Research Group for Spin-Energy Transformation ScienceGroup Leader: Eiji Saitoh
Members : Michiyasu Mori, Hiroaki Onishi, Jun’ichi Ieda, Mamoru Matsuo, Bo Gu, Zhuo Xu,Yuichi Ohnuma, Satoru Okayasu, Masao Ono, Hiroyuki Chudo, Kazuya Harii, Yudai Ogata, RyoTakahashi, Masaki Imai

A spin current is a flow of the angular momentum andbecomes the most important issue in spintronics. It will
dramatically reduce energy consumption, because of the special
property of spin, i.e., its rotational motion is limited in one
direction under a magnetic field. Hence, we can expect someinteresting functionalities such as spin Seebeck effect, spin
motive force, and rectification of heat flow. Using thisadvantage of spins, we are pursuing our researches based on a
new principle to control mechanical, electromagnetic, andthermal energy flows. In this fiscal year, a spin-hydrodynamicgeneration, which was theoretically predicted by ourselves, hasbeen observed experimentally [1]. This subject is explained in
the Research Highlights. Other two interesting results are statedbelow.
Barnett Effect in Paramagnetic States
The angular momentum is an important quantity of rotating
object and a spin of electron is also one kind of angularmomentum, although the spin does not literally correspond to
the rotating motion. On a rotating frame, the rotational motion
plays a role of magnetic field. In 1915, Barnett found that amagnetization is induced in iron by a rotational motion. On theother hand, the Barnet effect has not been so far observed in aparamagnet, because of zero coercivity and small susceptibility,
which requires in situ observation under rapid rotation.
In this fiscal year, we have successfully observed the Barnett
effect in paramagnetic states of gadolinium (Gd) metal withrotational frequencies of up to 1.5 kHz above the Curie
temperature [2]. Figure 1 (a) shows the capsule and the Gd
sample used in our experiment, and their schematic figures areshown in Fig. 1 (b). The sample used in our study shows
ferromagnetic transition at 292.5±0.5 K. The Curie constant islarge because of Gd's 4f local moment with J=7/2 (S=7/2, L=0).
Therefore, magnetic susceptibility around room temperature ishigh. It allows us to measure small stray fields from themagnetized Gd sample by the rotation, even in paramagneticstates (See also Fig. 1 (b)). The relation between the inducedmagnetization and the frequency of rotation is plotted in Fig. 1(c). The ratio of the magnetization and the susceptibility
provides an effective magnetic field induced by the rotation.
From the gradient of the effective field as a function of thefrequency, one can estimate the gyromagnetic ratio of Gd as−29±5GHz/T, which is comparable to −28 GHz/T for anelectron in a vacuum or Gd compounds.

Gd sample (orange dots) and blank capsule (open circles) as afunction of the rotational frequency at 300±0.5 K [2].

Magnetic Excitations of Spin Nematic State in a Frustrated
Quantum Spin System
Correlated many-body systems have rich variety of quantum
phenomena. A frustrated quantum magnet with competinginteractions is an interesting example of correlated many-bodysystem of spins. In general, the combination of frustration andquantum ﬂuctuation prevents a magnetic order and then somenovel spin states are stabilized such as spin nemtic state. It is aspin analogue of the nematic liquid crystal and is currently
attracting much attention as a novel quantum state in magnetic
materials. However, it is not straightforward to observe the spin
nematic state, since it does not simply couple to a magnetic nor
an electric field. In order to clarify the properties of the spin
nematic state, we studied dynamical spin structure factors of afrustrated ferromagnetic chain in a magnetic field using
dynamical density matrix renormalization group (DMRG)
method [3]. As shown in Fig. 2, the longitudinal mode isgapless, while the transverse one has a gap. This result is inaccordance with quasi-long-ranged longitudinal and shortranged transverse spin correlations, respectively. We further
analyzed dynamical quadrupole structure factors to reveal
excitation dynamics of the nematic state, since the nematic stateis a multiple spin state. We found the gapless quadrupole
excitations indicating a quasi-long-ranged quadrupole
correlation characteristic to the spin nematic order. We hope thatthese features could be examined by inelastic neutron scatteringexperiments in a frustrated magnet such as, LiCuVO4.
Furthermore, we should observe gapless excitations in thequadrupole channel as an interesting future problem.
Fig.2 Intensity plots of the dynamical spin structure factor S(q,ω) (=x,y, z) with wave number q and energy  calculated by the dynamicalDMRG method. (a) z-component of S(q,ω) with magnetization, m=0,(b) Sz(q,ω) with m=0.125, and (c) x-component of S(q,ω) with
m=0.125. Note that, the lowest excitation with finite q is shifted fromq/=0.5 in the case of (b). This is a common character to the spin spiralstate.

References[1] R. Takahashi et al., Nature Phys. 12, 52 (2015)[2] M. Ono et al., Phys. Rev. B 92, 174424 (2015).
[3] H. Onishi, J. Phys. Soc. Jpn. 84, 083702 (2015).
Fig.1 (a) Capsule (left) and Gd sample (right) used in the experiment.
(b) Schematic figures corresponding to (a). (c) The magnetization of