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TALK #3

Newman-Janis Algorithm on Asymptotically Flat Spacetimes
Tadashi Sasaki
Division of Physics, Graduate School of Science,
Hokkaido University, Sapporo 060-0810, JapanThe Newman-Janis algorithm was originally discovered as a curious transformation which generate a rotating
black hole solution of the Einstein equation from a non-rotating one[1]. The algorithm has been generalized toseveral classes of solutions[2][3], where the transformation typically takes the following form:iu′ = u + iT (θ, φ), r′ = r + D2 T (θ, φ), θ′ = θ, φ′ = φ,2where i is the imaginary unit, T is a function on S 2 , and D is covariant derivative on S 2 . Although there areseveral examples for the algorithm, the physical reason why such a complex transformation can work is notknown.
Interestingly, the above form of transformation resembles that of the BMS supertranslation[4],1u′ = u + α(θ, φ) + O(r−1 ), r′ = r + D2 α(θ, φ) + O(r−1 ), θ′ = θ, φ′ = φ,2where α(θ, φ) is an arbitrary function on S 2 . The supertranslation is one of the BMS transformations, whichis the symmetry of asymptotically flat spacetimes and has recently been studied as a key ingredient for solving
the black hole information loss problem.
Is this similarity accidental or not? For the first step to answer this question, we have investigated whether
the Newman-Janis-like complex transformation can apply to asymptotically flat spacetimes or not. We applied
generalized complex transformationu′ = u + U (θ, φ), r′ = r + R(θ, φ), θ′ = θ, φ′ = φ,to asymptotically flat spacetime, and obtaind a condition for the resultant spacetime to be a solution of theEinstein equation,"!
1i∂z ImR − D2 ImU + ∂u σ(0) ∂z̄ ReU = 0,2where z = eiφ cot(θ/2) is the stereographic coordinate on S 2 and σ(0) is called asymptotic shear.
If we consider the same transformation as the original NJ algorithm, that is, ReU = ReR = 0, then thecondition reduces to ImR = D2 ImU/2 + const., which is almost the same relation as the previously known
examples for NJ algorithm up to a constant.
Finally, we will discuss the possibility for unified understanding of the BMS symmetry and the Newman-Janisalgorithm, and future perspectives.

References[1] E. T. Newman and A. I. Janis, J. Math. Phys. 6 915 (1965)[2] C. J. Talbot, Commun. math. Phys. 13, 45-61 (1969)[3] H. Erbin, arXiv:1701.00037[gr-qc][4] H. Bondi, F.R.S., M. G. J. van der Burg, and A. W. K. Metzner, Proc. Roy. Soc. Ser. A, 269, 21-52(1962)[5] S. W. Hawking, M. J. Perry, and A. Strominger, Phys. Rev. Lett. 116, 231301 (2016)

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Chimera states in nonlocally coupled phase oscillatorswith higher harmonic interaction
Division of Physics, Hokkaido Univ.
Yusuke Suda, Koji Okuda
Under the balance of inflow and dissipation of energy, there often appear nonlinear oscillators
in various natural or artificial systems. In many cases, these oscillators interact with one
another, and compose a many-body system. Such systems are called coupled oscillator systems,
and studied numerously in a wide range of scientific fields for many years [1].
Synchronization is a famous phenomenon as a typical collective behavior of oscillators, while
there often appears a strange phenomenon called the chimera state, which is characterized by
the coexistence of the coherent synchronous and the incoherent not-synchronous regions, innonlocally coupled phase oscillators [2]! π∂dx′ G(x − x′ ) Γ (θ(x, t) − θ(x′ , t)),(1)
θ(x, t) = ω −
∂t
−π

(a) !

(b) !

"(x)

"(x)

where θ(x) is 2π-periodic phase on one-dimensional space x ∈ [−π, π] under the periodic boundary condition and ω is the natural frequency. The coupling kernel function G(x) characterizes
nonlocal coupling. The interaction between oscillators is described as the coupling function Γ ,and the sine coupling Γ (φ) = − sin(φ + α) with phase lag parameter α is generally used. It is
known that chimera states for Eq. (1) with the sine coupling, for example, as shown in Fig. 1(a)are spatial steady states which have steady mean fields. This steady mean field is a solution of
the self-consistent equation [2].
In contrast, when we especially use the Hansel-Mato-Meunier coupling Γ (φ) = − sin(φ +α) + r sin(2φ) where r is the amplitude ratio of the second harmonic component, chimera
states become more complicated [3]. In this study, we study the properties of such chimera
states numerically. For example, the mean field of the chimera state as shown in Fig. 1(b) is
temporally periodic, namely, not steady, so the phase distribution in the incoherent regions
change periodically. Furthermore, the coherent regions with different average frequencies exist
together. These properties can not be seen for steady chimera states mentioned above.

