Phase boundary near a magnetic percolation transition

Abstract

Motivated by recent experimental observations [Rowley et al. in 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 $p_\mathrm{c}$, we find that the magnetic ordering temperature $T_\mathrm{c}$ depends on the dilution p via the power law $T_\mathrm{c} \sim |p-p_\mathrm{c}|^\phi$ with exponent $\phi =1.09$, in agreement with classical percolation theory. However, this asymptotic critical region is very narrow, $|p-p_\mathrm{c}| \lesssim 0.04$. 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 $T_\mathrm{c} \sim (x_\mathrm{c} -x)^{2/3}$ 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.

Graphic abstract