Theoretical $T_1$ Calculation for Isotropic High Spin Molecules

TL;DR

This paper presents a theoretical calculation of the spin-lattice relaxation rate ($1/T_1$) in isotropic high spin molecules, comparing results with experiments and highlighting the importance of hyperfine interactions at low temperatures.

Contribution

It introduces a spin-phonon interaction-based model for $1/T_1$ in high spin molecules and discusses its limitations at low temperatures, emphasizing the role of hyperfine interactions.

Findings

The model agrees with experiments at high and intermediate temperatures.

Discrepancies appear at low temperatures, indicating other mechanisms are involved.

Hyperfine interactions are crucial for understanding low-temperature spin dynamics.

Abstract

We calculate the molecular-spin ($S$), temperature ($T$), and field ($H$) dependence of $1/T_1$ for a local magnetic probe coupled to an isotropic high spin molecule, based on spin-phonon interaction. We compare the calculation to recent NMR and $\mu$SR experiments in CrCu$_6$ ($S = 9/2$), CrNi$_6$ ($S = 15/2$) and CrMn$_6$ ($S = 27/2$). Although we can account for the high and intermediate temperature regimes, the calculation is fundamentally different from the data at $T \longrightarrow 0$. Since $1/T_1$ must be due to coupling of the molecular spin to an external heat bath, and since phonon contribution is ruled out at low $T$, we conclude that at these temperatures hyperfine interactions must play an important role in the molecular spin dynamic.