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Ferroelectric gate control of Rashba–Dresselhaus spin–orbit coupling in ferromagnetic semiconductor (Zn, Co)O Cite as: Appl. Phys. Lett. 119, 012403 (2021); doi: 10.1063/5.0047430 Submitted: 13 February 2021 .Accepted: 23 June 2021 . Published Online: 7 July 2021 Maoxiang Fu,1Jiahui Liu,1 Qiang Cao,2 Zhen Zhang,1Guolei Liu,1,a) Shishou Kang,1 Yanxue Chen,1 Shishen Yan,1,2Liangmo Mei,1and Zhen-Dong Sun1,3,a) AFFILIATIONS 1School of Physics, Shandong University, Jinan 250100, China 2Spintronics Institute, University of Jinan, Jinan 250022, China 3School of Physics and Electrical Engineering, Kashi University, Kashgar 844006, China a)Authors to whom correspondence should be addressed: liu-guolei@sdu.edu.cn and zdsun@sdu.edu.cn ABSTRACT In this paper, we demonstrate the ferroelectric gate control of Rashba–Dresselhaus spin–orbit coupling (R–D SOC) in a hybrid heterostructure consisting of a ferromagnetic semiconductor channel (Zn, Co)O(0001) and a ferroelectric substrate PMN-PT(111). The R–D SOC causes a transverse spin current via the charge-spin conversion, which results in unbalanced transverse spin and charge accumulations due to the spin-polarized band in the ferromagnetic (Zn, Co)O channel. By the reversal of gated ferroelectric polarization, we observed 55%modulation of the R–D SOC correlated Hall resistivity to the magnetization correlated anomalous Hall resistivity and 70% modulation of thelow-field magnetoresistance at 50 K. Our experimental results pave a way toward semiconductor-based spintronic-integrated circuits with anultralow power consumption in ferromagnetic semiconductors. Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0047430 The electric field control of ferromagnetism and spin phenomena has been intensively pursued in an information technique, since it offers a promising method for ultra-low power spin manipulation. 1–3 The electric field control of magnetic properties has been demon-strated in several classes of materials such as ferromagnetic semicon-ductors (In, Mn)As, 4(Ga, Mn)As,5–13(In, Fe)Sb,14(Ti, Co)O 2,15 ultrathin ferromagnetic metals,16–20and complex oxides.3,21,22By applying the gate voltage on the ferromagnetic semiconductor chan- nel, the accumulated (or depleted) carriers enhance (or suppress) the carrier density leading to the modulation of magnetization and theCurie temperature, and this type of electric field control of ferromag- netism can be attributed to the carrier-mediated ferromagne- tism. 4,6,14,15On the other hand, on device concept of the spin field effect transistor (spin-FET),23,24the electric field controlled Rashba25 and Dresselhaus26(R–D) spin–orbit coupling (SOC) is an effective and essential way to generate and manipulate a spin-polarized current in nanostructures without an external magnetic field. The Rashba SOC is due to the structure inversion asymmetry, and the Dresselhaus SOC is due to the bulk inversion asymmetry. The electric field con- trolled Rashba as well as Dresselhaus SOC has been demonstrated andextensively studied in non-magnetic semiconductor heterostructuresin the past decades. 24However, the electric field controlled R–D SOC has not yet been realized experimentally in the materials of the ferro- magnetic semiconductor. In this paper, we utilize the gated ferroelectric polarization to control the R–D SOC in the hybrid heterostructure (Zn, Co)O(0001)/ PMN-PT(111). The ferromagnetic semiconductor (Zn, Co)O films are n-type conductivity, and a space charge region is formed by applying t h eg a t ev o l t a g eo nt h ef e r r o e l e c t r i cs u b s t r a t eP M N - P T .T h ep o l eo f ferroelectric polarization induces the built-in electric field inside the(Zn, Co)O channel and also causes the variation of charge density, as shown in Fig. 1(a) . The Rashba spin–orbit coupling is ascribed to the structure inversion asymmetry of the (Zn, Co)O/PMN-PT hetero-strocture and the time inversion asymmetry of ferromagnetism in (Zn, Co)O. The Dresselhaus spin–orbit coupling is ascribed to the bulk inversion asymmetry of the wurtzite structure ZnO. The Hamiltonian by using the k/C1pmethod can be written as H R¼aRðrxky/C0rykxÞ andHD¼c½bkz/C0ðk2 xþk2 yÞ/C138ðrxky/C0rykxÞ,27,28where pxðyÞandrxðyÞ are the components of the electronic momentum operator and the spin Pauli matrices, respectively, and aRand bDare Rashba and Dresselhaus parameters, respectively. Both of the Rashba andDresselhaus SOCs are coexisted. Figure 1(b) shows the diagram of Appl. Phys. Lett. 119, 012403 (2021); doi: 10.1063/5.0047430 119, 012403-1 Published under an exclusive license by AIP PublishingApplied Physics Letters ARTICLE scitation.org/journal/aplspin-split of R–D SOC in the k-space without magnetization.24,27It is noted that there is a lack of spin-momentum locking due to the pre- sentation of ferromagnetic exchange coupling in ferromagnetic (Zn, Co)O, though it coexists with the R–D exchange coupling. On the reversal of gated ferroelectric polarization, the R–D SOC results in two aspects: (1) the modulation of the spin-polarized band structure in fer- romagnetic (Zn, Co)O, which relates to a modulated spin-polarized current and (2) a transverse spin accumulation and an unbalanced transverse charge accumulation due to the charge-spin conversion, which corresponds to the Rashba–Edelstein effect in ferromagnetic(Zn, Co)O. In this paper, we reported the ferroelectric gate controlled R–D SOC in the hybrid heterostructure (Zn, Co)O/PMN-PT through the measurements of the Anomalous Hall effect (AHE) and longitudi- nal magnetoresistance, where AHE is a magnetic response of itinerant band carriers caused by asymmetric carrier scattering in the presence of SOC. 29 The high quality (Zn, Co)O thin films in a thickness of 50–100 nm were epitaxially grown on ferroelectric substrates PMN- PT(111) with a 3 nm ZnO buffer layer by using radio frequency oxygen plasma-assisted molecular beam epitaxy. A smooth and high quality interface is very important to eliminate a residual space charge for the efficient carrier transmitting across the interface. The (Zn, Co)O thin film is doped with a high Co concentration 45% to achieve giant magnetization and strong AHE with the high Curie temperature. For Hall measurements, introducing tiny dose of donor dopants Ga of0.2% in atoms increases the conductivity of the (Zn, Co)O film, which helps to enhance the output Hall voltage. The growth temperature is 400/C14C under the oxygen partial pressure 3 /C210/C05Pa. The growth of (Zn, Co)O film is monitored by real time reflected high energy elec- tron deflection, and its chemical states are carried out by in situ x-ray photoelectron spectroscopy (XPS). The crystal structure is character- ized by high resolution x-ray diffraction (HRXRD). Magnetization is measured by a quantum designed superconducting quantum interfer- ence device (SQUID). Detailed growth and characterization refers to our previous works.30Hall effect is measured in the geometry of a Van der Pauw method in the size of 5 /C25m m2. The sheet resistivity of (Zn, Co)O thin films can be chemically tuned by introducing Ga donor dopants with the carrier density in the range of /C241018–1019cm/C03for different purposes of the Hall effect and magne- toresistance measurements.30Four Au electric contacts are deposited through mask shades by magnetron sputtering for the Hall and MR measurements, where (Zn, Co)O is not only a magnetic semiconduc- tor channel but also the top electric conducting layer. Figure 1(a) shows the schematic cross section of the hybrid heter- ostructure (Zn, Co)O(0001)/PMN-PT(111). By applying the gate volt- age between the ferroelectric substrates PMN-PT, the pole of ferroelectric polarization causes a space charge region, which induces a build-in electric field inside the (Zn, Co)O channel and the variation of charge density. The induced electric field results in the R–D SOC in the (Zn, Co)O layer.24,27When the direction of ferroelectric FIG. 1. (a) Cross section of the induced electric field and the carrier variation inside the (Zn, Co)O channel and related ferroelectric polarization in the PM N-PT substrate. (b) Schematic diagram of spin splitting of Rashba and Dresselhaus SOC in the k-space without magnetization. (c) Sheet resistance of (Zn, Co)O thin film s at 300 K as a function of the gate voltage Vgate, where a resistance platform refers to electron accumulation and depletion states. (d) Time duration measurements of a sheet resistance by applying the period pulse gating voltages ( þ300,/C0300 V). Gating voltage lasts 30 s at a 10 min interval.Applied Physics Letters ARTICLE scitation.org/journal/apl Appl. Phys. Lett. 119, 012403 (2021); doi: 10.1063/5.0047430 119, 012403-2 Published under an exclusive license by AIP Publishingpolarization points upward, it attracts more electrons from the electric circuit and forms an electron accumulation state in the (Zn, Co)O channel, vice versa, the downward ferroelectric polarization forms an electron depletion state in the (Zn, Co)O channel. Figure 1(c) shows the sheet resistance of the (Zn, Co)O channel by applying the gatevoltage, where the resistance platforms correspond to a high resistivity state (HRS) and a low resistivity state (LRS) as shown in Fig. 1(a) .H R S refers to the electron depletion state with carrier density 4.7/C210 18cm/C03and LRS to the electron accumulation state with carrier density 1.8 /C21018cm/C03. The modulation ratio of HRS to LRS is HR LR¼533%, and the modulation ratio of carrier density is 261%. In this paper, without loss of generality, we study the electron accumula- tion and depletion states by applying the remanent polarization P r,where P rþrefers to upward polarization and Pr-to downward polari- zation. Figure 1(d) shows the duration measurements of resistance by applying the period gating voltages þ300 V /C00/C0/C0 300 V /C00 /C0þ300 V, where the gate voltage lasts 30 s at a 10 min interval. It indicates that by the reversal of ferroelectric polarization, the transitionbetween HRS (or electron depletion state) and LRS (or electron accu- mulation state) is reversible and repeatable. It is necessary to exclude from the magnetostriction effect and carrier induced magnetization by the reversal of ferroelectric polariza-tion. Figure 2(a) shows the HRXRD h–2hscans of the (Zn, Co)O channel in the growth direction at electron accumulation (P rþ)a n d depletion (P r-) states. The unchanged lattice constant indicates the same piezoelectric strain at accumulation and depletion states. FIG. 2. (a) High resolution x-ray diffraction h–2hscans for (Zn, Co)O films at the electron accumulation state (blue line, P rþ) and the depletion state (red line, P r/C0). The inset shows theh–2hscans by the reversal of ferroelectric polarization 10 times. (b) XPS of Co 2p 1/2and 2p 3/2peaks and their satellites at electron accumulation and depletion states. The mag- netic hysteresis loops of (Zn, Co)O films at electron accumulation (blue solid lines) and depletion (red solid lines) states at (c) 300, (d) 150, (e) 50, (f) 20, (g) 10, and (h) 5 K.Applied Physics Letters ARTICLE scitation.org/journal/apl Appl. Phys. Lett. 119, 012403 (2021); doi: 10.1063/5.0047430 119, 012403-3 Published under an exclusive license by AIP PublishingFigure 2(b) shows the XPS measurements for Co 2p 1/2,2 p 3/2photo- emission peaks and their satellites at accumulation and depletion states, which indicates that the chemical states of cobalt dopants are not affected by the carrier variation. For further measurements, wechecked the magnetization of the (Zn, Co)O film at accumulation anddepletion states by using SQUID. Figures 2(c)–2(h) show the tempera- ture dependent magnetic hysteresis loops at accumulation and deple- tion states, which indicates that magnetization has nearly no influenceon the variation of carrier density except that there is /C243% change of the superparamagnetic background at 5 K. It is known that theferromagnetism of (Zn, Co)O is attributed to the percolation of bound magnetic polarons (BMPs). 31Our previous work of angle resolved photoemission spectroscopy shows that the impurity states of Co dop- ants in the case of diluted Co concentration are deep below the Fermilevel, and the impurity states disperse close to the Fermi level when theCo concentration increases up to 40%. 30The character of deep impu- rity states explains why magnetization is not affected by the carrier variation. In other side, because of the inhomogeneous distribution ofBMP, (Zn, Co)O coexists multiple magnetic phases: the ferromagneticregion with a long-rang percolation of BMP and superparamagnetic FIG. 3. Anomalous Hall resistivity qAHE yx as a function of the magnetic field for the 50 nm (Zn, Co)O film doped with 0.2% of Ga at as-grown, electron accumulation, and deple- tion states at (a)50, (b)150, and (c)300 K. The applied current is 1 mA. (d) Diagram of Hall measurements in the geometry of the van der Pauw method in a device size of 5/C25m m2. (e) Temperature dependent resistivity qxxat as-grown, electron accumulation, and depletion states. The inset is the plot of ln qxxvsT/C01=4. (f) Temperature depen- dent carrier density n at as-grown, electron accumulation, and depletion states.Applied Physics Letters ARTICLE scitation.org/journal/apl Appl. Phys. Lett. 119, 012403 (2021); doi: 10.1063/5.0047430 119, 012403-4 Published under an exclusive license by AIP Publishingclusters with short-rang BMPs,32where the accumulation charges enhance the enhancement of a superparamagnetic phase at low tem- perature 5 K. Figures 3(a)–3(c) show the evolution of anomalous Hall resistiv- ityqAHE yxas a function of magnetic field at as-grown, accumulation and depletion states at 300, 150, and 50 K, where the ordinary Hall resistiv- ity has been subtracted linearly from the raw Hall data. A large signal ofqAHE yxis achieved due to the giant magnetization of (Zn, Co)O films with a high Co concentration (45%). In Fig. 3(c) ,t h em a g n i t u d e so f qAHE yxat 50 K are 2.0, 2.6, and 3.5 lXcm at accumulation, as-grown, and depletion states, respectively, which indicates that qAHE yxis ferro- electric tunable. As expected, qAHE yxhas two origins: the spontaneous magnetization and R–D SOC: qAHE yx¼RsMþqSOC yx. At a fixed ferro- electric polarization, we find out that qAHE yx remains constant ontemperature in the range of 50–300 K, and it also remains constant on the carrier density in the range of 1.8–6.0 /C21019cm/C03,a ss h o w ni n Fig. 3 . Therefore, the magnitude of qAHE yxdepends on magnetization and gated ferroelectric polarization, and it has no influence on thepure carrier variation. 30We also checked the temperature dependent resistivity qxxand the linear fitting of ln qxx/T/C01 4,33which indicates the Mott variable range hopping at as-grown, accumulation, and depletion states, as shown in Fig. 3 . At accumulation and depletion states, we have excluded of the possible magnetic origins of magneto-striction and carrier induced magnetization. The contribution of R sM is constant for the fixed magnetization, while the contribution of qSOC yx is gated controlled. For a simple estimation, we assume that the R–D SOC is symmetric at accumulation and depletion states, then thevariation of q SOC yxbetween accumulation and depletion states is: FIG. 4. (a) Diagram of MR measurements in a device size of 5 /C25m m2. (b) Plots of temperature dependent longitudinal resistivity qxxfor a 100 nm (Zn, Co)O film, the inset shows ln qxxas a function of T/C01=2.l nqxxis linearly depended on T/C01=2at low temperature, and the solid lines show the fitting curve. Plots of MR at electron accumulation and depletion states at (c) 300, (d) 150, (e) 50, (f) 20, (g) 10, and (h) 5 K. The applied charge current is 100 nA at 5 and 10 K, 1 lA at 20 K, and 10 lA at 50–300 K. Solid lines in (e) and (f) are fitting the MR curve by using Eq. (1)with the fitting parameters in Table S2 of the supplementary material .Applied Physics Letters ARTICLE scitation.org/journal/apl Appl. Phys. Lett. 119, 012403 (2021); doi: 10.1063/5.0047430 119, 012403-5 Published under an exclusive license by AIP PublishingDqSOC yx¼½qAHE yxðdepletion Þ/C0qAHE yxðaccumulation Þ/C138 ¼ 1:5lXcm, and the contribution of RSM¼½qAHE yxðdepletion ÞþqAHE yxðaccumulation Þ/C138=2 ¼2:75lXcm. Then we can estimate the modulation of AHE by the gated ferroelectric polarizationDqSOC yx RSM¼55%. The R–D SOC exerts an efficient transverse magnetic field, which results in a spin–orbit torque on the magnetization. However, we do not observe the spin–orbit tor- que in our experiments. We carried out the magnetoresistance (MR) measurements in the (Zn, Co)O film to study the spin-dependent scattering under gatedferroelectric polarization. MR is defined as MRðHÞ¼½ q xxðHÞ /C0qxxð0Þ/C138=qxxð0Þ,w h e r e qxxðHÞis the resistivity at magnetic field Hperpendicular to the (Zn, Co)O film. Figure 4(a) shows the sche- matic diagram of MR measurements in a device size of 5 /C25c m2. Figure 4(b) shows the temperature dependent qxx(0T) and qxx(1.5T) at electron accumulation and depletion states. The linear fitting of lnqxxdepending on T/C01=2at low temperature indicates Efros variable range hopping (VRH)34at electron accumulation and depletion states. Figure 4(c)–4(h) show the low field MR- Hcurves for the accumulation and depletion states at 300, 150, 50, 20, 10, and 5 K. The MR– Hcurves show clear hysteresis characteristics, in which the two peak positionsagree with the coercivity of the (Zn, Co)O layer. This finding indicates that MR has the same magnetic origins as magnetization in the (Zn, Co)O layer. Concerning to the magnitude modulation of MR by agated ferroelectric polarization, we estimate the variation DMR at tem- perature 50 K by applying the magnetic field 2 T for the accumulation and depletion states, DMR MR min¼70%. For a qualitative interpretation, the hysteretic MRis attributed to spin dependent scattering according to the phenomenological model of spin-dependent Efros VRH,34where the resistivity qxxcan be written as qxx¼q0 1þP2hcoshiexphTESi T/C18/C19 1 2 ; (1) where hTESioriginates from sum of the effective Coulomb interaction and the effective exchange coupling interaction, Pis the carrier spin polarization ratio, q0is a resistance prefacter, hcoshi¼m2with m stands for the reduced magnetization of whole system, and his the angle between the occupied state and the final vacant state. To avoid the influence of a high-field magnetoresistance, we use qxx(1.5T) as a saturated magnetization state ( hcoshi¼1) and qxx(0T) as a hcoshi ¼0 state to fit qxxandhTESiat accumulation and depletion states. Figures 4(e) and4(f)show the fitting curves at 50 and 20 K by using Eq.