# Pseudo-Spin Versus Magnetic Dipole Moment Ordering in the Isosceles Triangular Lattice Material K$_3$Er(VO$_4$)$_2$

## TL;DR

This study investigates the magnetic ordering in the rare-earth triangular lattice material K$_3$Er(VO$_4$)$_2$, revealing a low-temperature transition to long-range order influenced by anisotropic pseudo-spin interactions and frustration effects.

## Contribution

It provides the first detailed experimental analysis of magnetic order and anisotropy in K$_3$Er(VO$_4$)$_2$, highlighting the interplay between pseudo-spin and magnetic dipole moment ordering in a frustrated lattice.

## Key findings

- Long-range magnetic order at 155 mK with entropy release
- Anisotropic Warren-like Bragg peaks indicating layered order
- Strong XY single-ion anisotropy in Er$^{3+}$ ions

## Abstract

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 pseudo-spin-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 K$_3$Er(VO$_4$)$_2$, which is a quasi-2D isosceles triangular antiferromagnet. Our specific heat and neutron powder diffraction data from K$_3$Er(VO$_4$)$_2$ reveal a transition to long range magnetic order at 155 $\pm$ 5 mK which accounts for all R$\ln$2 entropy. The quasi-2D magnetic order leads to anisotropic Warren-like Bragg peak profiles, and is best described by alternating layers of b-axis aligned antiferromagnetism and zero moment layers. Our magnetic susceptibility data reveal that Er$^{3+}$ takes on a strong XY single-ion anisotropy in K$_3$Er(VO$_4$)$_2$, leading to vanishing moments when pseudo-spins are oriented along c. Thus, the magnetic structure, when considered from the pseudo-spin point of view comprises alternating layers of b-axis and c-axis aligned antiferromagnetism.