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首页> 外文期刊>Physical review. B, Condensed Matter And Materials Physics >Description of spin transport and precession in spin-orbit coupling systems and general equation of continuity
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Description of spin transport and precession in spin-orbit coupling systems and general equation of continuity

机译：自旋轨道耦合系统中自旋输运和进动的描述以及连续性的一般方程

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摘要

By generalizing the usual current density to a matrix with respect to spin variables, a general equation of continuity satisfied by the density matrix and current density matrix has been derived. This equation holds in arbitrary spin-orbit coupling systems as long as its Hamiltonian can be expressed in terms of a power series in momentum. Thereby, the expressions of the current density matrix and a torque density matrix are obtained. The current density matrix completely describes both the usual current and spin current as well, while the torque density matrix describes the spin precession caused by a total effective magnetic field, which may include a realistic and an effective one due to the spin-orbit coupling. In contrast to the conventional definition of spin current, this expression contains an additional term if the Hamiltonian includes nonlinear spin-orbit couplings. Moreover, if the degree of the full Hamiltonian ≥3, then the particle current must also be modified in order to satisfy the local conservation law of number.
机译：通过将通常的电流密度归纳为关于自旋变量的矩阵，得出了密度矩阵和电流密度矩阵所满足的一般连续性方程。只要可以用动量的幂级数表示哈密顿量，该方程就可以在任意自旋轨道耦合系统中成立。由此，获得电流密度矩阵和转矩密度矩阵的表达式。电流密度矩阵还完整地描述了常规电流和自旋电流，而转矩密度矩阵描述了由总有效磁场引起的自旋进动，由于自旋轨道耦合，该总有效磁场可能包括现实的和有效的磁场。与自旋电流的常规定义相反，如果哈密顿量包含非线性自旋轨道耦合，则该表达式包含一个附加项。此外，如果全汉密尔顿度≥3，则还必须修改粒子流，以满足局部数守恒律。

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