0
-!

0
-!

-!

0

x

!

-!

0

!

x

Figure 1: Chimera state in nonlocally coupled phase oscillators, Eq. (1). These figures show
the snapshot of phase θ(x). As the coupling function Γ , (a) the sine coupling and (b) the
Hansel-Mato-Meunier coupling are respectively used.
[1] Y. Kuramoto, Chemical Oscillation, Waves, and Turbulence (Springer, Berlin, 1984).
[2] Y. Kuramoto and D. Battogtokh, Nonlinear Phenom. Complex Syst. 5, 380 (2002).
[3] Y. Suda and K. Okuda, Phys. Rev. E 92, 060901(R) (2015).

TALK #7
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Resistivity Measurement under pressurein pseudo-N-(BEDT-TTF)4[(H3O)Ga(C2O4)3]·C6H5NO2

TALK #9

Dept. of Phys. Graduate School of Science Hokkaido Univ.
Kazuto MORIBE , Yosuke FUTAMI , Yoshihiko IHARA , Atsushi KAWAMOTO

Organic
conductor(BEDT-TTF)4[(H3O)Ga(C2O4)3]·C6H5NO2[BEDT-TTF(ET):bis(ethylenedithio)tetrathiafuluvalene] consists of conducting layers of
ET molecules and insulating layers of anions alternately. There are two isomorphic
materials E´ type salt and pseudo-N type salt. These salts have quasi-2-dimendional
electronic system. These salts have the different packing structure of ET molecules. In
the E´ type salt, ET molecules are stacking parallel each other. In the pseudo-N salt, one
ET dimmer is surrounded by six monomers. The E´-type salt shows superconducting
transition at 7 K [1]. On the other hand, the behavior of the temperature dependence ofresistivity in pseudo-N type salt is of insulator at ambient pressure. The band gap ofpseudo-N type salt can be estimated about 90 meV. The gap seems to be related to thecharge ordering. We can estimate the charge distribution from the bonding length ofcentral C=C bond [2]. The estimation of the charge on the ET molecules gives the value
about +1 for rich ET molecules (dimers) and 0 for poor ET molecules (monomers). This
distribution suggests the possibility of the difference of the physical properties.
Therefore this salt is so interesting. In general, the transfer integral of ET molecules
increases by applying pressures. This increase means that the band width becomes
broad and the band gap can disappear. Therefore this salt has the possibility to become
metal state by applying pressures. To investigate the behavior of the temperaturedependence of resistivity under pressure and the relationship with superconducting state,
we performed resistivity measurement under pressure using PPMS designed by
Quantum Design. For this measurement, wedeveloped a holder to mount a pressure cell on
the PPMS. Fig. 1 shows the temperaturedependence of resistivity at 1.3GPa andambient pressure. The behavior of resistivity
remains semiconducting behavior, but theabsolute value of resistivity is suppressed byapplying pressures. Now further measurement
under pressures is in progress.
Fig. 1 Temperature dependence of R
[1] H.Akutsu et al. , J. AM. CHEM. SOC. (2002) 124, 12430[2] P.Guionneau et al. , Synthetic Metals (1997)86, 1973

