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The spin relaxation time in solids is determined by several competing energyscales and processes and distinct methods are called for to analyze the variousregimes. We present a stochastic model for the spin dynamics in solids which isequivalent to solving the spin Boltzmann equation and takes the relevantprocesses into account on equal footing. The calculations reveal yet unknownparts of the spin-relaxation phase diagram, where strong spin-dephasing occursin addition to spin-relaxation. Spin-relaxation times are obtained for thisregime by introducing the numerical Loschmidt echo. This allows us to constructa 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$\hbar/\tau_{\text{s}}\approx \Gamma\cdot \mathcal{L}^2/(\Gamma^2+\mathcal{L}^2+\Delta_{\text{Z}}^2)$.

The generic phase diagram of spin relaxation in solids and the Loschmidt echo