1/z-renormalization of the mean-field behavior of the dipole-coupled singlet-singlet system HoF_3

TL;DR

This paper refines the mean-field theory for HoF_3 by incorporating 1/z-expansion corrections and effective medium theory, improving the understanding of its magnetic behavior dominated by dipole interactions and singlet states.

Contribution

It introduces a first-order 1/z-expansion correction and an effective medium approach to better model HoF_3's magnetic properties beyond standard mean-field theory.

Findings

Enhanced agreement with experimental magnetic data

Significant correction to mean-field predictions

Effective medium theory captures single-site fluctuations

Abstract

The two main characteristics of the holmium ions in HoF_3 are that their local electronic properties are dominated by two singlet states lying well below the remaining 4f-levels, and that the classical dipole-coupling is an order of magnitude larger than any other two-ion interactions between the Ho-moments. This combination makes the system particularly suitable for testing refinements of the mean-field theory. There are four Ho-ions per unit cell and the hyperfine coupled electronic and nuclear moments on the Ho-ions order in a ferrimagnetic structure at T_C=0.53 K. The corrections to the mean-field behavior of holmium triflouride, both in the paramagnetic and ferrimagnetic phase, have been calculated to first order in the high-density 1/z-expansion. The effective medium theory, which includes the effects of the single-site fluctuations, leads to a substantially improved description of the magnetic properties of HoF_3, in comparison with that based on the mean-field approximation.