An experimental realization is thus highly desired. However a bonding directional coupling of varying spin components in matter is generally quite unnatural and thus difficult to engineer.

In a seminal work, Jackeli and Khaliullin have predicted Kitaev exchange to arise in a certain class of ‘spin-orbit’ Mott insulating transition-metal (TM) oxides [250]. Figure 35(a), shows the d electron levels for heavy TM atoms in octahedral oxygen environment, as relevant e.g. for iridates with 5 electrons in the 5d shell. Here, the six $t_{2g}$ levels are split by spin-orbit coupling (which amounts to ~0.4 eV for iridates) in four $J_{eff} = 3/2$ and two $J_{eff} = 1/2$ states, the former being filled, the latter being half filled [251]. The resulting $J_{eff} = 1/2$ pseudospin has a wave function with orbital and spin contributions and one complex component. For the case of a 90° TM–O–TM bonding angle, as illustrated in figure 35(b), there appears a destructive interference between two different hopping processes. This leads to a bond-directional Ising type magnetic exchange (figure 35(c)) where only the $J_{eff} = 1/2$ components perpendicular to the plane formed by the two TM atoms and its O connections are coupled, like in a ‘quantum compass’ [251]. In $Na_2IrO_3$, edge-shared $IrO_6$ octahedra are connected as displayed in figure 35(d), leading to a honeycomb configuration with three different bonds that couple x, y, and z-components of the $J_{eff} = 1/2$ pseudospins, respectively, as required for the Kitaev exchange.

**Current and future challenges.** $Na_2IrO_3$ crystallizes in a layered C2/m structure with alternating stacks of Na-hexagonal layers and $IrO_6$ honeycomb layers filled by another Na-atom [252]. Its electronic and magnetic properties indicate a Mott insulating state with a gap of order 0.35 eV and spin-orbit coupled $J_{eff} = 1/2$ moments. However, instead of displaying the desired Kitaev QSL ground state the material shows a

zigzag antiferromagnetic ordering below $T_N = 15$ K. While the observed spin-orbital entanglement of fluctuations above $T_N$ directly points to the dominance of the Kitaev interaction [253], small admixture of additional interactions, which are allowed by crystal structure symmetry in $Na_2IrO_3$, prevent the formation of the QSL. These are in particular next-neighbour Heisenberg and off-diagonal anisotropic exchange interactions as well as various further neighbour couplings [254]. The isoelectronic $Li_2IrO_3$ crystallizes in three different structures illustrated in figure 36. Honeycomb $\alpha$-$Li_2IrO_3$ has so far only been synthesized in polycrystalline form [255]. Compared to $Na_2IrO_3$ it has compressed lattice parameters and a reduced gap ~0.16 eV. The Curie Weiss temperature of ~33 K is significantly smaller than for $Na_2IrO_3$ (~116 K). An incommensurate magnetic ordering appears at 15 K whose exact structure is yet unknown. Isostructural honeycomb $Li_2RhO_3$ with $Rh^{4+}$ is another most promising candidate material for Kitaev exchange [254]. Polycrystals did not show long-range ordering, but this needs to be confirmed on high-quality single crystals. $\alpha$-$RuCl_3$ is another honeycomb material with spin-orbit $J_{eff} = 1/2$ moments [256]. Advantageous compared to honeycomb iridates and rhodates, the $RuCl_6$ octahedra in this material are likely closer to cubic symmetry because of only very weak van der Waals forces between the honeycomb layers. This is ideal for undisturbed Kitaev physics.

**Advances in science and technology to meet challenges.** Crystal quality is a very important aspect for the characterization of candidate materials such as $\alpha$-$Li_2IrO_3$ or isostructural $Li_2RhO_3$. Clean single crystals are required in order to determine the magnetic ground state and the dynamical properties related to the Kitaev interaction. Furthermore, it is promising to search for new materials with other than planar honeycomb structures. The three-fold coordination needed for Kitaev physics can also be realized in 3D structures. Figure 36 shows different synthesized variants of $Li_2IrO_3$ which realize ‘hyper’- and ‘stripy’-honeycomb configurations [257]. Unfortunately, $\beta$- and $\gamma$-$Li_2IrO_3$ both display long-range magnetic ordering at 38 K, though the configuration of the spins within the ground state could only be explained by a highly dominating Kitaev exchange. In order to achieve a Kitaev QSL, fine tuning of structural properties by chemical composition, hydrostatic or uniaxial pressure is required. Respectively for thin films epitaxial strain can be used.

