# Magnetic phase diagram of Eu$_2$CuSi$_3$ derived from thermal expansion and magnetostriction studies

## TL;DR

This study maps the magnetic phase diagram of Eu$_2$CuSi$_3$ using thermal expansion and magnetostriction, revealing strong magneto-structural coupling, anisotropic magnetic interactions, and ferromagnetic correlations above the Curie temperature.

## Contribution

It provides the first detailed thermal and magnetostriction analysis of Eu$_2$CuSi$_3$, highlighting anisotropic magnetic coupling and complex magnetic phases.

## Key findings

- Identified ferromagnetic transition at 34 K with strong magneto-structural coupling.
- Revealed anisotropic thermal expansion between c-axis and ab-plane.
- Constructed magnetic phase diagram showing evolution of magnetic order up to 15 T.

## Abstract

Precise thermal expansion and magnetostriction studies of the intermetallic compound Eu$_2$CuSi$_3$ in the temperature range between 5 and 300 K are presented. A clear sign of magnetic second order phase transition at the ferromagnetic Curie temperature $T_{\rm C}$ = 34 K indicates strong magneto-structural coupling. Uniaxial thermal expansion data show a large anisotropy between the magnetic easy $c$-axis and the hexagonal $ab$-plane, which is associated with a strongly anisotropic magnetic coupling. A spin-reorientation regime as well as a non-uniform energy scale are indicated by Gr\"uneisen analysis of the data at low temperatures. Anomalous contributions to the thermal expansion imply ferromagnetic correlations far above in zero magnetic field. The magnetic phase diagram is constructed, showing the evolution of short- and long-range magnetic order in magnetic fields up to 15 T. The anisotropic magnetic field effect yields anomalous magnetostrictive effects up to about 200 K.