Research Highlights
Field-Induced Switching of
Ferro-Quadrupole Order Parameterin PrTi2Al20
Takigawa, Sakakibara, and Nakatsuji Groups
The series of Pr-based cubic compounds PrT2X20 (T =Ir, Rh, X = Zn; T = V, Ti, X = Al) has been actively studied
recently to explore novel phenomena caused by multipolesof 4f electrons because the non-Kramers Γ3 doublet groundstates in the crystalline electric field (CEF) has active−
quadrupole (OZ = 3z2-r2 and OX = √3 (x2-y2)) and an octupole(TXYZ = xyz) moments but no magnetic dipole moment [1].
Among this series, PrTi2Al20 shows the highest transition
temperature of 2 K into a simple ferro-ordered state of OZ
quadrupole moment.
We have performed 27Ai-NMR and magnetization
measurements on high quality single crystals of PrTi2Al20
and unexpectedly observed discontinuous switching of
quadrupole order parameter by applying small magnetic
fields B of a few tesla along [001] and [110] but not along[111] directions [2]. The symmetry of order parameters
for different field directions were determined as shown in
Fig. 1. For B along [111], there is a single ordered phaseof OZ type below TQ = 2.2 K, which is independent of
B. Here we expect coexistence of three domains, where
the symmetry axis Z of the quadrupole moment points
along three equivalent <001> directions. The quadrupole order parameter can be conveniently represented as a
two-dimensional vector with OZ and OX chosen to be thebasis (rightmost panel of Fig. 1) [3]. For example, orderparameters of the three domains for B ∥ [111] is given by−−
OZ = 3x2– r2 = –OZ / 2 + √3 OX / 2 and 3y2– r2 = –OZ / 2 + √3−
OX / 2, corresponding to the polar angle of 0 and ±2π /√3 .
For B along [001], however, discontinuous jump of the
NMR frequency occurs near 2 tesla with a finite range offield where two lines coexist, indicating a first order phasetransition (Fig. 2a). From the analysis of NMR spectra andFig. 1. The temperature vs. magnetic field phase diagram of the ferroquadrupole order in PrTi2Al20 for B ∥ [111], [001], and [110]. The
order parameters are indicated by graphical symbols corresponding
to specific values of θ in the order parameter space shown in therightmost panel. The phase boundaries are determined by the peak ofd(C/T)/dt, C being the specific heat, splitting of the NMR lines, or kinkin the Knight shift. The dashed lines for B ∥ [001] and [110] indicate
the region of coexistence of high- and low-field phases. For B ∥ [001]and [110], there is no phase transition but only a crossover as a functionof temperature in high fields.

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ISSP Activity Report 2019

Fig. 2. (a) Magnetic-field dependence of the NMR spectrum (plotted asa function of shift from the nuclear Zeeman frequency) for B ∥ [001] at
1.5 K. ( b) The temperature dependences of the Knight shift at low (1T)and high (6.6T) magnetic field along [001] are compared with those of
the magnetic susceptibility.

magnetic susceptibility, we conclude that while the high field
phase has ferro-order of OZ with Z ∥ B, the order parameterof the low field phase is closer to OX type (θ ~ ±π/2). For B
along [110], the order parameter changes from OZ with Z ∥B in low fields to Z ~ –B in high fields. The field-induced
transition was also confirmed by measurements of heat
capacity and magnetocaloric effect [4].
We have developed a Landau theory to identify symmetry
allowed interactions between quadrupole and magnetic field,
which can account for the experimentally observed switchingof the order parameter [2]. Frist, the magnetic field induces
mixing between Γ3 ground doublet and excited CEF levels,
leading to the van-Vleck paramagnetism. This anisotropic
Zeeman interaction, which is quadratic in B, turns out tostabilize the order parameters observed in the high field
phases both for B ∥ [001] and B ∥ [110], leaving only a crossover as a function of temperature. On the other hand, we
found that symmetry allows interaction between quadrupoles
on neighboring Pr sites, which is responsible for the ferroquadrupole order, to depend also quadratically on B for small
B. This anisotropic interaction competes against the Zeeman
interaction and can stabilize the order parameter of the low
field phases. Therefore, the observed switching of the orderparameter can be explained if the anisotropy of the quadrupole-quadrupole interaction wins the Zeeman interaction at
low fields but becomes suppressed at high fields comparedwith the Zeeman interaction. We have indeed succeeded in
reproducing the experimental phase diagram by assuming a
non-monotonic field dependence of the anisotropic quadrupole interaction.
Although the mechanism for such a non-trivial fielddependence of the quadrupole interaction is not understoodyet, anomalous behavior of the NMR Knight shift in thequadrupole ordered states provides an important insight.
As shown in Fig. 2(b), the Knight shift at Al sites, whichprobes the polarization of conduction electron spin, shows
the identical temperature dependence to the magnetic susceptibility at a high field (6.6T). At a low field (1T), however,they show remarkable separation below the orderingtemperature, indicating that the hybridization between 4f andconduction electrons (c-f hybridization) is strongly influenced by the quadrupole order. Since the quadrupole-quadrupole interaction is mediated by the c-f hybridization, thismeans that the quadrupole order modifies the quadrupolequadrupole interaction via redistribution of 4f charge density,
which in turn should affect the order itself. We suspect thatsuch a feedback mechanism may be the key to understand thefield-induced discontinuous transition.
References[1] T. Onimaru and H. Kusunose, J. Phys. Soc. Jpn. 85, 082002 (2016).
[2] T. Taniguchi et al., J. Phys. Soc. Jpn. 88, 084707 (2019).
[3] K. Hattori and H. Tsunetsugu, J. Phys. Soc. Jpn. 83, 034709 (2014).

[4] S. Kittaka et al., J. Phys. Soc. Jpn. 89, 043701 (2020).

Authors
T. Taniguchi, K. Hattoria, M. Yoshida, H. Takeda, S. Nakamura,T. Sakakibara, M. Tsujimoto, A. Sakai, Y. Matsumoto, S. Nakatsuji, and
M. Takigawa
aTokyo Metropolitan University

Fluctuation-Induced First-Order
Transition and Tricritical Pointin a Cubic Chiral Magnet EuPtSi
Sakakibara GroupThe cubic chiral compound EuPtSi (space group P213)
helimagneitcally orders at TN=4.0 K with the propagation
vector q1*=(0.2,0.3,0.04). There has been growing interestin this compound because a skyrmion lattice phase with atriple-q structure emerges in a magnetic field applied along
the [111] direction [1,2]. One of the intriguing features of thiscompound is that the transition at TN is of first order [1-3].
We studied the helimagnetic transition on a single crystal of
EuPtSi by means of high-precision magnetization measurements, and found that the transition, which is of first order at
low fields, becomes of second order at high fields, and there
exists a tricritical point (TCP) in the phase diagram [4].
Figure 1 shows the temperature derivative of the magnetization, dM/dT, in magnetic fields H applied along the [110]direction. At H = 1.8 kOe, the first-order transition (FOT)
is characterized by a sharp peak in dM/dT at T = 4.0 K. By
increasing H, TN(H) defined by the peak position in dM/dTmoves to the lower temperature side with a decrease in thepeak amplitude. Above H = 8.8 kOe, the shape of dM/dT

Fig. 2. Phase boundary between the paramagnetic and the single-q
helical (conical) states of EuPtSi, constructed by colour contour
mapping of the dM/dT data with H||[110]. The bright line in low fields
indicates the first-order boundary, whereas the dashed line shows thesecond-order one. TCP denotes the position of the tricritical point.

dramatically changes and excibits a step function like jumpat TN(H), implying that the transition becomes of second
order above 8.8 kOe.
In order to construct the phase boundary between theparamagnetic and the ordered states, we show in Fig. 2
the color contour mapping of the dM/dT data for H||[110].
The bright line in the low-field region indicates the FOTboundary, and the dashed line in the high-field region
denotes the second-order one. In between there is a TCP as
indicated in the figure. A similar crossover of the transition
has also been observed for [111] and [100] directions [4].
In systems described by order parameters with n>4components, a usual second-order phase transition is
avoided due to interactions among critical fluctuations of
the order parameters [5]. FOT then takes place when thecorrelation length exceeds a certain limit, where a discontinuous phase transition occurs to a state energeticallyfavorable. This fluctuation-induced FOT takes place evenfor systems in which the mean-field theory predicts secondorder phase transitions, and the actual transition temperature
is suppressed much below the mean-field transition temperature. In EuPtSi, the lattice-symmetry operations on q1*
yields 12 distinct propagation vectors, which is large enoughin number to drive the transition to be first order. Applying amagnetic field reduces the symmetry of the system, and thenumber of components of the order parameter is effectively
decreased, leading to a second-order phase transition. The
presence of TCP in the phase diagram in Fig. 2 supports this
scenario of a fluctuation-induced FOT in EuPtSi. This situation is favorable for the occurrence of multi-q orders such as
the skyrmion lattice phase, since they need to be stabilizedagainst a single-q helical (or a conical) phase.
References[1] M. Kakihana et al., J. Phys. Soc. Jpn. 87, 023701 (2018).
[2] K. Kaneko et al., J. Phys. Soc. Jpn. 88, 013702 (2019).
[3] D.G. Franco et al., Phys. Rev. B 96, 014401, (2017).
[4] T. Sakakibara et al., J. Phys. Soc. Jpn. 88, 093701 (2019).
[5] P. Bak, S. Krinsky and D. Mukamel, Phys. Rev. Lett. 36, 52 (1976).

Fig. 1. Temperature derivative of the magnetization dM/dT of EuPtSi infields applied along the [110] direction.

Authors
T. Sakakibara, S. Nakamura, S. Kittaka
M. Kakihanaa, M. Hedoa, T. Nakamaa, and Y. Onukia
aUniversity of Ryukyus

ISSP Activity Report 20193

Effects of Molecular Dynamics on the
Anhydrous Proton Conductivity of
Imidazolium Hydrogen Dicarboxylates
Mori Group
Hydrogen (H) is a ubiquitous element, which plays
important role in a wide range of fields from the deep underground to the interstellar space, and from inorganic oxides
to biosystems. Proton (H+) migration in solids is one of suchextensively studied research topics. Recently, anhydrous
organic proton conductors, which can show proton conductivity at above 100 °C without humidification, have attracted
scientific interests owing not only to their wide applicability as solid-state electrolytes for fuel cells, but also totheir peculiar proton conduction mechanism mediated notby water molecules. However, there have been only a few
reports about anhydrous organic proton conductors.
Previously, we investigated the “intrinsic” proton conductivities of imidazolium succinate (= Im-Suc; Fig. 1a) andglutarate (= Im-Glu; Fig. 1b), by single-crystal measurements, and successfully disclosed two key factors for realization of anhydrous proton conductivity: (1) the hydrogenbond (H-bond) network structures, and (2) difference of the
proton donating/accepting abilities between acid and basemolecules, i.e., ΔpKa [1]. In this study, we newly preparedhigh-quality single crystals of another salt, imidazolium
fumarate (Im-Fum; Fig. 1c), in addition to Im-Suc and
Im-Glu, and investigated the effect of molecular “dynamics”
on the anhydrous proton conductivities of these three salts[2].
Im-Fum has similar 2D H-bond network structure as
Im-Suc and Im-Glu (Fig. 1), and showed the anisotropic
proton conductivity consistent with the previously disclosed“static” key factors (1) and (2). Interestingly, Im-Fum
exhibits linear dependence on the reciprocal temperature incontrast to non-linear dependence in Im-Suc and Im-Glu.
We speculated that it is contributed by the imidazolium
cation in the 2D H-bond network because the Ea showed
quite high values in Im-Suc and Im-Glu similar to the otherimidazolium-based salts, and that the molecular orientationof imidazolium cation is different between Im-Fum and theother two. Thus, we investigated the dynamic property ofimidazolium cations in these salts by high-temperature X-ray
structure analyses and solid-state 2H NMR.
In Im-Suc, a structural transition was observed in X-ray
structural analysis at ca. 80 °C, accompanied with thein-plane orientational disorder of imidazolium molecules in
one out of two layers. Consistently, the proton conductivity
showed abrupt increase at ca. 80 °C, which indicates that theimidazolium libration motion promotes proton conduction
in Im-Suc (Fig. 2 upper). On the other hand, no significant

Fig. 1. (upper) Chemical structures and (lower) H-bond network structures of (a) Im-Suc, (b) Im-Glu, and (c) Im-Fum. Red and black dashedlines denote N–H…O and O–H…O H-bonds, respectively.

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ISSP Activity Report 2019

Fig. 2. (upper) The single-crystal proton conductivity (σ) and (lower)
libration angle θlib vs. 1000/T plots for Im-Suc (orange and dark orange
circles), Im-Glu (green diamonds), and Im-Fum (pink squares). In
upper graph, the lines denote the Arrhenius fitting, and the inset figures
show ordered/disordered imidazolium cation in Im-Suc below/above
the transition temperature, ca. 80 °C. In bottom graph, filled circles,
diamonds, and squares denote libration angles of Im-Suc (orange)[3],Im-Glu (green), and Im-Fum (pink) in the proton-conducting temperatures, and open markers denote those below proton-conducting temperatures. Inset shows the model for the libration motion of imidazolium
cations.

changes were observed for Im-Glu and Im-Fum in X-ray
analyses.
Then, in order to investigate the local dynamics ofimidazolium cations, we performed the solid-state 2H NMR
experiments for Im-Glu and Im-Fum using imidazoled3 molecules (Fig. 2 lower inset). By spectral simulations
assuming the two-site jump model describing the libration motion of imidazolium molecules, we estimated thelibrational rates klib and angles θlib. Comparing the libration angles θlib and proton conductivities σ of Im-Glu and
Im-Fum together with the reported values of Im-Suc [3],magnitude of θlib is Im-Glu > Im-Suc > Im-Fum, in consistent with the same relationship of σ. This result clearly
indicates that the libration motion of the imidazolium cations
promotes proton conduction in these salts.
We consider that this “dynamic” factor synergistically contributes to anhydrous proton conductivity withthe already mentioned the “static” factors. Imidazolium
molecules lie within the 2D H-bond network in Im-Suc and
Im-Glu whereas imidazolium sticks out from the networkin Im-Fum (Fig. 1). In former case, directions of librationand proton conduction matches, and the libration can makeadditional H-bonds or short contacts to promote the protontransfer in the H-bond network, leading to the nonlinear
dependence of σ in the Arrhenius plot, whereas it is not for
the latter case.

In conclusion, in addition to previously disclosed “static”
key factors, (1) H-bond network structures and (2) ΔpKa
between acid and base molecules, we revealed that (3) the
molecular “dynamics” is another key factor for realization ofanhydrous proton conductivity. These “static” and “dynamic”
factors synergistically play important roles, which is thought
as peculiar nature of Grotthuss-type conduction in anhydrous
solids.
References[1] Y. Sunairi, A. Ueda, J. Yoshida, K. Suzuki, and H. Mori, J. Phys.
Chem. C 122, 11623 (2018).
[2] Y. Sunairi, S. Dekura, A. Ueda, T. Ida, M. Mizuno, and H. Mori,
J. Phys. Soc. Jpn. 89, 051008 (2020).
[3] T. Umiyama, R. Ohashi, T. Ida, and M. Mizuno, Chem. Lett. 42,1323 (2013).
Authors
Y. Sunairi, S. Dekura, A. Uedaa, T. Idab, M. Mizunob, and H. MoriaKumamoto University
bKanazawa University

Topological Properties ofτ-Type Organic Conductors
Osada Group
It is desirable that topological phases can be realized inorganic molecular crystals with high designability. However,the search for topological states in organic crystals has met
with some challenges. Generally, organic molecular crystals
have too poor symmetry to protect topological states. The
width of their tight-binding band is too narrow to cause theband inversion. Moreover, organic molecules consist of lightelements with correspondingly small spin–orbit coupling(SOC). So far, only a few molecular crystals, such as a

Fig. 1. (a) Schematics of a conducting layer of τ-type organic conductors. A and B indicate donor molecule sites, and X indicates anion
sites. (b) Bulk band dispersion of τ-type conductors with finite spinorbit coupling (SOC). A gap opens at the quadratic band contact point
at M. (c) Energy dispersion of the system with finite width. Helicaledge states along AA and BB edges appear in the gap. (d) Hofstadterbutterfly (energy spectra as a function of magnetic field) of τ-typeconductors. Blue and Red patterns correspond to up-spin and downspin, respectively. The value of SOC is enlarged to see its effect easily.

two-dimensional (2D) Dirac semimetal α-(BEDT-TTF)2I3
and a 3D nodal-line Dirac semimetal Pd(dddt)2, have beenstudied as topological materials in the field of organic
conductors.
Here, we demonstrate that the conducting layer of τ-typeorganic layered conductor, τ-(EDO-S,S-DMEDT-TTF)2X1+yand τ-(P-S,S-DMEDT-TTF)2X1+y (X=AuBr2, I3, IBr2), is a
2D electron system with unique topological properties [1].
On each layer, donor molecules (EDO-S,S-DMEDT-TTF
or P-S,S-DMEDT-TTF) form a square lattice, and anion
molecules (X) are arranged on it with a checkerboard pattern
as shown in Fig. 1(a). This lattice structure is a modification of Mielke's lattice, which is a typical flat band system,so that topological natures of Mielke's lattice are inherited.
In addition, rather strong spin-orbit coupling (SOC) can be
expected in τ-type conductors, although SOC is generally
weak in organic materials. It results from the strong in-planepotential modulation generated by the inorganic anion X.
Using a Kane-Mele type model, we discuss possible topological properties of the τ-type organic conductors.
In the absence of SOC, the conduction and valence bands
with four-fold rotational symmetry show quadratic band
touching. Since the Fermi level is located in the conduction
band, the actual τ-type organic conductors (y = 0.75~0.875)
have is a star-shaped electron Fermi surface. Under thein-plane uniaxial strain breaking the four-fold symmetry, theband contact point splits into a pair of Dirac cones. This is akind of Lifshitz transition from a 2D Luttinger semimetal toa 2D Dirac semimetal.
Once the SOC becomes finite, a small gap opens at theband contact point as seen in Fig. 1(b). The product of thevalence band parity values at symmetric point (time-reversal
invariant momentums) is -1. This fact indicates that the
gapped state is a topologically nontrivial insulator with bandinversion. In fact, there exists a helical edge state characteristic to the quantum spin Hall insulator (Z2-topologicalinsulator) along each edge as shown in Fig. 1(c). Therefore,
the actual τ-type conductors could be regarded as heavilydoped topological insulators. Since they have finite spindependent Berry curvature at the Fermi level, finite spin Hall
effect could appear although its experimental detection needs
microfabrication of samples.
Because of finite spin-dependent orbital magnetic
moment due to SOC, the Landau levels (LLs) have additional
spin splitting to the Zeeman effect. Figure 1(d) shows the
Hofstadter butterfly of the LLs for each spin subband. Since
the Zeeman effect is not included in this figure, the difference of both spin levels indicates the orbital contribution to
the spin splitting due to SOC. At the zero-field limit, we cansee the Chern number below the SOC gap takes finite valuesof -1 or +1 depending on the spin. As actual τ-type conductors are doped up to 10% of the conduction band, the orbital
contribution to the spin splitting is about several % of the
Zeeman splitting, which is possible to detect experimentallyin the Shubnikov-de Haas oscillations at low temperature andhigh magnetic fields.
Reference[1] T. Osada, J. Phys. Soc. Jpn. 88, 114707 (2019).
Authors
T. Osada, T. Taen, K. Uchida, M. Sato, and A. Kiswandhi

ISSP Activity Report 20195

Nonequilibrium Dynamics in Strongly
Correlated Electrons in One Dimension
and Clogged Charge Current
Tsunetsugu Group
Understanding nonequilibrium dynamics in strongly
correlated systems is an important issue and a big challenge
for both theorists and experimentalists. Recently proposed
generalized hydrodynamic (GHD) theory [1] succeeds indescribing nonequilibrium dynamics in one-dimensionalmodels that are exactly solvable through the Bethe ansatz(BA) equations. Its fundamental degrees of freedom are
local distribution function of multiple types of “quasiparticles” corresponding to real roots and complex roots (strings)
in the BA equations. These distribution functions evolve inspace and time following continuity equations, and theseequations include effective velocities that need to be determined self-consistently from the local distribution functions.
We have applied the GHD theory to the one-dimensional Hubbard model and studied quench dynamics witha partitioning protocol [2]. The system is initially divided
at the origin x = 0 to two semi-infinite parts. The left partis equilibrated at a fixed temperature with half-fillingelectron density, while the right part is set empty and has
no electrons. At time t = 0, the two parts are connected
and start to evolve. In this case, local physical quantities
depend only on the ray ξ = x/t, and vary continuously in thetransient region VL < ξ < VR. We have calculated charge andenergy densities, n(ξ), e(ξ), and their currents, jn(ξ), je(ξ), andexamined the proportionality relation between jn(ξ) and je(ξ).
An interesting finding is a phenomenon we named clogging.
Inside the transition region, there appears at high temperatures a region that has zero charge current although nonzero
energy current flows. This clogged region locates next to theleft part with half-filling electron density. A similar behavior
was found for spin current in quantum spin systems [3]. We
proved its presence in the infinite temperature limit, and also
confirmed by numerical calculations a finite region size,
which shrinks with decreasing temperature. In the clogged
region, one type of quasiparticles have the same charge
as electron and they flow towards the empty side as one
expects. This charge current is cancelled by the counterflow
carried by other types of quasiparticles that are bound statesof multiple electrons. All the types of quasiparticles carrynegative energy towards the empty part, thus leading to anonzero energy current in the clogged region.
The clogging of charge current is an interestingFig. 1. Profile of charge and energy currents at reciprocal temperature
β = 0.5 and 1.0. Coulomb repulsion is U = 8, and energy units are theelectron transfer energy. Charge current jn is normalized by the electron
charge –|e|.

