Phase boundary near a magnetic percolation transition

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 $T_c\sim |p-p_c{|}^{\varphi }$ with exponent $\varphi =1.09$, 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.

9 pages, 11 figures included, final version as published

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