Pseudospin versus magnetic dipole moment ordering in the isosceles triangular lattice material K3Er(VO4)2

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 ${\mathrm{K}}_{3}\mathrm{Er}{({\mathrm{VO}}_{4})}_{2}$, 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 ${T}_{N}=155\ifmmode\pm\else\textpm\fi{}5$ 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 $(hk0)$ 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 ${\mathrm{K}}_{3}\mathrm{Er}{({\mathrm{VO}}_{4})}_{2}$, 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.