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ISSP Activity Report 2019

Fig. 2. Change of clogged region with reciprocal temperature β at U=8.

unexpected behavior in nonequilibrium dynamics of strongly
correlated electrons in one dimension, and it is worth trying
to observe it in experiments.
References[1] O.A. Castro-Alvaredo, et al., Phys. Rev. X 6, 041065 (2016); B.
Bertini et al., Phys. Rev. Lett. 117, 207201 (2016).
[2] Y. Nozawa and H. Tsunetsugu, Phys. Rev. B 101, 035121 (2020).
[3] L. Piroli et al., Phys. Rev. B 96, 115124 (2017).
Authors
H. Tsunetsugu and Y. Nozawa

High-Harmonic Generation in Solids
Kato Group
Recently, high-harmonic generation (HHG) in solids
has been experimentally observed. In contrast to that of thegaseous media, solids have the vastly diverse nature such as
in their band structures, energy gaps, crystalline anisotropy,
magnetism, and so on. Thus, HHG shows various properties depending on the materials, and clarifying the universal
properties of HHG in solids should be needed to progress thehigh-intensity optical technology.
Based on this motivation, we have theoretically investigated HHG mechanism in solids. In Ref. [1] and [2], we haveshown that the HHG mechanism can be classified into three
regimes depending on the field intensity: (i) the multiphoton
absorption regime, (ii) ac Zener regime, and (iii) semimetal
regime. This consideration enables us to predict that HHG
in graphene would show unique properties in its ellipticity
dependence, and this was identified in the experiment [3]. In
this consideration, a concept of the field-induced dynamic
band structure is essential to gaining a full understanding of
extreme nonlinear optics in solids. Although fundamental
mechanisms of HHG in solids have already been revealed[3], the connection between HHG and other high-field
phenomena, such as the dynamical Franz-Keldysh effect,
above-threshold ionization, and dynamical localization has

Fig. 1. NIR frequency dependence of 2nd HSG for Eg = 21ωTHz in thecase of (a) ΩTHz = 0.5ωTHz, (b) ΩTHz = ωTHz, and (c) ΩTHz = 2ωTHz. The
blue and red lines indicate positive and negative 2nd HSG, respectively.

not been clarified yet. It appears that HHG and these opticalphenomena are different aspects of the same electron interaction with the strong light field. We tried to clarify the relation
between HHG and these phenomena, by supposing thepump-probe spectroscopy where weak near infrared (NIR)
and strong terahertz (THz) light are simultaneously imposed.
The weak NIR and strong THz lights induce the highorder sideband generation (HSG), which changes dependingon the THz intensity and NIR frequency. These changes are
considered as a probe of the modified states of solids understrong THz light irradiation. Figures 1 (a)-(c) show theintensities of 2nd positive and negative HSG as a function of
NIR frequency (ωNIR) for different THz intensities (ΩTHz).
These figures indicate that with increasing the THz intensities, more peaks at different frequencies of ωTHz become
visible, which reflects the modified state of the system has
new energy levels around the band-gap energy. By an analytical consideration, we have shown that these energy levels(subbands) are derived from a concept of the field-induced
dynamic band structure, as shown in Fig. 2(a). We have also
shown that kth Bessel function, ΩTHz Jk(ΩTHz/ωTHz), effectively describes mixing matrix elements between the kth
subband and the valence band, which can be used for a roughestimate of the transition amplitude. This presumption could
be identified by numerical calculation, as shown in Fig. 2(b),where the positive 2nd HSG resonates to subbands with theirenergy levels Eg = 20ωTHz, Eg = 19ωTHz, and Eg = 18ωTHz,

respectively (see Fig. 2(a)). These non-monotonic properties are generally confirmed in other high-field phenomena
such as the dynamical Franz-Keldysh effect and dynamical
localization. Thus, we could clarify the relationship between
HHG and other high-field phenomena and suggest a newexperiment for identifying oscillatory behavior that would beobserved in field-intensity dependence of HHG in solids [5].

Fig. 2. (a) Schematic diagram of the subband picture originating from
temporally changing band structure. (b) Numerical results of positive
2nd HSG as a function of ΩTHz/ωTHz. Here, the red, blue, and green
dots indicate (A) ωNIR = 18ωTHz, (B) ωNIR = 17ωTHz, and (C) ωNIR =16ωTHz, respectively, whose processes are illustrated in (a). Inset figure:
Analytic results of 2nd HSG as a function of ΩTHz/ωTHz. The red, blue,and green lines show |xJ-1(x)|2, |xJ-2(x)|2, and |xJ-3(x)|2, respectively,
where x = ΩTHz/ωTHz.

Fig. 1. (a) Schematic diagram of unitary operation on an electron spin
flying qubit. An FQ is injected to channel-1 and some portion of the
wave packet tunnels into channel-2 with down spin (gaining of zenith
angle.) During the travel, the FQ gains azimuth angle via the differencein the kinetic phase. The spin state is detected as the overall transmission amplitude. (b) Optical micrograph of metallic gates (regions withorange color) configuration fabricated on a 2DES. Edge conduction
channels and measurement circuits are illustrated and superposed.

References[1] T. Tamaya et al., Phys. Rev. Lett. 116, 016601 (2016).
[2] T. Tamaya et al., Phys. Rev. B 94, 241107(R) (2016).
[3] N. Yoshikawa, T. Tamaya, and K. Tanaka, Science 356, 736 (2017).
[4] T. Tamaya and T. Kato, Phys. Rev. B 100, 081203(R) (2019).
[5] P. Xia*, T. Tamaya*, C. Kim, F. Lu, T. Kanai, N. Ishii, J. Itatani,
H. Akiyama, and T. Kato: arXiv:2004.04492. (*equally contributed)
Authors
T. Tamaya and T. Kato

Electric Control of Flying Qubit on
Quantum Hall Edge Channels
Katsumoto GroupFor composing a quantum circuit with electron spins,“flying qubits” (FQs) are used for transferring quantum
information between qubit clusters. A simple realization of
FQ is an electron wave packet, which brings 1 qubit information as its spin. In a flight process, quantum decoherence,
i.e. loss of information should be avoided, and also a unitary
operation on the FQ is desirable. In the quantum Hall effectone-dimensional channels are formed at the sample edges(quantum Hall edge channel, QHEC) and the quantum
coherence of electronic states on them are robust against
disturbances from the environment. Also when the magnetic

ISSP Activity Report 20197

Reference[1] T. Nakajima, K. T. Lin, and S. Komiyama, AIP Conf. Proc. 1566,
301 (2013).
Authors
T. Shimizu, Y. Hashimoto, A. Endo, T. Nakamura, and S. Katsumoto

Spin Excitations Propagation Dynamics
along Skyrmion Strings
Otani Group
Fig. 2. Current distribution ratio to drain L, which is equal to the overall
transmission coefficient of channel-1 in Fig.1(b) as a function of centergate voltage.

field is strong enough, the electronic states of QHECs are
spin-polarized due to the Zeeman energy and the exchange
effect (quantum Hall ferromagnet). Hence in a spin up anddown pair of QHEC, the spin and orbital degrees of freedom
are quantum mechanically entangled. If one can separate
an electron wave packet into two QHECs in such a pair,
operations on the orbitals readily change the spin states.
For example, spin precession can be realized through the
Aharonov-Bohm (AB) interference. Here we report unitary
operation of FQs on QHECs by using non-adiabatic interedge channel tunneling.
Figure 1(a) shows the scheme of the unitary operation. From the right end, an electron wave packet with up
spin is injected into QHEC-1 and experiences partial interedge tunneling to QHEC-2, which corresponds to a gainof zenith angle in electron. During the travel to the left
crossing, a phase difference is given, which corresponds
to an azimuth angle rotation. The partition rate to QHEC-1
reflects both zenith and azimuth angles. We realized such
quantum interference circuits on semiconductor (AlGaAs/
GaAs) two-dimensional system (2DES) and micro-fabricated
Schottky gates on it. In Fig.1(b), we illustrate the channels
for FQs, the terminals and measurement circuits superposedon an optical micrograph of the sample gate configuration on
a 2DES. The first crossing point is realized by Gate SR as a
sharp corner, where inter edge tunneling is caused by spinorbit interaction. The phase difference between QHEC-1
and 2 is developed during the travel along the down edges ofGate SR, C and SL. This process corresponds to the precession of the spin around the zenith axis (z-axis). At the left
end of the device, the two QHEC are intermixed again andthe total transmission rate to the electrode L reflects bothzenith and azimuth angles.
In Fig. 2, we plot the current partition ratio (distribution
ratio, D) to drain L as a function of the gate voltage applied
to gate C (VC). The parameter is the gate voltage applied togate SR (VSR). A large oscillation versus VC is visible andthe amplitude strongly depends on VSR. The oscillation is aconsequence of interference in kinetic phases of QHEC-1
and 2, or equivalently precession of electron spin (azimuth
angle rotation) [1]. Here VC is changing the distance between
the two channels. The amplitude depends on the zenith
angle of the spin, and should be largest making the visibility
100%, when the spin is in xy-plane. Hence from the amplitude we can deduce the zenith angle, e.g. 14 degree for VSR=
-0.549 V.
From the above, we conclude that unitary operation onelectron spin FQ can be done electrically by using spinpolarized QHEC.

8ISSP Activity Report 2019

Magnetic skyrmions, topological solitons characterized
by a two-dimensional swirling spin texture, have recently
attracted attention as stable particle-like objects. In threedimensional systems, the skyrmion can form a string structure by extending in the third dimension, which consists of
the uniform stacking of two-dimensional skyrmions along
the string direction. Skyrmion strings can be considered as
an analog of the vortex line in a superfluid, type-II superconductors, and trapped dilute-gas Bose-Einstein condensates orthe cosmic string in the universe. They are all flexible, andsome of these strings are proposed to host a resonant oscillation mode propagating through the string path. This implies
the possible coherent signal transfer along skyrmion strings,
whereas the propagation character of their excitations has
rarely been investigated before.
Experimentally, such skyrmion strings appear in aseries of bulk magnets with chiral cubic atomic lattice.
The examples are metallic B20 or β-Mn-type Co-Zn-Mn
alloys and insulating Cu2OSeO3, the latter of which is thetarget of this work. In these materials, the Dzyaloshinskii–
Moriya (DM) interaction is the key to the skyrmion formation. For a limited temperature range, these compounds
host a hexagonal lattice of skyrmion strings aligned along
the static magnetic field (H) direction. This skyrmion
crystal (SkX) phase is predicted to host three distinctive
magnetic resonance modes (Fig. 1a–c), i.e., the counterclockwise (CCW) and clockwise (CW) rotational modes
both excited by an oscillating magnetic field Hν⊥H, as wellas the breathing (B) mode excited by Hν⁄⁄H, which have

Fig. 1. a-c Schematic illustration of CCW, breathing, and CW excitation modes on skyrmion strings. The central part represents the local
oscillation manner of skyrmion at the z = 0 plane. The upper andlower parts are the snapshot images describing how the spin excitation launched at z = 0 propagates on the skyrmion strings, along the ±z
direction parallel and antiparallel to H, respectively. The cross-sectional
images describing the size and position of skyrmion at selected z-planes(shown by red layers) are also indicated. d The direction of the local
magnetic moment at the core and edge position of skyrmion in each z
layer. Black rounded arrows denote the sense of local moment precession in the time domain, and ± symbols indicate the sign of local
Dzyaloshinskii-Moriya interaction energy gain DM.

recently been identified by magnetic resonance experiments. However, these previous works mostly focused on thecharacter of non-propagating uniform excitations with wave
number kSW = 0. To understand their propagation character,the employment of a different experimental approach sensitive to the kSW ≠ 0 regime, as well as the theoretical identification of their dispersion relation, is essential.
In the present study, we experimentally demonstrate thecoherent propagation of spin excitations along skyrmion
strings for the chiral-lattice magnet Cu2OSeO3. We findthat the counter-propagating spin excitations show different
propagation behavior, and the degree of non-reciprocity,
as well as the associated group velocity and decay length,
are strongly dependent on the character of the excitation
modes. Our theoretically calculated dispersion relations well
reproduce these experimental features. The observed decay
lengths exceed 50 μm, reflecting the excellent long-rangeorder of the skyrmion-string structure. The present results
revealed the peculiar propagation dynamics of skyrmionstring excitations and suggest that skyrmion string can be
an excellent medium for magnon transport with uniquefunctionalities. Our combined experimental and theoreticalanalyses offer a comprehensive account of the propagation
dynamics of skyrmion-string excitations and suggest thepossibility of unidirectional information transfer along such
topologically protected strings.
Reference[1] S. Seki, M. Garst, J. Waizner, R. Takagi, N. D. Khanh, Y. Okamura,
K. Kondou, F. Kagawa, Y. Otani, and Y. Tokura, Nat. Commun. 11, 256(2020).
Authors
S. Sekia,b,c, M. Garstd, J. Waiznere, R. Takagia,b, N. D. Khanhb, Y.
Okamuraa, K. Kondoub, F. Kagawaa,b, Y. Otani and Y. Tokuraa,baThe University of Tokyo
bRIKEN Center for Emergent Matter Science (CEMS)
cPRESTO, Japan Science and Technology Agency (JST)dInstitut für Theoretische Festkörperphysik, Karlsruher Institut fürTechnologie
eInstitut für Theoretische Physik, Universität zu Köln

Creation of Magnetic Skyrmionsby Surface Acoustic Waves
Otani Group
Non-collinear and non-coplanar spin textures, such as
chiral domain walls and helical or triangular spin structures,bring about diverse functionalities. Among them, magnetic
skyrmions, particle-like non-coplanar topological spin
structures characterized by a non-zero integer topologicalcharge called the skyrmion number (Nsk), have great potential for various spintronic applications, such as energysaving, non-volatile memory, and non-von Neumanndevices. Current pulses can nucleate skyrmion in thin-film
samples but require relatively large current densities, which
probably causes Joule heating. Moreover, skyrmion creation
is localized at a specific position in the film, dependingon the sample design. Here, we experimentally demonstrate an approach to skyrmion creation employing surface
acoustic waves (SAWs); in asymmetric multilayers of Pt/
Co/Ir, propagating SAWs induce skyrmions in a wide areaof the magnetic film (Fig. 1a,b). We use multilayer filmsof Pt/Co/Ir in which the formation of thermodynamicallystable skyrmions has already been well-studied in previous

Fig. 1. a, Schematic spin configuration of Néel skyrmion. b, Schematic
illustration of the device structure. Pt/Co/Ir films are deposited on
LiNbO3 substrates, and interdigital transducers (IDTs) are fabricated on both sides of a rectangular-shaped Pt/Co/Ir film. Surface
acoustic waves (SAWs) are excited by applying radio-frequency (RF)voltage to IDTs. c-e, Polar Kerr images before (a), during (b), andafter (c) exciting a propagating surface acoustic wave (SAW) with thewavelength (λSAW) of 16 μm by applying radio-frequency (RF) voltage
with the power (P) of 251 mW. The white dashed lines represent theboundaries between Pt/Co/Ir film and LiNbO3 substrate. The orange
arrow represents the propagation direction of SAW.

research. All measurements were performed at room temperature, and the magnetic field (H) was applied perpendicular
to the film plane. Firstly, we determined, from magnetic
images taken before and after the application of SAWs
at various H, the magnetic field Hsk at which skyrmions
begin to appear in the ferromagnetic state without SAWs.
The magnetic field evolution of polar Kerr images in a Pt/
Co/Ir film with the nominal Co thickness of dCo = 0.55 nm
shows that maze domains firstly appear at μ0H = 0.01 mT
and transforms to thermodynamically stable skyrmions 3 μm
in diameter at 0.21 mT. A further increase in H makes theskyrmions annihilate and leads to the ferromagnetic state at
μ0H = 0.31 mT. Here, we note that the size of the observed
skyrmions is relatively large, indicating that the dipole-dipole
interaction plays an essential role in their stabilization, in
addition to the interfacial DMI, and these types of skyrmion
are sometimes called a ‘skyrmion bubble’.
Figures 1c–e represent the magnetic images before andduring excitation by the propagating SAWs. Before exciting
with SAWs, we observe no magnetic contrast (Fig. 1c),which indicates that the sample is in the single-domain
ferromagnetic state. When the SAW is continuously excited,skyrmions appear (Fig. 1d); skyrmions are nucleated overalmost the whole region of a rectangular-shaped Pt/Co/
Ir film of width 100 μm and length 400 μm because of thelong propagation length of the SAWs. Even after turning
off the SAW, most of the skyrmions survive, indicating the
emergence of metastable skyrmions (Fig. 1e). The density(nsk) of the nucleated skyrmions in the ferromagnetic state
gradually increases with RF power above the threshold of P
= 100 mW (Fig. 2a). When H is close to Hsk, the number ofskyrmions dramatically increases after exciting with SAWs.
Besides, when the skyrmions coexist with the ferromagnetic
state before exciting with SAWs, that is, H < Hsk, skyrmions

ISSP Activity Report 20199

Fig. 2. a, Density of skyrmions (nsk) as a function of the power of the
RF signal that excites the SAWs. b, Magnetic field dependence of nsk
before and after exciting a SAW with λSAW = 16 μm and P = 251 mW.

are also created. The value of nsk after exciting with SAWs ismuch larger than that before exciting with SAWs (Fig. 2b).
In contrast, skyrmions cannot be created in the high fieldregion. This is probably because, in the high field region, theenergetically stable ferromagnetic state cannot accommodate
skyrmions due to the gain in Zeeman energy, even when
SAWs are excited.
Micromagnetic simulations reveal that inhomogeneous
torque arising from both SAWs and thermal fluctuations
creates magnetic textures, with pair structures consistingof a Néel skyrmion like and an antiskyrmion-like structure.
Subsequently, such pairs transform into a Néel skyrmion
due to the instability of the antiskyrmion-like structure ina system with interfacial Dzyaloshinskii–Moriya interaction. Our findings provide a tool for efficient manipulationof topological spin objects without heat dissipation and overlarge areas, given that the propagation length of SAWs is of
the order of millimeters.
Reference[1] T. Yokouchi, S. Sugimoto, B. Rana, S. Seki, N. Ogawa, S.
Kasai, and Y. Otani, Nat. Nanotechnol. 15, 361 (2020).
Authors
T. Yokouchia, S. Sugimotob, B. Ranaa, S. Sekia,c,d, N. Ogawaa,c, S.
Kasaiab,c and Y. Otani
aRIKEN Center for Emergent Matter Science (CEMS)
bNational Institute for Materials Science (NIMS)
cPRESTO, Japan Science and Technology Agency (JST)dThe University of Tokyo

Fig. 1. (a) Schematic model of an FeN/Ni/Fe/Ni film formation process
on Cu(001) by surfactant epitaxy using N atoms. First, monolayerc(2x2) Ni2N is formed on Cu(001) surface as shown in (b) by N adsorption and Ni deposition. Then, 1-ML Fe is deposited below 150 K. Afterannealing above 300 K, N atoms segregate to the Fe surface and Fe2N
monolayer is formed. Next, on top of this surface, 1-ML Ni is deposited
below 150 K. By repeating deposition and annealing, the L10 FeNi film
is prepared. (b) STM image of a Ni2N atomic layer on Cu(001) (left)
and its ball model (right). The 0.5-ML N form c(2x2) structure with
1x1 Ni atoms [1].

dicular to the film has not been realized because the in-plane
film shape anisotropy is larger than the magnetocrystalline
anisotropy. The limitation in the epitaxial films has been
attributed to the imperfect atomic layer-by-layer mode in thealternative deposition process of Fe and Ni atoms and theintermixing of the two elements at the interface.
We have demonstrated significant improvement of
the uniaxial magnetic anisotropy of an L10 FeNi epitaxial
film prepared by surfactant epitaxy of Fe and Ni atomic
layers using nitrogen (N) atoms and the deposition on acooled Cu(001) substrate [1]. The N-surfactant epitaxy,
that is, successive and selected segregation of the N atoms
to the surface during the alternate Fe and Ni monolayer

Large Magnetic Anisotropy of
L10 Ultrathin Film Grown by
Nitrogen-surfactant Epitaxy
Komori GroupFor the development of useful magnetic materials, important are uniaxial magnetic anisotropy with high magnetic
moment, coercivity, and transition temperature. Moreover,for their wide use, rare-element free materials are strongly
required. One of the excellent candidates of such magnetic
materials is L10 FeNi with large uniaxial anisotropy energy,
Ku, up to 1.3 MJm-3. While its single crystal cannot be
prepared by conventional macroscopic crystal growth,
the single-crystal films have been fabricated by layer-bylayer epitaxial growth on Cu(001) and other substrates in a
vacuum. The Ku values of the films are, however, lower than
the above ideal one. Thus, the magnetic anisotropy perpen-

10

ISSP Activity Report 2019

Fig. 2. (a) Fe L-edge XAS (upper) and XMCD (lower) spectra of
the NiN/Fe/Ni trilayer for the NI and GI geometries. In the NI (GI)geometry, the magnetic field direction is 0° (55°) off from the surface
normal to the [100] direction of the Cu(001) substrate. The XAS intensity was measured with the photon helicity parallel (I+) and antiparallel(I−) to the external magnetic field of 5 T at 8 K. (b) Narrow- (upper)
and wide- (lower) range Fe magnetization (M) curves of the NiN/Fe/Ni
trilayer [1].

(ML) deposition in the present case, suppresses the mixing
between Fe and Ni atoms during the deposition andannealing. The schema is given in Fig. 1(a). It was previously shown on the N-adsorbed Cu(001) substrate that N
atoms segregate to the surface during the Fe and Co deposition without mixing between the deposited metal and thesubstrate Cu atoms [2]. This is quite in contrast to the mixing
during the deposition of magnetic transition metals on thesame substrate [3]. Sharp interface between the atomic layersof Fe and Ni in the film is ensured by the present method.
A monatomic layer is grown on the cooled substrate whilebilayer islands are formed at room temperature. Satisfactory growth of the L10 FeNi films up to four monolayers
was confirmed after post-annealing process at 430 K byin-situ X-ray photoelectron spectroscopy, scanning tunnelingmicroscopy and low energy electron diffraction. Magnetic
properties were studied using element-specific soft-X-ray
magnetic circular dichroism (XMCD). The value of Fe L2,3
XMCD is an order of magnitude larger than that of Ni L2,3
XMCD, and thus the Fe monolayer dominates the magnetismof the film. The results of the NiN/Fe/Ni trilayer are shownin Fig. 2. The Fe hysteresis curve measured at 8 K indicatesthe out-of-plane magnetocrystalline anisotropy is large
enough for overcoming the in-plane film shape anisotropy.
According to the XMCD sum rule analyses, both Fe and Ni
magnetic moments increase with increasing the thickness ofthe FeNi film.
References[1] K. Kawaguchi et al., Phys. Rev. Material 4, 054403 (2020).
[2] D. Sekiba et al., Surf. Sci. 590, 138 (2005).
[3] H. L. Meyerheim et al., Phys. Rev. B 71, 035409 (2005).
Authors
K. Kawaguchi,T. Miyamachi, T. Iimori, Y. Takahashi, T. Hattori,
T. Yokoyamaa, M. Kotsugib, and F. Komori
aInstitute for Molecular SciencebTokyo University of Science

Enhanced Critical Magnetic Field
for Mono-Layer Superconductor
by Step Confinement
Hasegawa GroupIn a usual superconductor, electrons that have opposite
momentum are bound to form a Cooper pair. Under magnetic
fields, the pairs lose their stability as the field exerts forcesthat unbalance the electrons’ momenta. Since breaking thepairs costs an energy, however, superconductivity survives up
to a certain magnetic field. Enhancing the robustness against
magnetic field is technically important, e.g. for generatinghigh magnetic fields. In the case of thin films, superconductivity is naturally robust against the in-plane magnetic field
because the above-mentioned orbital breaking mechanism issuppressed due to the geometrical limitation. It would therefore be an impact if one finds approaches that make themrobust against magnetic fields in other directions. We report
here that for a single atomic layer superconductor narrowing
terraces by steps improves the tolerance against the out-ofplane magnetic field.
Here as a monolayer (ML) superconductor, we used a−−Pb-induced reconstructed structure, √ 3 × √ 43 Pb/Si(111),
whose nominal Pb coverage is 1.23 ML. An STM image
and a tunneling spectrum taken on the structure at 0.4 K

Fig. 1. (a) Atomically −resolved− image and (b) tunneling conductancespectrum taken on the √ 3 × √ 43 Pb/Si(111) structure at 0.4 K.

are presented in Fig. 1. From a fitting of the spectrum with
the Dynes function, whose curve is drawn with a red line in
Fig. 1(b), we found the gap is 0.28 meV. Figures 2(a) show
an STM image taken in a wider area (1μm×1μm). The whole− −surface is covered with the √ 3 × √ 43 phase including the area
close to the step edges. In the same area as Fig. 2(a), we havetaken spatial mappings of tunneling conductance at zero bias
voltage (ZBC: zero bias conductance), which corresponds
to the minimum conductance in the superconducting gap,
under various out-of-plane magnetic fields. The amount of
the magnetic field ranges from 0 to 400 mT, as shown in
Figs. 2(b-h). The ZBC mapping taken under zero field(Fig. 2(b)) demonstrates almost uniform distribution of the
deep gaps (low ZBC value) over the entire surface, indicting
uniform superconductivity including the area of steps. The
steps do not locally break the superconductivity of the ML
Pb structure.
When the out-of-plane magnetic fields of 30-100 mT(Figs. 2(c-f)) are applied, several round protrusions ofhigh-ZBC (light green) area are observed. The size of the
protrusion is mostly uniform and the diameter is ~100 nm.