(1), where the fitting matches well with experimental measure- ments. The fitting parameters are shown in Table S2 of the supple- mentary material . According to the phenomenological model, we may evaluate the spin polarization, which is 21% at the accumulation state and 28% at the depletion state. The larger spin polarization at thedepletion state indicates the larger equivalent spin splitting due to the exchange coupling and R–D SOC, which agrees to a larger q AHE yxat the depletion state. The results of MR measurements provide anotherexperimental evidence of ferroelectric controlled R–D SOC in (Zn,Co)O. We also check that the ferroelectric controlled MR in (Zn, Co)O has no dependence on the applied current and the external mag- netic field in contrast with the unidirectional magnetoresistance in theRashba system, 35–37where the measurements are shown in Fig. S4 of thesupplementary material .In conclusion, we have epitaxially grown the hybrid heterostruc- ture (Zn, Co)O(0001)/PMN-PT(111) by MBE. We observed the ferro-electric gate controlled AHE in the (Zn, Co)O layer and q AHE yx¼RsMþqSOC yx. It also shows that qAHE yxis not influenced by the variation of temperature and the carrier density at fixed ferroelectric polarization. The modulation change isDqSOC yx RSM¼55% between the accumulation and depletion states. MR measurements provide another experimental evidence for ferroelectric controlled R–D SOC in (Zn,Co)O. The calculated spin polarization is 21% at the accumulationstate and 28% at the depletion state, respectively. Our experimentalresults pave a way toward semiconductor spintronic-integrated circuitswith ultralow power consumption. See the supplementary material for crystal and magnetization of (Zn, Co)O, MR for the Ga 0.002(Zn, Co)O film, and detailed R–T fitting. This research was partially supported by the Natural Science Foundation of Shandong Province Nos. ZR2019MA023 andZR2020ZD28, the National Natural Science Foundation of ChinaNos. 12074216 and 11974145, 111 Project B13029, and the StateKey Project of Fundamental Research of China under Grant No.2015CB921402. DATA AVAILABILITY The data that support the findings of this study are available within the article and its supplementary material . REFERENCES 1J. F. I. Zutic and S. D. Sarma, Rev. Mod. Phys. 76, 323 (2004). 2C. Song, B. Cui, F. Li, X. Zhou, and F. Pan, Prog. Mater. Sci. 87, 33 (2017). 3F. Matsukura, Y. Tokura, and H. Ohno, Nat. Nanotechnol. 10, 209 (2015). 4D. C. H. Ohno, F. Matsukura, T. Omiya, E. Abe, T. Dietl, Y. Ohno, and K. Ohtani, Nature 408, 944 (2000). 5F. M. D. Chiba and H. Ohno, Appl. Phys. Lett. 89, 162505 (2006). 6I. Stolichnov, S. W. Riester, H. J. Trodahl, N. Setter, A. W. Rushforth, K. W. Edmonds, R. P. Campion, C. T. Foxon, B. L. Gallagher, and T. Jungwirth, Nat. Mater. 7, 464 (2008). 7S. W. E. R. Riester, I. Stolichnov, H. J. Trodahl, N. Setter, A. W. 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5.0054874.pdf

The Journal of Chemical PhysicsARTICLE scitation.org/journal/jcp Understanding carbon dioxide capture on metal–organic frameworks from first-principles theory: The case of MIL-53(X), with X =Fe3+, Al3+, and Cu2+ Cite as: J. Chem. Phys. 155, 024701 (2021); doi: 10.1063/5.0054874 Submitted: 22 April 2021 •Accepted: 18 June 2021 • Published Online: 9 July 2021 Giane B. Damas,1,2,a) Luciano T. Costa,3 Rajeev Ahuja,1 and C. Moyses Araujo1,4,a) AFFILIATIONS 1Materials Theory Division, Department of Physics and Astronomy, Uppsala University, 75120 Uppsala, Sweden 2Department of Physics, Chemistry and Biology, Linköping University, 58330 Linköping, Sweden 3MolMod-CS- Department of Physical-Chemistry, Campus Valonguinho, Institute of Chemistry, Fluminense Federal University, Niterói, Rio de Janeiro, Brazil 4Department of Engineering and Physics, Karlstad University, 65188 Karlstad, Sweden a)Authors to whom correspondence should be addressed: giane.benvinda.damas@liu.se and moyses.araujo@physics.uu.se ABSTRACT Metal–organic frameworks (MOFs) constitute a class of three-dimensional porous materials that have shown applicability for carbon dioxide capture at low pressures, which is particularly advantageous in dealing with the well-known environmental problem related to the carbon dioxide emissions into the atmosphere. In this work, the effect of changing the metallic center in the inorganic counterpart of MIL-53 (X), where X=Fe3+, Al3+, and Cu2+, has been assessed over the ability of the porous material to adsorb carbon dioxide by means of first-principles theory. In general, the non-spin polarized computational method has led to adsorption energies in fair agreement with the experimental outcomes, where the carbon dioxide stabilizes at the pore center through long-range interactions via oxygen atoms with the axial hydroxyl groups in the inorganic counterpart. However, spin-polarization effects in connection with the Hubbard corrections, on Fe 3 dand Cu 3 d states, were needed to properly describe the metal orbital occupancy in the open-shell systems (Fe- and Cu-based MOFs). This methodology gave rise to a coherent high-spin configuration, with five unpaired electrons, for Fe atoms leading to a better agreement with the experimental results. Within the GGA +U level of theory, the binding energy for the Cu-based MOF is found to be E b=−35.85 kJ/mol, which is within the desirable values for gas capture applications. Moreover, it has been verified that the adsorption energetics is dominated by the gas–framework and internal weak interactions. ©2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0054874 I. INTRODUCTION The World Meteorological Organization (WMO) has pointed out an expected average temperature of 1.5○C higher than the pre- industrial levels in less than 35 years, as the most abundant green- house gas, carbon dioxide, has reached an increase in 3.3 ppm (0.83%) in one year of analysis, which corresponds to an overall increase of about 145% compared to the pre-industrial levels.1In this context, great efforts are necessary from different sectors of our society for a further change in the current scenario.2,3The carboncapture and storage (CCS) program4–6has different technologies to partially deal with the carbon emissions, finding applications in several industrial installations that include thermodynamic power plants and steel production. In the post-combustion approach, car- bon dioxide is captured from the gas stream due to its affinity to amine-based solutions.7–9In general, these compounds present kinetically favored reactivity with carbon dioxide, as well as low solubility of hydrocarbon compounds that are quite interesting.10 Nonetheless, the low selectivity in the presence of sulfur dioxide and the high energy necessary for solvent regeneration represent a J. Chem. Phys. 155, 024701 (2021); doi: 10.1063/5.0054874 155, 024701-1 © Author(s) 2021The Journal of Chemical PhysicsARTICLE scitation.org/journal/jcp major problem for capture-related applications.11Thus, the devel- opment and synthesis of new chemical absorbers that can address these problems without losing the capacity for gas adsorption are highly desired.6 Metal–organic frameworks (MOFs) constitute a class of three- dimensional porous materials formed by interconnecting inorganic and organic counterparts, which has found large applicability in this field.12–16In particular, the MIL-53 frameworks comprise an inorganic region formed by the metallic centers connecting oxy- gen atoms from hydroxyl groups (axial positions) or benzene dicar- boxylate (BDC) ligands (equatorial positions) in an octahedral con- figuration.17–19In recent years, the applicability of this series has been widely evaluated by means of experimental14,18,20–25and the- oretical methods17,26for gas adsorption, including carbon diox- ide,14,18,20–23,26,27methane,18,23,25,26and hydrogen sulfide.24 In general, the presence of open metal sites with appropri- ate geometry and pore size in metal–organic frameworks is directly associated with high adsorption capacity and selectivity.12,28Addi- tionally, the material should present high heat or enthalpy of adsorption for good performance at low pressures.28This important macroscopic quantity is directly associated with the gas–framework interaction strength, which is expected to be strong enough to main- tain the latter inside the pore through weak interactions at the end of the process and also provide a suitable post-processing based cat- alytic reaction where the activated carbon dioxide can be converted in raw materials.29On the other hand, the ideal condition of process reversibility is maintained with intermediate values for this quantity. It is important to emphasize that further developments in the field are still made necessary in order to turn these mate- rials competitive in an industrial point of view. In this context, different strategies have been proposed to improve the perfor- mance of metal–organic frameworks for gas capture applications. In analogy with the amine-based solvents that are traditionally employed in post-combustion methods, the functionalization by amine groups has been widely considered to increase the storage capacity and selectivity by improving the interaction strength with carbon dioxide.13,27,28,30For instance, Hu et al.13have evaluated the effects of anchoring alkylamine groups in unsaturated Cr3+cen- ters of MOF-101 at room temperature conditions. In their series, the diethylenetriamine-functionalized MOF exhibits the best CO 2 uptake (3.5 mmol g−1) even with a significant reduction in the sur- face area. In another work, 2-aminoterephthalic acid has been tested as an organic linker in an amino-functionalized Cu-based MOF to increase the gas uptake to 5.85 mmol g−1.15Methacrylamides have also been employed to enhance the carbon dioxide capture in MOFs.31 Furthermore, pore functionalization by other chemical groups, including methyl, hydroxyl, and carboxyl groups, has been reported.12,27,28In this sense, Torrisi et al.27have shown that embed- ding carboxyl and hydroxyl groups into MIL-53(Al3+) is particu- larly advantageous for gas capture applications in comparison to amine functionalities. Nonetheless, anchoring chemical groups in metal–organic frameworks is not always straightforward in a practi- cal point of view since the synthesis conditions, given by high pres- sures and temperatures, do not favor the anchoring process of sev- eral chemical functionalities.32To overcome this issue, Yan et al.32 have initially synthesized the template with active amine groups that were further substituted by the desired acetic acid and trimesoylchloride groups. Although still containing amine groups in the struc- ture, the extra adsorption sites promote an increase of about ∼20% in gas uptake by the resulting MOFs when compared to the initial amine-functionalized material.32 Traces of water can also affect the adsorption capacity and selectivity for carbon dioxide capture in a gas mixture.33–36 Huang et al. have found that strong interactions between water molecules and the framework lead to enhanced water adsorption that could be beneficial or not for gas capture.24In another work, Siegelman et al. have found an improvement in efficiency by an amine-functionalized Mg-based MOF due to hydrogen-bonding interactions between water molecules and carbamate nitrogen atoms, which favor carbon dioxide binding.37However, it is more common that trace amounts of water can exert a negative impact on the adsorption capacity.33For instance, Liu et al.33have verified a decrease in carbon dioxide adsorption from 3.74 to 2.69 mol/kg in a Ni-based MOF with water traces besides the negative effect on the CO 2/N2selectivity. This work aims at understanding the influence of the metal- lic center from MIL-53 (X), where X =Fe3+, Al3+, or Cu2+, on the carbon dioxide capture. Such analysis is performed on a ther- modynamic point of view by means of first-principles calculations based on density functional theory (DFT). The outcomes suggest that the organic counterpart of the metal–organic framework also participates in the adsorption energetics as the oxygen atoms in this region and hydroxyl groups interact in a different extent in each material. In general, the non-spin polarized results have shown consistency to describe the energetics for these systems, but the open shell configuration exhibited by Fe- and Cu-based MOFs is better described with inclusion of such effects. Additionally, the Hubbard corrections have led to a consistent description of the atomic magnetic moment for the metallic center in these systems, a property that has been found to affect severely the adsorption energetics. II. COMPUTATIONAL METHODS The applicability of metal–organic frameworks to gas capture at low pressures has direct association with certain macroscopic properties, such as adsorption capacity and heat/enthalpy of adsorption.12,28The latter has a thermodynamic definition that requires the inclusion of thermal corrections to the total energies for its full assessment, i.e., zero point energies and thermal effects acting over the internal energy of each system, but the main contributing term is the total energy itself.17Hence, variations in this property prior and posterior to adsorption give a reliable estimation of the enthalpy of reaction/adsorption that is crucial to evaluate how good the material is for gas capture. From a microscopic standpoint, such variations are generally dictated by the interaction strength between the metal–organic framework and the guest molecule (carbon dioxide), namely, the binding energy (E b). Therefore, the heat/enthalpy of adsorption has been assessed by calculating the binding energy (E b) of the solid-state system within the framework of the density functional theory (DFT) as imple- mented in the Vienna Ab-Initio Simulation Package (VASP).38Fur- ther details on the computational methodology for modeling the metal–organic framework are given in Subsections II A and II B. J. Chem. Phys. 155, 024701 (2021); doi: 10.1063/5.0054874 155, 024701-2 © Author(s) 2021The Journal of Chemical PhysicsARTICLE scitation.org/journal/jcp A. Bulk structures To model the metal–organic frameworks here under consid- eration, the crystallographic data of MIL-53 (Fe3+) reported by Millange et al have been used .39The original structure has been modified to include hidden hydrogen atoms at the inorganic region, more specifically at the oxygen atoms that are displaced in axial posi- tions related to the metallic center.17Furthermore, it was necessary to remove the water molecules lying inside the pores in order to activate the material for gas adsorption (Fig. 1).40 The Perdew–Burke–Ernzerhof (PBE) functional41was the functional of choice to treat the exchange-correlation potential in the initial solid-state calculations, as it has provided good agree- ment with experimental data obtained for the evaluation of similar thermodynamic properties in previous reports.42–45In the current study, the ionic relaxations were carried out until the total ener- gies reached the convergence criterion of 1.0 ×10−3eV. Dispersion effects and weak interactions were taken into account by including the D3-Grimme corrections46in all steps. The plane wave-basis set was defined with a cutoff energy of 800 eV after convergence tests in the sampled region (400–1000 eV). The Brillouin zone was sam- pled by a 2 ×2×4 Monkhorst–Pack k-point mesh. Spin-polarization effects were further considered for the frameworks with an open shell configuration [MIL-53 (X), where X =Fe3+and Cu2+]. Alterna- tively, the lattice parameters have been fully relaxed for these systems as displayed in Table S1 of the supplementary material. The electronic structure has been attained by calculating the density of states (DOS) and its projected components (pDOS) onFe, Al, Cu, C, O, and H atoms. As the semi-local generalized gradi- ent approximation (GGA) functional fails to describe the bandgap of semiconducting materials, Hubbard corrections have been applied on Fe 3 dand Cu 3 dstates through spin-polarized static calculations within the tetrahedron method with Blöchl corrections. The partial occupancies for each orbital have also been determined by using the Gaussian