Magnetic phase diagram of an extendedJ1−J2model on a modulated square lattice and its implications for the antiferromagnetic phase of KyFexSe2

Abstract

Motivated by the experimentally observed $\sqrt{5}\ifmmode\times\else\texttimes\fi{}\sqrt{5}$ iron vacancy order and a block-spin antiferromagnetic phase with large magnetic moment in ${\mathrm{K}}_{0.8}{\mathrm{Fe}}_{1.6}{\mathrm{Se}}_{2}$, we study the magnetic phase diagram of an extended ${J}_{1}\ensuremath{-}{J}_{2}$ model on a $\frac{1}{5}$-depleted square lattice with $\sqrt{5}\ifmmode\times\else\texttimes\fi{}\sqrt{5}$ 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 ${J}_{1}\ensuremath{-}{J}_{2}$ model on two different modulated square lattices relevant to ${\mathrm{K}}_{y}{\mathrm{Fe}}_{1.5}{\mathrm{Se}}_{2}$, which respectively exhibit $\frac{1}{4}$-depleted $2\ifmmode\times\else\texttimes\fi{}2$ and $4\ifmmode\times\else\texttimes\fi{}2$ vacancy ordering.