TALK
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Microscopic theory of the vortex-core charging insuperconductors
Dept. of Phys., Hokkaido Univ.
M. Ohuchi, H. Ueki and T. Kita
The vortex-core charging in a type-II superconductor has been observed experimentally [1].
Although a number of studies on vortex-charging have been carried out by using the mean
field theory of superconductivity such as the Bogoliubov–de Gennes (BdG) equations [2, 3],
the BdG equations cannot clarify dominant contribution to the vortex-charging. In addition,
it is difficult to incorporate Fermi-surface and gap anisotropies. On the other hand, all force
terms for describing charging in superconductors is missing from the standard Eilenberger
equations (i.e., the quasiclassical equations of superconductivity) that have been used to
study superconductors in a magnetic field microscopically.
Recently, study on the flux-flow Hall effect has been carried out by using the augmented
quasiclassical equations in the Keldysh formalism with the Lorentz and pair-potential gradient forces, which are effects of first order in quasiclassical parameter [4]. In addition, we havetransformed the augmented quasiclassical equations into Matsubara formalism, so that charging in superconductors can be calculated microscopically and quantitatively [5]. However, theresult obtained from the augmented quasiclassical equations may include an unreliable quantitative result depending on the parameter region, because the derivation of the equations
have been performed by using the perturbation expansion in the quasiclassical parameter andthe gradient expansion with the Moyal product.
We study the validity of the augmented quasiclassical equations by calculating the vortexcore charging of a two-dimensional s-wave superconductor in comparison with the result basedon the BdG equations and clarify dominant contribution to the vortex-charging. Since theaugmented quasiclassical equations has the possibility to clarify the transport phenomenon
in type-II superconductors such as the flux-flow Hall effect in the presences of the spatial
inhomogeneity and vortex motion, it is very important to verify the validity of the equation.

[1] K. Kumagai, K. Nozaki, and Y. Matsuda, Phys. Rev. B 63, 144502 (2001).
[2] M. Matsumoto and R. Heeb, Phys. Rev. B 65, 014504 (2001).
[3] M. Machida and T. Koyama, Phys. Rev. Lett. 90, 077003 (2003).
[4] E. Arahata and Y. Kato, J. Low Temp. Phys. 175, 346 (2014).
[5] M. Ohuchi, H. Ueki, T. Kita, J. Phys. Soc. Jpn. 86, 073702 (2017).

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K[[S)M-"'9):"69)B[S)B[BBdB[\ZTALK #13

Magnetic ordering in the Hubbard model with two types ofantisymmetric spin-orbit couplings on a zigzag chain
Dept. of Phys., Hokkaido Univ.
M. Yatsushiro and S. Hayami
An effective antisymmetric spin-orbit coupling (ASOC), which originates from the atomic
spin-orbit coupling without the inversion symmetry, has attracted since it gives rise to various fascinating phenomena, such as the Dirac electrons at the surface of topological insulator
and noncentrosymmetric superconductivity. In these systems, spontaneous magnetic orderings lead to magnetoelectric phenomena, where the magnetization (electric polarization) is
induced by an electric (magnetic) field, since time reversal symmetry is no longer presereved.
Meanwhile, similar situations occur even in the centrosymmetric systems, e.g. a zigzag chain
and honeycomb structure, where the inversion center is missing at each lattice site [1, 2].
Reflecting the lack of the inversion center at lattice sites, the ASOC is induced in a staggered
way. Once the staggered magnetic ordering breaking the spatial inversion symmetry occurs,
the uniform ASOC is activated, which results in similar magnetoelectric phenomena. Furthermore, the staggered magnetic ordering on such lattice structures simultaneously activates
odd-parity multipoles, such as magnetic quadrupole and toroidal dipole [3]. Thus, it is intriguing problem to clarify when and how the magnetic orderings with odd-parity multipoles
are stabilized in the fundamental model.
In this study, we focus on how the ASOC affects the magnetic orderings from the viewpointof stability. We consider the minimal Hubbard model including the staggered ASOC on a
one-dimensional zigzag chain [4]. By performing the mean field calculations, we obtain the
ground-state phase diagram by changing the amplitude of the ASOC. In addition to thestaggered ASOC, we consider the contribution of the uniform ASOC, which appears by thesurface and domain effect. We show the parameter space where the magnetic orderings with
odd-parity multipoles are realized and discuss how the band structures are modified under
odd-parity multipoles.

[1] Y. Yanase: J. Phys. Soc. Jpn. 83 (2014) 014703.
[2] S. Hayami, H. Kusunose, and Y. Motome: Phys. Rev. B 90 (2014) 024432.
[3] S. Hayami, H. Kusunose, and Y. Motome: J. Phys.: Condens. Matter 28 (2016) 395601.
[4] Y. Yanase and H. Harima: Kotai Butsuri 46 (2011) 229-239; 46 (2011) 283-292; 47 (2012)
101-111.

