Quantum degradation of a second-order phase transition

The specific heat, magnetization, and thermal expansion of single crystals of the antiferromagnetic insulator EuTe, measured at temperatures down to 2 K and in magnetic fields up to 90 kOe, demonstrate nontrivial properties. The Néel temperature, being $\sim 9.8$ at $H=0$, decreases with magnetic field and tends to zero at $\sim 76 \mathrm{kOe}$, therefore forming a quantum critical point. The heat capacity and thermal expansion coefficient reveal $\lambda$-type anomalies at the second order magnetic phase transition at low magnetic fields, evolving into simple jumps at high magnetic fields and low temperatures; these are well described in a fluctuation-free mean-field theory. The experimental data and the corresponding analysis favor the quantum concept of an effective increase in spatial dimensionality at low temperatures that suppresses a fluctuation-driven divergence at a second-order phase transition.

Figure 1

Temperature dependence of the ratio $M/H$ at different magnetic fields applied to EuTe. $M=$ magnetic moment (emu/gm), $H=$ applied magnetic field (Oe). The inset plots the Curie temperature $T_c$ as a function of the applied magnetic field (circles taken from a maximum in the temperature derivative of $M/H$; squares taken as points where $M/H$ vs $H$ decreases in Fig. 2).

Figure 2

Ratio $M/H$ for EuTe as a function of applied magnetic fields. The quasilinear parts of the curves at high magnetic fields reveal saturation of the magnetization occurring in the field-polarized paramagnetic phase.

Figure 3

Heat capacity of EuTe around its field-dependent phase transition. The inset displays change in shape of the specific heat around the transition temperature for the three highest fields.

Figure 4

Thermal expansion of EuTe across the phase transition in applied magnetic fields.

Figure 5

Thermal expansion coefficient of EuTe around the phase transition in applied magnetic fields. The curves for 20–68 kOe are arbitrary shifted down for better viewing.