We report thermal-expansion and heat-capacity studies on ${\mathrm{Li}}_2{\mathrm{FeSiO}}_4$ single crystals which enable us to investigate critical behavior in magnetically quasi-two-dimensional (2D) material. Pronounced $\lambda$-shaped anomalies at the magnetic ordering temperature $T_{\mathrm{N}}$ imply significant magnetoelastic 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 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 ${\mathrm{Fe}}^{2+}$ ions, thereby illustrating how magnetic order evolves in a 2D Ising-like system with orbital degrees of freedom.

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• Critical exponents
• Magnetism
• Magnetoelastic effect
• Specific heat
• Thermal expansion
• 2-dimensional systems