TALK #14

The New Muon Spin Relaxation Functions for One-Two sourcesof Distributed Field on Muon Sites
Muhamad Darwis Umar 1,2) and Isao Watanabe1,2
1)
2)

RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan,
Department of Physics, Hokkaido University, Sapporo, Hokkaido, 060-0810, Japan,

Lineshapes of muon spin relaxation functions for some materials, for instance a quasi onedimensional spin-1/2 molecular chain [1] and spin gap antiferromagnetic materials: SpinPeierls [2]-spin ladder [3,4], show neither purely Gaussian nor purely Gaussian. The
distributed internal field on muon sites of these lineshape for both static or dynamics
behaviour can be produced by one source or more. To get appropiate physical information ofthese materials via Muon Spin Spectroscopy, we use Kubo Golden Formula (KGR) to
developed analytical muon spin relaxation functions for intermediate static field distribution
for both one source and two-source cases. Our derivation for zero field cases corfirms theprevious results [3] and proposes new analytical forms for zero field and applied longitudinal
field cases. In our derivation, we can consistently show that KGR can be applied tolongitudinal field cases included to recovery the known function for longitudinal fieldLorentzian Kubo-Toyabe (LF-GKT)[5].
( (1t )0 %( (1t )0 %
exp&"
exp&"
#
#
0
0 $
0
+
21
1
$ 21 .,'')) J 1 (2 0 t )Pµ (Bext , t ) = 1 + 2
cos 2 0 t
1"",
"20 +2" 0 +1
2 0 - (" 0 + 3) */t
2 0 (" 0 + 3)(" 2 0 + 2 )20

21 2 0J 0 (2 0 t )" 2
2 0 (" 0 + 3)(" 20 + 3)

( (1t )0 %( (1t )0 %cos 2 0 t exp&"
exp&"
#
#
0 $
0 $
21 2 0''"(" 20 + 3)(" 0 + 3)(" 20 + 2)2 02
t "20 +2
t "20 +2

213 0
J (2 / )"(" 0 + 3)(" 20 + 3)2 02 !0 0 0t( (1/ )0 %
exp&"
#
0 $
'

/ "30 + 3.
+.
+t
21 2 01)),," ,," 1)) ! J 0 (2 0/ )- (" 0 + 3)(" 2 0 + 2 ) *- (" 2 0 + 3) * 0"

21 3 0.
,1(" 0 + 3)(" 20 + 2)2 02 ,- (" 20 + 3)+t" 1)) ! cos 2 0/
*0

21 0
d/ "
J (2 / )(" 0 + 3) !0 0 0t( (1/ )0 %
exp&"
#
0 $
'

/ " 2 0 +1
( (1/ )0 %
exp&"
#
0 $
'

/ "30 + 3

( (1/ )0 %
exp&"
#
0 $
'

/ " 0 +1

" µ Bext ! = 10
" µ Bext ! = 5d/" µ Bext ! = 3d/" µ Bext ! = 2d/" µ Bext ! = 1

1< ! < 2) ("! )3 2 & 4 "3 t
) ("! )3 2 &
2"3 2Pµ (Bext , t ) = 1 *J1 (#0t )! 1 2 exp'*
J (#0! )exp'*
$+
$ d!
2 + 0
3#0
( 3 2 % 3 #0 0
( 32 %) ("! ) & 4 ") ("! ) &4
cos(#0! )exp'** "3 2 + J 0 (#0! )! 1 2 exp'*
$*
$ d!
2 +
3
0
( 3 2 % 3 #0 0
( 32 %t! = 1.5

32

3 t

32

! = 1.75# = 4.9 " 10 5 s !1
µs

The muon spin relaxation function of one source-between
Gaussian-Lorentzian distributions in longitudinal field plotted
for the different ratio of applied field to width.

References[1] T. Lancaster, et. al., Phys. Rev. B 73, 020410(R) (2006)[2] S. J. Blundel, et al., J. Phys.: Condens. Matter 9, L119-L124 (1997)[3] R. C. Williams, et. al., Phys. Rev. B 93, 140406(R) (2016)[4] M. I. Larkin, et al., Phys. Rev. Lett. 85, 9, 1982 (2000)[5] M.I. Larkin, et al., Physica B, 289-290, 153-156 (2000)

