Simulated nuclear spin-lattice relaxation in Heisenberg ferrimagnets: Indirect observation of quadratic dispersion relations

TL;DR

This paper investigates nuclear spin-lattice relaxation in Heisenberg ferrimagnets, revealing how relaxation rates relate to dispersion relations and magnetic interactions, with implications for understanding quantum magnetic systems.

Contribution

It introduces a theoretical framework for calculating relaxation times in spin-$(S,s)$ ferrimagnets, linking relaxation behavior to quadratic dispersion relations observed indirectly.

Findings

Relaxation rate $T_1^{-1}$ varies with temperature and field.

$T_1^{-1}$ is nearly proportional to $H^{-1/2}$ due to dispersion.

Low-temperature relaxation behavior depends on $(S,s)$.

Abstract

In response to recent proton spin relaxation-time measurements on NiCu(pba)(H$_2$O)$_3$$\cdot$2H$_2$O with ${pba}=1,3{-propylenebis(oxamato)}$, which is an excellent one-dimensional ferrimagnetic Heisenberg model system of spin-$(1,{1/2})$, we study the Raman relaxation process in spin-$(S,s)$ quantum ferrimagnets on the assumption of predominantly dipolar hyperfine interactions between protons and magnetic ions. The relaxation time $T_1$ is formulated within the spin-wave theory and is estimated as a function of temperature and an applied field $H$ by a quantum Monte Carlo method. The low-temperature behavior of the relaxation rate $T_1^{-1}$ qualitatively varies with $(S,s)$, while $T_1^{-1}$ is almost proportional to $H^{-1/2}$ due to the characteristic dispersion relations.