Specific heat of ${\mathrm{CeRhIn}}_5$ in high magnetic fields: Magnetic phase diagram revisited

${\mathrm{CeRhIn}}_5$ is a prototypical antiferromagnetic heavy-fermion compound, whose behavior in a magnetic field is unique. A magnetic field applied in the basal plane of the tetragonal crystal structure induces two additional phase transitions. When the magnetic field is applied along, or close to, the $c$ axis, a new phase characterized by a pronounced in-plane electronic anisotropy emerges at $B^{*}\approx$ 30 T, well below the critical field, $B_c\simeq$ 50 T, to suppress the antiferromagnetic order. The exact origin of this new phase, originally suggested to be an electronic-nematic state, remains elusive. Here we report low-temperature specific heat measurements in ${\mathrm{CeRhIn}}_5$ in high static magnetic fields up to 36 T applied along both the $a$ and $c$ axes. For fields applied along the $a$ axis, we confirmed the previously suggested phase diagram and extended it to higher fields. This allowed us to observe a triple point at $\sim 30$ T, where the first-order transition from an incommensurate to commensurate magnetic structure merges into the onset of the second-order antiferromagnetic transition. For fields applied along the $c$ axis, we observed a small but distinct anomaly at $B^{*}$, which we discuss in terms of a possible field-induced transition, probably weakly first-order. We further suggest that the transition corresponds to a change of magnetic structure. We revise magnetic phase diagrams of ${\mathrm{CeRhIn}}_5$ for both principal orientations of the magnetic field based entirely on thermodynamic anomalies.

Figure 1

Specific heat divided by temperature, $C/T$, of ${\mathrm{CeRhIn}}_5$ for a magnetic field applied along the $a$ axis. (a) $C/T$ as a function of $T$ obtained from relaxation technique for several values of a magnetic field. Curves are vertically shifted according to the magnetic field scale shown in the right axis. A zoom at low and high fields is shown in (b) and (c), respectively. (d) Total specific heat, $C$, obtained from field sweeps using the AC technique.

Figure 2

Magnetic phase diagram of ${\mathrm{CeRhIn}}_5$ obtained from relaxation (circles) and AC (triangles) specific heat measurements for a field applied along the $a$ axis. Closed and open symbols correspond to second- and first-order transitions, respectively.

Figure 3

$C/T$ of ${\mathrm{CeRhIn}}_5$ for a magnetic field applied along the $c$ axis obtained from temperature sweeps using the relaxation technique.

Figure 4

(a) Specific heat of ${\mathrm{CeRhIn}}_5$ for a magnetic field applied along the $c$ axis obtained from field sweeps using the AC technique. Curves are vertically shifted for clarity. (b) Second derivatives of the heat capacity shown in (a) with respect to a magnetic field. Arrows indicate the AFM transition and the anomaly at $B^{*}$.

Figure 5

Magnetic phase diagram of ${\mathrm{CeRhIn}}_5$ obtained from relaxation (circles) and AC (triangles) specific heat measurements. Closed symbols correspond to second-order transitions from AFM to PM phase. Open symbols indicate the anomaly at $B^{*}$, which presumably corresponds to a weakly first-order transition.