Spin-$1/2$ antiferromagnetic triangular lattice models are paradigms of geometrical frustration, revealing very different ground states and quantum effects depending on the nature of anisotropies in the model. Due to strong spin orbit coupling and crystal field effects, rare-earth ions can form pseudospin-$1/2$ magnetic moments with anisotropic single-ion and exchange properties. Thus, rare-earth-based triangular lattices enable the exploration of this interplay between frustration and anisotropy. Here we study one such case, the rare-earth double vanadate glaserite material ${\mathrm{K}}_3\mathrm{Er}{\left({\mathrm{VO}}_4\right)}_2$, which is a quasi-two-dimensional (2D) isosceles triangular antiferromagnet. Our specific heat and neutron powder diffraction data from ${\mathrm{K}}_3{\mathrm{Er}(\mathrm{VO}}_4{)}_2$ reveal a transition to long range magnetic order at $T_N=155\pm 5$ mK which accounts for all $Rln2$ entropy. We observe what appears to be a coexistence of three-dimensional (3D) and quasi-2D order below $T_N$. The quasi-2D order leads to an anisotropic Warren-like peak profile for $\left(hk0\right)$ reflections, while the 3D order is best-described by layers of antiferromagnetic $b$-aligned moments alternating with layers of zero moment. Our magnetic susceptibility data reveal that ${\mathrm{Er}}^{3+}$ takes on a strong $XY$ single-ion anisotropy in ${\mathrm{K}}_3\mathrm{Er}{\left({\mathrm{VO}}_4\right)}_2$, leading to vanishing moments when pseudospins are oriented along $c$. Thus, the magnetic structure, when considered from the pseudospin point of view could comprise of alternating layers of $b$-axis and $c$-axis aligned antiferromagnetism.

中文翻译：

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等腰三角形晶格材料K3Er（VO4）2中的假旋与磁偶极矩排序

自旋$\mathrm{1个}/2$反铁磁三角晶格模型是几何挫折的范例，根据模型各向异性的性质，它们揭示了截然不同的基态和量子效应。由于强烈的自旋轨道耦合和晶体场效应，稀土离子可形成伪自旋-$\mathrm{1个}/2$具有各向异性单离子和交换性质的磁矩。因此，基于稀土的三角形晶格使人们能够探索挫折与各向异性之间的这种相互作用。在这里我们研究一种这样的情况，稀土双钒酸盐辉石材料${\mathrm{ķ}}_3尔{（{\mathrm{VO}}_4）}_2$，它是准二维（2D）等腰三角形反铁磁体。我们的比热和中子粉末衍射数据来自${\mathrm{ķ}}_3{尔（\mathrm{VO}}_4{）}_2$ 揭示了向远距离磁阶的过渡 ${Ť}_{ñ}=155\pm 5$ 占全部的mK $\mathrm{[R}ln2$熵。我们在下面观察到三维（3D）和准2D顺序似乎并存${Ť}_{ñ}$。准2D阶导致各向异性的Warren峰形$（Hķ0）$ 反射，而3D顺序最好由反铁磁层描述 $b$对齐的力矩与零力矩层交替。我们的磁化率数据表明${尔}^{3+}$ 具有强大的 $Xÿ$ 单离子各向异性 ${\mathrm{ķ}}_3尔{（{\mathrm{VO}}_4）}_2$，导致伪旋转方向沿着消失的瞬间$C$。因此，从假自旋的角度考虑时，磁性结构可以包括交替的磁性层。$b$轴和 $C$轴排列的反铁磁性。