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Symmetries are widespread in nature. For instance, planetary motion is related to the conservation of angular momentum owing to rotational symmetry. In general, symmetries have important implications for physics, and new concepts based on symmetries open up new frontiers of research.

Crystals are one of the research objects in condensed matter physics, and have innumerable atoms arranged periodically with symmetries, including rotation, mirror, and inversion. Space-inversion (P) symmetry is of importance for physical properties; however, it is not always present in crystals. Magnetic ordering, a familiar example of spontaneous symmetry breaking in electron systems, may break P-symmetry depending on the spatial arrangement of electron spins even if the symmetry is innately given. Magnetic ordering itself also breaks time-reversal (T) symmetry owing to the nature of electron spin, as in the Zeeman effect. We investigate how electrons behave in crystal, and thereby know which symmetries are broken.

CeMnSi is a tetragonal intermetallic compound with P-symmetry, and has two magnetic elements: Ce and Mn. The spin degrees of freedom of their unpaired electrons must be frozen at low temperatures in some way according to a thermodynamic requirement. As for Mn, the way is an antiferromagnetic (AFM) ordering with an antiparallel spin arrangement. Consequently, the innate P-symmetry is broken, while the space-time inversion (PT) symmetry, a combination of P and T symmetries, is preserved. Hence, CeMnSi is classified as a PT-symmetric antiferromagnet.

As for Ce, there is no spontaneous magnetic ordering. However, this is not so surprising for Ce-based intermetallics because they have another way for the freezing, the Kondo coupling with conduction electrons. In this case, unpaired Ce-4f electrons become nonmagnetic below a characteristic temperature, and a correlated electron state called the heavy fermion state is realized. The most salient feature of the heavy fermion state in CeMnSi is the presence of the Mn-AFM ordering; heavy fermion states normally appear in paramagnetic state. In other words, CeMnSi provides a place where heavy fermion meets an “AFM sea”. The spin degeneracy protected by the PT-symmetry inherent in the Mn-AFM ordering would be crucial for the unique heavy fermion state in CeMnSi beyond the usual heavy fermion picture. The microscopic mechanisms need to be clarified by theoretical and further experimental studies.

(written by H. Tanida on behalf of all authors.)