smearing for visual analysis of the orbital hybridization. Here, the assessment of the electronic structure is basically intended to complement the material description. B. Structure model The gas capture process has been evaluated by expanding the initial bulk structure into a 2 ×2 supercell aiming to avoid adsor- bate interactions with their respective images in the periodic system. Initially, it has been assumed that the pore structures do not vary in a significant way upon gas uptake by allowing partial relaxation of the system, i.e., the ionic positions. This is an oversimplifica- tion that is expected to describe the gas adsorption process in a proper way. Nonetheless, we have also considered eventual changes in the crystal lattice by enabling full relaxation of the system. These results are briefly discussed in this publication. In the former case, the partial relaxations were performed within the Γ-point with a plane-wave cutoff energy of 550 eV. A tighter energy convergence criterion has been applied for electronic/ionic steps (1.0 ×10−5/1.0 ×10−4eV) in order to guarantee that the global minimum on the potential energy surface (PES) has been reached. The final atomic forces over the metal–organic frameworks are found to be less than FIG. 1. Bulk structure of MIL-53 (Fe3+) after ionic position relaxation at the PBE/800 eV level of theory including spin-polarization effects. In detail, it is possible to observe the narrow pore structure of this material. The red, gray, and white spheres correspond to oxygen, carbon, and hydrogen atoms, respectively, whereas the golden sphere is representative of Fe, Al, or Cu. Code: VASP. J. Chem. Phys. 155, 024701 (2021); doi: 10.1063/5.0054874 155, 024701-3 © Author(s) 2021The Journal of Chemical PhysicsARTICLE scitation.org/journal/jcp 0.01 and 0.03 eV/Å for the pore structure and the guest molecule, respectively. The GGA +U relaxations have been carried out using U=7 eV and J =1 eV as Hubbard parameters on Fe 3 dand Cu 3 d states, while employing the same energy convergence criteria for the electronic/ionic steps. The binding energy E bof the adsorbed species to the frame- work has been calculated by subtracting the total energy prior and posterior to the adsorption, i.e., Eb=EMOF−gas−(EMOF+Egas), (1) where E MOF-gas is the total energy of the gas–framework system and the last terms correspond to the individual total energies before adsorption. Zero-point energies and thermal corrections are not considered in this definition. Effects of spin-polarization and Hub- bard corrections (GGA +U) on Fe 3 dand Cu 3 dstates over the quantity expressed by Eq. (1) have also been evaluated for the Fe- and Cu-based metal–organic frameworks. III. RESULTS AND DISCUSSION A. Bulk structures In order to evaluate how the metallic center affects the ability of a non-functionalized metal–organic framework to capture carbon dioxide, we have considered the bulk structure from MIL-53 (Fe3+) with a diamond-shape pore, also called the narrow pore form. This material crystallizes in a P2 1/c space group with unit cell dimensions given by a =19.32 Å, b =15.04 Å, c=6.84 Å, and β=96.3○. Initially, lattice parameters have been constrained during the relaxation step in order to maintain the spatial group symmetry of the crystalline structure. Table S1 shows that the optimization of lattice parameters leads to a slight decrease of ∼1–2 Å of the blattice parameter and variation of <2○in the lattice angles for these systems that are not expected to affect the adsorption thermodynamics upon expansion into the 2 ×2 supercell. In MIL-53 (Fe3+), the inorganic counterpart formed by the iron metallic center is linked to the benzene dicarboxylate (BDC) ligands via oxygen atoms that are located in equatorial positions. In the axial positions, the hydroxyl groups form a region that can interact with the guest molecule as the hydrogen atoms are pointed out vertically to the pore center, while not presenting any steric hindrance. In this sense, the vertical distance between hydrogen atoms from different inorganic counterparts has been calculated as d H–H=5.20–5.40 Å, with iron atoms from adjacent parts being distanced by 19.32 Å. Replacing the metallic center by aluminum or copper in MIL-53 (Al) and MIL-53 (Cu) does not promote variations in the pore width (∼19.3 Å), but its size is diminished for the aluminum case (d H–H =5.11 Å). Additionally, there is a shortage in the Al–O chemical bond of about ∼0.2 Å in comparison to Fe–O or Cu–O, which might be resultant from a stronger interaction between the metallic center and the oxygen connecting the organic counterpart. At this point, it is necessary to emphasize that MIL-53 (Al3+) does not present the same crystal structure as the iron-based material; thus, it is an approximate model for this study.17 B. Electronic structure This analysis has been primarily considered to validate the density functional theory methodology, but also to establish thestructural parameters that are optimized during the relaxation pro- cess, i.e., the ionic positions are always considered but the lattice parameters are usually kept fixed throughout the relaxation. MIL-53 (Fe3+) has shown photoactivity in the visible light region with an experimental optical gap of 2.64 eV, which corre- sponds to an absorption edge at λ=470 nm.47Furthermore, the authors point out that the maximum absorption at λ=220 nm is due to the ligand to metal charge transfer, O (II) →Fe (II).47 Figure 2 and Fig. S1 depict the density of states of MIL-53 (X), where X=Fe3+, Al3+, and Cu2+, as obtained using the Gaussian smear- ing and tetrahedron method with Blöchl corrections, respectively. The latter choice is justified by the semiconducting nature of these materials, which requires such a methodology for an appropriate description of their intrinsic bandgaps, whereas the Gaussian smearing facilitates the plot visualization. For Fe- and Cu-based metal–organic frameworks, the GGA +U methodology has been used to deal with the self-interaction prob- lem from the GGA approximation to density functional theory that often leads to an underestimated bandgap.48–50In this sense, these calculations were performed in a static mode after spin-polarized ionic relaxation within the PBE level of theory. These open-shell systems present an octahedral dorbital splitting with the electron occupancy in Cu d-orbitals expressed as (t3↑↓ 2ge2↑,1↓ g), whereas the magnetic moment ( μ) for Fe3+(4.5μb/atom) suggests a high-spin state with electron occupancy given by (t3↑ 2ge2↑ g). An interesting point is that μfor oxygen atoms is slightly increased at the hydroxyl groups in the Cu-based MOF (∼0.3 μb/atom) in comparison with the Fe-based system (<0.2μb/atom), which is not verified for the oxygen atoms connected to the BDC ligands. Although the Cu-based MOF does not exhibit a significant change in the atomic μfor the metallic centers regarding the level of theory, the iron-based material does have a significant variation in this property (1.0–4.0 μb) within the PBE level, which would lead to Fe3+ions displaying different electronic configurations along the symmetric crystal environment. Such inaccuracy to describe the Fe-based MOF electronic structure could affect the thermodynamic properties if this effect is not propagated upon addition of the carbon dioxide molecule in the further steps. For MIL-53 (Fe3+), the optimum value for the Hubbard param- eter on Fe 3 dstates was estimated to be U =7 eV and J =1 eV to give a theoretical bandgap (E g=2.20 eV) that shows fair agree- ment with the experimental report.47As displayed in Fig. 2(a), this system has the valence band maximum (VBM) mainly com- posed of O 2 porbitals connecting to the metallic center, which persists until −2.6 eV. In the valence band, the spin-up contri- butions from Fe 3 dstates have a rising contribution from ∼−0.3 to−0.7 eV, but the conduction band minimum (CBM) is basi- cally determined by the position of the spin-down contributions from these atoms. Fingerprints from C–H and O–H bonds can be easily identified in the H 1 splot [Fig. 2(a)- bottom] with four clear peaks in the interval from −1.8 to −5.7 eV that match well with C 2 pstates and O 2 pstates that are present in the same interval. In Fig. S1(b), the calculated bandgap for MIL-53 (Al3+) is Eg=3.23 eV, which also shows good agreement with the experi- mental value reported by Guo et al. (Eexp=3.56 eV).51In the same work, the authors have found that this material has an absorption J. Chem. Phys. 155, 024701 (2021); doi: 10.1063/5.0054874 155, 024701-4 © Author(s) 2021The Journal of Chemical PhysicsARTICLE scitation.org/journal/jcp FIG. 2. Density of states obtained for the metal–organic frameworks under investigation at the level of theory: PBE/800 eV for MIL-53 (Al3+) and GGA +U/800 eV, with U=7 eV on Fe 3 dor Cu 3 dstates of MIL-53 (X =Fe3+, Cu2+). Code: VASP /Gaussian smearing method with σ=0.1. edge at λ=348 nm; therefore, it would not exhibit activity in the visible region for eventual photocatalytic purposes. Here, it is veri- fied that the valence band is formed mainly of O 2 pand C 2 pstates from the top ( −0.3 eV) until −2.3 eV. Al 3 pstates do not participate in the VBM or CBM composition, which are prominent just in the range of −2.1 to −7.1 eV with very low density of states ( <2.6 den- sity of states/eV). In the VBM, a very low contribution from Al 3 s states (0.11 DOS/eV) can be seen at −2.9 eV. This is the reason for the large bandgap shown by this material, since the CBM is formed by the overlapping of 2 pstates from carbon and oxygen atoms that lie much higher in energy than the unoccupied dstates from Fe and Cu atoms. Here, the C–H and O–H bonds are verified upon orbital overlapping from −1.74 to −10.0 eV with four major peaks that are shifted in about +0.25 eV compared to the Fe-based MOF. As displayed in Fig. 2(c), MIL-53 (Cu2+) has a similar den- sity of states profile shown by the iron-based system with Cu 3 d unoccupied states lying much lower in energy compared to Fe 3 d states. Therefore, the overlapping with unoccupied states from oxy- gen atoms is promoted initially at +0.23 eV (1.4 eV lower than Fe-based MOF) to significantly reduce the bandgap. On the other hand, carbon unoccupied orbitals will just appear with a higher intensity at about +3.0 eV. This material has a calculated bandgap of E g=0.83 eV using U =7 eV and J =1 eV for Cu 3 dstates [see Fig. S1(c)]. C. Gas capture Figure 3 displays the adsorption sites (labeled by different num- bers) here under consideration for CO 2capture. At site (1), the interaction takes place via hydrogen atoms from hydroxyl groupsthat are connected to the metallic center in the axial positions. At site (2), the interaction occurs with the ligand carbon and hydrogen atoms through the oxygen atom. At site (3), the molecule is expected to move freely inside the pore to interact via carbon or oxygen atoms. Horizontal interactions with hydrogen from the BDC ligand have been considered at site (4). Finally, at site (5), the guest molecule has been placed to interact with both inorganic (via hydroxyl groups) and organic (via carbon) counterparts. Table I contains the gas–framework binding energies (E b) calculated via Eq. (1) for all configurations (in kJ/mol). Inclusion of spin-polarization has been considered at the third and fourth columns, in which the latter column is estimated within the GGA +U level of the- ory. The experimental values are available in the last column for comparison. Mahdipoor et al. have previously determined the absolute heat of adsorption for MIL-53 (Fe3+) in 58.7 kJ/mol by experi- mental methods.52Table I (second column) indicates that E blies between −47.60 and −73.42 kJ/mol for this material, which gives an overestimation of ∼25% for the most favorable configuration (site 1). In this system, the final configuration shows a small angular shift for a better (CO 2)O⋅ ⋅ ⋅H(MOF) interaction at ∼1.97 Å. Such an interaction does not alter the O–H bond ( ∼0.98 Å) from the hydroxyl groups or the C =O bond (1.18 Å), a typical behavior for weak van der Waals interactions. Thus, one should not expect any changes in the electronic structure of this system since there is no orbital hybridization between O 2 p(CO 2) and H 1 sorbitals (-OH group). Here, the comparison between experiment/calculation methods is given with the absolute values for heat of adsorption. J. Chem. Phys. 155, 024701 (2021); doi: 10.1063/5.0054874 155, 024701-5 © Author(s) 2021The Journal of Chemical PhysicsARTICLE scitation.org/journal/jcp FIG. 3. Initial configurations for CO 2adsorption inside the MOF structures under investigation: the interaction takes place vertically in 1, 2, and 5, whereas in 3 (in detail) and 4, the carbon dioxide molecule has been placed in a horizontal position. The red, gray, and white spheres correspond to oxygen, carbon, and hydrogen atoms, respectively, whereas the golden sphere is representative of Fe, Al or Cu. It is interesting to note that applying spin-polarization effects, within the DFT/GGA theory level (third column), does not improve the theory–experiment agreement, instead leading to an even more significant overestimation in terms of absolute values(Eb=−189.58 to −245.43 kJ/mol). In order to investigate the under- lying reasons for such a discrepancy, the atomic magnetic moment (μ) at the metallic site has been evaluated for each case (see Table S2). The supercell prior to adsorption has ∼1–3 unpaired electrons at the TABLE I. Binding energies (E b) for several possible configurations upon carbon dioxide adsorption within the GGA level without spin-polarized effects (second column, ISPIN =1), as well as with its inclusion (third column, ISPIN-2). GGA +U values correspond to spin-polarized calculations with U =7 eV and J =1 eV on Fe 3 dor Cu 3 dstates. Note that the comparison between the heat of adsorption and E b, which is based on the total energy variation prior and posterior to the adsorption, is held using the absolute values. In the last column, the absolute values of heat of adsorption are taken from the literature. The boldfaces denote the most favorable Eb for each case. Binding energies (Eb, kJ/mol) GGA GGA +UHeat of adsorption Configuration ISPIN-1 ISPIN-2 ISPIN-2 (kJ/mol) MIL-53 (Fe3 +) 1 −73.42 −242.04 −47.13 58.752 2 −69.57 −198.47 −38.19 3 −48.34 −189.58 −21.26 4 −47.60 −215.50 −29.11 5 −51.55 −245.43 −17.71 MIL-53 (Al3+) 1 −36.19 ⋅ ⋅ ⋅ 2 −35.61 ⋅ ⋅ ⋅ 3 −36.73 ⋅ ⋅ ⋅ 35.018 4 −34.17 ⋅ ⋅ ⋅ 5 −19.39 ⋅ ⋅ ⋅ MIL-53 (Cu2+) 1 −39.80 −42.87 −35.85 2 −28.34 −39.90 −32.19 3 −33.23 −46.97 −33.66 n/a. 4 −30.38 −47.36 −30.97 5 −29.71 −37.49 −34.18 J. Chem. Phys. 155, 024701 (2021); doi: 10.1063/5.0054874 155, 024701-6 © Author(s) 2021The Journal of Chemical PhysicsARTICLE scitation.org/journal/jcp FIG. 4. Final configurations for CO 2 adsorption inside MIL-53 (Fe3+) after ionic relaxation. In (a), the most favor- able configuration at site 1 is shown, whereas the other systems are rep- resented in (b). Note: the position of the hydrogen (from -OH groups) slightly varies for each case. The red, gray, and white spheres correspond to oxygen, carbon, and hydrogen atoms, respec- tively, whereas the golden sphere is rep- resentative of Fe. metallic center ( μ=1.0–2.7 μB), but the introduction of the guest molecule promotes oscillations in the electron occupancy across the framework for all sites. As a result, the total magnetization does not remain constant in the series, even with multiple reoptimizations being carried out after the convergence is reached. These data clearly indicate the lack of consistency in the GGA level of theory to describe the open shell configuration of these frameworks, i.e., to find the correct minimum energy configuration in the potential energy surface, since the gas capture does not involve the metallic center in a direct way to justify the change in its electronic structure. On the other hand, μremains constant upon addition of car- bon dioxide within the GGA +U approximation as displayed in the fourth column in Table S2. In this case, the use of Hubbard cor- rections has returned E b=−47.13 kJ/mol, which has an agreement of 80.3% with the experimental reported value.52The total magne- tization determined for this material (mag =80.00 μB) establishes a coherent high spin configuration with five unpaired electrons for each Fe atom. Changes in the U parameter (U =6 and 8 eV) have been tested for better tuning of E b, but no significant improvement has been observed ( <1 kJ/mol) for site (1). The absolute heat of adsorption measured by Bourrelly et al.18 (35 kJ/mol) is indicative of a much weaker gas–framework inter- action in MIL-53 (Al3+) in comparison with the Fe-based MOF (58.7 kJ/mol).52This property has been properly described by our calculations, where the most favorable configuration (3) over- estimates the experimental value by only 1.73 kJ/mol ( <5%, Eb=−36.73 kJ/mol). For matters of comparison, Ramsahye et al. have determined E b=−41 kJ/mol for MIL-53 (Al3+) within the PW91 level of theory/double numerical basis set with polarizationfunctions applied on hydrogen atoms, using a different model for MIL-53 (Al3+) that is based on its crystallographic data.17Thus, the present study shows better agreement, and Fig. S2 (a) and (b) illus- trate the final structures after ionic relaxation with the experimental result than that found by previous works.17,27 The Cu-based MOF has site (1) as the most favorable