Magnetoelectric Behavior from S=1/2 Asymmetric Square Cupolas

Synthesis, Structure, and Anomalous Magnetic Ordering of the Spin-1/2 Coupled Square Tetramer System K(NbO)Cu4(PO4)4

Quasi-zero-dimensional antiferromagnets with weakly coupled clusters of multiple spins can provide an excellent platform for exploring exotic quantum states of matter. Here, we report the synthesis and the characterization of a copper-based insulating antiferromagnet, K(NbO)Cu₄(PO₄)₄. Single-crystal X-ray diffraction measurements reveal that the crystal structure belongs to the tetragonal space group P4/nmm, in which Cu²⁺ ions align to form a quasi-two-dimensional layer of spin-1/2 coupled square tetramers. The structure is quasi-isostructural to recently reported magnetoelectric antiferromagnets, A(TiO)Cu₄(PO₄)₄ (A = Ba, Sr, and Pb) with the P42₁2 space group. Despite their structural similarities, whereas the antiferromagnetic transition in A(TiO)Cu₄(PO₄)₄ produces conventional anomalies in magnetization and heat capacity, that in K(NbO)Cu₄(PO₄)₄ has several unusual features such as an upturn in magnetic susceptibility and a very weak specific heat anomaly that corresponds to a spin entropy release as small as 3%. These results indicate that the magnetism of K(NbO)Cu₄(PO₄)₄ is far different from that of A(TiO)Cu₄(PO₄)₄ and suggest that the ground state is very close to a quantum nonmagnetic singlet state. The origin of the distinct magnetism in K(NbO)Cu₄(PO₄)₄ is discussed in terms of structural modifications of a Cu₄O₁₂ unit forming a square tetramer. Our study demonstrates that the present material family, represented by an extended chemical formula A(BO)Cu₄(PO₄)₄ (AB = KNb, BaTi, SrTi, and PbTi), has broad chemical controllability of their magnetism. This makes this system an attractive material platform to study the physics of quantum spin-1/2 coupled square tetramers.

Electric Toroidal Quadrupoles in the Spin-Orbit-Coupled Metal Cd_{2}Re_{2}O_{7}

We report our theoretical results on the order parameters for the pyrochlore metal Cd_{2}Re_{2}O_{7}, which undergoes enigmatic phase transitions with inversion symmetry breaking. By carefully examining active electronic degrees of freedom based on the lattice symmetry, we propose that two parity-breaking phases at ambient pressure are described by unconventional multipoles, electric toroidal quadrupoles (ETQs) with different components, x^{2}-y^{2} and 3z^{2}-r^{2}, in the pyrochlore tetrahedral unit. We elucidate that the ETQs are activated by bond or spin-current order on Re─Re bonds. Our ETQ scenario provides a key to reconciling the experimental contradictions, by measuring ETQ specific phenomena, such as peculiar spin splittings in the electronic band structure, magnetocurrent effect, and nonreciprocal transport under a magnetic field.