We report magnetization (χ, $M$), magnetic specific heat ($C_{\mathrm{M}}$), and neutron powder diffraction results on a quasi-two-dimensional (2D) $S=2$ square lattice antiferromagnet ${\mathrm{Ba}}_2{\mathrm{FeSi}}_2{\mathrm{O}}_7$ consisting of ${\mathrm{FeO}}_4$ tetrahedrons with highly compressive tetragonal distortion (27%). Despite of the quasi-2D lattice structure, both χ and $C_{\mathrm{M}}$ present three-dimensional magnetic long-range ordering below the Néel temperature $T_{\mathrm{N}}=5.2\mathrm{K}$. Neutron diffraction data show a collinear ${\mathit{Q}}_{\mathit{m}}=$(1,0,1/2) antiferromagnetic (AFM) structure below $T_{\mathrm{N}}$ but the ordered moment aligned in the $ab$ plane is suppressed by 26% from the ionic spin $S=2$ value ($4{\mu }_{\mathrm{B}}$). Both the AFM structure and the suppressed moments are well explained by using Monte Carlo simulations with a large single-ion in-plane anisotropy $D=1$.4 meV and a rather small Heisenberg exchange $J_{\mathrm{intra}}=0$.15 meV in the plane. The characteristic 2D spin fluctuations are recognized in the magnetic entropy release and diffuse scattering above $T_{\mathrm{N}}$. This new quasi-2D magnetic system also displays unusual nonmonotonic dependence of $T_{\mathrm{N}}$ as a function of magnetic field $H$.

• Received 6 September 2021
• Revised 20 November 2021
• Accepted 14 December 2021

DOI:https://doi.org/10.1103/PhysRevB.104.214434