config- uration within the PBE level of theory, with E b=−39.80 kJ/mol in the non-spin polarized case. The final geometry can be visualized in Figs. S3(a) and S3(b), where the guest molecule is also rotated in rela- tion to site (1) in a similar position to that verified for the Fe-based MOF. Here, it is remarkable that the inclusion of spin-polarization effects provides a smoother trend with E b=−37.49 to −47.36 kJ/mol in comparison with the Fe-based MOF. This can be associated with the lower number of unpaired electrons in the Cu-based MOF that approximates the solution to the non-spin polarized case, but it still provides a different chemical trend for this framework series. In the GGA +U case, E b=−35.85 kJ/mol is 7.0 kJ/mol lower than that predicted by the PBE method, suggesting a very simi- lar heat of adsorption for this material in comparison with MIL-53 (Al3+). The final magnetization in the supercell (mag =32.00) is coherent with the presence of one unpaired electron in each metallic center (∼0.9μB/atom) and a slight magnetization on O atoms from the metal–organic framework ( ∼0.1–0.3 μB). Hence, the presence of an unpaired electron confirms the Cu d9electronic configuration arising from the Cu2+oxidation state in these systems. Therefore, this methodology is consistent to determine the electronic config- uration for these materials prior and posterior to the adsorption, thus providing total energies that can be compared with each other. The method itself determines the correct magnetization in the first J. Chem. Phys. 155, 024701 (2021); doi: 10.1063/5.0054874 155, 024701-7 © Author(s) 2021The Journal of Chemical PhysicsARTICLE scitation.org/journal/jcp FIG. 5. The main H ⋅ ⋅ ⋅O interactions in MIL-53 (X), where X =Fe3+, Al3+, or Cu2+before the gas adsorption. The red, gray, and white spheres correspond to oxygen, carbon, and hydrogen atoms, respectively, whereas the golden sphere is representative of Fe, Al, or Cu. Level of theory: PBE/non-spin polarized. electronic convergence that remains constant in the further steps until the ionic relaxation is finished. This is not verified for the PBE method, where the magnetization tuning along with the ionic relax- ation process could lead to different electronic structure descriptions for some systems. Albeit these frameworks have crystal structures that only dif- fer by the metallic center, it is noticeable that the Fe-based MOF has a binding energy (E b) for carbon dioxide capture that is much higher than the other frameworks (see Table I). Such disparity is not explained by the gas–framework interaction strength since the inter- action distance remains unaltered (1.97–2.04 Å) regardless of the material. Moreover, the van der Waals nature of these interactions points out the inactivity of the metallic center in the gas adsorp- tion. Thus, we should account for other weak interactions inside the framework that could play a significant role in the adsorption energetics. Subsection III D will address this point in detail. D. Structural analysis: The non-spin polarized case It has been discussed in Subsection III C that the inactivity of the metallic center to affect the gas–framework interactions should lead to more similar values for E b. In order to address this ques- tion, the main gas–framework and framework–framework interac- tions are investigated in this subsection. Figures 5 and 6 highlight these interactions prior andposterior to the gas adsorption, respec- tively, where O1–O3 correspond to oxygen atoms from the organic counterpart. This analysis has been performed using the non-spin polarized case for the same interaction site [site (1) for Fe has thesame final configuration as site (3) for Al and Cu] as the GGA +U methodology has not been employed for structural relaxation of the Al-based MOF. All relevant data are reported in Table II. It is noticeable that the vertical distance between hydrogen atoms from different inorganic counterparts d(H1 ⋅ ⋅ ⋅H2) increases in the order Fe <Al<Cu as the H–O bond in the hydroxyl group is bent toward the organic counterpart. Such geometrical distortion is an overall effect of the electrostatic attraction between hydrogen (H1) and the surrounding oxygen atoms connected to that counterpart. In MIL-53 (Cu2+), the attraction is more evident due to the shorter H1 ⋅ ⋅ ⋅O1 and H1 ⋅ ⋅ ⋅O2 distances (2.55 and 2.62 Å), while the (O1 ⋅ ⋅ ⋅H1⋅ ⋅ ⋅O2) angle is about 26○higher than that in the other MOFs. Nonetheless, these interactions are weakened upon gas adsorption, as indicated by the stretching of H1 ⋅ ⋅ ⋅O1 and H1⋅ ⋅ ⋅O2 distances to up to 2.98 Å (an increase of ∼0.4 Å) in MIL- 53 (Cu2+), which is a more significant variation than that observed for the other frameworks. Furthermore, the decrease of 56.4○in the a(O1 ⋅ ⋅ ⋅H1⋅ ⋅ ⋅O2) angle for this framework upon adsorption indicates a weakened interaction between the gas and the organic region. Other interactions inside the framework after adsorption are quite constant regardless of the metallic center. For instance, d(H1 ⋅ ⋅ ⋅O4) and d(H2 ⋅ ⋅ ⋅O5) distances lie in the range 1.97–2.05 Å for all systems, whereas the interaction between the oxygen atom from the organic counterpart and the carbon atom, i.e., d(C1⋅ ⋅ ⋅O6), is about 2.81–2.90 Å. Thus, these interactions are not dictating the differences seen in the gas adsorption energetics of these frameworks. FIG. 6. The main interactions after gas adsorption at site (1) inside the MIL-53 (Fe3+). Note that the interactions may vary according to each system. The red, gray, and white spheres correspond to oxygen, carbon, and hydrogen atoms, respectively, whereas the golden sphere is representative of Fe, Al, and Cu. Level of theory: PBE/non-spin polarized. J. Chem. Phys. 155, 024701 (2021); doi: 10.1063/5.0054874 155, 024701-8 © Author(s) 2021The Journal of Chemical PhysicsARTICLE scitation.org/journal/jcp TABLE II. Structural parameters given by atomic distances ( d, in Å) and angle ( a, in○) of the main contributions to the gas adsorption energetics in MIL-53 (X), with X =Fe3+, Al3+, or Cu2+. In the second column, the oxygen atoms (O1–O6) are located either at the organic counterpart (organic) or the gas molecule (CO 2). Level of theory: PBE/non-spin polarized. MIL-53 (Fe3+) MIL-53 (Al3+) MIL-53 (Cu2+) Atomic distance (Å)/Angle(○) Oxygen Initial +CO 2 Δd Initial +CO 2 Δd Initial +CO 2 Δd d(O1 ⋅ ⋅ ⋅H1) Organic 2.87 2.82 −0.05 2.90 2.85 −0.05 2.55 2.69 0.14 d(O2 ⋅ ⋅ ⋅H1) Organic 2.64 2.64 0.00 2.71 2.69 −0.02 2.62 2.98 0.36 d(O3 ⋅ ⋅ ⋅H1) Organic 2.71 2.95 0.14 2.68 2.89 0.21 3.12 2.97 −0.15 d(H1 ⋅ ⋅ ⋅H2) ⋅ ⋅ ⋅ 5.16 5.44 0.28 5.22 5.39 0.17 5.50 5.76 0.26 d(X–X) ⋅ ⋅ ⋅ 7.50 8.46 1.16 7.52 8.42 0.90 7.52 8.47 0.95 d(H1 ⋅ ⋅ ⋅O4) CO 2 ⋅ ⋅ ⋅ 1.97 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.98 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 2.04 ⋅ ⋅ ⋅ d(H2 ⋅ ⋅ ⋅O5) CO 2 ⋅ ⋅ ⋅ 1.97 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.98 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 2.05 ⋅ ⋅ ⋅ d(C1⋅ ⋅ ⋅O6) ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 2.88 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 2.90 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 2.81 ⋅ ⋅ ⋅ a(O1⋅ ⋅ ⋅H1⋅ ⋅ ⋅O2) Organic 114.6 115.1 0.5 112.0 113.2 1.2 138.9 82.5 −56.4 Eb(kJ/mol) −73.42 −36.73 −39.18 The process of gas accommodation inside the framework pore promotes an increase in the distance between metallic centers in about d(X–X) =0.9–1.2 Å. As this distance is decreased in the adja- cent unit cells by ∼0.5 Å, it is suggested that the presence of the guest molecule slightly opens the pore, whereas the flexibility of this model is clarified. Thus, the wider space opened between dif- ferent inorganic regions in MIL-53 (Cu2+) could slightly decrease the interaction strength with the guest molecule, i.e., the adsorp- tion enthalpy or heat of adsorption, as the hydrogen atoms are the main sites contributing to the adsorption. However, the constant gas–framework interactions suggest that internal interactions inside the framework involving the hydroxyl group and organic counter- part have significant contributions to the binding energy of these materials. IV. CONCLUSIONS In the current study, we have investigated the effect of vary- ing the metallic center in the inorganic counterpart of MIL-53 (X), where X =Fe3+, Al3+, Cu2+, on the carbon dioxide adsorp- tion by using first-principles methods. The relevance of applying spin-polarization and Hubbard corrections (GGA +U method) to describe the electronic structure and gas adsorption energetics has been investigated. The Hubbard parameters for Cu- and Fe-based MOFs have been initially estimated through electronic structure assessment, in which the values of U =7 eV and J =1 eV are found to be appropriate to treat the Fe dand Cu dstates. Within this theory level, MIL-53 (Cu2+) has a calculated bandgap of 0.83 eV, whereas MIL-53 (Fe3+) and MIL-53 (Al3+) display bandgaps of 2.20 and 3.23 eV, respectively, in fair agreement with experimental reports. In fact, the proper description of the metal orbital occupancy in the open shell systems is achieved using the spin-polarized GGA +U calculations. The atomic magnetic moment on the metallic center is, in this context, an important parameter to be tracked throughout the adsorption process, as it should remain constant prior andpos- terior to the adsorption. Here, MIL-53(Fe3+) is found to stabilize on the high-spin configuration with five unpaired electrons per atomand with a CO 2binding energy of −47.13 kJ/mol in good agreement with the experimental finding for heat of adsorption. It should be pointed out that our thermodynamics assessment includes only the total energy contribution for the reaction enthalpy, i.e., temperature- dependent contributions to the internal energy, zero-point energy, and pV term are not included. Therefore, the agreement with the experimental outcome could be further improved if such contri- butions are included and specific thermodynamics conditions are properly simulated. However, it lays beyond the scope of the cur- rent study. In the case of the Cu-based MOF, we have obtained a CO 2binding energy of −35.85 kJ/mol. The latter is similar to the one obtained for the Al-based MOF, viz., −36.73 kJ/mol. These results indicate that Cu-based MIL-53 is a promising framework for CO 2capture applications. Concerning the structure, the CO 2guest molecule is stabilized within the MOF pore center through weak interactions with the hydroxyl groups of the inorganic counterpart, which shows the relevance of the coordinating molecule on the metal site. These results provide insights for future design of suitable MOF compounds for CO 2capture and storage. SUPPLEMENTARY MATERIAL See the supplementary material for density of states obtained for the metal–organic frameworks under investigation using the tetrahedron method with Blöchl corrections and final configura- tion for gas adsorption inside MIL-53(Al3+) and MIL-53(Cu2+) after ionic relaxation. The supplementary material is available free of charge on the ACS Publications website. ACKNOWLEDGMENTS This research project received financial support from the Swedish Research Council (VR) and STandUP for Energy collab- oration, with computational resources provided by the Swedish National Infrastructure for Computing (SNIC) at the PDC Cen- ter for High Performance Computing and National Supercom- puter Centre (NSC). G.B.D. acknowledges CAPES (Coordenação de Aperfeiçoamento de Pessoal de Ensino Superior) for financial J. Chem. Phys. 155, 024701 (2021); doi: 10.1063/5.0054874 155, 024701-9 © Author(s) 2021The Journal of Chemical PhysicsARTICLE scitation.org/journal/jcp support of her Ph.D. studies. L.T.C. acknowledges support from CAPES/Print/UFF Grant No. 8881.310460/2018-01 and CAPES- STINT Grant No. 88887.465528/2019-00 and the CNPq Fellowship. The authors declare no conflicts of interest. DATA AVAILABILITY The data that support the findings of this study are available within the article. 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5.0048612.pdf

APL Materials ARTICLE scitation.org/journal/apm Engineering the spin conversion in graphene monolayer epitaxial structures Cite as: APL Mater. 9, 061113 (2021); doi: 10.1063/5.0048612 Submitted: 24 February 2021 •Accepted: 3 June 2021 • Published Online: 23 June 2021 Alberto Anadón,1,a) Adrián Gudín,1 Rubén Guerrero,1Iciar Arnay,1Alejandra Guedeja-Marron,1,2 Pilar Jiménez-Cavero,3,4 Jose Manuel Díez Toledano,1,5Fernando Ajejas,1,b)María Varela,6 Sebastien Petit-Watelot,7 Irene Lucas,3,4Luis Morellón,3,4 Pedro Antonio Algarabel,3,4 Manuel Ricardo Ibarra,3,4,8 Rodolfo Miranda,1,5,9Julio Camarero,1,5,9Juan Carlos Rojas-Sánchez,7 and Paolo Perna1,c) AFFILIATIONS 1IMDEA Nanociencia, C/Faraday 9, 28049 Madrid, Spain 2Departamento de Física de Materiales and Instituto Pluridisciplinar, Universidad Complutense de Madrid, Ciudad Universitaria, 28040 Madrid, Spain 3Instituto de Nanociencia y Materiales de Aragón, Universidad de Zaragoza and Consejo Superior de Investigaciones Científicas, 50018 Zaragoza, Spain 4Departamento de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain 5Departamento de Física de la Materia Condensada and Departamento de Física Aplicada and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, 28049 Madrid, Spain 6Departamento de Física de Materiales and Instituto Pluridisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain 7Université de Lorraine, CNRS, IJL, Nancy, France 8Laboratorio de Microscopías Avanzadas, Universidad de Zaragoza, 50018 Zaragoza, Spain 9IFIMAC, Universidad Autónoma de Madrid, 28049 Madrid, Spain Note: This paper is part of the Special Topic on Emerging Materials for Spin–Charge Interconversion. a)Author to whom correspondence should be addressed: alberto.anadon@univ-lorraine.fr b)Current address: Unité Mixte de Physique, CNRS, Thales, Univ. Paris-Sud, Université Paris-Saclay, Palaiseau, France. c)Electronic mail: paolo.perna@imdea.org ABSTRACT Spin Hall and Rashba–Edelstein effects, which are spin-to-charge conversion phenomena due to spin–orbit coupling (SOC), are attracting increasing interest as pathways to manage rapidly and at low consumption cost the storage and processing of a large amount of data in spintronic devices as well as more efficient energy harvesting by spin-caloritronics devices. Materials with large SOC, such as heavy metals (HMs), are traditionally employed to get large spin-to-charge conversion. More recently, the use of graphene (gr) in proximity with large SOC layers has been proposed as an efficient and tunable spin transport channel. Here, we explore the role of a graphene monolayer between Co and a HM and its interfacial spin transport properties by means of thermo-spin measurements. The gr/HM (Pt and Ta) stacks have been prepared on epitaxial Ir(111)/Co(111) structures grown on sapphire crystals, in which the spin detector (i.e., top HM) and the spin injector (i.e., Co) are all grown in situ under controlled conditions and present clean and sharp interfaces. We find that a gr monolayer retains the spin current injected into the HM from the bottom Co layer. This has been observed by detecting a net reduction in the sum of the spin Seebeck and interfacial contributions due to the presence of gr and independent from the spin Hall angle sign of the HM used. ©2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0048612 APL Mater. 