In addition to the search for new candidate materials, it is promising to investigate signatures of Kitaev physics in dynamical properties. Recent Raman scattering on $\alpha$-$RuCl_3$ has shown a broad continuum below 100 K which cannot be explained by conventional two-magnon scattering and is compatible with theoretical expectations for fractionalized Majorana excitations in Kitaev materials [258]. Further dynamical investigations e.g. by inelastic neutron scattering, magnetic resonant x-ray scattering and ultrafast optical spectroscopy are following this direction.

**Concluding remarks.** Driven by the discovery of topological insulators and motivated by the theoretical proposal of various
<figure><img src="image_40.png" /><figcaption>**Figure 35.** Kitaev magnetic exchange in spin-orbit Mott insulators. Splitting of 5d levels in an octahedral oxygen crystal electric field in the presence of strong spin-orbit coupling (a) Reprinted figure with permission from [250]. Copyright 2008 by the American Physical Society. Active bonds (in color) for edge-shared TM octahedra (b) Reprinted figure with permission from [251]. Copyright 2009 by the American Physical Society. Bond dependent Ising interactions in structural units with 90° TM–O–TM bonds (c). Design of the Kitaev model by combination of those units (d) Reprinted figure with permission from [251]. Copyright 2009 by the American Physical Society.</figcaption></figure>

<figure><img src="image_41.png" /><figcaption>**Figure 36.** Various structures with three-fold configuration required for the Kitaev interaction that are derived from the planar honeycomb structure by out-of-plane rotations and their realization in various materials. Reprinted figure with permission from [257]. Copyright 2014 by the American Physical Society.</figcaption></figure>

novel states in correlated materials with large spin-orbit cou-
pling, transition metal compounds with 4d and 5d elements
such as Ru, Rh or Ir are currently the focus of strong interest.
One field of intensive research concerns the search for solid
state realizations of the Kitaev magnetic exchange. The lat-
ter induces strong dynamical frustration and supports a QSL
with emergent Majonara fermion excitations that can be used
for topological quantum computation. The required bond-
directional exchange between differing spin components can
be realized in three-fold coordinated structures of spin-orbit
coupled moments. Several planar and ‘hyper’ honeycomb

materials have been shown to realize Kitaev exchange. Struc-
tural fine tuning by chemical substitution, hydrostatic and
uniaxial pressure or strain by choosing proper substrates
for thin films can diminish additional exchange interactions
which currently are spoiling pure Kitaev physics in real mat-
erials. Furthermore, the dynamical signature of Kitaev phys-
ics can be investigated in the paramagnetic state at elevated
temperatures.

***Acknowledgments.*** Research supported by the German Sci-
ence Foundation within SFB/TRR 80 and SPP1666.
<figure><img src="image_41.png" /><figcaption>**Figure 35.** Kitaev magnetic exchange in spin-orbit Mott insulators. Splitting of 5d levels in an octahedral oxygen crystal electric field in the presence of strong spin-orbit coupling (a) Reprinted figure with permission from [250]. Copyright 2008 by the American Physical Society. Active bonds (in color) for edge-shared TM octahedra (b) Reprinted figure with permission from [251]. Copyright 2009 by the American Physical Society. Bond dependent Ising interactions in structural units with 90° TM–O–TM bonds (c). Design of the Kitaev model by combination of those units (d) Reprinted figure with permission from [251]. Copyright 2009 by the American Physical Society.</figcaption></figure>

