Multiphase region of helimagnetic superlattices at low temperature in an extended six-state clock model

TL;DR

This paper investigates the complex magnetic phase regions in a six-state clock model for helimagnetic superlattices, revealing multiphase regions and the effects of temperature and layer number on phase degeneracy.

Contribution

It extends previous models by exploring a three-dimensional parameter space, uncovering two-dimensional multiphase regions and analyzing the impact of low temperature on phase degeneracy.

Findings

Discovered two-dimensional multiphase regions in the model.

Identified that temperature lifts degeneracy except along specific lines.

For L=4, phase hierarchy resembles the ANNNI model more than the bulk six-state clock model.

Abstract

The variety of magnetic phases observed in rare-earth heterostructures at low temperatures \cite{Jehan}, such as Ho/Y, may be elucidated by an ANNNI-like model Hamiltonian. In previous work modelling bulk Ho \cite{Seno}, such a Hamiltonian with a one-dimensional parameter space produced a single multiphase point. In contrast, the parameter space of the heterostructure model is three-dimensional, and instead of an isolated multiphase point, we find two-dimensional multiphase regions. In an example of Villain's ``order from disorder'' \cite{Villain80a,Villain91}, an infinitesimal temperature breaks the ground-state degeneracy. In first order of a low-temperature expansion, we find that the degeneracy is broken everywhere in a multiphase region except on a line. A segment of the line appears to remain multiphase to all orders in a low-temperature expansion when the number $L$ of magnetic layers between non-magnetic spacers is 4 but not for other values of $L$. For L=4, the hierarchy of phases more closely resembles that in the ANNNI model than in the bulk six-state clock model on which the present model is based.