− −Fig. 2. (a) STM image of √ 3 × √ 43 Pb/Si(111). (b-h) zero bias conductance mappings in the same field of view with (a) taken under theout-of-plane magnetic field of 0, 30 mT, 50 mT, 80 mT, 100 mT,
150 mT, and 400 mT, respectively.

ISSP Activity Report 201911

The number of the protrusions increases with the magnetic
field, and the ZBC value at the center of the protrusions isalmost same as the saturated ZBC measured at high magnetic
fields (e.g. 400 mT of Fig. 2(h)). These features lead us to
identify these protrusions as a vortex. We noticed in the
mapping of 80 and 100 mT (Figs. 2(e, f)) that the vortices
are formed only around the middle of wide terraces, apparently repelled from the step edges. In a narrow terrace thatis observed vertically around the center of the images, novortices are found. The apparent repelling of vortices by
step edges can be explained with the presence of Josephson
vortices at the step edges [1]. A Josephson vortex, formed
at a Josephson junction, has an extended core along thejunction with suppressed breaking of superconductivity,
and therefore appeared dark (blue) along the junction, that
is, along the step edges in our case. Since all the vortices
including Josephson’s exhibit repulsive interaction with eachother, the conventional vortices seem repelled from the stepedges.
In parallel with the vortex formation, the amount of ZBC
behind the vortices gradually increases with the appliedmagnetic field. At 150 mT (Fig. 2(g)), the vortices almost
lose their contrast with the background, which signals saturation of ZBC. Strikingly, in the narrow terrace, ZBC is still
low, clearly demonstrating suppression of the superconductivity breaking there. In order to break the superconductivityof the narrow terrace, further increase in the magnetic field
was required up to 400 mT (Fig. 2(h)), where all the area
reached the saturated ZBC value. The spatially resolved ZBC
evolution presented in Fig. 2 clearly demonstrates that thefield that makes ZBC saturated, which corresponds to thecritical magnetic field, is larger in the narrow terrace than thewide terraces.
From the ZBC evolutions we then investigated how thecritical field (Hc2) depends on the terrace width w. For thequantitative analysis we first estimated Hc2 at various sites bymeasuring the amount of the out-of-plane magnetic field thatsaturates ZBC, and then dependence of the estimated Hc2 onterrace width w was investigated. Our analysis indicated aclear crossover around w = 200 nm; for w > 200 nm Hc2 isconstant whereas for w < 200 nm Hc2 increases steeply withthe reduction in w.
According to the Ginzburg-Landau (GL) equation,
H c2 of low dimensional superconductors whose cross−section is narrower than 2√ 2 ξ is given by a formula of Hc2 =2
4 0/πw , where w is the width (the length of short side) of
the cross-section and 0 is magnetic flux quantum. We thus
expected our Hc2 measured on narrow terraces (< 200 nm)
are also explained with the formula. However, Hc2 of our
step-confined terraces was found markedly larger than theformula. In order to explain our results, we had to introduce a width-reduction factor w0 in the formula as Hc2 =4 0/π(w-w0)2, and found good agreements with w0 = 37 nm.
The effective reduction in terrace width is probably due tothe presence of Josephson vortices; their presence effectively
reduces the terrace width through the modification of theboundary condition at the edges. Based on our experimental
results we thus conclude that the step confinement makes thesuperconductor tolerant against the out-of-plane magnetic
field more effectively than the geometrical confinement. It
should be noted here that since the steps work as a Josephson
junction, the superconductivity is not totally disconnected;
coherent supercurrent flows across the steps, which is an
important aspect for practical applications.

12

ISSP Activity Report 2019

Reference[1] S. Yoshizawa et al., Phys. Rev. Lett. 113, 247004 (2014).
Authors
F. Oguro, Y. Sato, K. Asakawa, M. Haze, and Y. Hasegawa

Carrier Transport in Gradient-Doped
Photoelectrochemical Electrodes
Lippmaa GroupThe interest in developing electrode materials for photoelectrochemical water splitting cells stems from a visionof a sustainable and pollution-free hydrogen-based energy
cycle. In essence, the technique is reliant on the development of wide-gap semiconductor materials that are electrochemically and structurally stable over an extended time
period, measured in years, in a hydrogen or oxygen evolution
reaction under sunlight illumination. Perovskite titanates
such as SrTiO3 provide the prerequisite stability in water, butsuffer from a variety of intrinsic factors that rate-limit thesolar-to-chemical energy conversion process. The primaryrate-limiting issues are the non-optimal band gap of 3.2
eV and a short, sub nanosecond photocarrier lifetime. Theband gap can be brought down closer to the optimal value ofaround 2 eV by doping, but adding dopants to the crystal also
tends to further shorten the carrier lifetime to picosecond
range, negating any possibility of high-efficiency diffusive
photocarrier transport from the bulk of the semiconductor to
the water interface to drive the water splitting reaction.
We have recently attempted to determine the role ofTi-site dopants on the energy conversion efficiency underultraviolet band-gap excitation using non-doped andNb-doped SrTiO3 single crystals (A-D) shown in Fig. 1.

Fig. 1. (A to D) Nb:SrTiO3 single-crystal electrode materials, withdoping levels of A:0%, B:1%, C:0.1%, D:0.04%. (A-D) photoelectrochemical cell configuration. Electrode crystal shown in violet, surface
depletion layer in yellow. (E,F) Cell configuration for thin film samples
consisting of a SrTiO3 film (yellow) on a metallic Nb:SrTiO3 substrate(violet).

Fig. 2. Illustration of energy conversion efficiency, which is proportional to the cyclic voltammetry current for crystals A to F. The atomic
force microscope images for films E and F illustrate the difference insurface morphology related to lower (E) and higher (F) point defectdensities in the films.

The corresponding cyclic voltammetry curves are shownin Fig. 2, where the current density is directly proportional
to the efficiency of the energy conversion process, i.e., thenumber of generated gas molecules. The photoresponse ofa non-doped 0.5-mm-thick SrTiO3 crystal (A) is zero due tothe large resistance of the insulating crystal, which preventscurrent flow in an electrochemical cell (PEC) illustrated inFig. 1(A-D). Photoinduced holes in the surface depletion
layer of the substrate crystal, marked with a yellow gradientin the PEC diagram in Fig. 1, drive the oxygen evolution
reaction but the short lifetime of photocarriers prevents
diffusive photoelectron transport through the bulk part of thecrystal, stopping the water splitting reaction.
Electron transport becomes possible when bulk conductivity is induced by slight Nb doping of SrTiO3 at the Ti site.
As shown in Fig. 2, the efficiency gradually increases as thedoping level is reduced from 1% to 0.04% (B to D). Further
doping reduction will lead to reduced efficiency due toincreasing internal resistance of the substrate crystals.
Improvement of the PEC efficiency can be achieved witha bilayer heterostructure design that combines a non-doped
defect-free SrTiO3 crystal in the ~100 nm thick surface
depletion region of the electrode with a slightly-doped
Nb:SrTiO3 substrate, illustrated in Fig. 1(E,F). Photocarrier recombination losses are minimized and extraction
efficiency maximized in the depletion region where thehigh internal field associated with the surface band bending
drives fast carrier transport, whereas bulk doping is used topromote electron transport in the bulk diffusive region of theelectrode. Ideally, a continuously varying doping gradientcould be used to match the bulk doping level to the width of
the surface depletion layer by growing a crystal with a depthdirection gradient of the doping level.
As a simplified demonstration of this concept, we grewa high-crystallinity film with a minimal point defect density
and an atomically flat surface morphology (Fig. 2, E) on ahighly-doped Nb:SrTiO3 substrate [1]. The importance of
defect density control can be seen in a comparison electrode,which was grown at a low temperature and thus contained ahigh density of point defects (Fig. 2, F). The energy conversion performance of the defect-rich film was, as expected,
nearly zero.
This work demonstrates the importance of point defectdensity control in PEC electrode materials and shows that
depth-graded doping control can be a viable strategy fordesigning efficient hydrogen generation photoelectrochemical electrodes.

The Roles of Step-Site and Zinc in
Surface Chemistry of Formic Acid on
Clean and Zn-mModified Cu(111)and Cu(997) Surfaces
Yoshinobu Group
Methanol is of great interest as a source of futurehydrogen energy systems, because it is a useful chemicalthat can produce hydrogen. On the other hand, the synthesisof methanol from CO2 and H2 (CO2 + 3H2 → CH3OH +H2O) is one of the effective use of CO2, where the Cu/ZnO
catalyst has been used for this reaction. However, the detailsof reaction mechanism including intermediate species havenot been fully elucidated yet. The chemistry of formic acid(HCOOH) on Cu surfaces is important, because the formate
species (HCOO) is one of the stable intermediate species inmethanol synthesis.
In this study, we systematically investigated the adsorption, desorption and decomposition of formic acid (HCOOH)
on Cu(111), Cu(997), Zn-Cu(111) and Zn-Cu(997)using high-resolution X-ray photoelectron spectroscopy(HR-XPS), temperature programmed desorption (TPD) andinfrared reflection absorption spectroscopy (IRAS) [1]. On
the clean Cu(111) surface, 13% of formic acid molecules
adsorbed at 83 K were dissociated to form bidentate formate
species by heating at 300 K (Fig. 1a); however, on the
Zn-Cu(111) surface, only 4% or less of adsorbed HCOOH
were dissociated into the bidentate formate species (Fig. 1b).
On the other hand, 13% of adsorbed HCOOH were alreadydissociated into monodentate formate species on Cu(997)

Reference[1] S. Kawasaki, R. Takahashi, and M. Lippmaa, J. Phys. Chem. C,
123, 15551 (2019).
Authors
S. Kawasakia, R. Takahashi, and M. Lippmaa
aNIMS

Fig. 1. C 1s XPS spectra of formic acid and formate species as afunction of temperature on (a) Cu(111), (b) Zn-Cu(111), (c) Cu(997)
and (d) Zn-Cu(997)

ISSP Activity Report 201913

even at 83 K and 17% of adsorbed formic acid molecules
were transformed to bidentate formate species by heating(Fig.1c). Thus, the stepped Cu surface has higher reactivity
for HCOOH dissociation at low temperature. On the
Zn-Cu(997) surface, 20% of formic acid became bidentate
formate species in contrast to the case with Zn-Cu(111) (Fig.
1d); the Zn deposited Cu step surface shows special activity
for adsorption and dissociation of formic acid.
The desorption peak maxima of the formate decomposition products (CO2 and H2) on Zn-Cu(997) were shifted tohigher temperature than those on Cu(997) in TPD results.
Thus, the Zn on Cu surfaces plays an important role in thestabilization of formate species, which probably leads to thedecrease in the activation barrier for hydrogenation on the
Zn-Cu surface. The bidentate formate species at the Zn-Cu
sites can remain after heating at 472 K on Zn-Cu(997); we
found that the formate species at Zn-Cu step sites are further
stabilized. Therefore, in the real Zn-Cu catalysts that have
many step sites, we think that the synergy by the Zn and Cu
step site can play a vital role in methanol synthesis.
Reference[1] Y. Shiozawa, T. Koitaya, K. Mukai, S. Yoshimoto, and J. Yoshinobu,
J. Chem. Phys. 152, 044703 (2020).
AuthorJ. Yoshinobu

The Structural Study on Microbial
Rhodopsins and the Characterizationof New Microbial Rhodopsin Families
Inoue Group
Rhodopsin is photo-receptive heptahelical transmembrane protein in which a retinal chromophore is covalently
bound to a conserved lysine residue in the seventh transmembrane helix (TM7), and animal and microbial rhodopsin
families are known so far. Animal rhodopsins are present
in animal retina to transfer visual signal to brain and arealso related to non-visual light sensing in various tissues.
Microbial rhodopsins show diverse functions: light-driven
ion pump, light-gated ion channel, phototactic sensor, lightdependent regulation of gene expression and enzyme, andso on. Both types of rhodopsins are being widely used in
optogenetics to control various cellular events, such as neuralactivity, gene expression, dynamic protein localization, andso on, by light.

Fig. 1. The x-ray crystallographic structure of HeR

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ISSP Activity Report 2019

Recently, we discovered the third class of rhodopsin,
heliorhodopsin (HeR), which is evolutionally distinct fromboth of microbial and animal rhodopsins. In 2019, we
reported the three-dimensional structure of HeR at atomic
level by the x-ray crystallographic analysis (Fig. 1) [1].
It revealed that HeR forms dimers and a fenestration ispresent near the β-ionone ring of the retinal chromophore.
The biochemical experiment suggested that this fenestration is used for the uptake of the retinal chromophore fromthe environment. This molecular character unique for HeR
is considered to be physiologically important for microorganisms having HeR without retinal synthetic genes.
Also, the bioinformatic analysis suggested that, while HeR
is widely distributed in many gram-positive bacteria, nogram-negative bacteria do not have HeR in their genomes.
Because many typical microbial rhodopsins are used bymany gram-negative bacteria, the absence of HeR in themis a highly unexpected fact suggesting that the physiological
function of HeR would be related to the structure of thecellular membrane of gram-positive bacteria without outermembranes. The study on the ultrafast photoisomerization
process of the retinal chromophore in HeR revealed that its
isomerization process is similar to those of typical microbial rhodopsins despite of considerably different amino acidresidues surrounding the chromophore. A convergent evolution may have occurred in typical microbial rhodopsins and
HeR to achieve efficient retinal isomerization with highquantum yields.
The three-dimensional atomic structure of Gloeobacterrhodopsin (GR) was solved by the x-ray crystallographic
analysis. The electron microscopic observation revealed that
GR exists as a pentamer, and the structural detail obtained inour study will provide new insights to understand the mechanism of oligomerization of membrane protein.
A new type of rhodopsin showing unique isomerization
process and microbial rhodopsin without retinal binding
lysine (Rh-noK) were also identified from bacteria [2]. The
former has a new type of amino acid residues in the TM3
consisting of threonine, alanine and threonine called the“TAT motif” at the position where typical proton pumping
rhodopsin has the DTD (aspartic acid-threonine-asparticacid) or DTE (aspartic acid-threonine-glutamic acid) motifs.
In the study of Rh-noK, we revealed that ca. 10% of 5,558

Fig. 2. The phylogenetic tree of microbial rhodopsins. The Rh-noK
sub-family is shown in cyan.

microbial rhodopsins do not have the lysine residue in TM7
which typically is used to bind the retinal chromophore bymaking a covalent Schiff base linkage (Fig. 2). A colored
protein was formed by introducing a lysine residue at thisposition, and, interestingly, additional introduction of an
aspartate functioning as a counterion to the protonatedretinal Schiff-base recovered the light-driven outward proton
pumping function. This suggests that the Rh-noK protein
was recently evolved from natural outward proton pumping
rhodopsin, and most of structural elements important for thepump function has been retained even after the lack of theretinal binding lysine and counterion aspartate. The physiological roles of TAT rhodopsin and Rh-noK have not been
revealed yet, and they will be investigated in the near future.
References[1] W. Shihoya, K. Inoue et al., Nature 574, 132 (2019).
[2] C. Kataoka, K. Inoue et al., J. Phys. Chem. Lett. 10, 5117 (2019).
Authors
K. Inoue, T. Nagata, and H. Yawo

Electrical Manipulation of a Topological
Antiferromagnetic State
Nakatsuji, Otani, and Miwa Groups
Recently, materials with nontrivial band topology haveattracted considerable attention due to their novel physicalproperties. One such example is a Weyl semimetal, in which
two non-degenerate bands linearly touch in momentum
space, forming gapless Weyl fermions with different
chiralities in a time-reversal-symmetry (TRS) or inversionsymmetry breaking state. These touching points or Weylnodes act as topologically protected, unit-strength monopoles
or antimonopoles of underlying Berry curvature such as alarge anomalous Hall effect (AHE) and chiral anomaly. The
electrical manipulation of these novel properties becomes
an important topic for developing new technologies utilizing
novel topological state. For this purpose, TRS-breaking or

Fig. 1. (a) Mn3Sn crystal structure and inverse triangular spin (ITS)
structure. The large blue and red spheres (small gray and black spheres)
represent Mn atoms (Sn atoms) at z = 0 and 1/2, respectively. The Mn
magnetic moments (light blue and pink cylindrical arrows) lie within
the kagome-layer with the AB-AB stacking sequence and form the
ITS structure at room temperature. The spin structure on the kagome
bilayers can be viewed as a ferroic ordering of a cluster magnetic
octupole. (b) Left: cluster magnetic octupole (orange cylindrical arrow)consisting of the six spins on the kagome bilayer. Right: schematic
distribution of the Weyl points near the Fermi energy in the momentum
space (kx-ky plane at kz = 0) for the magnetic structure shown in theleft-side figure. Red and blue spheres correspond to Weyl nodes, which
respectively act as sources (+) and drains (-) of the Berry curvature(green arrows). Inset: three-dimensional schematic picture of a pair of
Weyl nodes.

magnetic Weyl semimetals would be suitable owing to theirmagnetic texture. Moreover, given the prospects of antiferromagnetic (AF) spintronics for realizing high-density devices
with ultrafast operation [1], electrical manipulation of an AF
Weyl metal is ideal, but have not yet been reported. In thisstudy, we demonstrate the electrical switching of a topological AF state and its detection by AHE at room temperature
in a Weyl antiferromagnet Mn3Sn by using spin-orbit torque(SOT) switching method.
Mn3Sn has a hexagonal D019 structure with the ABABstacking sequence of a (0001)-kagome layer of Mn, andthe geometrical frustration leads to a three-sublattice
non-collinear AF ordering of Mn spins below the Néel
temperature TN ~ 430 K (Fig. 1(a)) [2]. The magnetic
octupole’s polarization direction determines the locationof Weyl nodes and the associated distribution of the Berrycurvature in the momentum space (Fig. 1(b) right). To
induce possible SOT switching in Mn3Sn, we prepared the
Mn 3Sn/nonmagnetic metal (NM = Pt, W, Cu) bilayer
devices. Figure 2(a) shows the schematic image of the
SOT switching in Mn3Sn/Pt bilayer devices. When an
electrical current flows into the Pt layer, a spin polarized current generated by the spin Hall effect of Pt
induces the SOT on the Mn 3Sn layer and causes theswitching of the polarization direction of the magnetic
octupole. The measurement configuration and optical
micrograph of the fabricated bilayer Hall bar devices
are shown in Fig. 2(b). In our study, we first perform themagnetic field switching of the Hall voltage VH by using
an out-of-plane magnetic field Hz with a read current of
0.2 mA. A clear hysteresis of V H with the zero-fieldchange of ΔVHfield (= VH(+Hz→0) − VH(−Hz→0)) is observed(Fig. 2(c)). To examine the possible SOT switching ofFig. 2. (a) Schematic image for the spin-orbit torque switching. The
spin-polarized current (green cylindrical arrows on yellow spheres)
generated in Pt exerts a spin-orbit torque, causing the switching of thepolarization axis of the cluster magnetic octupole (orange cylindricalarrow) in the polycrystalline Mn3Sn under a write current and a bias
field along the x-direction. (b) Measurement configuration and optical
micrograph of the fabricated Mn3Sn-nonmagnet bilayer Hall bar
devices. (c) Hall voltage VH vs. magnetic field along the z-direction Hz
for the Mn3Sn/Pt 7.2 nm device at room temperature. Inset: Schematic
figures illustrating the direction of the cluster magnetic octupole. (d)Hall voltage VH vs. write current Iwrite for the Pt 7.2 nm, Cu 5 nm, andW 7.2 nm devices at room temperature. The Hall voltage is normalized
by the zero-field Hall voltage |ΔVHfield| in the magnetic field dependence for each sample.

ISSP Activity Report 201915

Mn3Sn, we pass a 100 ms write-pulse current Iwrite along thex-direction; then, we wait for 600 ms after the pulse current
and measure VH with a 0.2 mA read current. Fig. 2(d) shows
VH as a function of Iwrite in Pt, W, and Cu devices. For the
NM = Pt (spin Hall angle θSH > 0), a clear negative (positive)
jump appeared in the Hall voltage under a positive (negative)
current larger than a critical threshold write-current Ic witha bias field Hx along the current direction x. The magnitudeof the jump reaches ~30 % of the total Hall voltage change|ΔVHfield | in the field sweep measurements. To confirm that
this switching of VH is related to the SOT from the spin
Hall effect in the NM layer, we prepared NM = W (θSH < 0)and Cu (θSH ~ 0) instead of Pt. For NM = W, the switchingpolarity is opposite to the Pt one, while for NM = Cu, there
is almost no hysteresis with the electrical current cycle. The
difference in switching polarity between Pt and W devices
and the absence of switching in Cu devices cannot be
accounted for by the Oersted field generated by the electricalcurrent but agree well with the sign of θSH of the NM layer.
These results demonstrate that SOT from the NM layer
induces the perpendicular switching of the AF domain andthus manipulates the direction of Weyl nodes.
In recent years, utilizing antiferromagnets in spintronics
devices have attracted significant attention as its vanishingsmall stray fields and much faster spin dynamics than ferromagnets [1]. Our electrical switching measurement of AF
Weyl metals is made by using the same protocol as the oneused for ferromagnetic metals [3,4]. Moreover, the switchingor critical write current density Jc in the NM layer is foundreasonably small. It is estimated to be 2 × 1011 A/m2 for
7.2 nm thick Pt and 5 × 1010 A/m2 for 7.2 nm thick W
devices, which are smaller than the original values reported
for the first observations of the electrical switching in
the NM/FM devices (Jc ~ 1012 A/m2) [3,4]. These results
indicate that topological antiferromagnets may replace ferromagnets in spintronics devices.
In summary, we demonstrated the electrical switchingof Weyl antiferromagnets Mn 3Sn by using Mn 3Sn/NM
bilayer devices. Our findings indicate that SOT switching isa useful tool for electrically manipulating the distribution of
Weyl points and Berry curvature in momentum space. Theseobservations may lead to further scientific and technologicaladvances in topological magnetism and antiferromagnetic
spintronics [5].
References[1] T. Jungwirth et al., Nat. Nanotechnol. 11, 231 (2016).
[2] S. Nakatsuji, N. Kiyohara, and T. Higo. Nature 527, 212 (2015).
[3] I. M. Miron et al., Nature 476, 189 (2011).
[4] L. Liu et al., Science 336, 555 (2012).
[5] H. Tsai, T. Higo, K. Kondou, T. Nomoto, A. Sakai, A. Kobayashi,
T. Nakano, K. Yakushiji, R. Arita, S. Miwa, Y. Otani, and S. Nakatsuji,
Nature 580, 608 (2020).

