Phase Boundary Near a Magnetic Percolation Transition

Hexagonal ferrites such as PbFe₁₂O₁₉, SrFe₁₂O₁₉, BaFe₁₂O₁₉ show interesting magnetic and ferroelectric properties at low temperatures. The magnetic ordering temperature of these compounds can be tuned by random site dilution replacing Fe ions by Ga ions, for example in PbFe_12−xGa_xO₁₉. According to recent experiments, the critical temperature of these compounds varies as T_c ∝ (1 − x/x_c )^2/3, where x_c is very close to the percolation threshold of the lattice [1]. Motivated by these results, we re-examine the shape of the magnetic phase boundary over the entire x range from 0 to x_c. We perform large scale Monte-Carlo simulation of diluted XY and Heisenberg models for both cubic lattices and lattices representing the crystal structure of the hexaferrites. In particular, we study the critical behavior of the percolation transition and width of the critical region.

References:
[1] S. E. Rowley et al, Phys. Rev. B 96, 020407(R) (2017)