Critical behavior and evidence of dimensional crossover in quasi-two-dimensional Li${}_2$FeSiO${}_4$

Abstract

We report thermal expansion and heat capacity studies on Li${}_2$FeSiO${}_4$ single crystals which enable us to investigate the critical behavior in the magnetically quasi-two-dimensional (2D) material. Pronounced $\lambda$-shaped anomalies at the magnetic ordering temperature $T_{\mathrm{N}}$ imply significant magneto-elastic coupling. Our analysis of both the thermal expansion and the specific heat data implies the crossover from 2D Ising-like behavior for $|(T-T_{\mathrm{N}})/T_{\mathrm{N}}|>0.3$ to 3D Ising behavior \rev{below $\simeq 1.3\times T_{\mathrm{N}}$. The 2D-like behavior is further supported by density functional calculations which show minimal dispersion perpendicular to the crystallographic $ac$ planes of the layered structure, thereby indicating the 2D nature of magnetism at higher temperatures.} Our results extend the available model materials of quasi-2D magnetism to a high-spin $S=2$ system with tetrahedrally coordinated Fe${}^{2+}$-ions, thereby illustrating how magnetic order evolves in a 2D Ising-like system with orbital degrees of freedom.

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