<figure><img src="image_42.png" /><figcaption>**Figure 36.** Various structures with three-fold configuration required for the Kitaev interaction that are derived from the planar honeycomb structure by out-of-plane rotations and their realization in various materials. Reprinted figure with permission from [257]. Copyright 2014 by the American Physical Society.</figcaption></figure>

novel states in correlated materials with large spin-orbit cou-
pling, transition metal compounds with 4d and 5d elements
such as Ru, Rh or Ir are currently the focus of strong interest.
One field of intensive research concerns the search for solid
state realizations of the Kitaev magnetic exchange. The lat-
ter induces strong dynamical frustration and supports a QSL
with emergent Majonara fermion excitations that can be used
for topological quantum computation. The required bond-
directional exchange between differing spin components can
be realized in three-fold coordinated structures of spin-orbit
coupled moments. Several planar and ‘hyper’ honeycomb

materials have been shown to realize Kitaev exchange. Struc-
tural fine tuning by chemical substitution, hydrostatic and
uniaxial pressure or strain by choosing proper substrates
for thin films can diminish additional exchange interactions
which currently are spoiling pure Kitaev physics in real mat-
erials. Furthermore, the dynamical signature of Kitaev phys-
ics can be investigated in the paramagnetic state at elevated
temperatures.

***Acknowledgments.*** Research supported by the German Sci-
ence Foundation within SFB/TRR 80 and SPP1666.
## 21. A European action tracing the roadmap towards oxide electronics: perspective on nonvolatile oxide memories

Fabio Miletto Granziozio¹, Josep Fontcuberta² and Nini Pryds³

¹ CNR-SPIN UOS Napoli, Complesso Universitario di Monte Sant'Angelo, Via Cinthia 80126, Napoli, Italy

² Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Campus UAB, Bellaterra 08193, Catalonia, Spain

³ Department of Energy Conversion and Storage, Technical University of Denmark, Risø Campus, Roskilde 4000, Denmark

**Status.** The TO-BE COST action ‘towards oxide-based electronics’ (TO-BE)<fnref n="26" />, funded by the European Commission through the COST Association within the EU Framework Programme Horizon 2020, was started in 2014 and will run until 2018. The action gathers, at a European level, scientists from 29 European countries. TO-BE aims to create a strongly networked community of EU scientists active on synthesis, analysis, modelling and applications of transition metal oxides, with special emphasis on epitaxial heterostructures. TO-BE organises and funds semestral (spring and fall) meetings, biennial training schools and frequent international scientific missions between participating laboratories. The scientific activity is framed into three main work packages (WPs), as sketched in figure 37, named ‘fundamental understanding’, ‘growth control’ and ‘towards application’. The last WP is focused on a wide range of applications as nanoelectronics, microactuation and microsensing, and energy conversion.

TO-BE main objectives include the publication by 2018 of an International Technology Roadmap for Transition Metal Oxides (ITR-TMOs). Our future roadmap aims to (i) trigger a ‘paradigm shift’ within the oxide-related research community, helping the scientists in the field to more effectively contextualize their research in the framework of the needs and trends of the mainstream semiconductor industry; (ii) identify oxide material and oxide-based devices that are really bound to play a role in the industrial development of novel technologies, (iii) increase awareness of the perspectives offered by oxide materials among the solid state community, the semiconductor industry, the general public and the policy makers. This section contributed to this roadmap is a first output of the activity that will eventually produce the future TO-BE roadmap.

**Current and future challenges.** An overview of current and future challenges related to oxides is extensively provided by the other section published in this roadmap. To complete such an overview, it is mandatory in our opinion to include non-volatile memory technologies, a crucial topic in our action activity. We limit ourselves for brevity to emphasizing the role of oxides in so-called storage class memory devices. These are non-volatile memory (NVM) devices, i.e. memories that retain their information when power is switched off. They show promise to bridge the latency (time-access)

gap presently open between fast volatile memories currently employed for code storage and execution (e.g. dynamic random access memories, DRAMs) and the slower non-volatile devices employed for data storage (traditionally magnetic hard disk drives and now, increasingly, flash NANDs). In the list below, following [261], a broad categorization of novel storage class memory devices is divided in two blocks: ‘prototypical’, for which the involvement of industry has already started, and ‘emerging’, for which research is still largely limited to the academic sector. Highlighted in bold in the lists below are the storage class memory types where oxides are expected to play a key role.

Prototypical non-volatile memory technologies are: (P₁) **FeRAM** (ferroelectric-RAM); (P₂) **PCM** (phase change materials); (P₃) **MRAM** (magnetic-RAM) and (P₄) **STT-RAM** (spin transfer torque-RAM).

