Quasi-two-dimensional magnetism and antiferromagnetic ground state in Li 2 FeSiO 4

Our experimental (neutron diffraction, M\"ossbauer spectroscopy, magnetic susceptibility, specific heat) and numerical studies on the evolution of short- and long-range magnetic order in ${\ensuremath{\gamma}}_{\mathrm{II}}\text{\ensuremath{-}}{\mathrm{Li}}₂{\mathrm{FeSiO}}₄$ suggest a quasi-two-dimensional (2D) nature of magnetism. The experimental data obtained on single crystals imply long-range antiferromagnetic order below ${T}_{\mathrm{N}}=17$ K. A broad maximum in magnetic susceptibility $\ensuremath{\chi}$ at ${T}_{\mathrm{m}}\ensuremath{\simeq}28$ K, observation of magnetic entropy changes up to 100 K, and anisotropy in $\ensuremath{\chi}$ are indicative of low-dimensional magnetism and suggest short-range magnetic correlations up to 200 K. Neutron diffraction shows that long-range antiferromagnetic order is characterized by the propagation vector $\mathbf{k}=(\frac{1}{2},0,\frac{1}{2})$. The ordered moment $\ensuremath{\mu}=2.50(2)$ ${\ensuremath{\mu}}_{\mathrm{B}}$/Fe, at $T=1.5$ K, is along the crystallographic $a$ axis. This is consistent with the observed static hyperfine field of ${B}_{\mathrm{hyp}}=14.8(3)\phantom{\rule{0.28em}{0ex}}\mathrm{T}$ by M\"ossbauer spectroscopy which indicates significant orbital contributions. The temperature dependence of ${B}_{\mathrm{hyp}}$ yields the critical exponent $\ensuremath{\beta}=0.116(12)$ which is in the regime of the 2D Ising behavior. $\mathrm{LSDA}+\mathrm{U}$ studies exploiting the experimental spin structure suggest dominating magnetic exchange coupling within the $ac$ layers (i.e., ${J}₃\ensuremath{\simeq}\ensuremath{-}6$ K and ${J}₆\ensuremath{\simeq}\ensuremath{-}2$ K) while interlayer coupling is much smaller and partly frustrated. This confirms the 2D nature of magnetism and is in full agreement with the experimental findings.