Current-induced spin injection and surface torque in ferromagnetic metallic junctions

Effect of current on magnetization oscillations in the ferromagnet-antiferromagnet junction

“…The details of such calculations can be found in our previous publi cations [9,25]. Here, we will write the result for the case when thickness L AFM of the antiferromagnetic layer is much smaller than spin diffusion length l for the direction of current corresponding to the electron flux from the ferromagnet to the antiferromagnet: (7) where is the equilibrium (for zero current) magne tization of conduction electrons, Δm is the nonequi librium correction produced by the current, = M/ is the unit vector in the direction of magneti zation of the ferromagnet, is the analogous vector for the ferromagnet, μ B is the Bohr magneton, e is the electron charge, τ is the electron spin relaxation time, and j is the current density.…”

“…In our termi nology, these are (i) the transfer of spins and torque to the lattice by the current and (ii) injection of nonequi librium spins by current to the conduction band. Both modes were discussed by us earlier [22][23][24][25]. It will be shown below that these modes also affect the interac tion of polarized current with the AFM layer in differ ent ways.…”

Disturbance of spin equilibrium by current through the interface of noncollinear ferromagnets

“…In the both cases, there is a single quantization axis. Meanwhile, the boundary conditions determining spin current through a contact of two noncollinear ferromagnets are significant for a number of problems concerning spin-polarized current induced spin switching [7]. Such type of boundary conditions are treated in the present work.…”

“…Very different spin relaxation times correspond to the longitudinal and transverse polarizations, so only the longitudinal component J z ′ x = J zx cos χ survives beyond a thin layer of Fermi wavelength thickness (the so called Berger-Slonczewski layer, see [7] for details). This gives a boundary condition for the electron magnetization flux density at the interface between the ferromagnets x = 0:…”

“…whereD = (D + σ − +D − σ + )/σ is effective spin diffusion constant, D ± are partial electron diffusion constants, σ ± are partial conductivities, σ = σ + + σ − is total conductivity, Q = (σ + − σ − )/σ is conduction polarization coefficient (see [7] for details). The stationary solution of Eq.…”