9, 061113 (2021); doi: 10.1063/5.0048612 9, 061113-1 © Author(s) 2021APL Materials ARTICLE scitation.org/journal/apm Spin–charge current interconversion based on spin–orbit cou- pling is an essential operation in present spintronics applications.1–6 Systems showing these properties are promising candidates for the realization, for instance, of a new generation of nonvolatile magnetic random access memories or efficient energy harvesting devices,7–9 among other examples. The most widespread systems providing large spin Hall conversion efficiency toward these applications are based on heavy metals, e.g., Pt, Ta, or W, because of their strong spin–orbit coupling (SOC). Recently, two-dimensional (2D) materials, such as Rashba interfaces,10,11topological insulator surfaces,12–14and transition metal dichalcogenides,15–24have been proposed to obtain efficient spin–charge current interconversion25and their wide range of func- tional properties. Some can present large SOC,15,17,19,26while oth- ers such as gr can exhibit micrometer spin diffusion lengths and long spin lifetimes.27In addition, the properties of gr can be tuned by proximity with other materials, such as ferromagnets (FMs),28,29 heavy metals,30or even other 2D materials.17 In this regard, it has been observed recently that the gr/Pt inter- face presents a very high spin-to-charge output voltage at room temperature (RT) in lateral spin valve devices using exfoliated gr and electrodes grown ex situ by electron beam lithography.31,32The enhanced spin–charge signal was due to the combination of current shunting suppression, highly resistive platinum, and efficient spin injection into gr. However, in contrast, it has also been observed that gr can significantly reduce the spin pumping voltage33,34or even generate a spin pumping voltage by itself without the necessity of a HM due to interfacial spin–orbit interactions.35,36These discre- pancies, together with the low intrinsic SOC of gr, point toward the relevance of the quality of the interfaces in determining the overall spin transport properties. Here, we study the interface between the gr monolayer and a HM and its effect on spin-to-charge current conversion in epi- taxial systems in which the spin detector (i.e., top HM), the gr layer, and the spin injector (i.e., Co) are all grown in situ under controlled conditions and with clean and sharp interfaces. All the samples have an (111)Ir 10 nm buffer layer and a 1.6 nm-thick Co layer on top of it. Then, we have two different types of stacks on top of the Ir/Co: gr/HM and HM. The role of gr in determining the overall spin-to-charge current conversion has been disentan- gled by means of thermo-spin experiments, as shown in Fig. 1. In these experiments, which are done in the so-called longitudinal spin Seebeck effect (SSE) configuration,8,37the SSE and the anomalous Nernst effect (ANE)38coexist in this geometry. In order to sepa- rate both contributions, we first use an Ir/Co/Ir control sample to obtain the ANE in the Co layer. We subtract this contribution in all the other heterostructures in order to obtain the overall spin–charge current contribution. We demonstrate that the spin–charge conver- sion in a Co/gr/HM system is not enhanced compared to the refer- ence Co/HM and independent from the spin Hall angle sign of the HM used as spin detectors, i.e., Pt or Ta. This experimental find- ing highlights the importance of gr to engineer the spin conversion and for the development of spin-caloritronics and spin-orbitronics devices. The samples incorporating gr (i.e., gr/HM) and the ones without gr (i.e., HM) were all fabricated in situ on epitaxial Ir(111)/Co(111) grown on sapphire crystals under controlled conditions, that is, they present similar structural quality and clean FIG. 1. Schematic of thermo-spin measurements in graphene metal hybrid het- erostructures. When a thermal gradient is applied in an Ir/Co/Pt structure in the z direction as well as a magnetic field in the y direction, a spin current ( Js) is gener- ated in the z direction and we will observe two different thermo-spin contributions, the anomalous Nernst effect ( EANE) and the spin Seebeck effect ( ESSE). When a graphene monolayer is introduced, we will need to consider not only the effect of graphene itself but also the additional contributions of the two new interfaces in the system ( Egr), which may induce the inverse Rashba–Edelstein effect as well as spin memory loss, a partial loss of spin current coherence. interfaces. We followed the methodology described in Refs. 28 and 39. In brief, we first deposited a 10 nm-thick epitaxial Ir(111) on Al2O3(0001) single crystal substrates by DC sputtering at 670 K with a partial Ar pressure of 8 ⋅10−3mbar and low deposition rate (of 0.3 Å/s). Subsequently, in the case of the gr-based heterostructures, the monolayer gr was prepared by chemical vapor deposition by ethylene dissociation at 1025 K at a partial pressure of 5.5 ⋅10−6 mbar. The samples were then cooled down to RT and Co was deposited by molecular beam epitaxy, and then, the Co intercalation below gr was promoted by thermal annealing at 550 K. This proce- dure produces the formation of a homogeneous Co layer with high structural order and sharp interfaces.28,39The Co layer is monitored in every step of the growth by x-ray photoemission spectroscopy to assure that it is not oxidized. In the case of samples without gr, we deposited a 1.6 nm-thick Co layer by DC sputtering at RT on top of the Ir(111) buffer. Finally, in all samples, a 5 nm capping layer of Pt or Ta was DC sputtered at RT. To prove the structural quality of the samples, we resorted to x-ray diffraction (XRD) and high resolution scanning transmis- sion electron measurements (STEMs) at RT. The XRD measure- ments were performed using a commercial Rigaku SmartLab SE multipurpose diffractometer with a monochromatic Cu K αsource (λ=1.54 Å). STEM observations were carried out in a JEOL ARM200cF at 200 kV and RT. The microscope is equipped with a CEOS spherical aberration corrector and a Gatan Quantum electron energy-loss spectrometer.28Specimens were prepared by mechanical polishing and Ar ion milling. Figure 2(a) shows a θ–2θdiffraction pattern recorded in a Al 2O3//Ir/Co/gr/Ta heterostructure. Besides the Al 2O3[0006] and Al 2O3[00012] crystallographic reflections from the substrate, maximum intensity appears at 2 θ=40.6○and 87.9○, which corre- sponds with Ir[111] and Ir[222] reflections, respectively. The forma- tion of thickness fringes around the Ir[111] and Ir[222] reflections confirms the low roughness of the interfaces. In the inset, the ωscan (rocking curve) around the Ir[222] reflection shows a sharp pro- file. The curve was fitted using a pseudo-voigt function obtaining a full width at half maximum (FWHM) of 0.27○, which proves a low degree of mosaicity in the deposited films. Figure 2(b) shows φscans APL Mater. 9, 061113 (2021); doi: 10.1063/5.0048612 9, 061113-2 © Author(s) 2021APL Materials ARTICLE scitation.org/journal/apm FIG. 2. Structural and microscopic char- acterization of epitaxial Ir/Co/gr/HM het- erostructures. (a) X-ray θ–2θdiffraction pattern recorded in an Al 2O3//Ir/Co/gr heterostructure. In the inset, a θ–2θ scan recorded around the Ir(111) reflec- tion is shown. (b) φscan plots of the Al2O3[20–210] and Ir[002] reflections. (c) and (d) Scanning transmission elec- tron microscopy characterization of a Ir[111]/Co/gr sample grown on a SrTiO 3 substrate (with tCo=1 nm and tIr =10 nm), capped with a Ta oxide thick layer in order to protect the gr sur- face. Atomic resolution high-angle annu- lar dark-field images of the STO/Ir and Ir/Co interfaces, respectively. The scale bars represent a length of 2 nm. around the Al 2O3[202⋅110]and Ir[002] reflections. The rotation scan around the Ir[002] reflection shows a sixfold symmetry instead of the expected threefold symmetry. This is related with the presence of two equivalent twin-boundary domains rotated by 180○.40Similar curves, including ω- andφ-scans, are obtained for samples with- out gr (not shown). From Figs. 2(a) and 2(b), the following epi- taxial relations are obtained: out-of-plane [0001]Al2O3∣∣[111]Ir and two in-plane configurations, (1) [01–10]Al2O3∣∣[1–10]Ir (−90○and 30○) and (2) [01–10]Al2O3∣∣[1–10]Ir (30○and 90○). The positions of the Ir[111] and Ir[002] reflections indicate an incommensurate growth of iridium with a bulk-like afcc lattice parameter within the experimental error. This is explained by the large mismatch ( ∼13%) between Al 2O3[0001] (0.4785 nm) and Ir[111]. The STEM observations confirm the quality of the stacks. Figures 2(c) and 2(d) display the atomic resolution STEM high- angle dark-field image of an Ir/Co/gr/Ta heterostructure, showing a high crystalline quality and sharp and coherent interface. No major hints of chemical interdiffusion or disorder are visible. These results, along with x-ray diffraction, suggest that the Co layer is epitaxial and the Co layer on the Ir buffer is fully strained and coherent. Thermo-spin measurements were performed in an Oxford spectrostat NMR40 continuous flow He cryostat with a thermoelec- tric measurement system.41–43Experimentally, the sample is put in place between two ceramic AlN plates, which are electrically insu- lating but have high thermal conductivity. They are attached using thermal paste to a large Cu piece that acts as a cold feet and is in direct contact with the cryostat. A resistive heater on the upper AlN piece provides the thermal gradient by application of an elec- tric current in the order of several milliamperes. The temperature difference between the upper and lower plate is measured by two T-type thermocouples near to the sample in order to obtain accu- rate temperature values. The samples were contacted electrically with thin Al wires with a diameter of 25 μm using commercial thermal silver paste. The voltage was measured using a Keithley2182A nanovoltmeter. The sketch of the measurement geometry is shown in Fig. 1: the thermal gradient is applied in the z direction, while a magnetic field is swept in the y direction. A thermo-spin voltage is then measured in the x direction. It is worth recalling that in systems containing metallic FMs, the thermo-spin voltage has three main contributions: (1) the anoma- lous Nernst effect (ANE), i.e., the thermal counterpart of the anoma- lous Hall effect, which has a similar physical origin;8,38,43(2) the spin Seebeck effect, which comprises the generation of a spin cur- rent from incoherent thermal excitation and its conversion on an electric voltage by means of the inverse spin Hall effect (ISHE); and (3) the interfacial spin–orbit contribution, arising from the Rashba interfacial spin–orbit field, which can give rise to a wide range of phenomena, from spin memory loss to spin current generation.6,10,44 We first identified the ANE signal contribution of the Co layer, which is proportional to the Co magnetization. We acquired the thermo-spin voltage in a symmetric epitaxial Ir(10)/Co(1.6)/Ir(5) stack [panel (b)] as a function of the in-plane applied magnetic field and compared it to the sample magnetization along the y direc- tion normalized by the saturation value. The identical behavior of both magnitudes is shown in Fig. 3(b), as expected from the ANE phenomenological relation EANE=QS(μ0M×∇T), (1) with QS,μ0,M, and∇T being the Nernst coefficient, the vacuum magnetic permeability, the thermal gradient, and the magnetization of the FM, respectively. Since Ir has a much smaller spin Hall than other heavy metals, such as Pt,45this symmetric stack can be hence used as a reference to check the size of the anomalous Nernst effect of the Co layer in the asymmetric stacks, which will be subtracted from the overall voltage measured. Note that in Figs. 3(a) and 3(b), we can observe a very APL Mater. 9, 061113 (2021); doi: 10.1063/5.0048612 9, 061113-3 © Author(s) 2021APL Materials ARTICLE scitation.org/journal/apm FIG. 3. Thermo-spin voltage in epitaxial hybrid gr/HM and HM stacks. (a) Thermo- spin voltage in Ir/Co/Ir, Ir/Co/Pt, and Ir/Co/gr/Pt. The observed thermo-spin voltage in the sample with the Ir capping layer (yellow) is significantly smaller than the that with Pt, and it is mainly due to the anomalous Nernst effect in Co. A reduction in the voltage at saturation field is observed when gr is introduced into the stack. (b) Close-up view on the anomalous Nerst effect voltage in the Ir/Co/Ir sample and its magnetization measured by vibrating sample magnetometry. (c) Angular dependence on the thermo-spin voltage in the Ir/Co/Pt sample. The angle θrep- resents the relative angle between the measured voltage (x direction) and the applied magnetic field (xy plane). small voltage in the Co/Ir sample mainly due to the electrical screen- ing by the buffer layer of Ir because of its low resistivity, about three times lower than Pt in this range of thickness.46–48This is specially the case for epitaxial Ir,49which leads to smaller values of the spin Hall angle when comparing to polycrystalline metals (see Ref. 48). The second contribution to the measured voltage is the SSE generated by the inverse spin Hall effect,50,51which has a similar geo- metric behavior, since the spin current lies in the z direction as it is induced by an out-of-plane thermal gradient, JC=θSHρ A(2e ̵h)JS×σ, (2) where JCandJsare the charge and spin currents in the HM, respec- tively,θSHandρare the spin Hall angle and the electrical resistivity of the HM, respectively, Arepresents the contact area between the FM and the HM, eis the elementary charge, and σis the mean spin polarization direction of the electrons in the FM close to the interface with the HM. It is important to note here that JS∝∇Tandσ∝M in the FM at saturation. We have thus performed thermo-spin measurements in the Pt and gr/Pt samples. This is shown in Fig. 3(a) where we observe that the introduction of gr reduces the total observed thermo-spin voltage in the Ir/Co/Pt system by about 40%. As can be seen in Eqs. (1) and (2), the SSE and ANE voltages follow a cross product relation between the thermal gradient and the magnetization; therefore, when magnetization rotates in the xy plane and the x component of the thermo-spin electric field is measured, we will observe a sinusoidal relation, as shown in Fig. 3(c), where the angleθrepresents the relative angle between the measured voltage and the applied magnetic field. At this point, it is important to notice that (i) the dependence of the thermo-spin voltage with an external magnetic field is simi- lar for both effects and (ii) the comparison of thermal gradients in Co in these stacks is reliable. For the latter, we routinely checked that the total thermal conductivity of the system, i.e., the sample(mainly substrate) with its holder, is maintained unchanged in all experiments and all samples. In fact, the main contributions to the thermal resistance of the system come from the substrate and sample holder because their total thermal resistance is orders of magnitude larger than that of the thin film stack. Consequently, the heat current that flows through Co, which has the same thickness in all samples, is similar in all the cases. This implies that the inclusion of gr or dif- ferent metallic detecting layers does not modify the (perpendicular) thermal gradient in Co and that the corresponding spin current is kept reasonably unchanged for all samples. As remarked before, the ANE signal of the Co layer taken from the measurements of the symmetric Ir/Co/Ir system is subtracted from the voltages acquired in the asymmetric stacks with the Pt detecting layer with and without gr. We carefully considered the resistivities and thickness of the films in the system. This is shown in the supplementary material. Thus, the ANE (Vcontr ANE) contribution to the voltage in the xdirection for a multilayer system can be estimated for each sample as42,51 Vcontr ANE=(r 1+r)VANE, (3) where VANEis the anomalous Nernst effect voltage of a single metal- lic FM layer with the same thickness subjected to the same thermal gradient and r=ρHM ρFMtFM tHM, withρHMandρFMrepresenting the HM and Co resistivities and tHMand tFMrepresenting their thickness, respectively. The resulting voltage dependences on the applied magnetic field after subtraction of the ANE contribution are shown in Fig. 4. Here, the voltage signals are normalized by the sample resistance to rule out the possibility of a shunting effect in the gr monolayer in the inverse spin Hall signal. We also assume for this calculation that FIG. 4. Interfacial contribution to the thermo-spin voltage. (a) Thermo-spin volt- age after subtraction of the anomalous Nernst effect component. This value is divided by the sample resistance in order to reduce artifacts and compare the val- ues adequately. L x=0.8 mm represents the lateral dimension of the sample in the x direction and ∇T=(Thot−Tcold)/Lz, where Lz=0.4 mm is the sample thickness, including the substrate. The absolute saturation voltage observed in the Pt sample (blue open circles) is reduced by 60% when comparing with the gr/Pt sample (green triangles). This is also the case for the absolute voltage in the Ta sample (wine squares) compared to gr/Ta (red filled circles) where the observed reduction is 11%. APL Mater. 