High-field NMR study of the spin correlations in the spin-cluster mineral Na$_2$Cu$_3$O(SO$_4$)$_3$

TL;DR

This study uses high-field NMR to investigate spin correlations and excitation gaps in the spin-cluster mineral Na$_2$Cu$_3$O(SO$_4$)$_3$, revealing long-range order, spin anisotropy, and field-dependent gaps.

Contribution

It provides the first detailed high-field NMR analysis of spin correlations and excitation gaps in Na$_2$Cu$_3$O(SO$_4$)$_3$, highlighting short-range order and anisotropy effects.

Findings

Long-range magnetic order observed at $T_N$

Spin excitation gap increases linearly with magnetic field

Presence of short-range order and easy-plane anisotropy

Abstract

We report NMR study on the spin correlations in the spin-cluster based mineral Na$_2$Cu$_3$O(SO$_4$)$_3$ with magnetic fields ranged from 1 T to 33 T. The long-range magnetic order is observed from both the sudden spectral broadening at $T_N$ and critical slowing down behavior in the temperature dependence of spin-lattice relaxation rates ($1/T_1(T)$). The hump behavior of $1/T_1(T)$ persists to $\mu_0H=7.25$ T, above which a spin excitation gap is observed from the thermally activated temperature dependence of $1/T_1$. The gap size shows a linear field dependence, whose slope and intercept respectively yield an effective magnetic moment of 2.54 $\mu_B$ and a 0.94 meV spin excitation gap under zero magnetic field. These results indicate the existence of short-range order and prominent easy-plane spin anisotropy, which are important for understanding the spin excitation spectrum in A$_2$Cu$_3$O(SO$_4$)$_3$.