# Quasi-two-dimensional Bose-Einstein condensation of lattice bosons in spin-1/2 XXZ ferromagnet K$_2$CuF$_4$

## TL;DR

This study investigates the quasi-two-dimensional Bose-Einstein condensation in the spin-1/2 XXZ ferromagnet K$_2$CuF$_4$, confirming theoretical predictions through magnetization and specific heat measurements.

## Contribution

It provides experimental evidence of quasi-2D BEC in a real magnetic material, aligning with theoretical models and expanding understanding of magnetic phase transitions.

## Key findings

- Phase boundary follows a power law with exponent ~1.0
- Magnetization and specific heat data support quasi-2D BEC behavior
- Experimental phase diagram matches theoretical predictions

## Abstract

K$_2$CuF$_4$ is magnetically described as a spin-1/2, quasi-two-dimensional (2D), square-lattice XXZ ferromagnet with weak easy-plane anisotropy. The magnetic ordering for an applied magnetic field $H$ parallel to the $c$ axis is equivalent to the Bose\,--\,Einstein condensation (BEC) of lattice bosons, as discussed by Matsubara and Matsuda [Prog. Theor. Phys. \textbf{16}, 569 (1956)]. Magnetization and specific heat measurements were performed to obtain the temperature vs magnetic field phase diagram for $H\,{\parallel}\,c$. The phase boundary between polarized and ordered phases was found to be expressed by the power law $H_{\rm c}(T)\,{-}\,H_{\rm c}(0)\,{\propto}\,T^\phi$ with exponent $\phi\,{\approx}\,1.0$ in a wide temperature range, in agreement with the theory of quasi-2D BEC.