Theory of commensurable magnetic structures in holmium

TL;DR

This paper provides a theoretical analysis of the conditions under which holmium's magnetic moments lock into commensurable structures with the lattice, comparing predictions with experimental data across temperature and magnetic field variations.

Contribution

It introduces a mean-field theoretical framework to explain the stability of various commensurable magnetic structures in holmium, aligning with experimental observations and explaining recent findings.

Findings

Theoretical predictions match most experimental stability data.

The trigonal coupling explains increased stability of certain structures.

Discrepancy observed for the tau=5/18 structure below T_N.

Abstract

The tendency for the period of the helically ordered moments in holmium to lock into values which are commensurable with the lattice is studied theoretically as a function of temperature and magnetic field. The commensurable effects are derived in the mean-field approximation from numerical calculations of the free energy of various commensurable structures, and the results are compared with the extensive experimental evidence collected during the last ten years on the magnetic structures in holmium. In general the stability of the different commensurable structures is found to be in accord with the experiments, except for the tau=5/18 structure observed a few degrees below T_N in a b-axis field. The trigonal coupling recently detected in holmium is found to be the interaction required to explain the increased stability of the tau=1/5 structure around 42 K, and of the tau=1/4 structure around 96 K, when a field is applied along the c-axis.