9, 061113 (2021); doi: 10.1063/5.0048612 9, 061113-4 © Author(s) 2021APL Materials ARTICLE scitation.org/journal/apm Ms is the same in all the samples. To break down the contribution of the gr monolayer, in addition to the gr/Pt- and Pt-based stacks, we have considered a second set of samples capped by a 5 nm-thick Ta layer with a naturally oxidized surface (i.e., gr/Ta- and Ta-based stacks). As clearly shown in Fig. 4, the voltage dependence with the external magnetic field has an opposite sign when comparing Ta and Pt samples, as expected from their different signs of the spin Hall angle. Although the signal reductions in the two types of samples are of different magnitudes, that is, 60% in Pt-based samples and 11% in the Ta-based samples, our experimental finding suggests a uni- versal behavior regardless of the detecting layer. Here, the reduction percentage is calculated by subtracting the voltage at μ0H=0.7 T as ∣(VHM−Vgr/HM)/Vgr/HM⋅100∣. There are different mechanisms that may be behind the ori- gin of this observation. In this experiment, gr may support a non- negligible SOC, induced by the adjacent metals through electronic hybridization. This, in turn, produces a significant Rashba-type Dzyaloshinskii–Moriya interaction (DMI).28,29,40On this basis, we envisage three different mechanisms responsible for the reduction of the measured thermo-spin signals. (i) The introduction of gr could produce a shunting of the ISHE current, reducing the effective spin- to-charge conversion in the HM. This artifact is avoided normalizing the thermo-spin voltages by the sample resistance, as shown in Fig. 4. (ii) A Rashba interface, such as the Co/gr in our system, can induce spin–charge conversion by the so-called inverse Rashba–Edelstein effect (IREE). This would be translated in a voltage contribution of similar sign and magnitude for both systems. As we observe, this sce- nario cannot explain our findings unless the hybridization of gr due to the HM changes substantially the effective IREE of the interface. The IREE has already been observed in YIG/gr by spin pumping,35,36 and after normalization by sample resistance, its magnitude is signif- icantly smaller than the ISHE in Pt, although it could be different in the case of Co/gr. (iii) The gr interfaces are characterized by the pres- ence of an interfacial spin–orbit coupling field that can affect the spin coherence,6,46,52–54depolarizing the spin current traveling across it and thus reducing the total observed signal. This effect, referred to as spin memory loss (SML), may happen in both Co/gr28and gr/HM46 interfaces. The fact that the reduction is smaller in the case of Ta could be explained by its smaller SML when compared to Pt inter- faces.6,55Another plausible scenario could also arise considering a combination of the IREE effect and SML. In summary, we may have a different enhancement or attenuation depending on the nature of the HM. In addition, even though saturation magnetization can play an important role in ANE measurements,42,56this interpretation still holds even if the value of the saturation magnetization (Ms) is sig- nificantly different in both systems. As shown in the supplementary material, we obtain a higher average Ms in the gr samples, sug- gesting that the thermo-spin voltage suppression by graphene could be even larger than the estimation that we provide in Fig. 4. Fur- ther experiments including the direct injection of spin current are necessary in order to discern between both contributions since while spin Hall and inverse spin Hall are reciprocal effects, this is not necessarily the case of the Rashba–Edelstein effect and its inverse counterpart. Summarizing, we have fabricated high quality epitaxial hybrid metallic/monolayer graphene stacks with coherent, roughness-free interfaces as confirmed by x-ray diffraction and atomically resolved scanning transmission electron microscopy experiments. We haveexplored the spin–charge conversion by means of thermo-spin mea- surements in which we have carefully disentangled the anoma- lous Nernst effect from the spin Seebeck and interfacial contribu- tions. Furthermore, we estimated the interfacial contribution when a graphene monolayer is inserted. Although in other experiments the gr/Pt system has been shown to increase the spin Hall effect efficiency, we demonstrate that, for thermally induced spin cur- rents in the longitudinal spin Seebeck configuration, the presence of graphene reduces the overall spin–charge conversion regardless of the heavy metal (Ta or Pt with different spin Hall angle signs) layer used. We disregard any possible effect of the introduction of graphene in the thermal gradient in Co due to the insignificant change that the thermal resistance of graphene introduces in the system compared to the total thermal resistance of the sample and sample holder. We ascribe the reduction in the thermo-spin volt- age mainly to the combination of spin memory loss and the inverse Rashba–Edelstein effect. See the supplementary material for more information on the anomalous Nernst effect contribution in thermo-spin measurements and the saturation magnetization in ultra-thin cobalt films. We thank V. P. Amin, S. Sangiao, A. Fert, and F. Casanova for valuable discussions. This research was supported by the Regional Government of Madrid through Project No. P2018/NMT-4321 (NANOMAGCOST-CM) and the Spanish Minis- try of Economy and Competitiveness (MINECO) through Project Nos. RTI2018-097895-B-C42, RTI2018-097895-B-C43 (FUN-SOC), PGC2018-098613-B-C21 (SpOrQuMat), PGC2018-098265-B-C31, and PCI2019-111867-2 (FLAG ERA 3 grant SOgraphMEM). J.M.D.T. and A.G. acknowledge support from MINECO and CM through Grant Nos. BES-2017-080617 and PEJD-2017-PREIND- 4690, respectively. I.A. acknowledges financial support from the Regional Government of Madrid through Contract No. PEJD- 2019-POST/IND-15343. IMDEA Nanoscience is supported by the “Severo Ochoa” Program for Centres of Excellence in R & D, MINECO (Grant No. SEV-2016-0686). A.A., S.P.-W., and J.-C.R.-S. acknowledge support from Toptronic ANR through Project No. ANR-19-CE24-0016-01. P.J.-C., I.L., L.M., P.A.A., and M.R.I. acknowledge support from Project No. MAT2017-82970-C2-R. Electron microscopy observations were carried out at the Cen- tro Nacional de Microscopía Electrónica at the Universidad Com- plutense de Madrid. DATA AVAILABILITY The data that support the findings of this study are available from the corresponding author upon reasonable request. REFERENCES 1I. M. Miron, K. Garello, G. Gaudin, P.-J. Zermatten, M. V. Costache, S. Auffret, S. Bandiera, B. Rodmacq, A. Schuhl, and P. Gambardella, Nature 476, 189 (2011). 2X. Fan, H. Celik, J. Wu, C. Ni, K.-J. Lee, V. O. Lorenz, and J. Q. Xiao, Nat. Commun. 5, 3042 (2014). 3K. Jhuria, J. Hohlfeld, A. Pattabi, E. Martin, A. Y. A. Córdova, X. Shi, R. L. Conte, S. 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APL Mater. 9, 061113 (2021); doi: 10.1063/5.0048612 9, 061113-6 © Author(s) 2021

5.0057392.pdf

Characteristics of Thin Film Organic Photovoltaic Solar Cells Jagriti Dewan1Dand Mani Kant Yadav2E 1Pt. J.L.N. Government College, Faridabad ,QGLD 2J.C. Bose University of Science and Technology, Faridabad ,QGLD Djagritidewan22@gmail.com E&RUUHVSRQGLQJDXWKRU yadavmanikant64@gmail.com Abstract. The field of Organic Photovoltaics is gaining widespread popularity owing to the cost-effectiveness, efficiency, and stability of Thin Film Organic Photovoltaic Solar cells (OSC’s) for application especially in the relevance of the needs of the poor and remote areas of our vast country. Thin Film OSC aims at reducing the thickness of the active layer too few nanometres. This can help in enhancing the light- trapping ability of the OSC’s and thereby reducing the number of optical losses. A major proble m in OSC’s is the poor mobility and recombination of photogenerated charge carriers. The key role is to create appropriate designs of the device architecture with feeble losses. This paper aims at the device and material study of the OSC’s which could enha ncethe Power Conversion Efficiency (PCE) of the Thin Film OSC’s. This research area is in tune with the present International R&D trends to develop flexible and cost-effective solar cells Keywords —Organic Solar cells, Photovoltaics, Thin film, Power Conversion Efficiency, nanometer, recombination. INTRODUCTION Organic Photovoltaic Solar cells have gained widespread popularity over the years. Recent researches have shown a marked improvement in the Power Conversion Efficiency (PCE) which has made this an extremely popular R&D activity in the Solar cells field. The Solar Cell which was developed at Bell Laboratories in 1954 is a type of Photovoltaic device that converts optical en ergy to electrical energy[1]. Though it seems to be an extremely simple concept, successful Photovoltaic (PV) devices for solar energy production will require the optimization of many crucial factors involving material electron donor properties, electrode configuration, substrate mechanics, light trapping schemes, and fabrication methods. This paper covers a study of varioustechniques of material development an d light trapping methodologies to develop efficient OSC’s. Thin-Film Organic Solar Cells Silicon (Si) based solar cell s are designed primarily owing to its non-toxic nature and availability. Si however has an indirect bandgap. This leads to high optical lo sses due to reflection and hence the light absorption capacity is poor. To meet the requirement of light-harvest ing, the thickness of the Si active layer should be no less than 100 μm. The thickness of silicon solar cells is accompanied by efficient crystallization and purification methods which makes Si-based solar cells expensive. To solve these problems, pr oper device architecture and light trapping methods such as periodic gratings, photon ic crystals, plasmonic structures Si nanowire arrays (SiNWs), and Si nanocone arrays(SiNCs) have been proposed and investigated widely.Though efficiencies of these thin-film organic devices have not reached their inorganic counterpart’s dynamic methodologies will help achieve an optimum PCE. The field of OPV began with the use of small organic Advanced Materials and Radiation Physics (AMRP-2020) AIP Conf. Proc. 2352, 020040-1–020040-4; https://doi.org/10.1063/5.0057392 Published by AIP Publishing. 978-0-7354-4105-7/$30.00020040-1molecules (pigments) and further developed with semico nducting polymers. Also, a variety of small-molecular- weight electron-acceptor materials are available easily . A major advantage of these small-molecule materials compared with large-molecule polymers is that vacuum sublimation can be used to form well-controlled amorphous or polycrystalline thin films on flexible polymeric substrates. As a result, they can be used to fabricate complex multilayer devices, and there is no need to make the molec ules soluble. Moreover, they also are very easy to purify [2]. Preparation Techniques The most common among various techniques employed ar e the dry thermal evaporation of organic constituents. For small molecules, evaporation is the best choice. Therm al evaporation involves high vacuum conditions. In addition to it, contaminants such as oxygen and water are eliminated. The mean free path of the molecules in such an ultra-vacuum condition is greatly enhanced as co mpared to the distance from the evaporating source to the sample. This method allows good thickness and dopant control, eliminates parasitic coating on the walls of the chamber, and allows the fabrication of complex multilayer devices [3]. In addition to it, there are numerous techniques one of wh ich is Spincoating. This technique has indisputably the most important for the development of solar cells. In spite of the complexity of film formation, it helps in producing a homogenous film over a large area. The typi cal form of spin coating involves the application of a liquid to a substrate followed by an acceleration of the substrate to a chosen rotational speed [4]. The acceleration results in the ejection of most of the liquid an d what is left is a thin film of liquid on the substrate. The film thickness d obtained can be expressed as [4] d = k ὠª where ὠis the angular speed and k and a are constants related to the properties of the liquid (solvent), solute, and substrate. Formation of (xcitons Inorganic solids, the intermolecular overlap of electron ic wavefunctions is very weak which results in making the energy bands very narrow, and thus they can be ap proximated as molecular orbitals [5]. This results in the formation of two energy levels termed as Highest Occu pied Molecular orbital (HOM O) which is analogous to the valence band and Lowest unoccupied Molecular Orbital (LUMO) which is analogous to the conduction band in the case of inorganic materials. The energy bandga p is the difference betwee n the two energy levels. When the solar radiation is incident on the thin fi lm OSC’s absorption of energy greater than or e qual to the bandgap results in the formation of an excited electron (e) in the LUMO and a corresponding hole (h) in the HOMO. Due to the attractive Coulomb potential, the excite d electron and hole get drawn closer towards each other and become bound in a hydrogenic electronic state called an exciton. An exciton is neutral in charge and is capable of moving throughout the material. The formatio n of excitons is unfavorable in OSCs because one needs to generate free electrons and holes to be co llected at the opposite electrodes to generate current. For the successful operation of an OSC, the excitons must be diss ociated into free charge ca rriers with the aid of an energy greater than their binding energy [6]. Types of Solar Cells The structure and design of the OSC’s have been improved over the ye ars and there are mainly four kinds of Organic cells (1) single layer (2) bilayer (3) bu lk heterojunction (4) hybrid OSC. The first organic solar cells were based on single th ermally evaporated molecular organic layers sandwiched between two metal electrodes of different work functions [4]. The top layer (anode) is kept transparent for the absorption of light and made up of a thin film of organic materials. On absorbing a photon of energy equal to or greater than the bandgap an exciton is created and the on ly external energy available to dissociate excitons and draw the free charge carriers to opposite electrodes is due to the electric field established by the difference in the work functions, Φanode and Φcathode , of the anode and the cathode, respectively. The efficiencies achieved in single layer OSCs is low because of the insufficient tr ansport of free charge carriers to the electrodes. The poor efficiency of single layer OSCs introduced the idea of a bilayer OSCs which consist of two layers of organic material. The first layer is of donor material and the second layer is of an acceptor material and both have different ionization potential and electr on affinities. In this design, exc iton dissociation and charge carrier 020040-2collection are far more efficient than in a single layer OSC. However, the exciton diffusion length is very less and thus the free charge carriers so generated ar e limited in number [5]. Electrode 1 Electrode 1 Organic materialElectron donor Electron acceptor Electrode 2 Electrode 2 (a) (b) ),*85( 6WUXFWXUHRI DVLQJOHOD\HUDQG EPXOWLOD\HURUJDQLF VRODUFHOOV The essence of the bulk heterojunction (BHJ) is to intimat ely mix the donor and acceptor components in a bulk volume so that each donor-acceptor interface is within a distance less than the exciton diffusion length of each absorbing site.[7] As a result, this stru cture enables charge carrier generation everywhere within the active layer, which increases the photon to electron conversion efficiency dramatically.[6-7] The structure and mechanism of a hybrid solar cell are sim ilar to that of a BHJ with the only difference that the organic acceptor is replaced by an inorganic material. This is done to enhance the PCE of solar cells by utilizing both the type of materials. A combination of silicon nanowires (SiNWs) and poly (3,4-ethylene dioxythiophene) poly(styrene sulfonate) (PEDOT: PSS) have produced the best power conversion efficiency of 8.40% in hybrid OSCs to-date [8]. Light Trapping Techniques A major problem in organic solar cells is the poor m obility and recombination of the photogenerated charge carriers. Optical losses result in the loss of a significant portion of the incoming radiation and hence proper light trapping techniques must be incorporated to achieve the desired PCE. Light trapping ability is the capacity of the OSCs to absorb the maximum amount of solar radiations incident on it with feeble optical losses. This can be done by using num erous refractive structures [9], random structures [10-11], random scatterers [12], aperture s [13] and micro lenses [14-16]. These structures can be integrated with proper architecture to avoid recombination losses.For example, Metal nanoparticles placed above the solar cells can scatter most amount of incident light to the substrate and increase the in-coupling efficiency. However, owing to the low refractive index of organic materials a high coupling efficiency is difficult to ach ieve. These nanoparticles can act as optical antennas for that matter and store energy in the form of lo calized surface plasmon resonance (LSPR) [17]. There are other methods also employed su ch as the use of a diffraction grating that couples reflected light into waveguide modes of the solar cell [18]. The structural pr operties of the grating influence the performance of the solar cell.Light trapping elements can be induced by directly st ructuring the substrate of organic solar cells [19-23]. Substrates that have wrinkles or folds were found to have an improved photocurrent as compared to solar cells on a flat substrate [23]. SUMMARY AND FUTURE OUTLOOK The field of OSCs is a promising domain in future res earch. The limited charge ca rrier transport in organic semiconductors requires a thin layer of the material. We need to design more techniques and novel designs to achieve a greater amount of PCE and with minimal losses. In this paper, we reviewed the various material and architectural designs and some of the light-trapping ways . Given the fact that the theoretical calculations have a remarkable effect, however, the experimental realization is an important tool. For this reason, this field of organic solar cells will be an active f ield of research in the coming years. 020040-3REFERENCES [1] "April 25, 1954: Bell Labs Demonstrates the Firs t Practical Silicon Solar Cell". APS News (American Physical Society) 18 (4). April 2009. [2] Organic solar cell research at Stanford University. [3] Organic solar cells: An overview Harald Hoppea and Niya zi Serdar Sariciftci Linz Institute for Organic Solar Cells (LIOS).[4] J-M. Nunzi: Organic photovoltaic materials and devices. C. R. Physique 3, 523 (2002)[5] L.A.A. Pettersson, L.S. Roman, and O. Ingana¨s: Modeling photocurrent action spectra of photovoltaic devices based on organic thin films. J. Appl. Phys. 86, 487 (1999).[6] P. Schilinsky, C. Waldauf, and C.J. Brabec: Reco mbination and loss analysis in polythiophene based bulk heterojunction photodetectors. Appl. Phys. Lett. 81, 3885 (2002).[7] J-M. Nunzi: Organic photovoltaic materials and devices. C. R. Physique 3, 523 (2002).[9] S. Esiner, et al. Adv. Energy Mater. 3 (2013) 1013.[10] C. Cho, et al. Sol. Energy Mater. Sol. Cells 115 (2013) 36. [11] D.H. Wang, et al. Org. Electron. 11 (2010) 285. [12] Z. Hu, J. Zhang, Y. Zhao, J. Appl. Phys. 111 (2012) 104516. [44] P. Peumans, V. Bulovic´, S.R. Forrest, Appl. Phys. Lett. 76 (2000) 2650. [13] K. Tvingstedt, et al. Opt. Express 16 (2008) 21608.[14] S.D. Zilio, et al. Microelectron. Eng. 86 (2009) 1150. [15] J.D. Myers, et al. Energy Environ. Sci. 5 (2012) 6900. [16] ] V.E. Ferry, et al. Appl. Phys. Lett. 95 (2009) 183503.[17] Light trapping in thin-film organic solar cells Zheng Tang, Wolfgang Tress and Olle Ingana¨ Biomolecular and Organic Electronics, IFM, and Center of Organic Electronics, Linko¨ping University, SE-581 83 Linko¨ping, Sweden.[18] Z. Tang, et al. Adv. Energy Mate C. Cocoyer, et al. Appl. Phys. Lett. 88 (2006) 133108. [19] C. Cocoyer, et al. Thin Solid Films 511 (2006) 517. [20] L. Mu¨ller-Meskamp, et al. Adv. Mater. 24 (2012) 906.[21] J.B. Kim, et al. Nat. Photonics 6 (2012) 327. [22] Y. Yang, et al. ACS Nano 6 (2012) 2877. [23] D. Ko, et al. J. Mater. Chem. 21 (2011) 16293.r. 2 (2012) 1467. 020040-4

