The phase diagram of heavy-fermion superconductor CeRhIn5
Different phases of matter are best described using a phase diagram. Each phase exhibits unique physical characteristics based on various types of external variables like pressure, temperature and magnetic field. In collaboration with Dr. Tuson Park and Dr. Joe Thompson at Los Alamos National Laboratory we visualized the phase diagram of the heavy-fermion superconductor CeRhIn5. One of the many exotic properties of this material is that the conduction electrons of CeRhIn5 turn out to be quite heavy and therefore move much slower than electrons in typical metals like copper. What is even more remarkable is that they live on the edge of two quantum states, which are usually mutually exclusive. The duality of their nature is expressed in a localized versus itinerant behavior that has been experimentally observed in their antiferromagnetic versus superconducting attributes.
Analysis of the CeRhIn5 phase transitions have been visually studied before using 2D and 1D plots. Here, using CINT's visualization capabilities the scant experimental set of phase transition points were integrated into a single 3D visual model to explore interactively the phase diagram. We interpolated the experimental data to create smooth and continuous surface boundaries that are consistent with the laws of thermodynamics and the theory of quantum phase transitions. These surfaces allowed us to study the phase transitions and in particular the interactions of the antiferromagnetic and superconducting phases.
Measurements in an external magnetic field revealed the dual nature of cerium’s single 4f electron and its role in creating the coexisting phase of antiferromagnetism and superconductivity. Figure 1 shows the pressure-field-temperature phase diagram for CeRhIn5 with its many different quantum phases. Regions of normal metal (N), local-moment antiferromagnetism (AFM), and superconductivity (SC) are separated by phase boundaries. A comparative visual study of the phase diagram is shown in Fig. 2. The remarkable quantum critical region where AFM and SC coexist is of great interest and intensely studied. The interpretation is that as pressure increases the 4f electron becomes more itinerant and the superconducting dome grows at the expense of antiferromagnetically ordered local moments. Consequently, the nature of field-tuned quantum criticality observed between pressures 1.7 GPa and 2.2 GPa can be understood as a multi-critical line where the Fermi surface of the conduction electrons reconstructs and magnetic quantum fluctuations diverge. The consequences of these divergent quantum fluctuations can be seen at temperatures as high as 5 K with a wedge-like shape in the color map of the resistivity, even at zero-magnetic field.
Figure 1: The phase diagram of CeRhIn5 as function of the temperature T (K= Kelvin), pressure P (GPa=Giga-Pascal) and magnetic field B (T=Tesla). N stands for “normal phase”, AFM for “antiferromagnetic” phase, and “SC” for the superconducting phase. The color bar gives the resistivity (in units of mW-cm) that goes to zero as the SC region is approached. The cubic and spherical points are the experimentally measured data points extracted from the jumps in the specific heat, and the surfaces are created using interpolation. The white surface separates the antiferromagnetic phase from the normal phase at high temperature. The pink surface surrounds the superconducting region at the lower temperature region. The white surface penetrates into the pink surface. The common region between the white and the pink surfaces, inside the pink region, defines the coexistence region of the AFM and SC phases. The AFM transition temperature decreases with pressure. At T=0 K, the system undergoes a transition as a function of pressure which characterizes the quantum critical region.
Figure 2: This comparative 3D visualization contains several elements. The phase transition surfaces are bounded at z=0, that means zero magnetic field, by a plane colored by resistivity (mW-cm) versus pressure and temperature. The origin is in the bottom left hand corner of each image. The image series progresses from left to right and top to bottom and shows various outputs of the clip visualization operation that removes the data from some side of a (clip) plane. As the clip plane moves through the volume of the phase diagram, one can see how the superconducting (pink) and antiferromagnetic (orange) phase boundaries intersect as the external magnetic field increases in steps of 1.1 T.