Tensorial Spin-Phonon Relaxation Reveals Mode-Selective Relaxation Pathways in a Single-Molecule Magnet

TL;DR

This paper introduces a first-principles computational framework to analyze spin relaxation in a single-molecule magnet, revealing mode-specific pathways and matching experimental relaxation times without empirical fitting.

Contribution

The authors develop a comprehensive first-principles method combining DFT and open-system formalism to compute mode-resolved spin relaxation in molecular qubits.

Findings

Only three vibrational modes dominate longitudinal relaxation.

A single mode largely accounts for transverse relaxation.

Computed relaxation times agree with experimental data.

Abstract

Understanding and controlling spin relaxation in molecular qubits is essential for developing chemically tunable quantum information platforms. We present a fully first-principles framework for computing the spin relaxation tensor in a single-molecule magnet, \ce{VOPc(OH)8}, by combining density functional theory with a mode-resolved open-system formalism. By expanding the spin Hamiltonian in vibrational normal modes and evaluating both linear and quadratic spin-phonon coupling tensors via finite differences of the $g$-tensor, we construct a relaxation tensor that enters a Lindblad-type quantum master equation. Our formalism captures both direct (one-phonon) and resonant-Raman (two-phonon) relaxation processes. Numerical analysis reveals a highly mode-selective structure: only three vibrational modes dominate longitudinal ($T_1$) decoherence, while a single mode accounts for the majority of transverse ($T_2$) relaxation. The computed relaxation times show excellent agreement with experimental measurements, without any empirical fitting. These results demonstrate that first-principles spin-phonon tensors can provide predictive insight into decoherence pathways and guide the rational design of molecular qubits.