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APL Photonics ARTICLE scitation.org/journal/app On-demand light wave manipulation enabled by single-layer dielectric metasurfaces Cite as: APL Photon. 6, 086106 (2021); doi: 10.1063/5.0057275 Submitted: 19 May 2021 •Accepted: 20 July 2021 • Published Online: 6 August 2021 Xuyue Guo, Bingjie Li, Xinhao Fan, Jinzhan Zhong, Shuxia Qi, Peng Li,a) Sheng Liu, Bingyan Wei, and Jianlin Zhaoa) AFFILIATIONS Key Laboratory of Light-field Manipulation and Information Acquisition, Ministry of Industry and Information Technology, and Shaanxi Key Laboratory of Optical Information Technology, School of Physical Science and Technology, Northwestern Polytechnical University, Xi’an 710129, China a)Authors to whom correspondence should be addressed: pengli@nwpu.edu.cn and jlzhao@nwpu.edu.cn ABSTRACT Dielectric metasurfaces have been widely developed as ultra-compact photonic elements based on which prominent miniaturized devices of general interest, such as spectrometers, achromatic lens, and polarization cameras, have been implemented. With metasurface applications taking off, realizing versatile manipulation of light waves is becoming crucial. Here, by detailedly analyzing the light wave modulation prin- ciples raising from an individual meta-atom, we discuss the minimalist design strategy of dielectric metasurfaces for multi-dimensionally manipulating light waves, including parameter and spatial dimensions. As proof-of-concepts, those on-demand manipulations in different dimensions and their application potentials are exemplified by metasurfaces composed of polycrystalline silicon rectangle nanopillars. This framework provides basic guidelines for the flexible design of functionalized metasurfaces and the expansion of their applications as well as implementation approaches of more abundant light wave manipulations and applications using hybrid structures. ©2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0057275 I. INTRODUCTION The available functionalities of optical elements come from the effective manipulation of the light wave’s fundamental parame- ters, e.g., amplitude, phase, and polarization. Therefore, structuring materials with capabilities to manipulate light waves has been a long- concerned issue and attracted significant interest. To overcome the physical limitations imposed by conventional natural materials and traditional optical devices, the emerging metamaterials1,2exhibit unprecedented properties and lead to various novel optical effects.3–9 However, challenging problems, e.g., high losses and costly fabrica- tion associated with bulky structures, especially hinder them from practical applications. Until recently, the advent of metasurfaces10–17 that are characterized as reduced dimensionality of metamaterials makes the breakthrough to dramatically reduce the fabrication com- plexity and increase the design flexibility,18–27providing an elegant solution to those problems aroused in metamaterial-based optical devices. In the past decade, metasurfaces have been extensively stud- ied for engineering the fundamental parameters of light waves.28–35A considerable amount of metasurfaces have been developed with impressive applications in realms of holographic imaging,36,37polar- ization conversion,38,39functional devices,16,17multiplexing,26,27and nonlinear optics.40–42Nowadays, particular initiatives have been taken to enable multifunctional metasurfaces, which are based on the multi-dimensional manipulation of light waves. Recent progress has made some achievements, for instance, the introduction of unique structures (few-layer,43diatomic,44and folding45) and com- positional materials (liquid crystal,46phase change material,47and two-dimensional material48) provides additional degree of free- doms (DoFs) for manipulating light waves with metasurfaces in both parameter and space dimensions. In contrast, the use of a simpler structure to achieve multi-dimensional light wave control has greater advantages in practical applications and device fabri- cations. Although some relevant studies have been reported,20,21 the characteristics of multi-dimensional light wave control that can be realized by a minimalist structure have not been sys- tematically analyzed, and the relationship between the manipula- tion of parameter dimension with spatial DoFs has not been well discussed. APL Photon. 6, 086106 (2021); doi: 10.1063/5.0057275 6, 086106-1 © Author(s) 2021APL Photonics ARTICLE scitation.org/journal/app Here, by detailedly analyzing the structural birefringence of an individual meta-atom in single-layer dielectric metasurfaces, the light wave modulation principle for different parameter dimen- sions and spatial DoFs is discussed, based on which the minimalist design strategy of dielectric metasurfaces for modulation require- ment of multiple dimensions and DoFs is demonstrated. Accord- ing to diverse control principles, we design metasurfaces composed of polycrystalline silicon rectangle nanopillars and then demon- strate multifunctional applications of such minimalist metasur- faces, including phase-only holography, complex-amplitude holog- raphy, 3D holographic scene, axial modulation of light field, and polarization-encrypted holography. Meanwhile, the applicable prin- ciples of manipulating light waves in broadband and 3D space are analyzed. II. THEORY To construct the modulation principles for different parame- ter dimensions, we first investigate the light wave modulation effect of an individual meta-atom in a single-layer dielectric metasur- face. Figure 1 presents the schematic illustration of the wavefront modulation mechanism of the single-layer dielectric metasurface. According to the effective medium theory,49the meta-atom is an effective anisotropic structure that supports large refractive index contrast between orthogonal polarizations of light. Therefore, the complex transmission property of such a birefringent meta-atom can be expressed as J=R(−θ)⎡⎢⎢⎢⎢⎢⎣Toeiφo0 0 Toeiφe⎤⎥⎥⎥⎥⎥⎦R(θ), (1) where R(θ) is the rotation matrix, and the middle matrix accounts for the transmission amplitudes ( To,Te) and phases ( φo,φe) alongthe ordinary and extraordinary axes, respectively, as shown in Fig. 1(a). Assuming that two orthogonal polarizations have uniform transmission amplitude, i.e., To=Te=T, one can further simplify the Jones matrix according to the incident polarization. It is well known that the light–matter interaction is generally described as the response of two kinds of polarization states, that is, the linear polarization (LP) and circular polarization (CP). Thus, we take these two typical polarizations as examples, and the corresponding Jones matrices in the CP basis [ EREL]Tand LP basis [ EHEV]Tsubse- quently can be written as (the subscript R/L denotes the right/left CP state, and H/V denotes the horizontal/vertical LP state, respectively) J(CP)=Teiφ0⎡⎢⎢⎢⎢⎢⎣cos(δ/2) i sin(δ/2)e−i2θ i sin(δ/2)ei2θcos(δ/2)⎤⎥⎥⎥⎥⎥⎦, (2) J(LP)=T⎡⎢⎢⎢⎢⎢⎣eiφ1eiφ2 eiφ2eiφ3⎤⎥⎥⎥⎥⎥⎦,⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩eiφ1=cos2θeiφo+sin2eiφe, eiφ2=cosθsinθeiφe−cosθsinθeiφo, eiφ3=sin2θeiφo+cos2θeiφe, (3) where δ=(φo−φe) and φ0=(φo+φe)/2 depict the phase retar- dation and propagation phase based on ordinary and extraordinary components, respectively. The above Jones matrices cannot be directly connected with the modulable parameter dimensions. Therefore, to address legible modulation principles, we further consider the whole output fields, which are the composition of different polarizations, as schemati- cally shown in Figs. 1(b) and 1(c). For the incidence of the ∣R⟩state, the output field naturally consists of two components with orthog- onal polarizations, namely, the co-polarized and cross-polarized components; thus, the output vector field is expressed as FIG. 1. Wavefront modulation mechanism of the single-layer dielectric metasurface. (a) Schematic illustration of the dielectric metasurface. Inset: transmission property of a meta-atom. (b) and (c) Transmission properties of a meta-atom corresponding to two kinds of bases. (d) Conversion of polarization states on the Poincaré sphere. APL Photon. 6, 086106 (2021); doi: 10.1063/5.0057275 6, 086106-2 © Author(s) 2021APL Photonics ARTICLE scitation.org/journal/app Ecp out=Teiφocos(δ/2)∣R⟩+iTeiφosin(δ/2)ei2θ∣L⟩. (4) As for the incidence of linear polarized light field with ∣H⟩or ∣V⟩state, the output field consequently presents a [eiφ1eiφ2]Tor [eiφ2eiφ3]Tstate. Here, we consider a superposition state of the ∣H⟩ and∣V⟩states, namely, the ∣D⟩state, as a generalized model, and thus, the output vector field can be further expressed as Elp out=Teiφ1∣H⟩+Teiφ2∣D⟩+Teiφ3∣V⟩. (5) The modulation process introduced by the conversion of polar- ization states on the Poincaré sphere is shown in Fig. 1(d). Clearly, the above equations provide intuitionally controllable parameter dimensions, including amplitude, phase, and polarization. Accord- ing to Eq. (1), meta-atoms can be regarded as waveplates with arbitrary phase retardation ( δ) achieved by structuring the bire- fringence. Meanwhile, this phase retardation results in that the two components with orthogonal CPs have complementary inten- sities of T2cos2(δ/2) and T2sin2(δ/2), as shown in Eq. (4). In this principle, some polarization transformers50and ultrathin energy tailorable splitters16,51have been designed. Obviously, this mod- ulation on amplitude or polarization only refers to single DoF control. To showcase the modulation capabilities of different param- eter dimensions and spatial DoFs, we categorize the correspond- ing controllable wavefront into different cases, which are shown in Table I. It is worth noting that, for the CP basis, this inherent intensity relationship disables the independent control of the wave- front amplitudes corresponding to these two components; therefore, the wavefront modulation has been focused on the cross-polarized component, and given that the co-polarized component is a back- ground noise.52For pure phase modulation, as Eq. (4) shows, these two components have a communal propagation phase exp(i φ0), and the cross-polarized component experiences an abrupt phase change of ±2θ, i.e., the well-known geometric phase.53These two types of phases are determined by the geometric size and azimuthal angle of the meta-atom, respectively, which can be directly modu- lated by the φ0(case 1) and θ(case 2), corresponding to two DoF modulations. The phase modulation has been widely utilized for two- dimensional holographic imaging and reproducing special phase pattern. While by contrast, the manipulation capability with respect to three DoFs greatly improves the performance of metasurfaces in integrated multifunctional optical devices. In scalar optics, thecomplete information of a light field requires both amplitude and phase, namely, complex amplitude. Here, from the complex ampli- tude distribution of the cross-polarized component in the CP basis, i.e.,Tsin(δ/2)exp[i( φ0+2θ)], one can recognize that the amplitude and phase are determined by T,δand φ0, 2θ, respectively (case 3 and case 4). Thus, both the amplitude and phase can be completely and independently controlled, and benefiting from this, the com- plex amplitude modulation has advantages in 3D space imaging over amplitude- or phase-only modulation schemes.52It is important to point out that these two methods have an unavoidable directly trans- mitted component, which especially affects the axial modulation. Therefore, a complex amplitude modulation method with extra axial DoF control is introduced here (case 5). The above discussions focus on the scalar field, while the pos- sibility in simultaneous control of polarization and phase provides huge prospect to develop polarization-dependent optical devices and introduces extra polarization channels to increase the DoFs. For this reason, the optical responses to each component should be taken into account. For instance, in the case of CP basis, the com- bined effect of propagation phase and opposite geometric phases endows independent modulation phases φ0±2θonto two orthog- onal bases54,55(case 6). While for the case of LP basis, as Eq. (3) shows, one can obtain φ1=φoand φ3=φewhen the meta-atoms are arranged without rotation ( θ=0), that is, two independent phase patterns can be implemented on two orthogonal linear polarization states (case 7). Then, taking rotation into consideration, as shown in Eq. (5), three phase patterns, φ1,φ2, and φ3, which are dependent on the geometric parameters φo,φe, and θ, can be implemented on three linear polarization states56(case 8). For modulation with more parameter dimensions, amplitude, phase, and polarization response are inevitably associated with each other, when adjusting the geometric parameters of individual meta- atom, that is, the number of controllable parameters is limited to two, as shown in Table I. To break this limitation, two orthogonal polarization bases whose amplitude and phase can be precisely and independently modulated are primarily required. For the CP basis, this expectation cannot be achieved due to their correlated ampli- tudes, while for the LP basis, the background noise arising from phase-only modulation leads to the inaccuracy of superposition state. Therefore, a capable implementation is using hybrid structures based on exploring the inherent relationship between meta-atoms and associating each parameter dimension with a certain structural parameter of meta-atom. TABLE I. Categorized modulation capabilities of a single meta-atom in a single-layer dielectric metasurface. PD: parameter dimension, SDoF: spatial degree of freedom. Master variable Controllable wavefront PD ×SDoF Case 1 φ0 Eout=exp(i φ0) 1 ×2 Case 2 θ Eout=exp(±i2θ) 1 ×2 Case 3 δ,θ Eout=sin(δ/2)exp(i2 θ) 2 ×3 Case 4 T,δ,θ Eout=Tsin(δ/2)exp(i2 θ) 2 ×3 Case 5 T,φ0,θ Eout=Texp[i( φ0+2θ)] 2 ×3, 1×1 Case 6 φ0,θ Eout=exp[i( φ0+2θ)]∣L⟩+exp[i( φ0−2θ)]∣R⟩ 2×2 Case 7 φo,φe Eout=exp(i φo)∣H⟩+exp(i φe)∣V⟩ 2×2 Case 8 φo,φe,θ Eout=exp(i φ1)∣H⟩+exp(i φ2)∣D⟩+exp(i φ3)∣V⟩ 2×2 APL Photon. 6, 086106 (2021); doi: 10.1063/5.0057275 6, 086106-3 © Author(s) 2021APL Photonics ARTICLE scitation.org/journal/app As a proof-of-concept, we design and fabricate metasurfaces corresponding to each case. Here, we choose the poly-Si meta-atoms on a fused silica substrate, which have rectangular cross sections with square lattice arrangement, to design and fabricate metasur- faces by using COMS compatible processes (details can be found in the Appendix). The geometric size (height H, length L, width W, and period P) of the meta-atom is variable for different cases, depend- ing on master variables. For simplicity and generality, computer- generated holograms (CGHs)57are chosen to implement most of the following experiments, which are succinct to testify the capability of manipulating the light wave. All experiments were performed at the wavelength of visible light band. III. EXPERIMENT AND RESULTS To testify the performance of pure phase modulation, that is, cases 1 and 2, two-dimensional holographic imaging is implemented experimentally. In practice, phase-only CGHs are generated by use of the typical Gerchberg–Saxton (GS) algorithm.58Crucially, thepure phase modulation based on propagation phase and geometric phase have different modulation precisions and distinct require- ments for the selection of meta-atoms. In the case of propagation phase modulation, the phase-only CGH needs to be discretized, and higher nanopillars are required to ensure sufficient phase modula- tion depth. In contrast, geometric phase modulation only requires a single geometry and has higher modulation accuracy and efficiency via rotating nanopillars. Figures 2(b) and 2(d) show the scanning electron microscope (SEM) images of fabricated metasurfaces cor- responding to cases 1 and 2, where the metasurfaces both have 1000 ×1000 meta-atoms, but different heights (case 1: 610 nm and case 2: 350 nm) and periods (case 1: 450 nm and case 2: 300 nm). Figure 2(a) shows two target images (grayscale and binary images, respectively) and experimentally reconstructed results in case 1 at a wavelength of 633 nm. It can be seen that these target images are reconstructed with high performance. As a contrast, the binary image is also reconstructed by means of case 2 under the same experimental condition, and the corresponding result is shown in the fourth column of Fig. 2(c). Clearly, the reconstructed image FIG. 2. Holographic imaging based on the phase-only modulations of metasurfaces. (a) Target images and experimental results of case 1 at a wavelength of 633 nm. (b) and (d) SEM images of fabricated metasurfaces corresponding to cases 1 and 2, respectively. Scale bars are 1 μm. (c) Experimental results of case 2 at the wavelengths of 473, 488, 532, 633, and 670 nm, respectively. (e) Simulated transmittance and sinusoidal term spectra of the selected meta-atom in case 2. The geometric parameters areL=174 nm and W=104 nm. APL Photon. 