Mechanical generation of spin current by spin-rotation coupling
M. Matsuo1,2), J. Ieda1,2), K. Harii2,3), E. Saitoh2,3,4) and S. Maekawa1,2)
1) : R.G. for Condensed Matter Theory, ASRC, JAEA 2): CREST, JST3): R.G. for Mechanical Control of Materials and Spin Systems, ASRC, JAEA 4): Tohoku Univ.

Spin current, a flow of spins, is a key concept in spintronics[1]. It can be generated by using couplings between an electronspin and other physical quantities such as a magnetic field,magnetization, and orbital degrees of freedom. These
conventional methods, however, force us to use magnetic
materials or rare metals with strong spin-orbit coupling. In thisstudy, we have presented a new route for spin-current
generation by considering the coupling between spin andmechanical rotation. Our method requires neither magnetic
moments nor spin-orbit coupling.
First we introduce spin-rotation coupling (SRC):H  S Ω ,where S is the electron spin angular momentum and Ω is themechanical rotation frequency. If we rewrite the SRC asH  S  B , where B  Ω 1 is an effective magnetic field
due to mechanical rotation with gyromagnetic ratio  , the SRC
can be regarded as the Zeeman coupling. Historically the SRC isknown as a fundamental origin of the Barnett and Einstein-deHaas effects and plays a crucial role in tests of general relativity
by use of gyroscopic effect in gravitational fields due to Earth.
However, it has not been used for controlling spin currents.
Here we consider rotational motion of the lattice:implies that larger spin current is obtained in a weaker spin-orbit
material such as Al and Cu.
Conventionally, generation of spin current in nonmagnetic
materials has required strong spin-orbit coupling because thespin Hall effect has been utilized. In other words, nonmagnetic
materials with short spin lifetimes have been used. On thecontrary, the mechanism proposed here requires longer spin
lifetimes to generate larger spin currents. This means that Al andCu, which have been considered as good materials for a spin
conducting channel, can be favorable for generating spin current.
In this sense, our findings offer more options for spin-current
generation in nonmagnets than ever before.

1Ω    t u2
where u is the displacement vector of the lattice. When thelattice vibration has transverse modes, Ω does not vanish. In
such a case, the mechanical angular momentum of the lattice
can be converted into spin angular momentum via SRC.
Especially, in the presence of surface acoustic waves (SAWs),
rotational deformations that vary in space and time are induced.
In this case, the gradient of rotational modes acts on an electron
spin as the gradient of a magnetic field. For an electron spin,
spin prefers to align to the effective magnetic field and to flow
form the bottom to the surface for smaller Zeeman energy [Fig.
1]. Consequently, the stripe pattern of the spin accumulationarises at the surface [Fig. 2].
We developed the spin diffusion equation in the presence ofSAWs [2,3] and solved it in the case of the SAW frequency
given byFig.1 Snapshot of mechanical generation of spin current induced by
the SAW. In the presence of a SAW propagating in the xdirection, a gradient of mechanical rotation around the z-axis isgenerated. The rotation can be regarded as an effective
magnetic field. Consequently, spins align to the z-axis and thez-polarized current flows along to the y direction.

Ω  x, y,t   Ω 0 exp  kt y  i  kx   t 

where Ω 0 is the amplitude of the SAW, k is the wave number,
kt is the transverse wave number, and ω is the frequency of themechanical resonator. From the solution, the spin current
generated by the SAW is given byJS  S  2 0 1  2
exp  kt y  i  kx   t   / 2 e ct

where  is the spin lifetime, ct is the transverse sound velocity,and ξ is related to the Poisson ratio ν as ξ = (0.875+1.12ν )/(1+ ν ). The result indicates that the spin current Js is
proportional to the spin lifetime. Generally, we have longer spin
lifetime in a material with weaker spin-orbit coupling. ThisFig.2 Spin accumulation induced on the surface.

References[1] S. Maekawa, S. Valenzuela, E. Saitoh, and T. Kimura, ed.,Spin Current (Oxford University Press, Oxford, 2012).
[2] M. Matsuo et al., Phys. Rev. B 87, 180402(R) (2013).
[3] J. Ieda et al., Solid State Comm. (Available online).