Phase boundary near a magnetic percolation transition

TL;DR

This study uses large-scale simulations to analyze the phase boundary near the magnetic percolation transition in diluted magnets, revealing a narrow critical region and a nonuniversal phase boundary shape, but not matching some experimental observations.

Contribution

It provides detailed simulation results on the phase boundary near percolation in diluted magnets, highlighting the narrow critical region and the limitations of the percolation scenario in explaining experiments.

Findings

Critical exponent near percolation threshold is approximately 1.09.

The phase boundary shape is well described by a nonuniversal power law.

The percolation scenario does not explain the experimental relation in PbFe$_{12-x}$Ga$_x$O$_{19}$.

Abstract

Motivated by recent experimental observations [Phys. Rev. 96, 020407 (2017)] on hexagonal ferrites, we revisit the phase diagrams of diluted magnets close to the lattice percolation threshold. We perform large-scale Monte Carlo simulations of XY and Heisenberg models on both simple cubic lattices and lattices representing the crystal structure of the hexagonal ferrites. Close to the percolation threshold $p_c$, we find that the magnetic ordering temperature $T_c$ depends on the dilution $p$ via the power law $T_c \sim |p-p_c|^\phi$ with exponent $\phi=1.09$, in agreement with classical percolation theory. However, this asymptotic critical region is very narrow, $|p-p_c| \lesssim 0.04$. Outside of it, the shape of the phase boundary is well described, over a wide range of dilutions, by a nonuniversal power law with an exponent somewhat below unity. Nonetheless, the percolation scenario does not reproduce the experimentally observed relation $T_c \sim (x_c -x)^{2/3}$ in PbFe$_{12-x}$Ga$_x$O$_{19}$. We discuss the generality of our findings as well as implications for the physics of diluted hexagonal ferrites.