Magnetic phase diagram of an extended ${J}_{1}\ensuremath{-}{J}_{2}$ model on a modulated square lattice and its implications for the antiferromagnetic phase of K${}_{y}$Fe${}_{x}$Se${}_{2}$

Magnetic phase diagram of an extended $J_{1} - J_{2}$ model on a modulated square lattice and its implications for the antiferromagnetic phase of K $_{y}$ Fe $_{x}$ Se $_{2}$

Rong Yu, Pallab Goswami, and Qimiao Si

Phys. Rev. B 84, 094451 – Published 28 September 2011

Abstract

Motivated by the experimentally observed $\sqrt{5} \times \sqrt{5}$ iron vacancy order and a block-spin antiferromagnetic phase with large magnetic moment in $K_{0.8} {Fe}_{1.6} {Se}_{2}$ , we study the magnetic phase diagram of an extended $J_{1} - J_{2}$ model on a $\frac{1}{5}$ -depleted square lattice with $\sqrt{5} \times \sqrt{5}$ vacancy order, using a classical Monte Carlo analysis. The magnetic phase diagram involves various antiferromagnetically ordered phases, and most of them have higher-order commensuration. We find that the experimentally relevant block-spin state occupies a significant portion of the phase diagram, and we discuss the spin dynamics of this phase using a linear spin-wave analysis. By comparing the calculated magnetization with the experimental values of magnetic moment, we determine the physical parameter regimes corresponding to the block-spin antiferromagnetic phase. Based on our spin-wave calculations in different parameter regimes, we show how spin-wave degeneracy along the high-symmetry directions of the magnetic Brillouin zone can provide information regarding the underlying exchange couplings. We have also analyzed the magnetic phase diagram of a $J_{1} - J_{2}$ model on two different modulated square lattices relevant to $K_{y} {Fe}_{1.5} {Se}_{2}$ , which respectively exhibit $\frac{1}{4}$ -depleted $2 \times 2$ and $4 \times 2$ vacancy ordering.