Non-volatile memory technologies classified as emerging are: (E₁) **ReRAM** (redox-RAM); (E₂) **ferroelectric memories** (*FeFET*, ferroeletric field effect transistor and *FTJ*, ferroelectric tunnel junction); (E₃) **Mott memories**; (E₄) carbon memories and (E₅) molecular memories. According to recent reviews from Marinella [259, 261], the performances of these devices are schematically reported and compared in table 1. Here, we restrict our revision only to **Redox-RAM** and **ferroelectric memories**, labelled as E₁ and E₂ in table 1.

**Redox-RAMs** (ReRAMs), presently considered as the most promising candidates for next-generation NVMs, are two-terminal passive device consisting of a nanometric thin oxide films, e.g. TaOₓ, TiO₂, Al₂O₃, HfO₂₋ₓ or SiOₓ, sandwiched between two metal electrodes. Under an applied electric field, a migration and redistribution of oxygen vacancies takes place [260], resulting in a large, measurable, reversible and non-volatile resistance switch between a high resistance state (HRS) and a low resistance state (LRS). Classified as emerging NVMs in 2013, ReRAMs are substantially shifting towards the prototypical class. ReRAM-based devices are commercially available<fnref n="27" /> today and are at the core of the 3D XPoint technology jointly released in 2015 by Micron and Intel<fnref n="28" />. ReRAMs are expected to be scalable below 10nm and have been shown to possess large endurance, good retention and short latency (i.e. short access times). Their fabrication processes can be made CMOS compatible and allow for multilayering.

ReRAMs can be divided in different classes [261]. In table 1, the potential of (E1.1) electrochemical metallization bridge, (E1.2) bipolar filamentary, (E1.3) unipolar filamentary, and (E1.4) bipolar non-filamentary ReRAMs is assessed. Some present weaknesses of ReRAM technology are related to the undesirable initial forming steps, to the requirement of large switching currents, to the subsequent limitations due to crosstalk in high density cell arrays and (for bipolar devices) to the need for a bipolar power supply. The generation/creation

<footnote n="26">²⁶ Further details about the MP1308 TO-BE COST action are found at the action web site http://to-be/spin.cnr.it/</footnote>

<footnote n="27">²⁷ See e.g. the Panasonic MN101L Resistive RAM based on a on a TaOₓ layer http://electronics360.globalspec.com/article/4246/embedded-reram-gets-into-distribution</footnote>

<footnote n="28">²⁸ See e.g. www.micron.com/about/emerging-technologies/3d-xpoint-technology.</footnote>
## 21. A European action tracing the roadmap towards oxide electronics: perspective on nonvolatile oxide memories

Fabio Miletto Granozio¹, Josep Fontcuberta² and Nini Pryds³

¹ CNR-SPIN UOS Napoli, Complesso Universitario di Monte Sant'Angelo, Via Cinthia 80126, Napoli, Italy

² Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Campus UAB, Bellaterra 08193, Catalonia, Spain

³ Department of Energy Conversion and Storage, Technical University of Denmark, Risø Campus, Roskilde 4000, Denmark

**Status.** The TO-BE COST action ‘towards oxide-based electronics’ (TO-BE)<fnref n="26" />, funded by the European Commission through the COST Association within the EU Framework Programme Horizon 2020, was started in 2014 and will run until 2018. The action gathers, at a European level, scientists from 29 European countries. TO-BE aims to create a strongly networked community of EU scientists active on synthesis, analysis, modelling and applications of transition metal oxides, with special emphasis on epitaxial heterostructures. TO-BE organises and funds semestral (spring and fall) meetings, biennial training schools and frequent international scientific missions between participating laboratories. The scientific activity is framed into three main work packages (WPs), as sketched in figure 37, named ‘fundamental understanding’, ‘growth control’ and ‘towards application’. The last WP is focused on a wide range of applications as nanoelectronics, microactuation and microsensing, and energy conversion.