Large Transverse Thermoelectric Effect inIron-Based Binary Ferromagnets
Nakatsuji and Miwa Groups
Thermoelectricity, conversion of heat current into
electric energy, provides key technology for versatile energy
harvesting and heat current sensors. To date, the technology
has relied on the longitudinal thermoelectric response known
as the Seebeck effect. Its transverse counterpart in ferromagnets, the anomalous Nernst effect (ANE), has gained
significant attention, as it has a number of potential benefits[1,2]. For example, the transverse geometry of the Nernst
effect enables the efficient, large area and flexible coverageof a curved heat source (Fig. 1(a)). Moreover, the transverse
geometry is hypothetically better suited for thermoelectric conversion, as the Ettingshausen heat current should
support the Nernst voltage while the Peltier heat current may
suppress the Seebeck voltage [3]. However, the anomalous
Nernst effect is too small compared to the Seebeck effect forany thermoelectric application. Thus, it is essential to design
a new class of materials that exhibit a large ANE at zeromagnetic field.
To find candidate compounds efficiently, we carried out
a high-throughput calculation to screen materials without
synthesizing them first. Here we found two iron-based cubic
compounds Fe3X (where X is Ga or Al) as materials suitablefor designing such low-cost, flexible thermoelectric devices,reaching about 6 μVK-1 and 4 μVK-1 at room temperature,
respectively, close to the highest value reported so far. Our
successful fabrication of epitaxial Fe3Ga and Fe3Al thinfilms enables us to obtain a large ANE of about 4 μVK-1 and
2 μVK-1 at room temperature using an in-plane temperature gradient. Moreover, these Fe3Ga and Fe3Al films
have in-plane magnetization with a coercivity BC of about
40 Oe and 20 Oe, respectively, and exhibit a spontaneous
ANE at zero field (Fig. 1(b)) for the out-of-plane temperature gradient. These features enable us to design a much
simpler thermoelectric device than the conventional Seebeck
analogues.
The comparison between experiment and theory indicatesthat the Fermi energy tuning to the nodal web is the key
for the substantial enhancement in the transverse thermoelectric coefficient, reaching a value of about 5 AK-1m-1
with logarithmic temperature dependence. Figure 2(a)shows a schematic of the nodal web, a flat band structure
made of interconnected nodal lines. The Berry curvature

Authors

H. Tsai, T. Higo, K. Kondoua, T. Nomotob, A. Sakai, A. Kobayashi,
T. Nakanoc, K. Yakushijic, R. Aritaa, S. Miwa, Y. Otani, and S. Nakatsuji
aRIKEN CEMS
bUniversity of Tokyo
cAIST

Fig. 1. (a) Thermopiles based on the ANE. V, M, and ∆T is the voltage,
magnetization, and temperature difference, respectively. (b) Magnetic
field dependence of the Nernst voltage −Vyx for the thin films of
Fe3Ga, Fe3Al and α-Fe. The temperature gradient in the sample (MgO
substrate/Fe3Ga, Fe3Al, or α-Fe /MgO), ∇Tall, is monitored to be
3.0 Kmm-1. The temperature gradient in the Fe3Ga (Fe3Al) layer isestimated to be ∇T ≈ 0.86 K mm-1 (1.0 K mm-1).

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Fig. 2. (a) Energy dispersion of the conduction band (red) and thevalence band (blue) around the L point on the BZ boundary for Fe3Ga.
The nodal web is made of nodal lines, shown by the yellow lines (thesame as in Fig. 2(b)), along which the flat portions of the conduction
and the valence bands touch around the L point. (b) Contour plot of the
Berry curvature Ωn,z of the lower-energy band n around the L point andnodal lines. The z direction is along [001] parallel to the magnetization.

is particularly enhanced at the momenta connecting theedge of the nodal web around the L point on the Brillouinzone boundary, extending over a quasi-2D area spanned by
the web (Fig. 2(b)). These results suggest that the strongly
enhanced Berry curvature occurs near the momenta originally belonging to the flat nodal web, such as the one aroundthe L point.
Our discovery of the significant spontaneous transverse thermoelectric effects indicates that two iron-based
compounds, Fe 3Ga and Fe 3Al, should be suitable fordesigning low-cost, flexible thermos electric generator byusing their thin-film form. It is vital to enhance the coercivity
further to achieve stable performance in daily use. Finally,
it would be an interesting future direction to look for anenhanced output by combining the ANE with the spin
Seebeck effect, both of which occur in the same transverse
geometry [4].
References[1] A. Sakai et al., Nat. Phys. 14, 1119 (2018).
[2] M. Ikhlas, T. Tomita et al., Nat. Phys. 13, 1085 (2017).
[3] M. Mizuguchi and S. Nakatsuji, Sci. Technol. Adv. Mater. 20, 262(2019).
[4] A. Sakai et al., Nature 581, 53 (2020).

curvature inherent to the linearly dispersing crossing points
between two electronic bands (i.e., the Weyl points) allows
for the emergence of surprisingly large anomalous transporteffects even in antiferromagnets or spin-liquid candidates.
While the WSM is earlier identified experimentally innonmagnetic materials with breaking inversion symmetry[1,2], the search for magnetic WSM states in strongly correlated systems remains challenging yet of great importance,
due to their excellent tunability and appealing potential for
innovative technological applications.
The earliest predicted magnetic WSM is the family of
pyrochlore iridates R2Ir2O7 (where R is a lanthanoid or
yttrium) [3], a 5d electron system featuring noncoplanar
spin configurations in both 5d and 4f electron sectors. The
5d series provides an ideal ground for realizing exotic
topological phases, owing to the comparable strength of
the spin-orbit interaction relative to the Coulomb repulsion, allowing the correlation physics to play a critical role.
Indeed, recent experiments identified Pr2Ir2O7, the metallic
end-member of the R2Ir2O7 family, as a Luttinger semimetal
comprising quadratic band touching of doubly degenerate valence and conduction bands at the Brillouin zone
center Γ near the Fermi level EF (Fig. 1a) [4]. Lattice strain
or magnetic field tuning of the Luttinger semimetal may
engender a rich topological phase diagram, and is considered
a promising route towards realization of a magnetic WSM[5,6].
Recent studies on Pr2Ir2O7 have focused on its bulk
properties, yet the difficulties of applying uniaxial strain on
bulk single crystals leave the magnetic WSM shrouded inmystery. In contrast, thin films allow for control over the
crystal growth orientation and lattice deformation via
compressive or tensile strain imposed by epitaxial latticemismatch with a substrate. Here, we report the transport
properties of our epitaxial Pr2Ir2O7 thin films, which provide
firm evidence for a magnetic WSM state induced by thetensile strain along the surface normal [111] direction [7].

Authors

A. Sakai, S. Minamia, T. Koretsuneb, T. Chen, T. Higo, Y. Wang,
T. Nomotoc, M. Hirayamad, S. Miwa, D. Nishio-Hamane, F. Ishiia,
R. Aritac,d, and S. Nakatsuji
aKanazawa University
bTohoku University
cThe University of Tokyo
dRIKEN CEMS

Strain-Induced Magnetic Weyl
Semimetal in an Epitaxial Thin
Film of a Luttinger Semimetal
Nakatsuji, Lippmaa, Katsumoto,and Kindo Groups
Strong electronic correlations serve as a central threadof highly unusual behaviors in quantum materials, ranging
from metal-insulator transitions to unconventional superconductivity. The interplay of correlated electron physics withrecently discovered novel topological phases establishes a
new, fascinating research direction that awaits a full exploration. A vital example of this kind is the magnetic Weyl
semimetal (WSM), in which the strongly enhanced BerryFig. 1. (a) Band structure of a Luttinger semimetal consisting of
quadratic band touching of 5d electrons at the Γ point near EF (b)Schematic for experimental configurations of magnetotransportmeasurements. (c) Temperature dependence of the spontaneous Hall
resistivity. (d) Magnetoresistance curves as a function of the magnetic
field B measured at 2 K for B || I and B ⊥ I configurations. The solidand dotted lines are up and down sweeps of B, respectively. The
difference between the two curves arises from the chiral anomaly andindicates that the film is in the Weyl semimetal state.

ISSP Activity Report 201917

Fig. 2. (a) Schematic for the experimental configuration of the planar
Hall effect measurements. (b) and (c) Angle dependence of longitudinaland planar Hall resistivities, respectively, obtained at 70K and 9T

Using strained Pr2Ir2O7 thin films, we observed a zerofield Hall effect persisting up to about 50K without detectable spontaneous magnetization (Fig.1c). This onset temperature of the spontaneous Hall effect is much higher than thevalue (~ 1.5K) observed in bulk single crystals and is nearly
two orders of magnitude higher than the exchange coupling(J ~ 0.7K) of Pr 4f moments [8], indicating the breaking oftime-reversal symmetry induced by the magnetic order of
Ir 5d electrons. Thus, the condition for realizing a magnetic
WSM state is fulfilled in the strained thin film. Moreover, we
identified a negative contribution to the magnetoresistancespecific to the chiral anomaly (Fig. 1 b and d) and the planar
Hall effect (Fig. 2); both phenomena are considered thefingerprints of Weyl points lying close to EF [9, 10, 11].
In summary, we succeeded in synthesizing epitaxial thinfilms of Pr2Ir2O7 and revealed key transport signatures of the
WSM under strain tuning. The discovery of strain-induced
magnetic Weyl semimetal state in pyrochlore iridates thinfilms paves a new avenue to explore topological phases instrongly correlated materials.
References[1] B. Q. Lv et al., Phys. Rev. X 5, 031013 (2015).
[2] S.-Y. Xu et al., Science 349, 613 (2015).
[3] X. Wan et al., Phys. Rev. B 83, 205101 (2011).
[4] B. Cheng, T. Ohtsuki et al., Nat. Commun. 8, 2097 (2017).
[5] E.-G. Moon et al., Phys. Rev. Lett. 111, 206401 (2013).
[6] T. Kondo et al., Nat. Commun. 6, 10042 (2015).
[7] T. Ohtsuki et al., Proc. Natl. Acad. Sci. U.S.A. 116, 8803 (2019).
[8] Y. Machida et al., Nature 463, 210 (2010).
[9] D. T. Son and B. Z. Spivak, Phys. Rev. B 88, 104412 (2013).
[10] A. A. Burkov, Phys. Rev. B 96, 041110(R) (2017).
[11] S. Nandy et al., Phys. Rev. Lett. 119, 176804 (2017).

Fig. 1. (a) Temperature dependence of the electric resistivity (left axis)
and 4f-electron contribution (right axis) of PrV2Al20 under various
magnetic fields along [110]. (b) Temperature dependence of the longitudinal magnetoresistance MR of PrV2Al20.

result of the competing interplay between the magnetic
Kondo effect and the Ruderman-Kittle-Kasuya-Yosida(RKKY) interaction among local dipolar moments. Such
NFL often appears at the boundary of magnetic instability
and is attributed to quantum criticality.
Heavy fermion metals hosting multipolar local
moments entail a new route to exotic spin-orbital entangled
quantum phases. In the case of quadrupolar systems, theconventional Kondo effect is replaced by a two-channel
Kondo mechanism, known as the quadrupolar Kondo effect.
Here Kondo entanglement takes place between the quadrupolar moments of f-electrons and the orbital fluctuationsof the conduction electrons, while the conduction electron
spins offer two separated scattering channels. This effectis considered a key mechanism behind the orbital-driven
NFL behavior and quantum critical phenomena. The heavy
fermion superconductor PrV2Al20 possesses a nonmagnetic
ground-state doublet, featuring both electric quadrupoles

Authors
T. Ohtsuki, Z. Tian, A. Endo, M. Halim, S. Katsumoto, Y. Kohama,
K. Kindo, M. Lippmaa, and S. Nakatsuji

Evidence for the Quadrupolar Kondo
Effect in the Heavy Fermion
Superconductor PrV2Al20
Nakatsuji GroupThe non-Fermi liquid (NFL) phase holds abiding fascination owing to its prime connections with unconventional
superconductivity and other intriguing emergent quantum
states in itinerant electron systems. Magnetic heavy-fermion
metals offer some prototypical examples of the NFL as a

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ISSP Activity Report 2019

Fig. 2. Universal scaling behavior of (a) the 4f-electron contribution to
the resistivity and of (b) the magnetic susceptibility measured under a[110] magnetic field.

and magnetic octupoles. It exhibits novel NFL behavior
above the antiferroquadrupolar ordering transition at ambient−−pressure, with ~ √ T dependent resistivity and ~ −√ T magnetic
susceptibility. The relation of this NFL phase with thequadrupolar Kondo effect is yet to be explored.
We report a comprehensive study of the NFL phenomena
in PrV2Al20 single crystals based on magnetoresistance (MR),magnetic susceptibility, and specific heat measurements
obtained under a [110] magnetic field. Upon entering the
NFL regime, we observed a universal scaling behavior
expected for the quadrupolar Kondo lattice, which reveals
the vital role of the quadrupolar Kondo effect in shaping the
NFL phase of PrV2Al20. Deviations from this scaling relation
occur below about 8 K, accompanied by a negative MR anda power-law divergent specific heat. Such behavior signifies
the emergence of an anomalous low-temperature state,
which is likely driven by heavy-fermion coherence in thequadrupolar Kondo lattice or critical quantum fluctuations ofmultipolar moments.
References[1] P. Gegenwart, Q. Si, and F. Steglich, Nat. Phys. 4, 186 (2008).
[2] D. L. Cox and A. Zawadowski, Adv. Phys. 47, 599 (1998).
[3] A. Sakai and S. Nakatsuji, J. Phys. Soc. Jpn. 80, 063701 (2011).
[4] M. Fu et al., J. Phys. Soc. Jpn. 89, 013704 (2020).
Authors
M. Fu, A. Sakai, N. Sogabe, M. Tsujimoto, Y. Matsumotoa, and
S. Nakatsuji
aMax Planck Institute for Solid State Research

Orbital-Driven Giant Anisotropic
Magnetoresistance in the Quadrupolar
Heavy Fermion Superconductor PrV2Al20
Nakatsuji and Sakakibara Groups
The quest for a mechanism that realizes significant
transport anomalies in non-ferromagnetic materials may
spark a breakthrough in developing ultrafast and energyefficient memory devices [1,2]. An example of such transport
anomaly is anisotropic magnetoresistance (AMR), definedas the difference between the resistance with current applied
parallel and perpendicular to the ordered spin direction.
To date, however, the AMR effect found in antiferromagnetic materials is limited to a small value of 1% - 2% [3,4].
Rearrangement of electron orbitals may hold the key tofurther enhancing the AMR in non-ferromagnetic systems, as
it should generate anisotropy in the electronic band structure,
thereby inducing dramatic effects on the transport properties.
A promising discovery along this line is the strongly aniso-

tropic magnetoresistance appearing within the nematic orderphase in iron-based superconductors.
Here, we focus on a cubic heavy fermion compound
PrV2Al20. A unique feature of this material is its nonmagnetic Γ3 ground-state doublet, in which the magnetic dipole
moment is absent, whereas the quadrupole and octupole
moments are active [5], offering an ideal stage for investigating transport phenomena driven solely by electron
orbitals. The strong hybridization of these multipolar
moments with conduction electrons leads to a rich phase
diagram involving a two-stage multipolar order below
0.6–0.7K, non-Fermi-liquid behavior driven by multipolar Kondo effect, and heavy-fermion superconductivity
below about 0.05K at ambient pressure [6]. Under a [100]magnetic field, earlier magnetization measurements revealed
a high-field phase lying between ~11 – 24T below about
1K [7] (Fig. 1a). This high-field phase is likely the result of
rearrangement of the quadrupole moments and therefore is apromising place to explore anisotropic transport properties.
We carried out magnetoresistance measurements underhigh magnetic fields up to 31.4T at the National High
Magnetic Field Laboratory, Tallahassee, USA [8]. Under a[100] magnetic field, we found that, on entering the highfield phase at about 12 T, the rearrangement of quadrupolar
moments yields a sharp jump in the magnetoresistance(ΔMR~100%), with a substantial AMR effect of about 30%(Fig. 1b). This feature signifies a Fermi surface reconstruction within the high-field quadrupolar ordered phase, owing
to the strong hybridization between the local quadrupolar
moment and the conduction electrons. This giant anisotropic
magnetoresistance induced by quadrupole rearrangement
may form the basis of conceptually new memories and information storage using multipolar states.
References[1] S. Nakatsuji, N. Kiyohara, and T. Higo, Nature 527, 212 (2015).
[2] T. Jungwirth et al., Nat. Nanotechnol. 11, 231 (2016).
[3] D. Kriegner et al., Nat. Commun. 7, 11623 (2016).
[4] X. Marti et al., Nat. Mater. 13, 367 (2014).
[5] A. Sakai and S. Nakatsuji, J. Phys. Soc. Jpn. 80, 063701 (2011).
[6] M. Tsujimoto et al., Phys. Rev. Lett. 113, 267001 (2014).
[7] Y. Shimura et al., J. Phys. Soc. Jpn. 82, 043705 (2013).
[8] Y. Shimura et al., Phys. Rev. Lett. 122, 256601 (2019).
Authors
Y. Shimuraa, Q. Zhangb, B. Zengb, D. Rhodesb, R. Schönemannb,
M. Tsujimoto, Y. Matsumotoc, A. Sakai, T. Sakakibara, K. Arakid,
W. Zhengb, Q. Zhoub, L. Balicasb, and S. Nakatsuji
aHiroshima University
bNational High Magnetic Field Laboratory
cMax Planck Institute for Solid State ResearchdNational Defense Academy

Magnetic Field Induced Quantum Phases ina Tensor Network Study of Kitaev Magnets
Kawashima Group

Fig. 1. (a) Temperature-magnetic field (T-B) phase diagram for a [100]magnetic field obtained from the magnetoresistance data. (b) The anisotropic magnetoresistance ratio as a function of magnetic field measured
at 0.45K and 1.6K

Tensor network (TN) is a useful concept in various fields,
not only in the condensed matter theory, but also in data
science and machine learning. Even in the condensed mattertheory alone, the application of the TN concept is multi-fold.
In variational principles calculation, the TN is used as a new
type of variational wave function. In the real-space renormalization group (RG) theory, it serves as a natural representation of a renormalized system. In the pure mathematicalphysics, it is used as a new language for discussing the

ISSP Activity Report 201919

topological nature of the quantum states.
In our previous study [Lee, Kaneko, Okubo andKawashima: Phys. Rev. Lett. 123, 087203 (2019)], we
studied the Kitaev model by the TN representation. We
proposed a new wave function that is extremely simple in the
TN representation but still shares many essential properties
with the ground state of the Kitaev model, such as the quasilong-range correlation, the short-range magnetic correlation, the flux-free property, the Z2 gauge structure, and the
2D Ising universality. We call this state the "loop gas state"because of its mathematical equivalence to the loop gas
model, one of the standard and solvable statistical physicalmodels. We showed that the loop gas state is adiabaticallyconnected to the ground state of the Kitaev model, indicating
a similar role to the AKLT state for the S = 1 AFH chain.
We then extended our method to several other models:S = 1 Kitaev model, and Kitaev-Gamma model. In this study,
we studied field-induced quantum phases in the theoreticalmodel of a real candidate material of Kitaev magnets, i.e.,
α-RuCl3. For this compound, there was an experimental
discovery of the half quantized thermal Hall conductivity,
which initiated a series of theoretical investigations aiming
at finding a concrete connection between the observed
quantum phenomena and the theoretical developments of
the Kitaev spin liquid. Our TN calculation suggested that afield-induced phase appears between the low field zig-zag
magnetic order and the high field polarized state. We foundthat the chiral Kitaev spin liquid occupies an area in thephase diagram, smaller than predicted by other groups.
Specifically, we studied the K-Γ-Γ' model on the honeycomb lattice represented by the following Hamiltonian,αij

H = ∑ H ij

may imply the importance of the thermodynamic limit. The
tensor network method provides us results for infinite system
in contrast to the methods used in the previous ones. At zero
field, there is a transition from KSL to a FM
_ _ (ferromagnetic) phase where spins are aligned in the [111] direction.
However, with a very weak magnetic field (h = 0.005), theFM phase disappears, and a direct phase transition from KSL
to ZZ (zigzag magnetic ordered) occurs. With increasing themagnetic field, the transition from KSL to the P (polarized)
phase occurs at a finite h, where spins start aligning in the[111]-direction.
Apart from the KSL phase, we discovered two
non-magnetic states, NP1 and NP2. These phases arecharacterized by spontaneously-broken 120-degree-latticerotational symmetry. When the magnetic field is tilted sothat the lattice-rotational symmetry is broken by the Hamiltonian, we found that the phase transition between the KSL
and NP2 is continuous in spite that both phases have thesame symmetry. This may indicate the non-trivial topologicalnature of the NP2 phase, which should be clarified in the
future study.
Reference[1] H.-Y. Lee, R. Kaneko, L. E. Chern, T. Okubo, Y. Yamaji,
N. Kawashima, and Y. B. Kim, Nature Communications 11, 1639
(2020)
Authors
H.-Y. Lee a, R. Kaneko b, L. E. Chern c, T. Okubo d, Y. Yamaji d,N. Kawashima, and Y. B. Kimce
aISSP and Korea University
bISSP and Kindai University
cUniversity of Toronto
dThe University of Tokyo
ePerimeter Instituteij

α h
H ij = −∙(Si + Sj) + STi Gα Sj
3where αij = x,y,z depending on the direction of the bond (ij).
The magnetic field is along the [111] direction. The matrix
Gα characterizes the two-body anisotropic interaction, e.g,
for α = z,
⎛ 0 Γ Γʹ ⎞Gz ≡ ⎜ Γ 0 Γʹ ⎜⎝ Γʹ Γʹ K ⎠The matrices for other directions are defined similarly.
In Fig. 1, the obtained phase diagram is presented. The
KSL ground state survives only in a small corner of thephase diagram. It disagrees with the previous results obtainedby 24-site exact diagonalization and DMRG studies, whichsuggested a largely extended KSL phase. The discrepancy

Fig. 1. (a) The magnetization and (b) the flux expectation value of theK-Γ-Γ' model at Γ'= - 0.03. Here "KSL" stands for the chiral Kitaev
spin liquid, "P" for a spin-polarized phase, and "NP1" and "NP2" fornematic paramagnet phase. The red solid line at h = 0 denotes a ferromagnetic phase.

