Deformation of the triangular spin-$\frac{1}{2}$ lattice in Na${}_2$SrCo(PO${}_4$)${}_2$

Abstract

Crystal structure and thermodynamic properties of Na${}_2$SrCo(PO${}_4$)${}_2$, the chemical sibling of the triangular quantum spin-liquid candidate Na${}_2$BaCo(PO${}_4$)${}_2$, are reported. From single crystal x-ray diffraction and high-resolution synchrotron x-ray powder diffraction, the compound was found to crystallize in the monoclinic space group $P{2}_1/a$ at room temperature, in contrast to the trigonal Na${}_2$BaCo(PO${}_4$)${}_2$. Above 650 K, the symmetry of Na${}_2$SrCo(PO${}_4$)${}_2$ changes to $C2/m$, while around 1025 K a further transformation toward trigonal symmetry is observed. The monoclinic symmetry leads to a small deformation of the CoO${}_6$ octahedra beyond the trigonal distortion ubiquitous in this structure type, and results in the stronger $g$-tensor anisotropy ($g_{\text{z}}/g_{\text{xy}}=1.6$) as well as the increased XXZ anisotropy ($J_{\text{z}}/J_{\text{xy}}=2.1$) compared to the Ba compound ($g_{\text{z}}/g_{\text{xy}}=1.1$, $J_{\text{z}}/J_{\text{xy}}=1.5$), while the average coupling strength, $J_{\text{av}}/k_{\text{B}}=(2J_{\text{xy}}+J_{\text{z}})/3k_{\text{B}}\simeq 1.3\text{K}$, remains unchanged. The Néel temperature increases from 140 mK (Ba) to 600 mK (Sr), and an uncompensated in-plane moment of $0.066(4){\mu }_{\text{B}}/\text{f.u.}$ appears. We show that the ordering temperature of a triangular antiferromagnet is capably controlled by its structural distortions.