Phase boundary near a magnetic percolation transition


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.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The datasets generated and analyzed during the current study are available from the corresponding author upon reasonable request.]


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    The lattice in question is the lattice of exchange interactions between the Fe ions.

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We acknowledge support from the NSF under Grant nos. DMR-1506152, DMR-1828489, and OAC-1919789. The simulations were performed on the Pegasus and Foundry clusters at Missouri S&T. We also thank Martin Puschmann for helpful discussions.

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Correspondence to Thomas Vojta.

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Khairnar, G., Lerch, C. & Vojta, T. Phase boundary near a magnetic percolation transition. Eur. Phys. J. B 94, 43 (2021).

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