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ISSP Activity Report 2019

Quantum Criticality of Valence
Transition for the Antiferromagnetic
Compound EuCu2Ge2 under Pressure
Uwatoko Group
Most Eu compounds order magnetically because of adivalent electronic state Eu2+. And, valence instability often
occurs in Eu compounds, from the divalent electronic stateof Eu2+ at high temperatures to the nearly nonmagnetic
electronic state Eu3+ at low temperatures, upon changing themagnetic field and pressure. These compounds can be used
to construct a conventional pressure phase diagram with very
similar to the Doniach phase diagram for the Ce compounds.
Recently, chemical- and high-pressure measurements havebeen carried out on single crystals of EuCu2(SixGe1-x)2 with
the ThCr2Si2-type tetragonal structure, which undergoes two
successive transitions at TN ~ 15 K and T'N ~ 9 K on x = 0,
and no magnetic orderings on x = 1, at ambient pressure. TN
slightly increases with increasing x and starts decreasing at
x = 0.5. and TN disappears around x ~ 0.7, revealing a mixedvalence or valence-fluctuating state.
In this report, we present the results of electrical resistivity measurements under pressure that revealed a new
aspect of the quantum criticality on Eu valence transition[1].
Figure 1 shows the temperature dependence of theelectrical resistivity ρ of EuCu2Ge2 under several pressures.
With increasing pressure, the resistivity at room temperature
increases because the c - f hybridization between conduction electrons and 4f electrons is enhanced. TN substantiallythe generalized Kadowaki-Woods plot, was about 510 mJ/(mol K2), suggesting that the effective mass of the quasiparticles is highly enhanced around Pc. From the analysisof the pressure effect on the exponent n of the power law
dependence of the resistivity: ρmag = ρmag0 + BTn, the fit of
the power law to the resistivity data provides valuable information on the pressure dependences of the exponent n of
EuCu2Ge2. It is predicted that n reaches 1.5 for the AF-QCP,
while it reaches 1 for the QCP of the valence transition. Inset
of Fig. 2 shows the pressure dependence of exponent n.
In the magnetic region n is larger than the Fermi liquidvalue n = 2, probably due to electron-magnon scattering.
Approaching Pc, the exponent n decreases as a functionof pressure and approaches n = 1. It suggests that the casecan be explained as QCP of the valence transition while thescenario based on critical AF-QCP cannot be applied to thepresent case [1]. This is the first observation of this phenomenon among the Eu compounds.
Reference

ˉ nuki,[1] J. Gouchi, K. Miyake, W. Iha, M. Hedo, T. Nakama, Y. O
and Y. Uwatoko, J. Phys. Soc. Jpn. 89, 053703 (2020).
Fig. 1. Temperature dependence of electrical resistivity in EuCu2Ge2
under several pressures together with the data for YCu2Si2 as a reference of the phonon parts of EuCu2Ge2. The inset shows the tetragonal
crystal structure of EuCu2Ge2.

increases from 15 K and becomes maximum at about 27
K at 6.2 GPa and then it is unclear in a wide temperature region. These results suggest that the valence of Eu
increases continuously from nearly divalent to trivalent withincreasing pressure. The resistivity at 6.5 GPa indicates noclear magnetic ordering and is typical for a moderate heavyfermion state. Tmax remains up to 6.5 GPa and shifts tohigher temperatures with further increasing pressure.
Figure 2 shows the P vs Néel temperature TN phase
diagram of EuCu2Ge2. With increasing pressure, TN substantially increases from 15 K and becomes maximum at about
27 K at 6.2 GPa. The resistivity at 6.5 GPa indicates noclear magnetic ordering. Note that T'N disappears rapidly
under pressure. In the present case, the Neel temperature
became zero abruptly at around 6.5 GPa. This suggeststhat the valence of Eu increased continuously up to 6.2
GPa, and then the quantum critical point(QCP) of thevalence transition arises abruptly at around Pc = 6.5 GPa.
The electronic specific heat coefficient, estimated from

Fig. 2. Pressure-Néel temperature phase diagram in EuCu2Ge2. The
inset shows pressure dependence of exponent n of the power law ρmag =ρmag0 + BTn of the magnetic resistivity at 0.05 K.

Authors
ˉ nukib, and
J. Gouchi, K. Miyakea, W. Ihab, M. Hedob, T. Nakamab, Y. O
Y. Uwatoko
aOsaka University
bUniversity of the Ryukyus

Kármán-Vortex Cavitation behind
Circular-Cylinder Arrays
Noguchi Group
Cavitation is a phenomenon in which bubbles are generated by local pressure changes in a liquid flow. Since cavitation has adverse effects on fluid machinery such as performance degradation, vibration and noise, and erosion, theelucidation of its mechanism is of great engineering importance. Numerically, cavitation has been mainly studied bysimulations based on the Navier–Stokes equation. However,it requires a bubble seed to simulate a vapor phase so thatit cannot treat the cavitation inception. Here, we directly
simulated the cavitation using molecular dynamics (MD) that

Fig. 1. Snapshots of density (left panels) and vorticity (right panels)
fields. The black circles in the figure represent cylinders. At the hightemperature, T = 2, Kármán vortex is formed without bubble generation. At the lower temperatures, cavitation occurs. A gas phase (thelow-density region in blue color) appears behind the cylinders.

ISSP Activity Report 201921

does not require the assumption of a phase transition modelor an equation of state for the bubble generation.
We employed Lennard-Jones fluids around periodicallyaligned side-by-side cylindrical objects at Reynolds number
Re~100. As shown in the top panels in Fig. 1, a Newtonian
fluid exhibits a Kármán vortex, in which vortexes are periodically generated behind the objects. The neighboring Kármán
vortex is synchronized in the antiphase. This synchronization
amplifies the vibrations acting on the cylinder. We decrease
the temperature to observe the cavitation. At the temperatures
T = 1.3 and 1.25, bubbles are generated in conjunction withthe shedding cycle of the Kármán vortex (the middle panels
in Fig. 1). The Kármán vortex remains synchronized in theanti-phase as in the non-cavitating flow. As the temperature
is further reduced to T = 1.2, the gas-phase region behindthe cylinder is further expanded, and the upper and lower
Kármán vortices become asymmetric (the bottom panels
in Fig. 1). This asymmetric structure is switched by a long
period of time. A similar dynamics is seen at more closely
packed cylindrical arrays in a Newtonian fluid. Thus, thebubbles give an effective increase in the cylindrical diameter.
The change in the vortex structure alters the vibrations
excited by the vortex. Because the generated bubbles inhibit
the propagation of the vibration associated with the ejectionof the vortex, the vibration amplitude decreases and eventually disappears as the cavitation develops.
In summary, the molecular-scale analysis reveals thatbubbles generated near the cylinder significantly change theproperties of the lift and flow fields.
Reference[1] Y. Asano, H. Watanabe, and H. Noguchi, J. Chem. Phys. 152,
034501 (2020).
Authors
Y. Asano, H. Watanabea, and H. Noguchi
aKeio University

Highly Homogeneous Gel without
Spatial Heterogeneity
Shibayama Group
Fabrication of ordered nanostructure is a crucial stepin a wide range of fields, although the typical size of theseobjects is still limited to a scale of µm3 even with current
technologies. Polymer gels are a familiar soft material
consisting of a nanoporous three-dimensional network thatis readily prepared in a large scale, in principle unlimited.
However, application of gels as a nanostructured object isobstructed by the fact that gel networks inevitably have asignificant level of defects including dangling ends, loops,
entanglements, and nonuniform pore sizes, as a result of
the fully stochastic gelation reaction. Numerous attempts
have been made to remove these defects from polymer gels,
including by synthesizing them from monodisperse polymer
chains, by using a relatively uniform cross-linking process
such as a photoreaction, by limiting unfavorable intramolecular reactions via the A-B type cross-coupling of starpolymers, and even by cross-linking polymer chains withmovable cross-linkers. Nevertheless, discernible signs ofspatial defects have been persistently observed in gels. Gels
have been believed to be inherently dis-ordered as a result of
the stochastic reaction.

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ISSP Activity Report 2019

Fig. 1. Illustration of synthesis scheme of highly homogeneous gel via
bond percolation. Four-armed star polymer units were dissolved in agood solvent at a concentration much higher than the chain overlapping limit of the polymers. Small crosslinkers were added into thepolymer solution. The crosslinkers gradually connect the star polymers
and eventually percolate the system. Because there is almost no spatial
defect in this polymer gel, the transparency of this material is extremelyhigh.

In this study, we broke this preconception: we present a
simple but yet universal scheme to fabricate polymer gelswith a highly ordered network. Our strategy is to bring ageometric constraint into the pregel solution so that the
space is always uniformly filled with the starting polymer
units throughout the gelation reaction (Fig. 1). This gelation
framework is known as “bond-percolation” in the classicalpercolation theory. The spatial and temporal heterogeneityof the synthesized gel network is investigated in the Fourier
space by using scattering techniques. Our gel did not show
any signatures of heterogeneity: no static laser speckles(Fig. 2), no anomalous small angle scattering, and fully
ergodic concentration fluctuations (Fig. 3) and ideal rubber
elasticity were observed. These results are completely
different from the widely accepted picture of gels. Because
both the spatial and temporal correlations of polymer chainsin our gels are identical to those of non-crosslinked pre-gel
solutions, we cannot even determine the physical state (sol orgel) of our sample by scattering techniques.
Gels have often been discussed in analogy with glass
because both gels and glass have a highly disordered structure. However, our results suggest that the bond percolation
gel is more like a crystal than glass because almost identicalstar polymers are closely packed in the space and no spatial
defects were detected. The Bragg peaks of the neighboring
polymer units were not observed in this gel because thepolymer chains can fluctuate much more than atoms in the
crystals. This fluctuation of the polymer chains would leadto substantial blurring of the observable correlation between
chains.
The simplicity of our gel preparation scheme will enable
us to synthesize homogeneous gels with highly ordered
network from a variety of polymers with different chemical
structures and functionalities (e.g. polydimethylsiloxane,
poly(acrylic acid), and poly(N-isopropylacrylamide)), which
will open the door to a wide range of new applications.

Fig. 2. Static laser speckle test to visualize the spatial defects in thegels synthesized via the bond percolation and conventional scheme. A
coherent laser beam was directed to the gel samples and the scattered
light was collected using an EMCCD camera. Each image was accumulated for 30 sec to obtain a time-averaged intensity. The bright spots(static laser speckles) in the images denote the static interference fromthe heterogeneous structures in the gels.

Fig. 3. Intensity time correlation function of the highly homogeneous
gel measured with dynamic light scattering at 100 randomly chosen
sample positions. All the intensity correlation functions well overlap,
indicating the high temporal homogeneity in this gel. The calculatedensemble-averaged intensity correlation function were in perfectconsistence with the individual local correlation function, suggesting
the ergodic concentration fluctuations of polymer chains in the highly
homogeneous gel.
Reference[1] X. Li, S. Nakagawa, Y. Tsuji, N. Watanabe, and M. Shibayama,

Science Advances. 5, eaax8647 (2019).
Authors
X. Li and M. Shibayama

Low-energy Excitations ofGlassy Carbon Tetrachloride
Yamamuro Group
There remain many unsolved problems in physicalproperties of glasses. One of the most important problems is
the low-energy excitations (LEE) characteristic to glasses.
A broad excitation peak appears around 2-5 meV in mostof Raman and inelastic neutron scattering (INS) spectra ofglasses. This peak is usually called “boson peak” since thetemperature dependence of the peak intensity is scaled wellby Bose factors. This peak is basically due to a local excitation since the peak position does not depends on momentum
transfer Q. Another interesting phenomenon is the phonon
dispersion which has been observed in network glasses [1].
It seems strange that the glasses have phonon dispersion
relations since they do not have periodicity. Nevertheless,broad dispersion-like excitations actually exist on dynamic
structure factor S(Q,E) planes of glasses. The origins of
the above phenomena should be associated with disordered(non-periodic) but locally-ordered structures of glasses.
However, their microscopic mechanisms are still unknown.
An essential approach to the LEE problems is the INS
study of molecular glasses with simple structures. The study
enables us to make direct comparison with the results ofvarious theoretical and computer simulation studies. Vitrification of simple molecules is not easy owing to their prompt
crystallization on cooling. Hence we utilize the vapor-deposition (VD) technique whose cooling rate is estimated to be
more than 107 Ks-1.
We have measured the INS spectra of VD carbon tetrachloride (CCl4) glass on AMATERAS, J-PARC. Fig. 1(a)Fig. 1. (a) Inelastic neutron scattering spectra of two glassy and one
crystalline states of CCl4 at 6 K. (b) Q dependence of the boson peakintensity integrated over E = 1.5–3.5 meV. Structure factor S(Q) of
glassy CCl4 is also plotted.

shows the S(Q,E) data in the boson peak energy region. A
clear boson peak appeared at around 2.5 meV in the glassy
state while a sharper peak, which corresponds to the Debye
cut-off of the acoustic phonon, at 4.5 meV in the crystalline
state. The annealing at 50 K slightly reduced the intensityof the boson peak in the lower-energy side as observed in
VD molecular glasses [2]. Fig. 1(b) gives the Q dependenceof the boson peak intensity. The intensity has a clear humpat 2.3 Å-1 and 3.4 Å-1 which coincides with the second andthird peak positions in S(Q). This is a similar Q dependence

Fig. 2. S(Q,E)/Q2 color contour map of the glassy CCl4 data at 6 Kfrom which normal phonon contribution proportional to Q2 has been
subtracted in advance.

ISSP Activity Report 201923

to that of the boson peak of SiO2 glass [3]. The phenomenon
is roughly explained by a coupled rotation model of the SiO4
tetrahedral unit. Fig. 3 shows the S(Q,E)/Q2 color contour
map of the data in which normal phonon contribution
proportional to Q2 has been subtracted. It is of interest that,as shown by red curves, the phonon excitation has a clear
dispersion relation starting at Q = 2.3 Å-1 where the boson
peak intensity has a maximum and S(Q) exhibits the second
peak. This is the first observation of the dispersion-like
excitation in molecular glasses. We are now trying a normal
mode analysis based on the local structure determined by thereverse Monte Carlo analysis on the X-ray diffraction data
which was obtained in SPring-8.
References[1] M. Arai, Y. Inamura, T. Otomo, N. Kitamura, S. M. Bennington, and
A. C. Hannon, Physica B 263, 268 (1999).
[2] O. Yamamuro, I. Tsukushi, T. Matsuo, K. Takeda, T. Kanaya, and
K. Kaji, J. Chem. Phys. 106, 2997 (1997).
[3] U. Buchenau, M. Prager, N. Nücker. A. J. Dianoux, N. Ahmad, andW. A. Phillips, Phys. Rev. B 34, 5665 (1986).
Authors
X. Wu, M. Kofua, Y. Mizuno, H. Akiba, T. Kikuchia, S. Kawamuraa,
K. Nakajimaa, and O. Yamamuro
aJ-PARC, JAEA

Novel Excitations near Quantum
Criticality in Geometrically Frustrated
Antiferromagnet CsFeCl3
Masuda GroupFor understanding condensed matter, the investigation of
the collective excitation in low energy range is indispensable.
According to the quantum field theory, the excitation in thesystem with spontaneously symmetry broking is characterized by phase and amplitude fluctuations of order parameters. The former is known as the Nambu-Goldstone (NG)mode, and the latter is called as the amplitude mode. Even
though these modes are usually separated, they are hybridized under some conditions, and interesting phenomena are
induced; for example in a crystal lattice system, acoustic
phonon (NG mode) and optical phonon (amplitude mode)
are hybridized through anharmonic terms in a thermoelectricmaterial PbTe, which renormalizes the phonon spectrum andleads to low thermal conductivity and high figure of meritin thermoelectric property [1]. Such a hybridization effectcould exist in other types of elementary excitations, however,no research has been reported to our knowledge partiallybecause longitudinal mode itself is not trivial.
Spin S = 1 easy-plane antiferromagnet is one of theFig. 1. Schematic diagram of the S = 1 easy-plane antiferromagnet.

In the ordered state, the doublet excited states |±1> splits into |L>and |T>. Here, the former and latter have longitudinal and transverse fluctuations, respectively.

24

ISSP Activity Report 2019

Fig. 2. Inelastic neutron scattering spectra. The spectra obtained at achopper spectrometer under (A) 0.0 GPa at 6 K, (B) 0.3 GPa at 2.7 K
and (C) 1.4 GPa at 0.9 K sliced by the energy transfer - wave vector(ħω – q) plane for q = (-k, 2k, 0). The yellow circles, squares, and red
diamonds are the peak positions of the excitations obtained from theconstant-q scans using a triple-axis spectrometer. The solid yellow
curves are the dispersions calculated by ESW. Calculated neutron crosssection by the ESW under (D) 1.4 GPa at 0 K. Calculated neutron
cross-section in the absence of the off-diagonal elements under (E) 1.4
GPa at 0 K. The black and red solid curves in (D) and (E) are gaplessand gapped modes, respectively.

prototypical quantum spin systems that allows to explore thequantum phase transition (QPT) [2]. When the anisotropy
D is large, the ground state is a quantum disordered (QD)
singlet as shown in Fig. 1 left panel. When D is small andthe exchange interaction is large, the ground state is magnetically long-range ordered state. A remarkable feature in therenormalized energy scheme in Fig. 1 right panel is that thesecond excited state can be excited only by the longitudinalcomponent of spin operator S||, meaning that the longitudinalmode is allowed in the system. Because the geometricalfrustration in magnets could induce the hybridization of thetransverse (T) and longitudinal (L) modes, spin S = 1 easyplane antiferromagnet having geometrically frustrated latticeis the best playground for the research of hybridized modes
in magnetic material.
CsFeCl3 is the S = 1 easy-plane triangular antiferromagnet. The inelastic neutron scattering (INS) study atambient pressure revealed that the ferromagnetic chains
along the crystallographic c axis are antiferromagneticallycoupled in the ab plane [3]. The ground state is the QD statebecause of large single-ion anisotropy. The magnetic susceptibility measurement under pressures exhibited a pressureinduced magnetic order above a critical pressure of about
0.9 GPa [4]. Owing to the strong easy-plane anisotropy,
the ordered moment aligns in the ab plane; the neutron
diffraction evidenced the noncollinear 120° structure in the
LRO phase [5]. CsFeCl3 is, thus, a promising host for thepressure-induced QPT in the geometrically frustrated lattice.
In 2019 our group reported a new hybridization of the phaseand amplitude fluctuations of the order parameter near QCP
in CsFeCl3 [6].
The INS spectrum measured at 0.0 GPa by using chopper
spectrometer in Fig. 2A exhibits a single dispersive excitation with the energy gap of 0.6 meV at the wave vectors
q = (-k, 2k, 0) for k = 1/3 and 2/3. The energy gap at 0.3 GPain Fig. 2B becomes softened when approaching the orderedstate. A qualitatively different spectrum is observed in theordered state at 1.4 GP in Fig. 2C. A well-defined gaplessexcitation emerges at k = 1/3 and 2/3 and another dispersive excitation are observed in the higher energy range.
The INS spectra were collected also by using a triple-axis
spectrometer in order to cover wide ħω – q range, and theextracted peak energies are overplotted by open symbols in
Figs 2A-2C. At 1.4 GPa, the spectral lineshape at k = 5/6
was reproduced by double Lorentzians with broad widths
which is reflected by large errorbars. The dispersion relations
calculated by the extended spin-wave theory (ESW) [7]
are indicated by the solid yellow curves. The calculationis consistent with the experiment both in the QD and LRO
phases.
In ESW calculation one can notice that noncollinearityof the magnetic structure makes off-diagonal elements in the
Hamiltonian nonzero, leading to the hybridization of L and
T modes in one-magnon process. To understand the effectsof LT-hybridization, we demonstrate the INS spectra after
dropping the off-diagonal element. The results are shownin Figs. 2E, where the black-gapless (red-gapped) modes
are pure transverse (longitudinal) modes in this case. The
result is inconsistent with the experiment in Fig. 2C. When
LT-hybridization is taken into account, the off-diagonal
elements lead to anticross of the modes at k~ 5/6 in Fig. 2D,
and novel magnetic excitations are formed; both gaplessand gapped modes are accompanied by strong longitudinal
and transverse fluctuations. The result is consistent with theexperiment, and, thus, the LT-hybridization plays an important role in magnon dynamics in noncollinear magnet near
QCP.
Since the newly found excitation exists in a noncollinear
spin structure, the search of the excitation in different typesof noncollinear structures such as cycloidal structure, all-inall-out structure, and skyrmion lattice would be interesting
topics. The search of the hybridized mode in other systems
including charge density wave, spin density wave, and ultracold atoms would be important. Finally, the effect of hybridization to the lifetime of the magnon and other elementary
excitations would be also interesting.
References[1] O. Delaire, J. Ma, K. Marty, A. F. May, M. A. McGuire, M. H. Du,
D. J. Singh, A. Podlesnyak, G. Ehlers, M. D. Lumsden, and B. C. Sales,Nat. Mat. 10, 614 (2011).
[2] M. Matsumoto and M. Koga, J. Phys. Soc. Jpn. 76, 073709 (2007).
[3] H. Yoshizawa,W. Kozukue, and K. Hirakawa, J. Phys. Soc. Jpn. 49,
144 (1980).
[4] N. Kurita and H. Tanaka, Phys. Rev. B 94, 104409 (2016).
[5] S. Hayashida, O. Zaharko, N. Kurita, H. Tanaka, M. Hagihala,
M. Soda, S. Itoh, Y. Uwatoko, and T. Masuda, Phys. Rev. B 97, 140405(2018).
[6] S. Hayashida, M. Matsumoto, M. Hagihala, N. Kurita, H. Tanaka,
S. Itoh, T. Hong, M. Soda, Y. Uwatoko, and T. Masuda, Sci. Adv. 5,
eaaw5639 (2019).

[7] R. Shiina, H. Shiba, P. Thalmeier, A. Takahashi, and O. Sakai,
J. Phys. Soc. Jpn. 72, 1216 (2003).
Authors

S. Hayashida, M. Matsumotoa, M. Hagihala, N. Kuritab, H.
Tanakab, S. Itohc, T. Hongd, M. Soda, Y. Uwatoko and T. Masuda
aShizuoka University
bTokyo Institute of Technology
cKEK
dOak Ridge National Laboratory

Magnetic Structure and Excitationof Quasi One-Dimensional
Antiferromagnet Ba2CoSi2O7
Masuda GroupThe relationship between magnetism and dielectricity
has been extensively studied. In the multiferroics, the ferroelectrics with the cycloidal and proper-screw magnetic
structures are explained by the spin-current mechanism andthe spin-dependent d–p hybridization mechanism, respectively [1,2]. On the other hand, the multiferroic property
has been reported even on a collinear antiferromagnet. Oneof the maultiferroics with the collinear magnetic structure
is an antiferromagnet Ba2CoGe2O7. Ba2CoGe2O7 with theCo-square lattice shows multiferroic properties, and the
local electric polarization of CoO4 tetrahedra is explainedby the spin-dependent d-p hybridization mechanism [3,4].
In contrast, the anomaly of the dielectric constant in similarmaterial Ba2CoSi2O7 is not observed at the antiferromagnetic transition temperature TN =6 K [5]. Ba2CoSi2O7 has
a distorted crystal structure formed by CoO4 and SiO4
networks, as shown in Fig. 1(a), and two kinds of Co-Co
bonds exist within the b-plane. In order to clarify themagnetic model of Ba2CoSi2O7, the magnetization andneutron scattering measurements have been performed.
In the neutron powder diffraction measurement using thehigh-resolution powder diffractometer ECHIDNA installed at
OPAL, ANSTO, Australia, the magnetic reflections indexedby the propagation vector (1/2, 1/2, 1/2) was observed below
TN = 6 K. By analyzing the powder neutron profile, we
found that a collinear antiferromagnetic structure shown in
Fig. 1(b) was realized below TN = 6 K. The magnetic
moments with the easy axis along the [10-1] form an antiferromagnetic arrangement along [101] and a ferromagnetic
arrangement along [10-1]. In the spin-dependent d-p hybridization mechanism, the local electric polarization of the
CoO4 tetrahedron is almost zero with the magnetic moment
along [10-1]. This is consistent with the dielectric property
where the temperature dependence of the dielectric constant
has no anomaly at TN = 6 K.
We have also measured the Q-dependencies of themagnetic excitations along the b * , [10-1], and [101]directions at 1.5 K to clarify the magnetic correlation of
Ba2CoSi2O7 by using a cold-neutron triple-axis spectrometer(CTAX) installed at HFIR, ORNL, USA. Figure 2(a) shows
the constant-Q scan profiles measured at (h, 1/2, h). Figure2(b) shows the h-dependence of integrated intensities andpeak energies obtained by Gaussian fitting of the constantQ profiles at (h, 1/2, h), which corresponds to the Q-dependence along the [101] direction. The excitation observed at
ħw = 2.9 meV is almost dispersionless, but the integrated

Fig. 1. (a) Crystal structure of Ba2CoSi2O7. (b) Schematic magnetic
structure of Ba2CoSi2O7.

