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

中文翻译：

---

磁渗过渡附近的相界

摘要

受到最近的实验观察的启发[Rowley等。[Phys Rev 96：020407，2017]]上，我们重新审视了接近晶格渗透阈值的稀释磁体的相图。我们在简单的立方晶格和代表六角形铁氧体晶体结构的晶格上执行XY和Heisenberg模型的大规模蒙特卡罗模拟。接近渗流阈值\（p_ \ mathrm {c} \），我们发现磁排序温度\（T_ \ mathrm {c} \）通过幂定律\ {T_ \ mathrm {c}取决于稀释度p \ sim | p-p_ \ mathrm {c} | ^ \ phi \），指数为\（\ phi = 1.09 \），与经典的渗流理论一致。但是，此渐近临界区域非常狭窄，\（| p-p_ \ mathrm {c} | \ lesssim 0.04 \）。在其外部，通过非普遍幂定律，在较宽的稀释范围内，很好地描述了相界的形状，其指数略低于单位。尽管如此，渗流方案仍无法在PbFe \（_ {12-x}中重现实验观察到的关系\（T_ \ mathrm {c} \ sim（x_ \ mathrm {c} -x）^ {2/3} \）\） Ga \（_ x \） O \（_ {19} \）。我们讨论了我们发现的一般性以及对稀释的六角形铁氧体的物理意义。

图形摘要