6, 086106 (2021); doi: 10.1063/5.0057275 6, 086106-4 © Author(s) 2021APL Photonics ARTICLE scitation.org/journal/app in this case exhibits a higher fidelity, which results from the high accuracy of geometric phase modulation. In addition, the charac- teristic of independence of wavelength enables us to operate geo- metric phase modulation in a broad bandwidth. Figures 2(c) and 2(e) show the reconstructed results and response spectrum of the selected meta-atom at multiple wavelengths. As shown, although the geometric phase modulation has lower transmittance at short wavelengths, it still exhibits good broadband characteristics as the experimental results present clear reconstructed holographic images at all operating wavelengths. Further testifications of complex amplitude modulation are shown in Figs. 3 and 4, where complex amplitude hologram and 3D holographic scenes are demonstrated. Figures 3(a) and 3(b) show the simulated transmittance, propagation phase, and sinusoidal term of selected meta-atoms in case 3. The complex amplitude holo- grams are calculated by the Fourier transform of the target image. Figures 3(d) and 3(e) show the fabricated metasurface ( H=610 nm, P=450 nm) and reconstructed result of case 3. The experiment is carried out with the setup shown in Fig. 3(c) at a wavelength of 670 nm, and the image reconstructed on the screen is photoed by a camera. Compared with these two previous phase-only modulation methods [Figs. 2(a) and 2(c)], the complex amplitude modulation method intuitively improves the imaging quality and reduces the background noise since both the amplitude and phase are faithfully reproduced. Figure 4(a) shows the combined amplitudes Tsin(δ/2) and propagation phases of selected meta-atoms in case 4. In case 3, the precondition that transmittances of these meta-atoms areconstant limits the geometry selectivity. While in case 4, the con- trol of parameter Tdoes not directly affect the final modulation effect but supplies a greater tolerance to the selection of the meta- atom in case 4. Consequently, under the same height of the meta- atom, the operating wavelength is reduced to 633 nm. In order to fully demonstrate the advantages of complex amplitude modu- lation, a 3D holographic scene, which consists of letters “N,” “P,” and “U” localized at three lateral planes, is performed. Figures 4(b) and 4(c) illustrate the operation principle and experimental setup. For the calculation of CGH, each letter image at certain diffrac- tion distances is back-propagated to the metasurface plane by the beam-propagation method. Figure 4(d) shows the simulated and experimentally observed results at three lateral planes, respectively. In this experiment, we introduce an optical microscopy setup with the cross-polarized analyzer in order to avoid the influence of the co-polarized component. It is noteworthy that the experimentally reconstructed images have almost identical profiles with simulated ones, which powerfully demonstrates the great capability of the com- plex amplitude modulation of the metasurface for reconstructing target images in 3D space. The full control of the amplitude and phase significantly improves the quality and capability of the reconstructed image. Nevertheless, in the above two cases, the unavoidable co-polarized component arising from the incomplete spin conversion, i.e., the non-zero Tcos(δ/2), leads to a drawback that prevents the above methods from axial modulation without polarization filtering. How- ever, eliminating the co-polarized component is difficult to imple- ment in some special situations, such as focusing. Therefore, FIG. 3. Holographic imaging of the metasurface with complex amplitude modulation. (a) and (b) Simulated transmission amplitudes, propagation phases, and sinusoidal term of these selected meta-atoms in case 3. (c) Schematic illustration of the experimental setup. HWP: half-wave plate and QWP: quarter-wave plate. (d) SEM image of the fabricated metasurface corresponding to case 3. The scale bar is 1 μm. (e) Reconstructed results of case 3 at a wavelength of 670 nm. APL Photon. 6, 086106 (2021); doi: 10.1063/5.0057275 6, 086106-5 © Author(s) 2021APL Photonics ARTICLE scitation.org/journal/app FIG. 4. 3D imaging of the metasurface with complex amplitude modulation. (a) Simulated amplitudes and propagation phase of the selected meta-atoms in case 4. (b) Schematic illustration of the 3D holographic scene. (c) Schematic illustration of the experimental setup. Inset: SEM image of the fabricated metasurface. The scale bar is 1μm. (d) Simulated and experiment results at a wavelength of 633 nm. in case 5, the phase retardation δis fixed as π, making sure that the incident spin polarization is totally transformed into the orthogo- nal one; hence, the amplitude and phase modulations are dependent onTand φ0+2θ, respectively, as shown in Fig. 5(a). Obviously, the amplitude is only dependent on the transmittance of meta-atom [Fig. 5(b)], but the phase term is related to both the propagation and geometric phases. Unfortunately, the transmittance and prop- agation phase are jointly related to the geometry of meta-atoms. To break this relationship, an opposite rotation angle φ0/2 should be added onto θ, i.e., θ’=θ−φ0/2, and then the amplitude and phase are independently and completely controllable. As an example, an axially structured light field with sinc- functional intensity distribution (calculated by the spatial spectrum optimization method based on the Durnin ring59,60) is demonstrated to assess this axial tailoring capability. Figure 5(d) shows the mea- sured intensity distribution (normalized) in the y–zplane, which is observed through the setup shown in Fig. 5(c). The microscope sys- tem is localized on a linear translation stage with a scanning interval of 10 μm. The simulated and measured on-axis intensity distribu- tions (normalized) are displayed in Fig. 5(e). As shown, this method can sustain the construction of axial light field. The above discussions all refer to the wavefront manipula- tion of scalar light field, namely, the cross-polarized component. Inaddition to the enhancement of multiplexing capability, numerous intriguing phenomena related to vector fields, such as their con- struction, enhanced longitudinally polarized component, and super- resolution focusing, are based on the combined modulation of two spin states.61,62To address polarization-dependent light field modu- lation, more parameters should be taken into account. As is known, the geometric phase is always accompanied by a “twin field,” which originates from the phase accumulation of opposite CP state tran- sition. Therefore, by combining the propagation phase, two CPs can obtain independent phase modulation of φ0±2θ, as shown in Fig. 6(a). However, in this case, the inherent amplitude correlation disables the independent amplitude modulation of two CPs. Thus two CPs are commonly considered to have unitary amplitude, i.e., sin(δ/2)=1. Here, a holographic reconstruction of two complemen- tary images [Figs. 6(c) and 6(d)] is employed to showcase the poten- tial in polarization-encrypted application. Figures 6(e)–6(g) display the experimental results under the incidences of light fields with dif- ferent polarizations. As shown, when a linear polarized light field illuminates, the metasurface outputs a uniform spot without pattern, but the polarization-dependent patterns show up for the CP incident light fields. In comparison, LP-based methods provide more optional channels. Thanks to the “structural birefringence” of meta-atoms, APL Photon. 6, 086106 (2021); doi: 10.1063/5.0057275 6, 086106-6 © Author(s) 2021APL Photonics ARTICLE scitation.org/journal/app FIG. 5. Longitudinal modulation enabled by the metasurface. (a) Schematic of the modulation effect in case 5. (b) Transmittances of 17 selected meta-atoms. (c) Schematic illustration of the experimental setup. Inset: SEM image of the metasurface. The scale bar is 100 μm. (d) Measured intensity distribution in the y–zplane. (e) Simulated and measured on-axis intensity distributions. arbitrary manipulation can be implemented on a certain polarized component modulated along ordinary or extraordinary axis theo- retically, as described in Eq. (1). Here, the transmittance of each meta-atom is set to be unitary. In Eq. (3), when θ=0, one obtains φ1=φoand φ3=φe, namely, two independent phase modulationscan be implemented on two orthogonal linear polarization chan- nels. While taking rotation into account, three independent phase modulations can be implemented on three linear polarization chan- nels. The experimental setup and SEM images of two LP-based metasurfaces without and with rotation are shown in Figs 7(a)–7(c). FIG. 6. Polarization-dependent holographic imaging of the metasurface based on the combined modulations of two CPs. (a) Schematic of the combined modulation of two CPs. (b) SEM image of the metasurface. The scale bar is 1 μm. (c) and (d) Target images encoded on two CPs; reconstructed results for the incidence of a (e) linearly polarized, (f) right-handed CP, and (g) left-handed CP light field. APL Photon. 6, 086106 (2021); doi: 10.1063/5.0057275 6, 086106-7 © Author(s) 2021APL Photonics ARTICLE scitation.org/journal/app FIG. 7. Polarization-encrypted imaging of the metasurface. (a) Schematic illustration of the experimental setup. (b) and (c) SEM images of the metasurface corresponding to cases 7 and 8. Scale bars are 0.5 μm. (d) and (e) Experimental results of polarization-encrypted imaging based on modulation mechanisms of cases 7 and 8. The red and blue arrows depict the incident and detected polarization directions, respectively. For the metasurface without rotation, four letters are encoded into the horizontal and vertical polarizations by phases φ1and φ3, respectively. The experimental results are depicted in Fig. 7(d). Under the illumination of a diagonal polarized light field, patterns encoded in two polarization channels are simultaneously recon- structed. By rotating the polarization analyzer, the reconstructed pattern is switched from “AB” to “CD.” For the second metasurface, an additional polarization channel is available due to the introduc- tion of geometry rotation. Three letter patterns are encoded into the horizontal, vertical, and diagonal linear polarizations by phases φ1, φ2, and φ3, respectively. As shown in Fig. 7(e), for the incidence of a diagonal polarized light field, three patterns in three polariza- tion channels are simultaneously reconstructed without the ana- lyzer. While for the cases of H- or V-polarization incidence, the pat- tern in the orthogonal polarization channel disappears, respectively. Furthermore, individual polarization channels can be switched by changing the incident and analyzed polarization directions. There- into, the “XYZ” pattern, namely, diagonal polarization channel, can be obtained with the orthogonal polarizer and analyzer. IV. DISCUSSIONS The on-demand modulation principles of single-layer dielectric metasurfaces for multiple dimension control have been theoretically and experimentally exhibited, but more details merit discussions. Notably, arbitrary modulation can be implemented through manip- ulating the “structural birefringence” of meta-atoms and various applications can be realized according to the above principle. How- ever, limited by the properties of natural materials, the modulation depth and width are restricted to meet some particular applications, which also results in confined operating wavelengths and repre- sents a daunting exploratory and computational problem. Therefore, invariant parameters and varying thicknesses are used in different cases to obtain an enough modulation range.Second, the systematic strategy for on-demand light wave manipulation demonstrated here avoids unnecessary complexity in both the design process and experimental operation, which presents the full potential of single-layer dielectric metasurfaces, and leads to a series of applications. The pure phase modulation can be realized in two ways, among which the geometric phase modulation has been widely used in device design due to its convenience, high precision, and broad bandwidth. By contrast, the complex amplitude mod- ulation has an advantage of information density over phase-only hologram, which leads to holographic images with higher quality, higher fidelity, and the reconstruction in 3D space. Moreover, for applications involving holographic data encryption or storage, the complex amplitude hologram can greatly increase the storage capac- ity. Furthermore, the axial modulation method in case 5 enriches the functionalities of complex amplitude modulation and provides an additional DoF in 3D light wave manipulation, as well as an approach for constructing tightly focusing fields with longitudi- nally oscillating polarization. In addition, the polarization-encrypted holography exhibited in cases 6–8 effectively enlarges the design space of polarization-dependent devices, and further applications, such as polarization-multiplexing and information encryption, can be expected. It is no doubt that such a strategy provides a basic guide- line for the flexible design of optical metasurfaces and an effective way for the expansion of their applications. Finally, besides the functionality, the modulation efficiency is another concerned issue. Notably, the pure phase modulation meth- ods have advantages of efficiency because of the excellent encoding techniques. On the other hand, the modulation efficiency is closely related to the amplitude coefficient of the Fourier transform CGHs, i.e.,Tsin(δ/2)≠1. In our experiment, taking the absorption of mate- rial into account, the diffraction efficiency in case 2 is 62.5% (with polarization conversion efficiency exceeding 95%), while in cases 3 and 4, it is about 10%. For axial modulation, the optimized spa- tial spectrum can significantly enhance the generation efficiency to about 20%, but it is still strongly dependent on the pre-established APL Photon. 6, 086106 (2021); doi: 10.1063/5.0057275 6, 086106-8 © Author(s) 2021APL Photonics ARTICLE scitation.org/journal/app distribution. In polarization-dependent modulations, the response of the meta-atoms and the quality of fabrication are the main factors affecting the efficiency; here, the diffraction efficiency of cases 6–8 is all about 50%. As a whole, the demonstrated design principles and devices can be characterized as low loss. V. CONCLUSION In summary, we have systematically discussed multi- dimensional light wave manipulation via single-layer dielectric metasurfaces. To showcase such a strategy, the “structural birefringence” of meta-atoms on different polarization bases is considered, and the modulation capabilities from single to multiple parameter dimensions are categorized. Based on the proposed mechanism, complete manipulation of the wavefront amplitude, phase, and polarization state has been achieved, and the poly-Si meta-atoms and holographic method are employed to experimen- tally demonstrate how various functionalities are achieved. The results show that single-layer dielectric metasurfaces exhibit strong modulation capability in various light wave manipulation, and the design principle is simple but has powerful extension for the flexible design of optical metasurfaces. This work offers a systematic and generalizable method toward manipulating light waves at will with meta-devices, and provides a possible approach for achieving more abundant manipulation and applications through hybrid structures. ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant Nos. 91850118, 11774289, 11634010, 61675168, 12074313, and 11804277), the National Key Research and Development Program of China (Grant No. 2017YFA0303800), the Natural Science Basic Research Program of Shaanxi (Grant No. 2020JM-104), the Fundamental Research Funds for the Central Universities (Grant Nos. 3102019JC008 and 310201911cx022), and the Innovation Foundation for Doctor Dissertation of Northwest- ern Polytechnical University (Grant Nos. CX202046, CX202047, and CX202048). We thank the Zhiwei Song of National Center for Nanoscience and Technology for supplying the materials as well as the Analytical and Testing Center of Northwestern Polytechnical University. APPENDIX: METHOD The metasurfaces were fabricated based on the process of deposition, patterning, lift off, and etching. At first, a 350 nm (610 nm)-thick poly-Si film was deposited on a 500 μm-thick fused silica substrate by inductively coupled plasma enhanced chemical vapor deposition (ICPECVD), and then a 100 nm-thick hydrogen silsesquioxane electron beam spin-on resist (HSQ, XR-1541) was spin-coated onto the poly-Si film and baked on a hot plate at 100○C for 2 min. Next, the desired structures were imprinted by using stan- dard electron beam lithography (EBL, Nanobeam Limited, NB5) and subsequently developed in NMD-3 solution (concentration 2.38%) for 2 min. 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