TO-BE main objectives include the publication by 2018 of an International Technology Roadmap for Transition Metal Oxides (ITR-TMOs). Our future roadmap aims to (i) trigger a ‘paradigm shift’ within the oxide-related research community, helping the scientists in the field to more effectively contextualize their research in the framework of the needs and trends of the mainstream semiconductor industry; (ii) identify oxide material and oxide-based devices that are really bound to play a role in the industrial development of novel technologies, (iii) increase awareness of the perspectives offered by oxide materials among the solid state community, the semiconductor industry, the general public and the policy makers. This section contributed to this roadmap is a first output of the activity that will eventually produce the future TO-BE roadmap.

**Current and future challenges.** An overview of current and future challenges related to oxides is extensively provided by the other section published in this roadmap. To complete such an overview, it is mandatory in our opinion to include non-volatile memory technologies, a crucial topic in our action activity. We limit ourselves for brevity to emphasizing the role of oxides in so-called storage class memory devices. These are non-volatile memory (NVM) devices, i.e. memories that retain their information when power is switched off. They show promise to bridge the latency (time-access)

gap presently open between fast volatile memories currently employed for code storage and execution (e.g. dynamic random access memories, DRAMs) and the slower non-volatile devices employed for data storage (traditionally magnetic hard disk drives and now, increasingly, flash NANDs). In the list below, following [261], a broad categorization of novel storage class memory devices is divided in two blocks: ‘prototypical’, for which the involvement of industry has already started, and ‘emerging’, for which research is still largely limited to the academic sector. Highlighted in bold in the lists below are the storage class memory types where oxides are expected to play a key role.

Prototypical non-volatile memory technologies are: (P₁) **FeRAM** (ferroelectric-RAM); (P₂) **PCM** (phase change materials); (P₃) **MRAM** (magnetic-RAM) and (P₄) **STT-RAM** (spin transfer torque-RAM).

Non-volatile memory technologies classified as emerging are: (E₁) **ReRAM** (redox-RAM); (E₂) **ferroelectric memories** (*FeFET*, ferroeletric field effect transistor and *FTJ*, ferroelectric tunnel junction); (E₃) **Mott memories**; (E₄) carbon memories and (E₅) molecular memories. According to recent reviews from Marinella [259, 261], the performances of these devices are schematically reported and compared in table 1. Here, we restrict our revision only to **Redox-RAM** and **ferroelectric memories**, labelled as E₁ and E₂ in table 1.

**Redox-RAMs** (ReRAMs), presently considered as the most promising candidates for next-generation NVMs, are two-terminal passive device consisting of a nanometric thin oxide films, e.g. TaOₓ, TiO₂, Al₂O₃, HfO₂₋ₓ or SiOₓ, sandwiched between two metal electrodes. Under an applied electric field, a migration and redistribution of oxygen vacancies takes place [260], resulting in a large, measurable, reversible and non-volatile resistance switch between a high resistance state (HRS) and a low resistance state (LRS). Classified as emerging NVMs in 2013, ReRAMs are substantially shifting towards the prototypical class. ReRAM-based devices are commercially available<fnref n="27" /> today and are at the core of the 3D XPoint technology jointly released in 2015 by Micron and Intel<fnref n="28" />. ReRAMs are expected to be scalable below 10nm and have been shown to possess large endurance, good retention and short latency (i.e. short access times). Their fabrication processes can be made CMOS compatible and allow for multilayering.

ReRAMs can be divided in different classes [261]. In table 1, the potential of (E1.1) electrochemical metallization bridge, (E1.2) bipolar filamentary, (E1.3) unipolar filamentary, and (E1.4) bipolar non-filamentary ReRAMs is assessed. Some present weaknesses of ReRAM technology are related to the undesirable initial forming steps, to the requirement of large switching currents, to the subsequent limitations due to crosstalk in high density cell arrays and (for bipolar devices) to the need for a bipolar power supply. The generation/creation

<footnote n="26">²⁶ Further details about the MP1308 TO-BE COST action are found at the action web site http://to-be.spin.cnr.it/</footnote>

<footnote n="27">²⁷ See e.g. the Panasonic MN101L Resistive RAM based on a on a TaOₓ layer http://electronics360.globalspec.com/article/4246/embedded-reram-gets-into-distribution</footnote>

<footnote n="28">²⁸ See e.g. www.micron.com/about/emerging-technologies/3d-xpoint-technology.</footnote>