Spin accumulation and longitudinal spin diffusion of magnets

Article

关键词: IRREVERSIBLE-PROCESSES;    RECIPROCAL RELATIONS;    RESONANCE;    TRANSMISSION;    RELAXATION;    ELECTRONS;   

DOI  :  10.1103/PhysRevB.105.174441

来源: SCIE

【 摘 要 】

We extend to the longitudinal component of the magnetization the spintronics idea that a magnet near equilibrium can be described by two magnetic variables. One is the usual magnetization (M) over right arrow. The other is the nonequilibrium quantity (m) over right arrow, called the spin accumulation, by which the nonequilibrium spin current can be transported. (M) over right arrow represents a correlated distribution of a very large number of degrees of freedom, as expressed in some equilibrium distribution function for the excitations; we therefore forbid (M) over right arrow to diffuse, but we permit (M) over right arrow to decay. On the other hand, we permit (m) over right arrow, due to spin excitations, to both diffuse and decay. For this physical picture, diffusion from a given region occurs by decay of (M) over right arrow to (m) over right arrow, then by diffusion of (m) over right arrow, and finally by decay of (m) over right arrow to (M) over right arrow in another region. This somewhat slows down the diffusion process. Restricting ourselves to the longitudinal variables M and m with equilibrium properties M-eq = M-0 + chi(M parallel to) H and m(eq) = 0, we argue that the effective energy density must include a new, thermodynamically required exchange constant lambda(M) = -1/chi(M parallel to). We then develop the appropriate macroscopic equations by applying Onsager's irreversible thermodynamics and use the resulting equations to study the space and time response. At fixed real frequency omega there is, as usual, a single pair of complex wave vectors +/- k but with an unusual dependence on omega. At fixed real wave vector, there are two decay constants, as opposed to one in the usual case. Extending the idea that nonequilibrium diffusion in other ordered systems involves a nonequilibrium quantity, this work suggests that, in a superconductor, the order parameter Delta can decay but not diffuse, but a nonequilibrium gap-like delta, due to pair excitations, can both decay and diffuse.

【 授权许可】

Free