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Anomalous antiferromagnetic resonance of-(BETS)2FeCl4 in antiferromagnetic insulating phase
Taehoon Lee1,2, Yugo Oshima1,2, Hengbo Cui1 and Reizo Kato1
RIKEN1, Hokkaido University2-(BETS)2FeCl4, where BETS is bis(ethylenedithio)tetraselenafulvalene, is awell-known charge transfer salt which shows a superconducting state at highmagnetic field. 7KLV V\VWHP LV FRPSRVHG IURP WKH FRQGXFWLQJ Œ-electrons of BETS
molecules and the magnetic d-electrons of Fe spins, and it is considered that strong
LQWHUDFWLRQ EHWZHHQ WKH Œ- and d-electrons exists. While paramagnetic and metallic
behaviors are observed in the high temperature phase, the system turn into an
antiferromagnetic insulating (AFI) state below 8.3 K. It was previously believed
WKDW WKH PHWDO WR LQVXODWRU WUDQVLWLRQ RI WKH Œ-electrons is due to theantiferromagnetic long-range order of the d-electrons. However, recent heat
capacity measurement observed a huge excess specific heat below 8.3 K, and its
origin was explained from the contribution of paramagnetic d-electrons [4]. It
suggests that the d-electron remains paramagnetic below 8.3 K and only WKH Œelectrons becomes antiferromagnetic and localized. However, this explanation is
QRW FRQVLVWHQW ZLWK WKH H[LVWHQFH RI VWURQJ Œ-d interaction, and contradicts withprevious electron spin resonance (ESR) studies [1-3].
To have a better understanding of the
AFI phase, we have performed ESR
measurements. When the magnetic field
is applied parallel to the easy-axis, wehave observed the easy-axis mode of
AFMR below 5 T, however, the easyaxis mode of AFMR changes to hardaxis mode of AFMR above 5 T (asshown Fig. 1). It suggests that a changeof the easy-axis occurs above 5 T. This
unconventional magnetic properties of-(BETS)2FeCl4 should be strongly
connected with the electronic state of
WKH Œ-electrons. Our ESR results will bepresented in detail, and the AFI phaseFig. 1 : Frequency-field dependence of
RI -(BETS)2FeCl4 will be discussed.
AFMR (B//easy-axis, T = 2 K)
The inset shows frequency-fielddependence of conventional AFMR
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5

TALK #17

Ground state of M-component Bose Einstein condensateswith 3/2-body interactions
Wataru Kohno, Akimitsu Kirikoshi, Takafumi Kita
Department of Physics, Hokkaido University, Sapporo 060-0810, Japan,
e-mail: wataruv@phys.sci.hpkudai.ac.jp

As for describing weakly interacting BEC systems, Bogoliubov theory [1] has been widely
accepted, which brings the approximated effective Hamiltonian by an order of O(N) (N :total-particle number) into diagonal form. This approximation provides us an interesting
result that low-lying “quasi-particles” (single-particle modes) are equivalent with “phonons”(collective modes). In other words, this result indicates that the system behaves as acollection of non-interacting quasi-particles. Moreover, these modes satisfy with the strict
theorem for the ground state of a BEC system given by Hugenholtz and Pines [2]. Thus, thistheory has been used for BEC systems extensively as a physical approximation.
On the other hand, the contributions of 2-body interactions (collisions between quasiparticles) and 3/2-body interactions (collisions of two quasi-particles throws one of theminto the condensate and visa versa) which should be incorporated self-consistently are
neglected in Bogoliubov theory since the contributions are by an order of O(! !!! ).
Girardeau and Arnowitt [3] constructed a variational wave function for the ground state ofhomogeneous systems to evaluate the ground-state energy incorporating 2-body interactionsof quasi-particles. However, this improvement caused an unphysical energy gap in the
single-particle excitation spectrum unlike the Bogoliubov spectrum with a gapless linear
dispersion and an infinite lifetime in the long-wavelength limit, which is in contradiction to
the Hugenholtz–Pines theorem. With these backgrounds, a variational wave function for the
ground state with the contributions of 3/2-body interactions has been constructed recently[4]. This study shows that (i) the unphysical energy gap caused by 2-body interactions issuppressed by considering 3/2-body interactions and (ii) the width of the single-particle
spectrum is finite even in the long-wavelength limit and thus the single-particle mode andthe collective mode in a BEC system are distinguishable in terms of respective lifetimes.
In this presentation, we develop the variational method [4] and construct a ground-state
wave function of weakly interacting M-component BECs. The method, results andconsiderations will be shown in detail in our presentation.
References[1] N. N. Bogoliubov, J. Phys. (USSR) 11, 23 (1947).
[2] N. M. Hugenholtz and D. Pines, Phys. Rev. 116, 489 (1959).
[3] M. Girardeau and R. Arnowitt, Phys. Rev. 113, 755 (1959).
[4] T. Kita, J. Phys. Soc. Jpn. 86, 044003 (2017).