ISSP Activity Report 201925

Authors
M. Sodaa, T. Hongb, M. Avdeevc, H. Yoshizawaa, T. Masuda, and
H. Kawano-Furukawaa,daRIKENbORNL
cANSTOdOchanomizu University

High-Field Ultrasonic Study of
Quadrupole Ordering and Crystal
Symmetry Breaking in CeRhIn5
Tokunaga Group

Fig. 2. (a) Constant-Q scans at (h, 1/2, h) measured at 1.5 K. Data
are shifted by vertical offsets. (b) Integrated intensities and the peakenergies at (h, 1/2, h). Solid lines are the calculated values with theclassical spin-wave theory.

intensity exhibits a clear modulation along the [101] direction. In the measurements along the b* and [10-1] directions,on the other hand, both the neutron intensity and peak energy
show less change. (not shown)
We analyzed the magnetic excitation by using the spin
Hamiltonian in order to clarify the magnetic model including
the magnetic interaction in Ba2CoSi2O7. To explain theobserved magnetic excitation, we consider the one-dimensional antiferromagnet in which the antiferromagnetic chain
is along the [101] direction. We performed the calculations of
the neutron intensity and the dispersion energy for both theeasy-axis and Ising-like antiferromagnet models; two models
cannot be distinguished in the classical spin-wave theory.
The magnetic dispersion relation shown in Fig. 2(b) is reproduced by the one-dimensional antiferromagnet model, as
shown by solid curves.
Our results of the neutron scattering suggest that the
Ba2CoSi2O7 is the one-dimensional antiferromagnet withthe easy-axis spin anisotropy or the Ising-like spin. On theother hand, Ba2CoGe2O7 with the tetragonal structure is
two-dimensional easy-plane antiferromagnet. The neutron
results suggest that the crystal structure affects both themagnetic interaction dimensionality and anisotropy inåkermanite-type materials.
References[1] T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, andY. Tokura. Nature 426, 55 (2003).
[2] S. Seki, Y. Onose, and Y. Tokura. Phys. Rev. Lett. 101 067204(2008).
[3] H. Murakawa, Y. Onose, S. Miyahara, N. Furukawa, and Y. Tokura.
Phys. Rev. Lett. 105, 137202 (2010).
[4] M. Soda, M. Matsumoto, M. Månsson, S. Ohira-Kawamura, K.
Nakajima, R. Shiina, and T. Masuda, Phys. Rev. Lett. 112, 127205(2014).
[5] M. Akaki, J. Tozawa, D. Akahoshi, and H. Kuwahara, J. Phys.:Conf. Ser. 150, 042001 (2009).

26

ISSP Activity Report 2019In a number of strongly correlated electron systems, theelectronic nematic (EN) state characterized by the lackingof the C4±-rotational operations has been focused because
the EN contribution to superconductivity and other exotic
phenomena have been proposed. Recently, the field-induced
EN phase above 30 T has been proposed in the D4h1 tetragonal compound of CeRhIn5 [1,2], which was well known as apressure-induced heavy-fermion superconductor.
To investigate the active representation and the orderparameter of the field-induced EN phase, we performed anultrasonic measurement for CeRhIn5 in pulsed magnetic
fields up to 56 T [3]. The ultrasound technique is a powerfultool to determine the active representation of a phase transition related to the crystal symmetry breaking because soundwaves can induce the symmetry strain belonging to theirreducible representation (IR) of the space group. Furthermore, we can propose the electric quadrupole as an orderparameter of the crystal symmetry breaking and the EN state
in terms of the electric quadrupole-strain interaction, which
is based on the selection rule of group theory.
To identify the active representation of the symmetry
breaking at the EN state, we measured all the elastic
constants of CeRhIn5 that can be detected in the tetragonal
system. As shown in Fig. 1, the transverse elastic constantCT = (C11 − C12)/2 with the B1g IR of D4h shows the anomaly
at BIM = 28.5 T at 1.4 K and 2.1 K. This BIM is consistent
with the previous studies [1, 2]. While CT shows an anomaly,
other elastic constants, which can identify the symmetry
breaking of B2g and Eg IR, do not exhibit anomaly at BIM.
Therefore, our ultrasonic measurements demonstrate theB 1g-type crystal symmetry breaking. Furthermore, theFig. 1. Magnetic field dependence of the transverse elastic constant
ΔCT/CT at several temperatures for B//[001].u(d)The vertical arrows
indicate the metamagnetic transition field Bm
for field up(down)
sweep, the EN transition field B*, and the critical field Bc. The right andleft arrows show hysteresis direction. The propagation direction q andpolarization direction of ultrasound are indicated.

Fig. 2. Schematic view of the B1g-type quadrupole ordering and crystal
symmetry breaking. (a) Crystal structure in the xy plane of CeRhIn5 in
the normal phase. (b) High-field symmetry breaking state of CeRhIn5.
The red arrows indicate the deformation direction of the crystal lattice
due to the strain εx2 - y2 = εxx - εyy.

electronic degree of freedom with the B1g IR, namely theelectric quadrupole Ox2 − y2 ∝ (x2 − y2) /r2, can be the orderparameter of the EN state. This symmetry breaking is attributed by the electric quadrupole-strain coupling written as
HQS = −gx2 − y2 Ox2 − y2 εx2 − y2.
We show the schematic view of the B1g-type ferroic
electric quadrupole ordering and crystal symmetry breaking
in Fig. 2. The square lattice of CeRhIn5 with the tetragonal
crystal structure of D4h1 is drawn in Fig. 2(a). In the fieldinduced EN state, the electric quadrupole Ox2 − y2 appearson the Ce site. The lattice changes from the square of thetetragonal structure to the rectangle of orthorhombic one dueto the quadrupole-strain coupling HQS accompanying thelattice distortion εx2 − y2 = εxx − εyy. A maximal nonisomorphic orthogonal subgroup D2h1 is an appropriate space-groupfor this symmetry lowering from D4h1.
Furthermore, we found the acoustic de Haas-van Alphen(AdHvA) oscillation in CT with the frequency 690 T, which
has not been observed experimentally. On the other hand, thetheoretical study treating 4f electrons as itinerant has shown ahole Fermi surface with the frequency ~ 690 T [4]. Thus, we
proposed the origin of the AdHvA oscillation in terms of thequadrupole-strain coupling in the k-space based on the deformation potential theory [5].
We also discussed the quantum state possessing theelectric quadrupole. The delocalization of 4f electrons andthe in-plane type p-f hybridization are candidate interactions
constructing the quantum state in high fields.

both experimentally and theoretically. One of the intriguing
phenomena in UTe2 recognized in the very early stage is
its large superconducting critical fields. For the magnetic
fields applied along the hard magnetization b-axis, thesuperconducting transition can survive well above the Pauliparamagnetic limit [1,2]. This fact suggests the realization of the long-sought spin-triplet superconductivity. Suchunconventional superconductivity is believed to realize in the
ferromagnetic superconductors (FMSCs), such as URhGeand UCoGe. In the case of UTe2, however, the ground stateis paramagnetic. Here, we introduce our observation ofmetamagnetic transition in UTe2 and discuss the relation
between metamagnetism and superconductivity by comparedto FMSCs [3].
The high-field magnetization was measured by using
the pulse magnets installed in the International MegaGauss
Science Laboratory. Figure 1(b) shows the magnetization curve for the field along the b axis at 1.4 K. At μ0Hm
~ 35 T, magnetization suddenly increases with a large stepof ~0.6 μB. Because of the hysteric behavior against themagnetic field, this metamagnetic transition is of first-order.
From the magnetization curves at various temperatures, wesummarized a magnetic phase diagram of UTe2 in Fig. 1(a).
The field hysteresis disappears above 11 K, indicating theexistence of the critical end point (CEP), and the transitionchanges to crossover. As known in many paramagnets, theenergy scale of metamagnetic transition, μ0Hm, corresponds
to Tχmax, where the temperature dependence of magnetic
susceptibility shows a broad maximum. This relation isfurther supported by the fact that μ0Hm(T) connects toTχmax(μ0H). At almost the same time, the high-field magnetoresistance measurements independently revealed a similarphase diagram [4]. A sharp step-like increase in the resistance across the Hm may reflect the modification of the
Fermi surface, although it is not clear yet. More interestingly,
the superconducting (SC) phase shows a reentrant behavior
above 16 T and is suddenly suppressed above μ0Hm [5] [seeReferences[1] P. J. Moll et al., Nat. Commun. 6, 6663 (2015).
[2] F. Ronning et al., Nature (London) 548, 313 (2017).
[3] R. Kurihara et al., Phys. Rev. B 101, 115125 (2020).
[4] D. Hall et al., Phys. Rev. B 64, 064506 (2001).
[5] M. Kataoka and T. Goto, J. Phys. Soc. Jpn. 62, 4352 (1993).
Authors
R. Kurihara, A. Miyake, M. Tokunaga, Y. Hirosea, and R. Settaia
aNiigata University

Discovery of Metamagnetic
Transition in New Unconventional
Superconductor UTe2
Tokunaga GroupNews of the discovery of unconventional superconductivity in a paramagnetic heavy-fermion system UTe2 at theend of 2018 has excited strongly the researchers working on
the condensed matter physics. Within a few years since thefirst report in arXiv, many new aspects have been unveiled

Fig. 1. (a) Magnetic phase diagram of UTe2 for H // b determined by
Hm and Tcmax. CEP denoted by a diamond is critical end point. (b)Magnetization curve for H // b at 1.4 K. (c) Magnetic field dependenceof the electronic specific heat derived from magnetization curves by theMaxwell relation.

ISSP Activity Report 201927

Fig. 1(a)]. This unusual Tc enhancement can be explained
qualitatively by a simple mass-enhancement model asfollows. Figure 1(c) represents the magnetic-field evolutionof the electronic specific heat g, derived by the thermodynamic Maxwell relation using the temperature dependencies of magnetization at constant fields [3]. With increasing
fields, the γ increases and shows a maximum at Hm. Thisenhancement is also confirmed by the direct specificheat measurement using a pulse magnet in ISSP [6]. Thisenhancement on going to metamagnetic transition indicatesthat the development of the fluctuation evolves around Hm.
This fluctuation may stabilize the SC phase even at highmagnetic fields as has been adapted to explain the reentrant
superconductivity in URhGe. Using a simplified McMillantype formula, the field-enhancement of the superconducting
transition temperature can be reproduced qualitatively [seeRefs. 3 and 6 for more detail and references therein].
Now, it is no doubt that the high-field studies make animportant role to reveal the superconductivity on UTe2. Soon
after our work [4], more exciting phenomena in high fields
were reported [7]: Surprisingly, another SC phase appears at
Hm when the field is applied intermediate angles between thea and c axis. This is in stark contrast to the fact of suppression of SC at Hm for the b axis. Our struggles continue.
References[1] S. Ran, C. Eckberg, Q.-P. Ding, Y. Furukawa, T. Metz, S. R. Saha,
I.-L. Liu, M. Zic, H. Kim, J. Paglione, and N. P. Butch, Science 365,684 (2019).
[2] D. Aoki, A. Nakamura, F. Honda, D. X. Li, Y. Homma, Y.
Shimizu, Y. J. Sato, G. Knebel, J.-P. Brison, A. Pourret, D. Braithwaite,
G. Lapertot, Q. Niu, M. Vališka, H. Harima, and J. Flouquet, J. Phys.
Soc. Jpn. 88, 043702 (2019).
[3] A. Miyake, Y. Shimizu, Y. J. Sato, D. Li, A. Nakamura,Y. Homma, F. Honda, J. Flouquet, M. Tokunaga, and D. Aoki, J. Phys.
Soc. Jpn. 88, 063706 (2019).
[4] W. Knafo, M. Vališka, D. Braithwaite, G. Lapertot, G. Knebel, A.
Pourret, J.-P. Brison, J. Flouquet, and D. Aoki, J. Phys. Soc. Jpn. 88,
063705 (2019).
[5] G. Knebel, W. Knafo, A. Pourret, Q. Niu, M. Vališka, D. Braithwaite, G. Lapertot, M. Nardone, A. Zitouni, S. Mishra, I. Sheikin, G.
Seyfarth, J.-P. Brison, D. Aoki, and J. Flouquet, J. Phys. Soc. Jpn. 88,
063707 (2019).
[6] S. Imajo, Y. Kohama, A. Miyake, C. Dong, J. Flouquet, K. Kindo,
and D. Aoki, J. Phys. Soc. Jpn. 88, 083705 (2019).
[7] S. Ran, I.-L. Liu, Y. S. Eo, D. J. Campbell, P. Neves, W. T.
Fuhrman, S. R. Saha, C. Eckberg, H. Kim, J. Paglione, D. Graf, J.
Singleton, and N. P. Butch, Nat. Phys. 15, 1250 (2019).
Authors
A. Miyake, Y. Shimizua, Y. J. Satoa, D. Lia, A. Nakamuraa, Y. Hommaa,
F. Hondaa, J. Flouquetb, M. Tokunaga, and D. Aokia, baTohoku University
bCEA-Grenoble

Fig. 1. High-magnetic-field X-ray diffraction profiles of the α-phase ofsolid oxygen at 10 K. Vertical dashed lines indicate the positions thatare expected from the previous report [2]. (a) 001 reflection peaks areshown. (b) -111 and -201 peaks are shown. Peaks with * are considered
to be due to impurities on the window of the sample cell.

meaning that the successive phase transitions are not merely
magnetic phase transitions but structural phase transitions.
The γ-phase, β-phase, and α-phase have a cubic, rhombohedral, and monoclinic crystal structure, respectively. The
lowest temperature phase, the α-phase is an antiferromagnet
at a low temperature below 24 K, while the β-phase only
exhibits a short-range antiferromagnetic correlation and the
γ-phase is paramagnetic. We have been sharing the idea thatmagnetic energy between oxygen molecules should play
an important role for having different crystal structure for along time. However, no direct experimental evidence of thestrong spin-lattice coupling had ever been obtained before
the discovery of the novel magnetic-field-induced θ-phase at
120 T [1]. It has been proved that controlling spins induces anovel oxygen crystal.
Microscopic investigation of the crystal lattice of solid
oxygen in magnetic fields is important. Actually, there
was a report of the high magnetic field x-ray diffraction of
the solid oxygen using a synchrotron x-rays up to 8 T andsignificantly large magnetostriction was likely to occur
in the α-phase of solid oxygen [2]. The volume striction
ΔV/V was found to reach around 10-2. In the present study,
we have extended the magnetic field range to 25 T for the
x-ray diffraction experiment.
The high-field XRD experiments have been performedat the Institute for Materials Research of Tohoku University
with a DC magnet up to 5 T, and at BL22XU in SPring- 8
up to 25 T using a pulsed magnet. Pure oxygen gas (purity> 99.99995%) was liquified by cooling into a sample cell
designed for each experiment. For the 5 T DC-magnet
experiment, a CuKα (1.54 Å) characteristic emission line

High-Magnetic-Field X-Ray
Diffraction Study in Solid Oxygen
Y. Matsuda Group
Molecular oxygen is a unique homonuclear diatomic
molecule because it possesses a spin quantum number S = 1.
After M. Faraday had noticed that gaseous oxygen exhibits
magnetism, condensed phases, namely liquid and solid
phases have been extensively studied as intriguing magnetic
materials. Solid oxygen undergoes successive phase transitions with lowering temperature, and three distinct phases,
γ-phase, β-phase, and α-phase appear at 54, 44, and 24 K,
respectively. One of the most intriguing findings on thesethree phases is that they have different crystal symmetries,

28

ISSP Activity Report 2019

Fig. 2. The relative changes of the diffraction plane spacing at 5 T are
shown at different reciprocal vectors.

was used as the x-ray source. The measurement temperature
was controlled to be 10 K. In the 25 T pulse-magnet experiments, the photon energy (wavelength) of the synchrotron
x-ray used is 15 keV (0.8266 Å). The time interval of thesuccessive pulsed magnetic field measurements is 10–20
min, which is necessary for cooling the magnet after heating
due to the discharge for field generation. The variation of themagnetic field ΔB/B during the measurement time (100 μs) isaround 2% [3].
The measured XRD profiles in pulsed magnetic fields
at 10 and 25 T are shown in Fig. 1 along with the zerofield profile. The XRD at 0 T is measured with an exposure
time of 10 ms. The profiles at 10 and 25 T are obtained byaverages of six times and five times the repetition of themeasurements, respectively. The obtained XRD profiles atdifferent magnetic fields seem to be identical at first glance.
In order to confirm the unexpectedly small magnetic
field effect, we have also analyzed the steady field XRD datathat have higher precision in terms of the longer accumulation time. And also, we need to exclude a possibility thatthe dynamics of the crustal lattice is slower than the pulsed
magnetic field of which duration time is 1 ms in this study.
Figure 2 shows the obtained linear magnetostriction
Δd/d at 5 T. The Δd/d of several diffraction plane spacing isfound to be as small as 10-4 which is more than one order ofmagnitude smaller than the values reported previously [2].
The reason for the contradiction between our results
and the previous study is not very clear. One of the possible
causes for the contradiction is that there had been somemechanical influence on the experimental configuration by
applying DC magnetic fields. Small mechanical movementsof measurement apparatuses can cause a change in theobserved XRD peak positions [3].
The high-field XRD experiments on α oxygen at 10 K
has revealed that the linear magnetostriction Δd/d is smaller
than 10−4 T−1 in magnetic fields of up to 25 T [3]. The
absence of the giant magnetostriction in α oxygen is also inagreement with the experimental fact that the magnetic field
induced α-θ transition is first order [1]. The deformation of
the crystal lattice in a magnetic field is not significant below
the critical magnetic field around 100 T. It is likely that adrastic symmetry change in the crystal lattice takes place
discontinuously at the phase transition.

Observation of Quantum Spin-Nematic
Phase in Volborthite
Kohama, Kindo and Hiroi Groups
For a long time, it was believed that matter could exist in
only three different forms, solid, liquid and gas. However, inthe second half of the nineteenth century, it became clear that
not all substances could be described as solid, liquid or gas.
Liquid crystals came of age in the twentieth century, as botha subject of fundamental research and the basis for modern
display technology. Since we know examples of quantum
gases, liquids and solids, it is natural to ask, are there
quantum liquid crystals, too? For a long time, this question
remained a mathematical curiosity. However, in recent years,
potential quantum analogues of a liquid crystal state havebeen discussed in real material, which is called a quantum
spin-nematic state. Its experimental observation has proved
much more challenging, since the order parameter of the spin
nematic state, spin quadrupole moment, is hard to detect withconventional magnetic probes.
In this research, with an exotic frustrated magnet,
volborthite, we provided the possible evidence of quantum
analogue of the nematic crystal, and resolved a long-standing
mystery about the magnetism of volborthite [1]. Here weapplied thermodynamic measurement techniques, the magnetocaloric effect (MCE) and specific heat(C) measurements,
which measure entropy and sensitive to any phase transition
irrespective of the type of the order parameter. The state-ofart experimental capability in IMGSL; high-field calorimetry
in magnetic fields up to 60 T and low temperatures down to
0.5 K, enabled observation of quantum spin-nematic state involborthite.
First, we show the MCE curves obtained in the adiabatic
condition, T(H), in Fig. 1(a). The adiabat T(H) initiallydecreases with increasing fields, before passing a broad
minimum at ~25 T and then increases at higher fields. Below
1.7 K, a notable change occurs as seen in the enlarged
plot (Fig. 1(b)). The broad minimum in T(H) acquires
small dips, indicative of phase transitions at 22.5, 25.5 and27.5 T. Each of these three critical fields has also been foundin measurements of MCE under nearly isothermal conditions

References[1] T. Nomura, Y. H. Matsuda, S. Takeyama, A. Matsuo, K. Kindo, J. L.
Her, and T. C. Kobayashi, Phys. Rev. Lett. 112, 247201 (2014).
[2] K. Katsumata, S. Kimura, U. Staub, Y. Narumi, Y. Tanaka, S.
Shimomura, T. Nakamura, S. W. Lovesey, T. Ishikawa, and H.
Kitamura, J. Phys.: Condens. Matter 17, L235 (2005).
[3] Y. H. Matsuda, A. Shimizu, A. Ikeda, T. Nomura, T. Yajima, T.
Inami, K. Takahashi, T. C. Kobayashi, Phys. Rev. B 100, 214105(2019).
Authors
Y. H. Matsuda, A. Shimizu, A. Ikeda, T. Nomura, T. Yajima, T. Inamia,
K. Takahashib, and T. C. Kobayashic
aNational Institutes for Quantum and Radiological Science andTechnology
bTohoku University
cOkayama University

Fig. 1. Magnetocaloric effect and magnetic phase diagram of volborthite. (a) Experimental data of the MCE in volborthite. (b) Enlarged
plot of MCE curve. The phase boundaries deduced from the MCE andC(T) measurements were plotted by solid symbols and open circles.

ISSP Activity Report 201929

Magnetization Process of the Breathing
Pyrochlore Magnet CuInCr4S8 in
Ultrahigh Magnetic Fields up to 150 T
Kohama Group

Fig. 2. Specific heat in volborthite. (a) Experimental results for specificheat C(T) for magnetic fields spanning the low-field phase I, phase II(SDW), and phase N1. (b) Specific heat within the hidden-order phaseN2 and the plateau state P.

as shown in Fig. 1(b) as black and green curves. In Fig. 1(b),we also plot the phase boundary deduced from MCE andC(T) measurements.
We have further investigated the temperature-dependenceof C in magnetic fields up to 30.2 T as seen in Fig. 2. In
the absence of magnetic field, C(T) exhibits small peaks
as reported previously (See Fig. 2(a)). The onset of SDWorder (Phase II) is also revealed as a broad shoulder inC(T). Different behavior is observed above 22.5T where
the transition is marked by a substantial λ-shaped anomaly.
An extremely sharp peak (Fig. 2(b)) is developed above
25.5 T, consistent with the phase boundary identified in
MCE. Above the crossover field to the plateau state (P) at
27.5T, no anomaly is observed in C(T). These observations
provide unequivocal evidence that there are two different
magnetic states between SDW and plateau states, i.e., Phases
N1 and N2 as seen in Fig. 1(b). It is important to note that theearlier NMR results [2], however, failed to resolve the phase
N2. Since the spin quadrupole moment cannot be detectedby conventional magnetic probes such as NMR, it is reasonable to consider the phase N2 between 25.5 and 27.5 T is
the ordered state of the quadruple moment that is so-called aquantum spin nematic state.

