Studies of transverse and longitudinal relaxations of $^{55}$Mn in molecular cluster magnet Mn$_{12}$Ac

TL;DR

This study measures the relaxation rates of $^{55}$Mn in Mn$_{12}$Ac at very low temperatures and high magnetic fields, revealing how these rates decrease with temperature and field, and explaining the results with a simple spin-phonon interaction model.

Contribution

It provides a detailed analysis of $^{55}$Mn relaxation rates in Mn$_{12}$Ac using a simplified model of thermal fluctuations due to spin-phonon interactions, linking experimental data to theoretical interpretation.

Findings

Both $1/T_2$ and $1/T_1$ decrease with lower temperature and higher magnetic field.

$T_1/T_2$ ratio is approximately 200 across conditions.

Relaxation rates are explained by a model involving excitation to the first excited state with specific lifetime assumptions.

Abstract

The transverse and longitudinal relaxation rates 1/$T_2$ and 1/$T_1$ of $^{55}$Mn in molecular cluster magnet Mn$_{12}$Ac have been measured al low temperatures down to 200mK and in the fields upto 9T. Both of 1/$T_2$ and 1/$T_1$ exhibit remarkable decreases with decreasing temperature and with increasing field, with the relative relation $T_1/T_2 \approx 200$. In the analysis, we adopt a simple model that the thermal fluctuation of the cluster spin $S$=10 associated with the spin-phonon interactionis, is only due to the excitation to the first excited state from the ground state with the average life-times $\tau_ 1$ and $\tau_0$ ($\tau_ 0$$\gg$$\tau_1$). We show that 1/$T_2$ is interpreted in terms of the strong collision regime as given by 1/$\tau_ 0$, and that 1/$T_1$ is understood by the high-frequency limit based on standard perturbation treatment for the step-wise fluctuating field, thus being proportional to 1/$\tau_0\omega_N^2$.