Magnetic field induced modification of a first-order ferromagnetic transition in Eu2In

Abstract

We present a comprehensive study of the temperature- and magnetic-field-dependent magnetization, specific heat, and local crystal structure across the first-order ferromagnetic-paramagnetic transition in Eu$_2$In. Anomalies in the magnetocaloric response are observed near $H \approx 25$~kOe, including changes in field scaling of magnetic entropy, local entropy exponent, and universal master curve, which suggest an apparent weakening of the first-order character of the transition. However, quantitative analysis of the magnetocaloric parameters together with modified Arrott plots demonstrates that the transition remains first order up to at least 70~kOe. Specific-heat measurements reveal a field-induced splitting of the sharp zero-field anomaly into a doublet, providing a natural explanation for the change in the magnetocaloric response. Magnetic field dependent extended x-ray absorption fine structure (EXAFS) measurements show no detectable field-induced changes in the local coordination environment of Eu. We therefore attribute these observations to a magnetic field induced two-step transition process in Eu$_2$In.

Figures (13)

• Figure 1: (a) Rietveld refinement of the room-temperature powder XRD pattern of Eu$_2$In collected using Mo $K_{\alpha}$ radiation. Red symbols represent the observed intensities, and the black solid line denotes the calculated profile. Vertical tick marks indicate the Bragg positions corresponding to the orthorhombic $Pnma$ (Co$_2$Si-type) phase. The bottom trace shows the difference between the observed and calculated patterns. An asterisk indicates the presence of a small amount ($\sim$2%) of a secondary Eu$_8$In$_3$ phase. (b) Three-dimensional representation of the crystal structure of Eu$_2$In, highlighting the two inequivalent Eu sites. (c) Temperature-dependent magnetic susceptibility ($\chi$--$T$) measured in zero field cooled (ZFC), field cooled warming (FCW), and field cooled cooling (FCC) protocols at 1 kOe in the temperature stable mode. Inset (c1) shows high resolution FCC and FCW data recorded in the temperature sweep mode in the vicinity of $T_{\rm c}$. Inset (c2) shows the Curie--Weiss fit to the FCW data between 60 to 300 K. (d) Field-dependent magnetization measured at 2 K. The inset shows an enlarged view of the low-field region.
• Figure 2: (a) Temperature-dependent magnetic entropy change ($\Delta S_{\rm M}$) of Eu$_2$In at different magnetic fields. The inset shows the field dependence of the maximum magnetic entropy change ($\Delta S^{\rm max}_{\rm M}$) on a log-log scale, where the solid black line represents the linear fit for $H > 25$ kOe. (b) Temperature-dependent local field exponent ($n$) of $\Delta S_{\rm M}$ at different fields. (c) Normalized $\Delta S_{\rm M}$ versus scaled temperature curves at different fields, with the dashed line representing the curve for $H = 25$ kOe. The inset shows the field dependence of the vertical dispersion at $\theta = -5$, where the solid black lines represent straight fits to the data below and above $H = 25$ kOe.
• Figure 3: (a) Temperature-dependent zero-field specific heat of Eu$_2$In measured using the standard $2\tau$ relaxation method. The solid and dashed black curves represent the best fit of the data using Eq. (\ref{['Debye']}) in the temperature range 70--100 K and the extrapolation of the fitted curve down to 2 K, respectively. The dotted horizontal line represents the classical Dulong--Petit limit of $C_P$ for Eu$_2$In. The inset shows the enlarged view of the low temperature region, where the solid black line represents the best fit using Eq. \ref{['HC_LT']}. (b) Magnetic contribution to the specific heat, $C_{\rm mag}/T$ (left axis), and the magnetic entropy, $S_{\rm mag}$ (right axis), of Eu$_2$In. The dashed horizontal line represents the theoretical magnetic entropy $S_{\rm mag} = R\ln(2J+1)$ expected for Eu$^{2+}$. The double-sided black arrow indicates the magnetic entropy associated solely with the magnetic transition.
• Figure 4: (a--o) The temperature dependent specific heat of Eu$_2$In in the vicinity of magnetic transition at different magnetic fields measured in both heating and cooling modes, using the long heat pulse method. T$_{\rm H}$ and T$_{\rm L}$ in panel (f) represent the temperatures corresponding to the HT and LT peaks, respectively, at 25 kOe.
• Figure 5: Magnetic-field dependence of the transition temperatures determined from magnetization and specific-heat measurements. The solid black line represents a linear fit to the $T_{\rm c}(H)$ curve, extracted from the magnetization data. The inset shows the field-dependent separation between the two peaks observed in the specific heat curves.