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Magnetic properties of S = 5/2 triangular lattice dimer Cs3 Fe2 Cl9
1

Y. Ishii, 2 Y. Matsushita, 1 H. Yoshida, 1 M. Oda, 3 M. Hagihala, 4 T. Masuda, 5 T. Kida,
5
Y. Narumi, and 5 M. Hagiwara.

1

Dept.of Phys.Grad .Sch.Sci ., Hokkaido Univ ., 2 National Institute for Material Science,
3
KEK − IMSS , 4 ISSP , 5 AHMF .Dept.of Phys.Grad .Sch.Sci .Osaka Univ .
Cs3 Fe2 Cl9 is one of the members of A3 M 2 X 9 (A = Cs, Rb ; M = Ti, V, Cr, Fe ; X= Cl, Br, I) series compounds. The crystal structure consists of the triangular lattice made of(Fe2 Cl9 )3− dimers (Fig. 1 (a)). Three dominant magnetic interactions, the intra-dimer interaction J , and the inter-dimer interactions J , J are considered in this system[1] . These competing0pcinteractions can evoke exotic phenomena.
We succeeded in synthesizing the single crystals of Cs3 Fe2 Cl9 by the hydrothermal synthesis
and measured the magnetic properties and the heat capacity on the single crystal. In the previous
reports, the magnetic susceptibility of the powder sample showed no magnetic order[2] . However,
our magnetic and heat capacity measurements on the single crystal revealed that Cs3 Fe2 Cl9 exhibited the antiferromagnetic long-range order at TN = 5.3 K under zero magnetic field. Unlike
a normal antiferromagnetic transition, the easy-axis (c-axis) magnetic susceptibility showed thesudden drop at TN and then it decreased toward zero with T-linear temperature dependence(Fig. 1 (b)). Increasing magnetic field, the susceptibilities below TN show drastic changes (Fig.
1 (b)). In addition, the magnetization show the metamagnetic transitions and the 1/2 magnetization plateau (Fig. 1 (c)).
In my presentation, I will show more detail experimental results and discuss the magnetismof Cs3 Fe2 Cl9 .

(a)

(b)

Fe3+

Cl-

H

±

±

¢

c axis³°²+

M / MS

5 T ZFC
5 T FC

3 T ZFC
3 T FC

H // c - axis 1.4 K
0.1 T ZFC
0.1 T FC
1 T ZFC
1 T FC

²° ²·

Jp

c

²° ²²

a

b

²°
·

²° ³²

dM/dH (a. u.)

J0

M / H (emu / mol Fe)

²° ³·

Jc
Cs

(c)
7 T ZFC
7 T FC

²

´

¶

¸

º

²°
²

²

³²

´²

µ²

³²

T (K)

H (T)

Fig. 1: (a)The perspective view of the crystal structure of Cs3 Fe2 Cl9 . (b)The magnetic susceptibilities of Cs3 Fe2 Cl9 under several fields (H // c - axis). (c)The high field magnetization (upperside) and the field differential of the high field magnetization (lower side) at 1.4 K (H // c axis).

References[1] B Leuenberger and Hans U. Güdel, Journal of Solid State Chemistry, 64, 90-101 (1986).
[2] A. P. Ginsberg and M. B. Robin, Inorg. Chem., 2, 817-822 (1963).
1

