Search for quantum-tricritical-point in antiferromagnet CeRu$_2$(Si$_{1-x}$Ge$_x$)$_2$

TL;DR

The study addresses how an Ising-type antiferromagnet near a quantum critical regime, CeRu$_2$(Si$_{1-x}$Ge$_x$)$_2$ with $x=0.12$, evolves under pressure to reveal a quantum tricritical point (QTCP) and an associated quantum critical line (QCL). Using magnetoresistance and Hall resistivity measurements under hydrostatic pressure up to $1.06$ GPa, the authors map the $H$-$P$ phase diagram and identify a likely QTCP near $P oughly 0.38$–$0.40$ GPa where first-order lines terminate and hysteresis disappears, accompanied by divergence in the $A$ coefficient along a QCL and a $T^{5/3}$ resistivity indicative of 3D ferromagnetic fluctuations. The results suggest a richer, pressure-tuned phase structure than simple TCP-to-QTCP pictures and underscore ferromagnetic fluctuations in the quantum-critical regime, though conclusive QTCP verification requires additional measurements (susceptibility, specific heat, $T_1$).

Abstract

CeRu$_2$Si$_2$ is a well-known heavy fermion paramagnet, and substituting Ge for Si induces antiferromagnetism. This antiferromagnetism is Ising-like and has a tricritical point in the magnetic field ($H$) -temperature ($T$) phase diagram. Since the temperature of the tricritical point is expected to decrease with increasing pressure ($P$), we investigated the pressure dependence of the magnetic phase transitions. We determined the $H$-$P$ phase diagram and revealed that a first-order phase-transition line changes to a quantum critical line, which implies the existence of the quantum tricritical point. A ferromagnetic quantum fluctuation arises in the vicinity of the possible quantum tricritical point.

Figures (5)

• Figure 1: (Color online) Temperature evolution of (a) Magnetoresistance $\rho_{xx}(H)$ and (b) Hall resistance $\rho_{yx}(H)$ of CeRu$_2$(Si$_{0.88}$Ge$_{0.12}$)$_2$ for $H\parallel c$ at ambient pressure. Each data is shifted vertically for clarity. The colored (gray) curves in (a) represent the field-raising process, while the black ones indicate the field-lowering process. The transition fields are indicated by arrows. Each transition field is almost the same in the magnetoresistance and Hall resistance. (c) Temperature dependence of the resistivity under magnetic fields. (d) Magnetic field variation of the difference in the resistivity between warming and cooling processes ($\rho^w$ and $\rho^c$). A finite difference indicates a hysteresis existing at a transition. (e) $H$-$T$ phase diagram constructed from (a) and (c). Hatching area means the hysteresis region. The red (thick) and green (thin) curves indicate the transition with and without hysteresis.
• Figure 2: (Color online) Pressure evolution of (a) Magnetoresistivity $\rho_{xx}(H)$ and (b) Hall resistivity $\rho_{yx}(H)$ at 0.03 K. Each data is shifted vertically for clarity. The colored curves in (a) represent the field-raising process, while the black ones indicate the field-lowering process. The transition fields are indicated by arrows. Since it was difficult to define the transition field from $\rho_{yx}(H)$, especially at higher pressure, for (b) we draw the arrows at the same fields as defined on $\rho_{xx}$ in (a). (c) Pressure dependence of $\rho_{xx}$ at 0.2 T. (d) Pressure dependence of $\rho_{yx}$ at 1.0 T. (e) The $\rho_{xx}(H)$-curves in raising- and lowering-field processes at pressures near the pressure at which hysteresis vanishes.
• Figure 3: (Color online) $H$-$P$ phase diagram at 0.03 K in CeRu$_2$(Si$_{0.88}$Ge$_{0.12}$)$_2$. The red (thick) and green (thin) curves indicate the transition with and without hysteresis. The black line represents the transition where the hysteresis cannot be confirmed. The dashed curve is a possible metamagnetic crossover. Hatching area means the hysteresis region.
• Figure 4: (Color online) Pressure evolution of the $A$ coefficient as a function of the magnetic field. The magnetic phases are indicated by different colors (intensities of gray).
• Figure 5: (Color online) (a) $T^2$ and (b) $T^{5/3}$ plots of the resistivity at 0.38 GPa and 2 T close to the QTCP.