Universal mechanism of spin relaxation in solids

TL;DR

This paper derives a universal expression for spin relaxation mechanisms in solids, linking lattice rotations to spin-phonon interactions, and provides insights into decoherence limits for spin-based qubits.

Contribution

It introduces a universal formula for spin-phonon matrix elements due to lattice rotations and analyzes their effects on spin relaxation in solids.

Findings

Derived a universal expression for spin-phonon interactions.

Demonstrated the field dependence of transition rates for uniaxial spins.

Provided a lower bound on decoherence for spin qubits.

Abstract

We consider relaxation of a rigid spin cluster in an elastic medium in the presence of the magnetic field. Universal simple expression for spin-phonon matrix elements due to local rotations of the lattice is derived. The equivalence of the lattice frame and the laboratory frame approaches is established. For spin Hamiltonians with strong uniaxial anisotropy the field dependence of the transition rates due to rotations is analytically calculated and its universality is demonstrated. The role of time reversal symmetry in spin-phonon transitions has been elucidated. The theory provides lower bound on the decoherence of any spin-based solid-state qubit.