Magnetic-field dependence of spin-phonon relaxation and dephasing due to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>g</mml:mi></mml:math>-factor fluctuations from first principles

The electron spin decay lifetime in materials can be characterized by relaxation (${T}_{1}$) and irreversible (${T}_{2}$) and reversible (${T}_{2}^{*}$) decoherence processes. Their interplay leads to a complex dependence of spin lifetimes on the direction and magnitude of magnetic fields, which is relevant for spintronics and quantum information applications. Here, we use real-time first-principles density matrix dynamics simulations to directly simulate Hahn echo measurements, disentangle dephasing from decoherence, and predict ${T}_{1}$, ${T}_{2}$, and ${T}_{2}^{*}$ spin lifetimes. We show that $g$-factor fluctuations lead to nontrivial magnetic field dependence of each of these lifetimes in inversion-symmetric crystals of ${\mathrm{CsPbBr}}_{3}$ and silicon, even when only intrinsic spin-phonon scattering is present. Most importantly, fluctuations in the off-diagonal components of the $g$ tensor lead to a strong magnetic-field dependence of even the ${T}_{1}$ lifetime in silicon. Our calculations elucidate the detailed role of anisotropic $g$ factors in determining the spin dynamics even in simple, low spin-orbit coupling materials such as silicon.