Breathing pyrochlore magnets with an alternating arrayof small and large tetrahedra have recently attracted attention because of their potential realization of exotic magnetic
states. One promising candidate is the S = 3/2 chromium
spinel oxide, LiInCr4O8, characterized by the small breathing
factor J’/J~0.1, where J and J’ are the exchange interactions
on the small and large tetrahedra, respectively (inset of Fig.
1) [1]. In this system, the spin-lattice coupling (SLC) as wellas the breathing factor govern its magnetic properties, as
represented by a tetramer-singlet formation [1] and a fieldinduced transition to a 1/2-magnetization plateau phase [2].
Another intriguing system is the sulfide, CuInCr4S8, where
the antiferromagnetic (AFM) J and the ferromagnetic (FM)J’ coexist [3]. As shown in Fig. 1, the previously reported
M-H curves at 1.4 K (orange and cyan lines for up anddown sweeps, respectively) show a metamagnetic behavior
with a large hysteresis loop at around Hc1=20~40 T, while
M reaches only 45 % of the saturation magnetization of~3.06 μB/Cr at 73 T [3].
In this work, we performed magnetization measurements
on a polycrystalline powder sample of CuInCr4S8 by using
a single-turn coil system. The observed M-H curve and its
derivative dM/dH at 5 K up to 150 T are shown in Fig. 1 (redand blue lines for up and down sweeps, respectively) [4].
Remarkably, a wide 1/2-plateau emerges from Hc2 ~ 65 T

References[1] Y. Kohama, H. Ishikawa, A. Matsuo, K. Kindo, N. Shannon, and
Z. Hiroi, PNAS 116(22) 10686 (2019).
[2] H. Ishikawa, M. Yoshida, K. Nawa, M. Jeong, S. Kramer, M.
Horvatic, C. Berthier, . Takigawa, M. Akaki, A. Miyake, M. Tokunaga,
K. Kindo, J. Yamaura, Y. Okamoto, and Z. Hiroi, Phys. Rev. Lett. 114,
227202 (2015).
[3] O. Janson, S. Furukawa, T. Momoi, P. Sindzingre, J. Richter, and
K. Held, Phys. Rev. Lett. 117, 037206 (2016).
Authors
Y. Kohama, H. Ishikawa, A. Matsuo, K. Kindo N.Shannona, and Z.
Hiroi
aOkinawa Institute of Science and Technology Graduate University

30

ISSP Activity Report 2019

Fig. 1. M-H curves of CuInCr4S8 measured at ~5 K in a single-turncoil megagauss generator up to 150 T (red and blue curves for up anddown sweeps, respectively). Derivatives dM/dH are shown in the upper
panel. The previously reported M-H curve measured at 1.4 K up to 73
T are also shown (orange and cyan curves for up and down sweeps,
respectively) [3]. Transition fields are denoted by brackets or arrows in
the upper panel, and drawn by the shaded areas (first order) or dashedlines (second order) in the lower panel. Inset shows the schematic of thebreathing pyrochlore lattice.

[4] M. Gen, Y. Okamoto, M. Mori, K. Takenaka, and Y. Kohama, Phys.
Rev. B 101, 054434 (2020).
[5] K. Aoyama and H. Kawamura, Phys. Rev. B 99, 144406 (2019).
Authors
M. Gen, Y. Okamotoa, M. Moria, K. Takenakaa, and Y. Kohama
aNagoya University

Femtosecond Laser Pulse Generation
with 20-GHz Repetition Rate
Kobayashi Group

Fig. 2. Calculated magnetization curves as a function of magnetic field
h for b/(1 + JFN/J) = 0 to 0.25 in steps of 0.05. The spin structures
corresponding to the curve for b/(1 + JFN/J) = 0.10 (thick green line)
are shown in the upper part of the figure.

to Hc3 ~ 112 T as in Cr spinel oxides. Besides, two inherent
features are observed: A slight change in the slope of theM-H curve at Hc2’ ~ 85 T and a shoulder like shape at Hc4~ 135 T. Both are accompanied by a hysteresis, suggesting
first-order transitions. The saturation is estimated to Hsat ~180 T under the assumption that M increases linearly above
150 T, where M already reaches ~2.7 μB/Cr.
For interpreting the observed magnetization process, weconstructed an effective spin model mapped onto the fcc
lattice, which is derived from the microscopic spin model on
the breathing pyrochlore lattice with the SLC as proposed inRef. [5]. Figure 2 summarizes the calculated M-H curves forgiven values of the SLC parameter b and the corresponding
spin structures. In spite of the simplification in our model,
the calculation well reproduces the main feature of the M-Hcurve of CuInCr4S8, including a relatively wide intermediate(canted 2:1:1) phase as well as the 1/2-plateau phase withcollinear 3:1 spin configuration.
It is noteworthy that the M-H curves of LiGaCr4S8 and
LiInCr4S8, where the FM interaction J’ is expected to bestrong, do not exhibit the 1/2-plateau [3]. Bearing this inmind, the exotic magnetic behaviors on CuInCr 4S8 canbe attributed to the relatively dominant AFM interactions
J+JFN compared to the FM J’, which is achieved only by
the moderate breathing distortion in the Cr spinel sulfide.
On the other hand, the origins of the hysteretic behaviors on
CuInCr4S8 at Hc2’ and Hc4 remain unsolved at the moment.
They might originate from the interplay between the SLC
and the further neighbor interactions JFN, or the thermal andquantum effects, which are not considered in the present
theory. The macroscopic spin structures beyond four sites
within small tetrahedra should also be clarified, which is
crucial to prove the novelty of the magnetic properties in
CuInCr4S8. Further experimental investigations such as
magnetostriction, ESR, and magnetocaloric effect measurements in high magnetic fields are ongoing to elucidate theessence of the successive phase transitions.
References[1] Y. Okamoto, G. J. Nilsen, J. P. Attfield, and Z. Hiroi, Phys. Rev.
Lett. 110, 097203 (2013).
[2] M. Gen, D. Nakamura, Y. Okamoto, and S. Takeyama, J. Magn.
Magn. Mater. 473, 387 (2019).
[3] Y. Okamoto, M. Mori, N. Katayama, A. Miyake, M. Tokunaga, A.
Matsuo, K. Kindo, and K. Takenaka, J. Phys. Soc. Jpn. 87, 034709(2018).

Femtosecond laser pulses have widely used in thefield of spectroscopy, metrology and material processing.
Especially, material processing using the femtosecond laser
has played an important role in the manufacturing because
it does not induce thermal damages around the processingarea, resulting in the high-quality micro-processing. One
important laser parameter for these applications is a pulse
repetition rate, which is typically in the range of 1 kHz to
100 MHz. Recent progress of the laser technologies has
succeeded to generate femtosecond laser pulses with thegigahertz repetition rate. These high repetition rate pulses
have performed efficient material processing compared withthe low repetition rate laser pulses. Although the high repetition rate pulses are one candidate of the next-generation laser
processing, mechanisms of the efficient material removal
have not understood ever before. One reason is a lack of themulti-GHz femtosecond laser sources. Especially, material
removal via laser pulses with the repetition rate above
10-GHz have not examined due to the difficulty of generating the multi-GHz laser pulses. We are interested in thegeneration of such kind of laser pulses.
Several methods have been used to generate multi-GHz
repetition rate pulses. We focused on the Kerr-lens mode
locked laser (KML), which provides the shortest pulse
duration in the femtosecond lasers. The repetition rate of the
KML is determined by the cavity length, with the relationof f = c/L, where f denotes the pulse repetition rate, c isthe speed of the light and L is the cavity length. Therefore,
the higher repetition rate is achieved with a shorter cavity
length. To date, KML has realized up to 15 GHz repetition
frequencies with a pulse duration of 150 fs. This repetition
frequency corresponds to a cavity length of 20 mm. To
increase the repetition rate above, the cavity length must be
shorter than 20 mm. However, the cavity length is limited by
the size of the optical element. In addition, typical KML isconfigured with 5 to 7 optical component, resulting in a large
cavity.
In this work [1], we developed the KML with the repletion rate above 20 GHz only using three optical components. This was achieved by designing new cavity geometry,
which includes a triangle-cut laser gain medium and multi-

Fig. 1. The cavity geometry

ISSP Activity Report 201931

Fig. 2. A part of the output spectrum

functional dielectric coating. The detail cavity configuration
is described in Figure 1. We use a gain medium of Yb:Y2O3
ceramic because an output light can be easily amplified byusing a Yb-doped fiber amplifier. The pump source wasan wavelength-stabilized laser diode coupled to a single
mode fiber. One side of the gain medium was coated witha dichroic chirped mirror, while the other side was wedgedat the Brewster angle. The concave mirror was dichroiccoated and its angle compensated an astigmatism that was
introduced by the Brewster-cut gain medium. The plane
mirror was high-reflection coated and was used as the output
coupler.
Femtosecond pulse generation was achieved with thecavity length of 15 mm, which determines the pulse repetition rate as 20 GHz. A pulse duration was measured as
120 fs. The pulse repetition rate corresponds to the spacingof longitudinal cavity mode, which can be identified fromthe optical spectrum. Figure 2 shows a part of the optical
spectrum. Each longitudinal mode is clearly observed
because the mode spacing is wider than a spectrometer
resolution of 4 GHz. To the best of our knowledge, therepetition rate of 20 GHz is the highest frequency in KMLs.
Our results will enable the investigation of the material
processing above the 10-GHz repetition rate.
Reference[1] S. Kimura, S. Tani, and Y. Kobayashi, Optica 6, 532 (2019).
Authors
S. Kimura S. Tani, and Y. Kobayashi

Geometrical Frustration of B-H Bonds
in Layered Hydrogen Borides
Accessible by Soft Chemistry
I. Matsuda GroupElectrically conducting materials have been essential elements for devices and also for redox reactions onelectrodes to sustain our electronic and information society.
Miniaturizations in nanotechnology have demanded toreduce the material size down to the atomic limit, however,there are only a few conducting atomic layers, such asgraphene, up to now. A search of a novel atomic layer issignificant to produce new physical/chemical properties
and also to promote various functionalities by combining
different types of layers.
In 2017, atomic sheets of hydrogen boride (HB) or
borophene are synthesized by the ion-exchange process[1]. The HB sheet has been theoretically predicted to be
conducting. However, preliminary experiments of the trans-

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ISSP Activity Report 2019

Fig. 1. (a) An image of scanning electron microscope of the hydrogen
boride sheet. (b) Current‐voltage curves acquired at various temperatures of the sheet [2].

Fig. 2. Atomic structure model of the special local structure in thehydrogen boride sheet [2].

port measurement have resulted in insulating properties.
This fact has lead experimentalists to take great efforts ofimproving the purity of the samples to develop the conductivity. Eventually, in the present research [2], high-purity HBsheets were successfully synthesized, as shown in Fig. 1(a),and achieved the highest conductivity in hydrogen borides(0.13 S/cm). Moreover, suppression of the conductivity inprevious samples were found to be due to adsorption ofresidual organic molecules on the sheet. Interestingly, the HB
sheet becomes insulating at 30 °C when there are residual
molecules and, reversely, returns to have high conductivity
below the temperature, as shown in Fig. 1(b).
To reveal the intriguing phenomena in terms of theatomic structure, an X-ray scattering experiment was carriedout at the synchrotron radiation facility, SPring-8. By
analyzing the experimental pair distribution function with theBayesian optimization, it became clear that there are locallyspecial arrangements of hydrogen atoms in the sheet thatallow adsorptions of the residual organic molecules. Figure 2
shows the atomic model. The structure consists of threecenter, two-electron (3c-2e) B-H-B bridging bonds as wellas ordinary two-center, two-electron (2c-2e) B-H terminal
bonds. The present research revealed that conductivity ofatomic sheets of hydrogen boride can be regulated by thetiny number of molecules, indicating promising functionalities in sensors or in catalysts.
References[1] H. Nishino, T. Fujita, N. T. Cuong, S. Tominaka, M. Miyauchi, S.
Iimura, A. Hirata, N. Umezawa, S. Okada, E. Nishibori, A. Fujino, T.
Fujimori, S. Ito, J. Nakamura, H. Hosono, and T. Kondo, J Am Chem
Soc. 139, 13761 (2017).
[2] S. Tominaka, R. Ishibiki, A. Fujino, K. Kawakami, K. Ohara, I.
Matsuda, H. Hosono, and T. Kondo, Chem 6, 406 (2020).
Authors
S. Tominakaa,b, I. Matsuda, and T. Kondoc,daInternational Center for Materials Nanoarchitectonics (MANA),
National Institute for Materials Science (NIMS)
bJapan Synchrotron Radiation Research InstitutecTokyo Institute of Technology
dUniversity of Tsukuba

Ultrafast Unbalanced Electron
Distributions in Quasicrystalline
30° Twisted Bilayer Graphene
I. Matsuda, Okazai, and Komori Groups
Layers of twisted bilayer graphene exhibit varieties
of exotic quantum phenomena and the twist angle Θ has
become an important degree of freedom for exploring novel
states of matters. At Θ = 1.1°, the two-dimensional superconductivity was observed, while, at Θ = 30°, a two-dimensional
quasicrystal is synthesized. For the quasi-crystalline twisted
bilayer graphene (QCTBG), the interlayer interaction is
the minimum due to the 30° twisted angle and the massless
Dirac Fermions remain in the two layers. The electronic state
results in the twelve-fold (dodecagonal) structure and it iscomposed of upper- and lower-layer Dirac cones, ULDs and
LLDs, as shown in Fig. 1.
We explored this electronic structure by focusing on

Fig. 1. Crystal and electronic structure of a twisted bilayer graphene
quasicrystal on the SiC substrate. The upper- and lower-layer
graphene sheets are twisted by 30 degrees with respect to each other.
In the momentum space, electronic structure of a TBG quasicrystal
is composed of the upper-layer Dirac (ULD) and lower-layer Dirac(LLD) bands. The inner-red and blue Dirac cones represent the replica
bands of ULD and LLD bands by the umklapp scattering induced by
the incommensurate interlayer stacking of the quasi-crystallinity. The
quasi-crystalline twisted bilayer graphene was n-type: Dirac point andequilibrium chemical potential are denoted as DP and μeq, respectively.

Fig. 2. Calculated band structures for the ULD and LLD bands in
QCTBG and for non-twisted bilayer graphene (NTBG) band, respectively. Dashed lines indicate the μeq level. d–f, Equilibrium angleresolved photoemission spectra for ULD, LLD, and NTBG bands. DP
is indicated by an arrow. g–i, Difference images of TARPES for the
ULD, LLD, and NBLG bands. Red and blue points represent increasing
and decreasing photoemission intensity, respectively.

Fig. 3. Chemical-potential shift as a function of pump-probe delay timefor LLD and ULD bands for QCTBG. For comparison, the result for
NTBLG is also shown.

the ultrafast dynamics through time- and angle-resolved
photoemission spectroscopy (TARPES), which allows us todirectly observe the temporal evolution of fermions in the
Dirac cones [1]. The measurement used the pump-probe
approach with an infrared pulse with hv = 1.55 eV serving
as pump and an extreme-ultraviolet pulse with hv = 21.7 eVserving as a probe to cover the entire two-dimensional Brillouin zone. Figure 2 shows a summary of the TARPES band
diagrams taken at selected delay time for the ULD and LLD
bands in a TBG quasicrystal. The results of the periodic
non-twisted bilayer graphene (NTBG) are also shown forcomparisons. After the pump pulse (intensity ~0.7 mJ/cm2),
the TARPES band diagram of individual bands of bilayers
evolves on the femtosecond time scale. To enhance thetemporal variations, the band diagrams are shown as thedifference between the spectra before and after photoexcitation. The spectral weights for all bands decrease immediately
below μeq and increase above μeq at Δt= 0.05 ps. This reflects
the excitation of electrons from the occupied bands to theunoccupied bands. At Δt= 0.16 and 0.32 ps, the difference
intensity decreases with delay time, which corresponds to therelaxation of photoexcited carriers.
To evaluate the occupation of Dirac cones by nonequilibrium carriers, we made energy distribution curves of
the Dirac bands by integrating over momentum space andsummarized the chemical-potential shift or the photoinduced potential as Fig. 3. As shown in the figure, thedifferent time evolution for potential indicates that the ULD
and LLD bands have the opposite behavior after Δt = 0.2 ps(i.e. the ULD undergoes a negative shift whereas the LLD
undergoes a positive shift). Interestingly, the photo-induced
potential for the NTBG band remains constant at essentiallyzero over the same time delay. The striking difference among
the three types of the Dirac cones provides clear evidenceof a carrier imbalance between the ULD and LLD bands of
the QCTBG on the ultrafast time scale. Through the kinetic
analysis, the key mechanism was found to involve the carriertransport between layers and the transient doping from thesubstrate interface. Our TARPES measurements on replicasof the ULD and LLD bands, shown in Fig.1, revealed thatthe ultrafast dynamics scheme continues after the Umklapp
scattering. The dynamics in the atomic layer opens the possibility of new applications and creates interdisciplinary links
in the optoelectronics of van der Waals crystals.

ISSP Activity Report 201933

Reference[1] T. Suzuki, T. Iimori, S. J. Ahn, Z. Yuhao, M. Watanabe, J. Xu,
M. Fujisawa, T. Kanai, N. Ishii, J. Itatani, K. Suwa, H. Fukidome, S.
Tanaka, J. R. Ahn, K. Okazaki, S. Shin, F. Komori, and I. Matsuda,
ACS Nano 13, 11981 (2019).
Authors
I. Matsuda, T. Suzuki, K. Okazaki, and F. Komori

Photoinduced Hydrogen Releasefrom Hydrogen Boride Sheets
I. Matsuda Group
Materials consisting of one atomic layer, such asgraphene, are one of the two-dimensional materials that haveshown various physical and chemical properties that are
different from ordinary ones. Recently, novel atomic layersof boron, so-called “borophene”, were reported and thematerials were found to surpass the performance of grapheneby theoretical works. However, the growth requires special
conditions such as appropriate metal substrates, high temperature and ultra-high vacuum.
Under these circumstances, we have succeeded in synthesizing a hydrogen boride (HB) sheet (Fig. 1(a)), which ishydrogenated borophene or borophane, under the ambientcondition. Since the HB sheet is composed only of the lightelements, boron and hydrogen, the mass hydrogen density
is as high as 8.5%, and it was expected to be applied asa safe and lightweight material for the hydrogen carrierthat replaces the conventional high-pressure hydrogen gas
cylinder with a risk of explosion. However, it has required toconsider a procedure to extract hydrogen atoms/moleculesfrom the sheet before the actual use. In the present research,
we designed and verified the hydrogen release by the lightirradiation [1].
According to the first-principles calculation of thehydrogen boride sheet, the optical transition (α → β) occurs
from the bonding orbital of boron to the antibonding
orbital, as shown in Fig. 1(b). On the other hand, there isalso an optical transition (α → γ) to the antibonding orbitalof hydrogen. Since this transition energy corresponds to a
photon energy of ultraviolet (UV) ray, it is hypothesized thathydrogen could be released from a hydrogen boride sheet
only by the UV irradiation even under the ambient condition.
The experimental verification was made by analyzing thegas molecules emitted from the hydrogen boride sheets withusing two types of light sources. One type of the sources
irradiates visible light that can cause the optical transition (α → γ), while the other type irradiates ultraviolet lightthat can induce the optical transition (α → β). As shown in
Fig. 2, it was confirmed that the hydrogen gas was generated
by exposure of the ultraviolet ray. By quantifying the amountFig. 1. (a) Top and side views of the atomic structure of the HB sheet.
The unit cell is indicated by the dashed lines. (b) Projected band structures of B- and H-originated orbitals [1].

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ISSP Activity Report 2019

Fig. 2. A amount of H2 production by the light irradiation with two
different light sources [1].

of the hydrogen production, it was found that 8% of the massof the hydrogen boride sheet was consumed for the hydrogen
release. For conventional hydrogen storage alloys, the masshydrogen density is up to 2%. Even a promising hydrogen
carrier of the organic hydrides reaches mass hydrogendensity of 6.2% with heating above 300 °C. Thus, thehydrogen boride sheet can be a safe, lightweight and simple
portable hydrogen carrier with a simple light operation of theextremely high hydrogen release.
Reference[1] R. Kawamura, N. T. Cuong, T. Fujita, R. Ishibiki, T. Hirabayashi, A.
Yamaguchi, I. Matsuda, S. Okada, T. Kondo, and M. Miyauchi, Nature
Commun. 10, 4880 (2019).
Authors
I. Matsuda, T. Kondoa,b, and M. Miyauchic
aTokyo Institute of Technology,
bUniversity of Tsukuba
cTokyo Institute of Technology

Surface-State Coulomb Repulsion
Accelerates a Metal-Insulator Transitionin Topological Semimetal Nanofilms
I. Matsuda, Sugino, and Komori Groups
By reducing the size of materials in the microscopic
scale, the electronic states are governed by the rules ofquantum mechanics and the various quantities, such asenergy levels, take discrete values (the quantum size effect,
QSE). Thus, there can be a case that gapless metal films
become insulating at the nanoscale. Such a QSE-induced
transition into an insulating phase in semimetallic nanofilms
was predicted more than half a century ago on bismuth (Bi)films [1]. Despite the researches of spectroscopy and transport experiments, the previous results have remained contradictions, indicating an interesting mechanism behind.
In the present research, we revealed an unexpectedmechanism of the transition in Bi by combining of highresolution measurements of angle-resolved photoemission
spectroscopy (ARPES) on high-quality films and the densityfunctional theory (DFT) calculations [2]. Figure 1 (a) shows
peak-enhanced ARPES images resolving all quantizedbulk bands and surface bands. One can see that the top
quantized levels are clearly shifting below the Fermi levelwith decreasing thickness. This is the first direct observationof the QSE-induced transition into an insulating phase in Bi
films.

Fig. 2. (a) Schematic of a self-consistent cycle for a total charge density
and an effective confinement potential. (b) Comparison of experimental
thickness dependence of quantized levels (markers) and a numericalsimulation (solid lines). The inset depicts wave function charactersobtained in the simulation. (c) Schematics of the new class of size
effects driven by increased Coulomb repulsion from surface states.

Fig. 1. (a) Peak-enhanced ARPES images measured on atomically thin
Bi films. 1 bilayer (BL) of Bi corresponds to 3.9 Å. (b) Schematic of
unusual band connections. The number indicates degeneracy of eachband. (c) DFT band structures calculated on a 14 BL Bi slab withenergy shifts manually induced. (d) Wave function characters calculated
for n = 1, 2, 3 quantized states.

