Theory of spin-charge conversion effects in spintronics are presented in terms of correlation functions of physical observables, spin and electric current. Direct and inverse spin Hall effects and spin pumping effect are studied considering metallic systems with random spin-orbit interaction and spatially nonuniform Rashba interaction.
The theory is free from ambiguity associated with spin current, and provides a clear physical picture of the spin-charge conversion effects. In the present approach, the spin current transmission efficiency turns out essentially to be the nonuniform component of magnetic susceptibility.
We concisely review the equivalence among the dynamics of spin, a spinning top, and an electron subjected to a magnetic monopole. The equivalence becomes clearer when the finite inertia of spin is taken into account. We describe how to calculate spin inertia, considering metallic ferromagnets as an example, where conduction electrons flow among localized magnetic moments. The presence of conduction electrons effectively changes the dynamics of the localized magnetic moments; in particular, the electrons add a finite inertial term to the magnetic moments. We also introduce the interesting history of monopole harmonics, which is a generalized concept of spherical harmonics describing an electron wave function subject to a monopole magnetic field. It is named by Wu and Yang in 1976, but the function itself appeared in much older literature, such as the Landau- Lifshitz's textbook on quantum mechanics. It appears in quantization of the motion of spinning tops or diatomic molecules, which was already considered in as early as 1926, soon after Schrodinger published his pioneering paper on quantum wave mechanics.
Current pumping by an external potential is studied on the basis of the Keldysh Green’s function method, and a pumping formula written in terms of retarded and advanced Green’s functions is obtained. The formula is used to study the spin pumping effect in the case of strong s-d exchange interaction, and the driving field is identified to be the spin gauge field. At the lowest order in the precession frequency of magnetization, the spin gauge field works as a constant potential, and the system is shown to reduce to a static problem of spin current generation by a time-independent potential with off-diagonal spin components.
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We theoretically explore the optical properties of a bulk Rashba conductor by calculating the transport coefficients at
finite frequencies. It is demonstrated that the combination of direct and inverse Edelstein effects leads to a softening of
the plasma frequency for the electric field perpendicular to the Rashba field, resulting in a hyperbolic electromagnetic
metamaterial. In the presence of magnetization, a significant enhancement of anisotropic propagation (directional
dichroism) is predicted because of the interband transition edge singularity. On the basis of an effective Hamiltonian
analysis, the dichroism is demonstrated to be driven by toroidal and quadratic moments of the magnetic Rashba system.
We theoretically explore the optical properties of a bulk Rashba conductor by calculating the transport coefficients at
finite frequencies. It is demonstrated that the combination of direct and inverse Edelstein effects leads to a softening of
the plasma frequency for the electric field perpendicular to the Rashba field, resulting in a hyperbolic electromagnetic
metamaterial. In the presence of magnetization, a significant enhancement of anisotropic propagation (directional
dichroism) is predicted because of the interband transition edge singularity. On the basis of an effective Hamiltonian
analysis, the dichroism is demonstrated to be driven by toroidal and quadratic moments of the magnetic Rashba system.
The effective theory of the cross-correlation effects has the same mathematical structure as that of insulating
multiferroics.
KEYWORDS: Ferromagnetics, Bismuth, System on a chip, Metals, Electron beams, Silicon, Resistance, Magnetism, Spintronics, Current controlled current source
Spin-charge conversion induced by spin-orbit coupling (SOC) is attractive topic for alternative magnetization manipulation and involved various novel phenomena. Particularly Bi-based structure draws interest due to its large Rashba-Edelstein effect (REE) at interface between non-magnetic metal and Bi [1]. A recent report showed that spin-to-charge current conversion becomes more efficient when Bi2O3 is employed on behalf of the Bi [2]. Here we report novel type of magnetoresistance (MR) in Co25Fe75/Cu/Bi2O3 multilayer. This novel MR comes from conversion between spin and charge current at Cu/Bi2O3 interface, and distinctive spin transfer torque dependent on magnetization of the ferromagnetic Co25Fe75 layer.
A Co25Fe75 (5)/Cu (0-30)/Bi2O3 (20) (unit:nm) multilayer was deposited with electron beam evaporation on shadow masked Si substrate. Hall bar shaped shadow mask was patterned with photo-lithography method. The MR measurement was performed via 4-point probe method with changing magnitude or angle of external field. Note that external field for angle dependent measurement was 6 T to make sure complete saturation of ferromagnetic layer. We found characteristic resistance drop when the magnetization of ferromagnetic layer is parallel to magnetic direction of spin accumulation, which is similar to spin Hall magnetoresistance (SMR) [3,4]. Further discussion will be given.
[1] J. C. Rojas Sanchez et al. Nature Comm. 4, 2944 (2013).
[2] S. Karube et al. Appl. Phys. Express. 9, 03301 (2016).
[3] H. Nakayama et al. Phys. Rev. Lett. 110, 206601 (2013).
[4] J. Kim et al. Phys. Rev. Lett. (in press).
We overview the recent developments in spin current generation mechanisms and study the spin pumping effect
and diffusive spin current in detail based on a microscopic theory. The spin-charge conversion using the inverse
spin Hall effect is also discussed. Spin chemical potential describing the diffusive spin current is calculated by
linear response theory and spin injection effect is discussed based on the result.
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