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

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.