TALK #20

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Rubidium superoxide is one of alkali metal superoxides (AO2; A = Na, K, Rb,
and Cs). The magnetic properties of these systems result from the partially filled
p-electron levels of the superoxide anion O2±. In the O2±, three electrons occupy a
SDLU RI GHJHQHUDWH DQWLERQWLQJ Œ PROHFXODU RUELWDOV WKXV WKHUH LV RQH XQSDLUHG
spin (5 L s t). All AO2 compounds undergo structural distortions splitting theGHJHQHUDF\ RI WKH Œ on cooling [1]. In the case of CsO2, a magnetic ordering isobserved below 10 K [2,3]. We have confirmed this ordered state to be a longrange one by usiQJ 65 7KH PDJQHWLF RUGHU was observed at the temperature
below ~ 9 K. This system also provides rare simple manifestations of the coupling
between spin, lattice, and orbital degrees of fredom [4].
We also studied another alkali metal superoxide, RbO2. We have checked thesample quality by the X-ray powder diffraction and the magnetic properties bysusceptibility
measurements. We havecarried out the ZF- and LF-PSR
measurements to investigate the magnetic
order in RbO2. As the temperature decreases,
the time spectrum started to change and themuon-spin precession behavior appear
below about 15 K. In our presentation, weare going to report detailed results recently
achieved in RbO2, in conjunction with theresults in CsO2.
)LJXUH =HUR ILHOG WLPH VSHFWUXP RI 5E2
DW WKH YDULRXV WHPSHUDWXUHReferences:[1] S. Riyadi et al., Phys. Rev. Lett. 108, 217206 (2012).
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Hysteretic response to electric current observed in toroidal
magnetic ordered state on UNi4B
A

Grad. School of Science, Hokkaido Univ., BKEK IMSS CMRC, CUK MFF

H. SaitoA, N. MiuraA, H HidakaA, T. YanagisawaA, H. AmitsukaA, C. TabataB,
0 9DOLãNDC . 8KOt RYiC - 3URNOHãNDC, and V. Sechovsk!C
Toroidal moment t is one of the parameters that describes the strength of the magnetoelectric coupling. It isdefined as the vector product of position r and spin S. It can be found in the Taylor expansion of Helmholtz
free energy with respect to electric field and magnetic field. In other words, toroidal moment t is one of thebasic notions in electromagnetism. In the last decade, the toroidal order, which is the ordered periodic arrayof toroidal moments, has attracted much interest in connection with multiferroic insulating materials.
Recently, S. Hayami et al. showed theoretically that such an exotic order can occur also in metallic systems,
and exotic phenomena such as magnetization induced by electric current can occur in the toroidal ordered
metal [1].
UNi4B is one of the candidate metals for the toroidal order. The orthorhombic structure in the present
compound (symmetry: Cmcm, D2h17, No. 63) is the structure slightly distorted from hexagonal
coordinates[2]. Since it is difficult to detect the distortion by Laue photography on single crystal, we
assume the structure as hexagonal in the present work. Below TN (= 20.4 K), it is suggested that it orders
antiferromagnetically in a magnetic structure where the magnetic moments carried by the 2/3 of U ions
make the vortices in each triangular planes [3]. This magnetic structure is the same as that assumed in theabove theory. In order to test the theory, we have performed magnetization measurements under electric
current on UNi4B. We observed that magnetization is induced by constant electric current in the orderedstate of UNi4B [4]. Therefore, the validity of the theory is confirmed in part by the experiments.
However, the accuracy of the previous measurements is not high because of the existence of the magnetic
field generated by applied electric current during the measurement. In order to achieve higher accuracy, we
have tried magnetization measurement after applying square-wave pulsed current (³SXOVHG-current
PDJQHWL]DWLRQ PHDVXUHPHQW´) and reported briefly that pulsed-current also cause the change ofmagnetization below TN.
Recently, we succeeded in growing higher-quality single crystalline sample of UNi4B and got the chance
to continue above measurements in Charles University, Prague, Czech Republic. The results ofpulsed-current magnetization measurement for each settings of B || a, b-axes and J || a, b, and c-axes will
be presented. Then, we'll discuss about the possible cause of the strange response of magnetization toelectric current.
This work was supported by JSPS KAKENHI Grant Number JP15H05885 and JP15K21732 (J-Physics).
Experiments were performed in the Materials Growth and Measurement Laboratory MGML (see:http://mgml.eu).
[1] S. Hayami, H. Kusunose, and Y. Motome, Phys. Rev. B 90, 024432 (2014).
% unki, Physica B 403 900-902 (2008).
[2] Y. Haga, A. Oyamada, T. D. Matsuda, S. Ikeda, and Y. 2
[3] S. A. M. Mentink, A. Drost, G. J. Nieuwenhuys, E. Frikkee, A. A. Menovsky, and J. A. Mydosh, Phys.
Rev. Lett. 73, 1031 (1994).
[4] H. Saito, K. Uenishi, N. Miura, C. Tabata, H. Hidaka, T. Yanagisawa, and H. Amitsuka, 20th
International Conference on Magnetism (Barcelona), TU.A-P67 (2015).

TALK
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