Three-dimensional critical phase diagram of the Ising antiferromagnet ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$ under intense magnetic field and pressure

Using novel instrumentation to combine extreme conditions of intense pulsed magnetic field up to 60 T and high pressure up to 4 GPa, we have established the three-dimensional (3D) magnetic field-pressure-temperature phase diagram of a pure stoichiometric heavy-fermion antiferromagnet (${\mathrm{CeRh}}_2{\mathrm{Si}}_2$). We find a temperature- and pressure-dependent decoupling of the critical and pseudometamagnetic fields at the borderlines of antiferromagnetism and strongly-correlated paramagnetism. This 3D phase diagram is representative of a class of heavy-fermion Ising antiferromagnets, where long-range magnetic ordering is decoupled from a maximum in the magnetic susceptibility. The combination of extreme conditions enabled us to characterize different quantum phase transitions, where peculiar quantum critical properties are revealed. The interest to couple the effects of magnetic field and pressure on quantum-critical correlated-electron systems is stressed.

Figure 1

Schematic magnetic field-pressure-temperature phase diagram of heavy-fermion antiferromagnets. AF, SC, CPM, and PPM denote the antiferromagnetic and superconducting phases, the correlated paramagnetic and polarized paramagnetic regimes, respectively. Sketches of antiferromagnetic moments, polarized moments, and fluctuating moments (assuming Ising magnetic anisotropy) are presented for the AF phase and the PPM and CPM regimes, respectively. All parameters $T_N, T_{\chi }^{\max }, T^{*}, T_{\mathrm{pol}}, T_{sc}, p_c, H_c$, and $H_m$ presented in this phase diagram have been defined in Section 1.

Figure 2

${\rho }_{x,x}$ of ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$ under pressures combined with fields up to 60 T applied along $\mathbf{c}$ and temperatures $1.4\le T\le 141$ K. Data are presented at (a) $p=0.65$ GPa (sample $♯2$), (b) $p=0.75$ GPa (sample $♯2$), (c) $p=1$ GPa (sample $♯2$), (d) $p=1.2$ GPa (sample $♯2$), (e) $p=1.5$ GPa (sample $♯2$), and (f) $p=4$ GPa (sample $♯3$).

Figure 3

Magnetic-field dependence of the resistivity ${\rho }_{x,x}$ of ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$ emphasizing the low-temperature decoupling of $H_c$ and $H_m$ at pressures just below $p_c$ (sample $♯4$). ${\rho }_{x,x}$ versus $H$ (a) at $T=4.2$ K and $p=0.75$, 0.85, and 0.9 GPa, and at $1.5\le T\le 10$ K, in fields ${\mu }_{0}H\le 35$ T: (b) at $p=0.85$ GPa and (c) at $p=0.9$ GPa.

Figure 4

($H,p,T$) phase diagram of ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$ under a magnetic field $\mathbf{H}\parallel \mathbf{c}$. (a) ($p,T$) phase diagram at $H=0$. (b),(c) ($H,T$) phase diagrams at $p=0.75$ and 1.2 GPa. (d) ($p,H$) phase diagram in the limit $T\to 0$.

Figure 5

3D ($H,p,T$) phase diagram of ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$ under a magnetic field $\mathbf{H}\parallel \mathbf{c}$, for ${\mu }_{0}H\le 60$ T, $p\le 1.2$ GPa, and $1.4\le T\le 100$ K. $T_N, T_{1,2}$, and $T_{sc}$ at zero field and $H_{sc}$ are reproduced from [35]; $T_{\chi }^{max}$ at zero field is reproduced from Ref. [33]. (a) emphasizes the 3D views of the AF and SC phases, while (b) emphasizes the 3D views of the CPM and PPM regimes.

Figure 6

Pressure dependence of $R_{AF}=T_N/\left({\mu }_0{H}_c\right)$ and $R_{AF}^{*}=T_{\chi }^{max}/\left({\mu }_0{H}_c\right)$ for $p<p_x$, and $R_{CPM}=T_{\chi }^{max}/\left({\mu }_0{H}_m\right)$ for $p>p_x$.

Figure 7

Evolution of the Fermi liquid coefficient $A$ as a function of magnetic field and pressure. (a) $A$ versus $H$, in magnetic fields up to 55 T, at different pressures. (b) $A$ versus $p$, in pressures up to 2 GPa, at different magnetic fields. (c) Pressure dependence of $A_{max}$ ($=A\left(H_c\right)$ for $p<p_x$ and $A\left(H_m\right)$ for $p>p_x$.

Figure 8

Definition of the transitions and crossovers in the magnetoresistivity and phase diagrams extracted at different pressures. (a)–(e) Magnetoresistivity of sample $♯1$ at ambient pressure, and of sample $♯2$ at pressures from 0.65 to 1.2 GPa, under pulsed magnetic fields up to 56 T, at various temperatures from 1.5 to 34 K, and (f)–(j). Corresponding magnetic-field–temperature phase diagrams obtained at constant pressures.

Figure 9

Magnetoresistivity (a) of sample $♯2$ at $p=1$ GPa and (b) of sample $♯3$ at $p=0.95$ GPa at various temperatures from 2.1 to 100 K.

Figure 10

(a),(b) Resistivity versus $T^2$ of sample $♯4$ at $p=0.9$ GPa, for different fields up to 52 T. Resistivity versus $T^2$, in extended temperature scales, of (c) sample $♯1$ at $p=1$ bar, (d) and (e) sample $♯4$ at $p=0.65$ and 0.85 GPa, and (f) $♯2$ at $p=1.2$ GPa, for selections of magnetic field values from 1 to 52 T. The lines correspond to the fit to the data by a $T^2$ law.

Figure 11

Magnetic-field- and pressure-dependence of the quadratic coefficient $A$ of the magnetoresistivity ${\rho }_{x,x}$ of ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$ in $\mathbf{H}\parallel \mathbf{c}$. (a) Comparison of $A$ versus $H$ at $p=1$ bar (sample $♯1$) and $A$ versus $p$ at $H=0$ (samples $♯2, ♯3, ♯4$).