Abstract
The spin relaxation time in solids is determined by several competing energy scales and processes and distinct methods are called for to analyze the various regimes. We present a stochastic model for the spin dynamics in solids which is equivalent to solving the spin Boltzmann equation and takes the relevant processes into account on equal footing. The calculations reveal yet unknown parts of the spin-relaxation phase diagram, where strong spin-dephasing occurs in addition to spin-relaxation. Spin-relaxation times are obtained for this regime by introducing the numerical Loschmidt echo. This allows us to construct a generic approximate formula for the spin-relaxation time, $\tau_{\text{s}}$, for the entire phase diagram, involving the quasiparticle scattering rate, $\Gamma$, spin-orbit coupling strength, $\mathcal{L}$, and a magnetic term, $\Delta_{\text{Z}}$ due to the Zeeman effect. The generic expression reads as $\hbar/\tau_{\text{s}}\approx \Gamma\cdot \mathcal{L}^2 /(\Gamma^2+\mathcal{L}^2+\Delta_{\text{Z}}^2)$.
Highlights
The emerging field of spintronics [1,2] envisions to employ the electron spin as an information carrier instead of the usual charge degree of freedom, allowing for more efficient and high-performance future informatics devices
Fabian et al (Ref. [31]) showed that a proper description of spin dynamics can be obtained by treating the electron spin quantum mechanically and the electron momentum quasiclassically
Spin-dephasing regime of spin dynamics, which occurs due to a strong spin-orbit coupling (SOC)
Summary
The emerging field of spintronics [1,2] envisions to employ the electron spin as an information carrier instead of the usual charge degree of freedom, allowing for more efficient and high-performance future informatics devices. The presence of reversible dephasing smears the irreversible effects and the determination of the spin-relaxation time. This motivated us to develop a numerical approach to the dynamics of spins of noninteracting electrons, which includes momentum scattering and spin precession under the action of an external and the SOC-related magnetic fields. Spin-relaxation time can be obtained even in the presence of strong reversible dephasing with the introduction of a numerical Loschmidt echo. This allowed us to construct the full phase diagram of ( , L, Z) and we find that a generic formula s≈.
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