Uniform and staggered magnetizations induced by Dzyaloshinskii-Moriya interactions in isolated and coupled spin 1/2 dimers in a magnetic field

TL;DR

This paper studies how Dzyaloshinskii-Moriya interactions influence magnetizations in spin 1/2 dimers under magnetic fields, revealing significant deviations in magnetization orientations and effects of inter-dimer coupling, supported by theoretical and experimental comparisons.

Contribution

It provides analytical expressions for magnetizations in isolated dimers and extends the analysis to coupled dimers using DMRG, highlighting the impact of Dzyaloshinskii-Moriya interactions on magnetic properties.

Findings

Uniform magnetization can deviate significantly from the external field direction.

Maximum staggered magnetization occurs near half polarization in small Dzyaloshinskii-Moriya interactions.

Simple models for isolated dimers are applicable to weakly coupled dimers with minor modifications.

Abstract

We investigate the interplay of Dzyaloshinskii-Moriya interactions and an external field in spin 1/2 dimers. For isolated dimers and at low field, we derive simple expressions for the staggered and uniform magnetizations which show that the orientation of the uniform magnetization can deviate significantly from that of the external field. In fact, in the limit where the ${\bf D}$ vector of the Dzyaloshinskii-Moriya interaction is parallel to the external field, the uniform magnetization actually becomes {\it perpendicular} to the field. For larger fields, we show that the staggered magnetization of an isolated dimer has a maximum close to one-half the polarization, with a large maximal value of $0.35 g\mu_B$ in the limit of very small Dzyaloshinskii-Moriya interaction. We investigate the effect of inter-dimer coupling in the context of ladders with Density Matrix Renormalization Group (DMRG) calculations and show that, as long as the values of the Dzyaloshinskii-Moriya and of the exchange interaction are compatible with respect to the development of a staggered magnetization, the simple picture that emerges for isolated dimers is also valid for weakly coupled dimers with minor modifications. The results are compared with torque measurements on Cu$_{2}$(C$_{5}$H$_{12}$N$_{2}$)$_{2}$Cl$_{4}$.