Research Group for Spin-Energy Transformation ScienceGroup Leader: SAITOH Eiji
Members: MORI Michiyasu, ONISHI Hiroaki, IEDA Jun’ichi, NAKATA Koki, YAMAMOTOKei, ARAKI Yasufumi, OKAYASU Satoru, ONO Masao, CHUDO Hiroyuki, SATO Nana, IMAIMasaki

Research on mutual energy conversion among various forms isa key for improving energy efficiency and further thesustainability of energy. We study the energy conversion using
electron spins and their couplings to another type of angularmomentum, including mechanical rotation.
Tuneable Nano-scale Inductor Toward Power-spintronics
A coil of a conducting wire induces an electromotive force(EMF) by applying an electric current. This is a classical inductor,
being an important element of power electronics for electric
voltage transformation and electric noise filtering. The magnitudeof the inductance, is proportional to the cross-section of the coil.
This feature, however, is a crucial restriction to reduce the size ofinductors (Fig.1 left). Recently, researchers in RIKEN haveproposed a quantum mechanical version of inductors called“emergent inductor” (EI) using a spiral magnet that exhibits
totally opposite system size dependence (Fig. 1 right) and theconcept has been experimentally demonstrated [1,2]. Motivatedby these findings, we have extended the theory of EI by including
the Rashba spin-orbit coupling (RSOC) and the electron spin
relaxation [3]. Notably, in the spiral magnet with the RSOC, theEMF of the spin origin, i.e., spinmotive force (SMF) is composedof two parts: One is RSOC-free and depends on the derivativesof magnetization both in time and space. The other one is inducedby the RSOC. The latter is missing in the original proposal [1],but it gives rise to a significant impact on the magnitude of EI. Inaddition, our results indicate that the spin relaxation effect that
was also discarded in [1] is crucial in determining the overall signof the EI. If one can prepare a spiral magnet with 20 nm half-pitch
and the RSOC with a magnitude ~104 m/s, the RSOC effectresults in a large enhancement of the EI about three orders ofmagnitude. Furthermore, this enhancement factor can be tuned byelectrical gating because of the RSOC. Surprisingly, the spinrelaxation effect leads to negative EI. These two factors can betuned independently by electrical gating and appropriate material
choice. More importantly, our EI is enhanced in the small size incontrast to the classical inductor made of conducting wire. Ourresults will contribute to a nano-scale power supply circuit and anoise canceller of electromagnetic noise.

Sound waves in a solid are small deformations and distortionsof solid transmitted as vibrations. The Rayleigh wave is a soundwave propagating only along a surface, i.e., surface acoustic wave
(SAW), and is widely used as sensors and filters, because it canpropagate in any solid with a slower velocity and lower
attenuation than ordinary bulk sound waves propagating throughthe solid volume. In addition, many studies on spintronics focus
on the SAW to develop a new information carrier using electron
spins. For this purpose, a directional control of SAW is crucial.
We have predicted that the SAWs can be generated
preferentially in one direction in a magnetic film by applying adriving magnetic field (Fig. 2) [4]. The non-reciprocity of SAW
arises from magneto-elastic coupling and magneto-rotation
coupling. Equations of motion of magnetization and latticedisplacement are simultaneously solved under certain
assumptions, where only one spin wave mode couples dominatly
to the SAW instead of bulk phonons. The magnetic susceptibility
resulting from the equations indicates that the hybridization
between SAW and spin wave is very different for positive wave
numbers, k>0, and negative wave numbers, k<0. The SAWs
themselves are reciprocal, because both senses of rotation of theatoms at the surface in SAWs, i.e., clockwise and anticlockwise,
are allowed. However, their couplings with the magnetization
depend on the handedness formed by the wave vector of SAW,
the surface normal of the sample, and the magnetization. This
frame is switched from the left-handed to the right-handed andvice versa with chaging sign of k. This means that the nonreciprocity is already implemented in the coupling. Although its
magnitude is rather small, we have found that the non-reciprocity
is enhanced by the magnon-polaron resonance.
Our results will contribute to the development of an acoustic
rectifier for information processors using SAWs and effective useof waste heat by controlling SAWs in insulators.

Fig.2 Schematic of the magnetic film [4]. The ring surrounding the thickarrow at the centre indicates the precessing magnetisation and the otherrings at the back represent the rotation of surface atoms. In this figure,energy is dominantly channelled into SAWs propagating in the negativedirection.

Fig.1 Comparison of classical and quantum inductors. The size (crosssection) dependence is totally different between two systems [3].

Non-reciprocal Pumping of Surface Acoustic Waves

References[1] N. Nagaosa, Jpn. J. Appl. Phys. 58, 120909 (2019).
[2] T. Yokouchi et al., Nature 586, 232 (2020).
[3] J. Ieda et al., Phys. Rev. B 103, L100402 (2021).
[4] K. Yamamoto et al., J. Phys. Soc. Jpn. 89, 113702 (2020).