The high-resolution ARPES observation reveals an
unusual signature: both of two surface bands connect to the
top quantized bulk band. Because of the presence of surface
states at the top and bottom of a film, these surface bands aredoubly degenerate. Thus, this band connection readily meansthat the top quantized level must be quadruply degenerate.
Although this breakup of conventional quantization rule wastotally unexpected, our first-principles calculations reproduced the behavior. In Fig. 1(c) shows band structures thatare intentionally shifted via modulation of lattice parameters.
In the leftmost panel, quantized energy levels are regularly
ordered, and n = 1, 2, 3 states possess wave function characters expected for ones confined in an ideal quantum well.
From the leftmost to the rightmost panels, the separation
between n = 1 and 2 levels is gradually reduced, and thewave function characters divert from the ideal cases and get
localized near surfaces.
What is the essential mechanism for the unexpectedlevel degeneracy and the bulk-to-surface transformation ofquantized wave functions? In the DFT framework, an effective one-body potential and a total charge density are determined by a self-consistent cycle reflecting Coulomb interaction. From left to right in Fig. 1(c), the occupation of thesurface bands increases and their relative contributions to thetotal charge density increase.
This tendency makes Coulomb repulsion among
electrons compress the total charge density toward the film
center. In the one-body picture of the DFT framework, apotential barrier around the film center is induced by thiscompressed total charge, which creates a double-well potential, as illustrated in Fig. 2(a). Such a double-well potential
supports degenerate ground states whose wave functions are
localized in both wells with opposite parity, which explainsobservations above. Furthermore, experimental thickness
dependence of quantized levels was excellently reproduced
by a numerical simulation using a single-well potential
which gradually deforms into a double well (Fig. 2(b)).
This unprecedented picture naturally reconciles thestrange contradiction observed in previous studies: even if
the top quantized levels can cross the Fermi level, the stateseffectively behave as surface-conducting states, and the film
interior is insulating as observed in transport experiments, as
shown in Fig.2(c). Thus, we established the complete pictureof the half-century problem in Bi, which demonstrates a newclass of size effects driven by increased Coulomb repulsion
from surface states.
References[1] V. B. Sandomirskii, Quantum size effect in a semimetal film. Soviet
Physics JETP 25, 101 (1967).
[2] S. Ito, M. Arita, J. Haruyama, B. Feng, W.-C. Chen, H. Namatame,
M. Taniguchi, C.-M. Cheng, G. Bian, S.-J. Tang, T.-C. Chiang, O.
Sugino, F. Komori, and I. Matsuda, Science Advances 6, eaaz5015(2020).
Authors
S. Ito, O. Sugino, F. Komori, and I. Matsuda

Real-Time Observation of Electronic,
Vibrational, and Rotational Dynamics
in Nitric Oxide with Attosecond SoftX-Ray Pulses at 400 eV
Itatani Group
Attosecond science has made tremendous progress inthe past two decades along with the advance of Ti:sapphirebased ultrafast laser technologies. Intense ultrashort pulses
in visible and near infrared regions are now routinely
produced, which allow to produce attosecond pulses in theextreme ultraviolet (EUV, photon energy <200 eV) by using
the physics of high harmonic generation (HHG). Since the

ISSP Activity Report 201935

maximum photon energy (or the high harmonic cut off) is
scaled by the ponderomotive potential that is proportional
to the square of laser wavelength, intense ultrashort-pulse
IR sources are required to extend the spectral range ofattosecond pulses towards the soft X-ray (SX) range. Suchspectral extension of high harmonics paves a way to elementspecific ultrafast spectroscopy using atomic absorption
edges. The features of atomic selectivity, photon-in/photonout methodology, and the preservation of temporal resolution on the attosecond time scale are attractive to constructattosecond transient spectroscopy that can generally be applicable to atoms, molecules, and condensed matters even in thepresence of strong external fields.
Since 2008, Our group developed a carrier-envelope
phase-stable ultrashort-pulse IR source that used BiB3O6(BiBO) crystals as an optical parametric chirped-pulse
amplification (OPCPA) medium. Because of the extremely
broadband gain of BiBO-OPCPA in 1.2-2.2 μm, we successfully produced CEP-stable sub-two-cycle IR pulses (1.5 mJ,
10 fs) at a repetition rate of 1 kHz [1]. The high pressure
gas cell that is filled with Ne or He gases allow to generate
attosecond continua that cover nearly all of the water
window.
Using the BiBO-OPCPA and a high-pressure He target(2.4 bar), we demonstrated attosecond SX spectroscopyof NO molecules that were exposed to intense IR fields
as shown in Fig. 1 [2]. The output from BiBO-OPCPA(1.6 µm, 10 fs, 1.5 mJ, 1 kHz, CEP stable) was split to pumpand probe pulses. The pump pulses induced field ionization,
followed by multi-scale coherent dynamics in NO molecules.
The probe pulses produced attosecond SX pulses thatmonitored the unoccupied energy levels by inner shell excitation. The transmitted SX spectra were then recorded with agrating-based spectrometer with a back-illuminated x-ray
CCD camera.
Figure 2(a) shows the measured transient differential
absorbance of NO (pump intensity: ~1×1014 W/cm2). The
static absorbance of NO without the pump pulses is shownin Fig. 2(b). The main feature in Fig. 2(a) is the appearanceof upshifted absorbance of the 1s-2π peak at 402.5 eV whenthe IR pulse precedes the SX pulse. This upshift comes fromNO+ generated by tunnel ionization. Figure 2(c) shows thedifferential absorbance at 403.1 eV around the time origin(pump intensity: ~2×1014 W/cm2). A step-like absorbanceincrease with a period of 2.7 fs (half cycle of the pumpIR pulse) was observed. These steps are characteristic oftunnel ionization. Figure 2(d) shows the oscillation of thecentral energy of the NO+ 1s-2π peak with a period of 14.5 ±0.1 fs. Figure 2(e) shows the differential absorbance of theNO 1s-2π peak (pump intensity: ~1×1014 W/cm2). The peakstructure around 100 fs can be explained by laser-induced
molecular alignment. As far as we know, this attosecond

Fig. 2. (a) Time-resolved absorption spectra of NO. (b) Static absorbance of NO without the pump pulses measured in our experiment(blue circles) and a synchrotron (red curve). (c) Absorbance changeof the NO+ 1s-2π peak at 403.1 eV (red circles) and its 3-point rolling
average (red curve). (d) Central energy of the NO+ 1s-2π peak (redcircles) and the fitting by a cosine and Gaussian function (red curve).
(d) Absorbance change of the NO 1s-2π peak (398.7 to 400.6 eV) withparallel (red circles) and perpendicular (blue circles) IR and SX polarizations. The solid curves are calculation results considering molecularalignment. The pump intensity is ~1×1014 W/cm2 for (a, b, d, e) and~2×1014 W/cm2 for (c). The polarizations of the IR and SX are parallelfor (a, c, d).

transient spectroscopy is at the highest photon energy, andthe first experiment to measure the field-induced alignmentof molecular ions.
Attosecond transient spectroscopy of NO molecules
reveals that the absorption spectra near the nitrogen K-edge(~400 eV) allow to capture full quantum dynamics (i. e.,electronic, vibrational, and rotational dynamics) with a single
spectrogram. These results show that attosecond soft-x-ray
absorption spectroscopy is a powerful technique to trace themolecular dynamics of various freedoms in a different timeand energy scales.
References[1] N. Ishii, K. Kaneshima, T. Kanai, S. Watanabe, and J. Itatani,
J. Opt. 20, 014003 (2018).
[2] N. Saito, H. Sannohe, N. Ishii, T. Kanai, N. Kosugi, Y. Wu,
A. Chew, S. Han, Z. Chang, and J. Itatani, Optica 6, 1542 (2019).
Authors
N. Ishii, K. Kaneshima, T. Kanai, S. Watanabea, N. Saito, H. Sannohe,
N. Kosugib, Y. Wuc, A. Chewc, S. Hanc, Z. Changc, and J. Itatani
aTokyo University of SciencebInstitute of Materials Structure Science, High Energy Accelerator
Research OrganizationcUniversity of Central Florida

Efficient Terahertz Harmonic Generation
with Coherent Acceleration of Electrons
in the Dirac Semimetal Cd3As2
Matsunaga, Tsunetsugu, and Itatani Groups

Fig. 1. (a) Schematic of the experimental setup. (b) Typical SX
spectrum obtained by HHG in Helium.

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ISSP Activity Report 2019

Intense waveform-controlled light field has revealed
highly-intriguing nonlinear and nonperturbative light-matterinteractions such as high-order harmonic generation (HHG).
Recently, HHG in solids with mid-infrared (IR) excitation
has been reported, opening a new route toward laser-based
stable and compact extreme ultraviolet (EUV) sources.
Meanwhile, in the long wavelength limit, efficient third
harmonic generation (THG) in the terahertz (THz) frequency
regime has also been reported in a superconducting film[1]. Realization of such extreme nonlinear photonics in theTHz region at room temperature is highly desired for highspeed THz electronics and for nonlinear frequency mixing insensitive detection of cosmic microwave background. Fromthese perspectives, graphene has attracted tremendous attention as a candidate for efficient THz frequency multiplication using massless Dirac electrons because the current flow
across the Dirac node in the momentum space is expected to
exhibit remarkably large nonlinearity [2], as schematicallyshown in Fig. 1(a). Very recently, HHG in the THz frequency
range in graphene was clearly demonstrated by using a very
intense light source that is based on a large-scale electron
accelerator [3]. In their experiment, the nonlinear coefficients in graphene were found to be much larger than typicalmaterials, whereas the conversion efficiency is still limited
by its monolayer nature.
In our work [4], we investigated THz nonlinear spectroscopy for thin films (thickness of 240 nm) of the three-dimensional Dirac semimetal Cd3As2 at room temperature using alaboratory-scale laser source. We have observed intense THz
pulse generation using this laser-based setup and performed
nonlinear transmission spectroscopy of quasi-monochromatic
intense THz pulse with the center frequency of 0.8 THz [4].
Figure 1(b) shows the results of the spectral amplitude fortransmitted pulses. A sharp peak of THG is clearly observed
at 2.4 THz, which demonstrates the efficient nonlinear
frequency conversion of the THz light. For comparison, we
examined monolayer graphene with the same excitation
condition, and also observed the THG signal. The nonlinear
coefficient for graphene was estimated as ~10-9 m2V-2, whichis consistent with the previous literature, and several ordersof magnitude larger than typical materials. Compared tographene, the conversion efficiency in Cd3As2 is much larger
due to the film thickness, and the observed THG field amplitude is ~100 V/cm under the pump field of 6.5 kV/cm inside
the film. In the next step, we can reduce the Fresnel reflection loss at the sample surface by using an antireflection
coating on the film or directly applying the field via contact
electrodes, which will allow to generate further stronger
harmonics for realistic applications in ultrafast electronics.
To understand the efficient HHG mechanism in Cd3As2
in a microscopic picture, we also performed THz pump-THz
probe spectroscopy. In the case of graphene, the origin of
the THz HHG was successfully explained by a thermodynamic model where electrons were assumed to be in quasiequilibrium with repeating heating and cooling processes
very rapidly within the THz timescale [3]. However, sucha picture of incoherent electron dynamics is essentiallydifferent from the originally proposed scheme to induce
large nonlinearity in massless Dirac systems [2]. Our timeresolved THz spectroscopy in this work has revealed thatthe relaxation rate of the carriers in Cd3As2 is ~8 ps, which

Fig. 2. (a) Pump THz field waveform (upper). THz pump-THz probe
signal as a function of the pump-probe delay time with different polarization configurations. (b) Calculated THG amplitude in the intraband
acceleration model as a function of the scattering time.

is much longer than one optical cycle of the pump field(1.25 ps) in contrast to the rapid cooling in graphene (<< 1ps). We performed the thermodynamic-model calculationand confirmed that this model cannot reproduce the efficient
THG with realistic parameters.
In addition, we experimentally investigated the electron
dynamics during the THz wave irradiation and found that thenonlinear response manifests itself almost only for the pumppolarization direction, as shown in Fig. 2(a). The result canbe well explained by the intraband current model [2]. Whenelectrons are accelerated by the pump field, the electron
distribution function in the momentum space moves rapidly
back and forth along with the pump polarization direction,
but it appears as if “nothing happens” in other probe polarization directions, which was observed as the anisotropic
nonlinearity. We also calculated the nonlinear current byconsidering the intraband acceleration in a simple linear
dispersion model and confirmed that the intraband acceleration model can reproduce the value of the THG amplitude
and its saturating behavior which we observed.
Our results show that, even though the scattering time of~145 fs in Cd3As2 is still shorter than the pump field cycleof 1.25 ps, the nonlinear response is well described by the
intraband current by coherent acceleration of electrons. It
can be explained by the fact that asymmetric non-thermal
electron population distribution in momentum space canbe developed as rapidly as in ~85 fs. Figure 2(b) shows thecalculated result of the THG amplitude as a function of thescattering time. If the scattering time is as long as 100 fs, theTHG amplitude strongly saturates. Therefore, the scattering
time of 145 fs in this material is “long enough” for nonperturbative intraband acceleration driven by the optical field of
a few-kV/cm.
In future, even longer scattering times might be achievedin other topological semimetals with massless dispersion,
which will allow us more efficient frequency conversion,
perhaps at sub-kV/cm field strength. Our results will open a
new pathway towards a novel frequency convertor in the THz
frequency based on Dirac semimetals.
References[1] R. Matsunaga et al., Science 345, 1145 (2014).
[2] S. A. Mikhailov, Europhys. Lett. (EPL) 79, 27002 (2007).
[3] H. A. Hafez et al., Nature 561, 507 (2018).
[4] B. Cheng†, N. Kanda†, T. N. Ikeda, T. Matsuda, P. Xia, T.
Schumann, S. Stemmer, J. Itatani, N. P. Armitage, and R. Matsunaga,
Phys. Rev. Lett. 124, 117402 (2020). (†: equal contribution)

Fig. 1. (a) A schematic of high harmonic generation due to the coherent
acceleration of Dirac electrons. (b) Amplitude spectra of the transmitted
intense THz pulse with appearance of the THz THG in Cd3As2 thin
film.

Authors
B. Chenga,†, N. Kanda†, T. N. Ikeda, T. Matsuda, P. Xia, T. Schumannb,
S. Stemmerb, J. Itatani, N. P. Armitagea, and R. Matsunaga (†: equal
contribution)aThe Johns Hopkins University
bUniversity of California

ISSP Activity Report 201937

Observation of Terahertz Anomalous
Hall Effect in Weyl Antiferromagnet
Mn3Sn Thin Films
Matsunaga and Nakatsuji Groups
Control of magnetism has been a key issue for modern
data processing and recording in spintronic devices. Fromthe viewpoint of manipulation speed, antiferromagnets arepromising materials because spin precession motion occurs
typically at terahertz (THz = 1012 per second) frequencies, a
few orders of magnitude higher than ferromagnets. Readoutof the magnetization information in antiferromagnets is,however, still very difficult since they are generally not sensitive to the external field because of the much smaller net
magnetization than in ferromagnets, which has made theirpractical application challenging. In 2015, Nakatsuji groupin ISSP has discovered large anomalous Hall effect (AHE) inan antiferromagnet Mn3Sn at room temperature comparable
to ferromagnets in spite of the vanishingly-small net magnetization [1]. The exceptionally-large response originatesfrom an inverse-triangular spin structure where the spins
form a 120-degree order with negative vector chirality in theab plane. Such noncollinear antiferromagnetic spin orderin the Kagome bilayer is characterized by cluster magnetic
octupole moments, which macroscopically breaks timereversal symmetry. Deep understanding of the dynamical
properties of Mn3Sn in the THz frequency range is highly
desired for ultrafast readout of the antiferromagnetic spinorder to develop novel functional devices.
In another point of view, Mn3Sn has also been interested
as a possible candidate for Weyl semimetals with broken
time-reversal symmetry, or “Weyl (antiferro)magnets”, whichhost massless electron dispersions with opposite chirality
in the vicinity of the Fermi energy [2]. Since the ac anomalous Hall effect is directly related to the interband excitation
across the Weyl nodes, a number of theoretical efforts havebeen recently devoted to investigating the ac anomalous Hall
conductivity in σxy(ω) Weyl semimetals. Investigating σxy(ω)

Fig. 1. (a) A schematic of THz wave polarization rotation in Mn3Sn
thin films depending on the antiferromagnetic spin order. (b)The experimental results of the polarization rotation spectra with different antiferromagnetic spin orders.

Fig. 2. (a) Frequency dependence of real- and imaginary-part anomalous Hall conductivity, indicating non-dissipative and dissipative part,respectively. (b) Temperature dependence of the real-part anomalous
Hall conductivity.

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ISSP Activity Report 2019

experimentally is therefore important for understanding
novel electromagnetic responses related with the Berrycurvature in Weyl semimetals.
Frequency dependence of the AHE can be observed in
an optical method by measuring the polarization rotation oftransmitted light. It is based on the relation between σxy(ω)
and the polarization rotation angle θ(ω):σxy(ω)Z0dθ (ω) + iη(ω) = ⎯⎯⎯⎯⎯⎯⎯⎯
1 + ns + σxy(ω)Z0d
where η(ω) an ellipticity angle, d the film thickness, Z0 thevacuum impedance, ns the substrate refractive index, and σxx
the longitudinal conductivity. In the present work, we developed polarization-resolved THz time-domain spectroscopy
setups with precise polarization resolution up to 0.05 mradin 0.5-2.0 THz frequency window for 20-min accumulation
time [3]. Figure 1(a) shows a schematic of our measurement.
Using Mn3Sn thin films with 50-200 nm thicknesses [4],we clearly observed the polarization rotation of transmitted
THz wave at room temperature and zero magnetic field asshown in Fig. 1(b), depending on the direction of the cluster
magnetic octupole moments. The result quantitatively agrees
with the large AHE previously reported in the DC resistivity
measurement.
We also performed the polarization-resolved THz
spectroscopy with broad band frequency range up to 6 THz(25 meV) [3]. Figure 2(a) shows the result of real- andimaginary-part σxy(ω), corresponding to the non-dissipativeand dissipative Hall current, respectively. The results demonstrate small dissipation in the AHE up to THz frequencies,
which is consistent with an intrinsic origin of it. Figure 2(b)shows the temperature dependence of σxy(ω). The strong
suppression of σxy(ω) below 250 K is consistent with thespin-reorientation phase transition from the inverse-triangular structure to a helical spin ordering along the c-axis.
The development of the helical spin ordering along the c-axis
recovers the macroscopic time-reversal symmetry, which
results in the disappearance of the AHE.
The observation of the THz AHE at room temperaturedemonstrates the ultrafast readout for the antiferromagnetic
spintronics using Mn3Sn. Our all-optical approach in anoncontact way with picosecond time resolution also opens
a new avenue for studying nonequilibrium dynamics in Weyl
antiferromagnets.
References[1] S. Nakatsuji, N. Kiyohara, and T. Higo, Nature 527, 212 (2015).
[2] K. Kuroda et al., Nature Mater. 16, 1090 (2017).
[3] T. Matsuda, N. Kanda, T. Higo, N. P. Armitage, S. Nakatsuji, and R.
Matsunaga, Nature Commun. 11, 909 (2020).
[4] T. Higo, D. Qu, Y. Li, C. L. Chien, Y. Otani, and S. Nakatsuji, Appl.
Phys. Lett. 113, 202402 (2018).
Authors
T. Matsuda, N. Kanda, T. Higoa, N. P. Armitageb, S. Nakatsuji, and R.
Matsunaga
aCREST, Japan Science and Technology Agency
bThe Johns Hopkins University

Photoinduced Possible Superconducting
State with Long-Lived Disproportionate
Band Filling in FeSe
Okazaki Group
Photoexcitation is a very powerful way to instantaneously
drive a material into a novel quantum state without any fabrication, and variable ultrafast techniques have been developed to observe how electron, lattice, and spin degrees of
freedom change. One of the most spectacular phenomena is
photoinduced superconductivity, and it has been suggested incuprates that the transition temperature Tc can be enhanced
from the original Tc with significant lattice modulations.
Here, we demonstrate the possibility for another photoinduced high-Tc superconducting state in the iron-based
superconductor FeSe using time- and angle-resolved photoemission spectroscopy (TARPES) [1]. We find that a photoinduced superconducting gap appears as a result of significant lattice modulation. Our demonstration of how we canchange electron- as well as lattice-structure in FeSe by strong
photo-excitation provides important insight into the nextgeneration devices using photo-induced superconductors,
e.g. ultrafast switches or quantum engineering.
Figures 1a and 1b show the time-dependent oscillatory components of the photoemission intensity integrated
above the Fermi level (EF) after photo-excitation for the holeand electron Fermi surfaces (FSs), respectively. The fits bysinusoidal functions are shown as black solid lines. The clear
appearance of single cosine-like signature is noticed both forthe hole and electron FSs. The frequency of this oscillationis 5.3 THz, which corresponds to the A1g coherent phononmode shown in Fig. 1c. Moreover, the amplitude of theoscillation significantly increases with the increase of pumpfluence shown in Fig. 1d. These signatures indicate that theobserved coherent phonons is explained by the displacive
excitation mechanism, in which coherent phonons are generated as a result of the photo-induced modulation of the lattice
structure.
In order to study the photo-induced electronic state inmore detail, we further conducted long time-scale measure-Fig. 2. a, b. Shifts of the leading-edge midpoints (LEM) as a functionof time and pump fluence for the hole and electron FSs. In Fig. 2b, theaveraged superconducting gap, <∆> is shown as black solid lines andmarkers. c. Illustration of photoinduced LEM shifts for the hole (Г) andelectron (M) bands. |G> and |E> represent the ground and photoexcitedstates, respectively.

ments. Figures 2a and 2b show the photo-induced leadingedge midpoint (LEM) shifts for the electron and holes FSs as
a function of time and pump fluence, respectively. One cannotice that the LEM shift at the hole FS is negative, while theLEM shift at the electron FS is negligibly small. This unbalanced shift is due to disproportionate band filling schematically shown in Fig. 2c. It is of note that the disproportionate
band filling lasts for a quite long time of ~1ns owing to theindirect semimetallic band structure, where the electron-hole
recombination must accompany the assistance of phonons
with a large momentum.
The origin of the disproportionate band filling is most
likely ascribed to the emergence of photo-induced superconducting gap because FeSe has no other competing orders
such as the anti-ferromagnetic order in the equilibrium state.
To further investigate the photo-induced superconducting
gap, we extract the superconducting gap and performed
photo-intensity dependent measurements, as shown in
Fig. 2b. We find that with increasing photo intensity, thesuperconducting gap also increases, which suggests that theenhancement of superconducting order is enabled by tuning
light intensity.
In summary, our finding of the possible photo-induced
superconducting state for FeSe can provide another platformof photo-induced superconductivity. The significant property
in this system is the longevity of the photo-induced state,
which is also called metastable. According to the report inphoto-induced superconducting state in cuprates, the carrier
lifetime of FeSe is more than two orders of magnitude longer
than that of cuprates. In terms of device applications, thissignature is quite powerful because one can perform multiple
and complicated processes during this metastable state.
Reference[1] T. Suzuki, T. Someya, T. Hashimoto, S. Michimae, M. Watanabe,
M. Fujiwara, T. Kanai, N. Ishii, J. Itatani, S. Kasahara, Y. Matsuda,
T. Shibauchi, K. Okazaki, and S. Shin, Communications Physics, 2,
115 (2019).

Fig. 1. a, b. Oscillatory components for the time-dependent photoemission intensities integrated above Fermi Energy for the hole and electron
Fermi surfaces. c. Illustration of lattice modulation by photoexcitation,corresponding to A1g phonon mode. d. Fast Fourier transform (FFT)
amplitude at 5.3 THz for the hole and electron FSs as a function of thepump fluence.

Authors
T. Suzuki, T. Someya, T. Hashimoto, S. Michimae, M. Watanabe,
M. Fujiwara, T. Kanai, N. Ishii, J. Itatani, S. Kasaharaa, Y. Matsudaa,
T. Shibauchib, K. Okazaki, and S. ShinaKyoto University
bThe University of Tokyo

ISSP Activity Report 201939