Magnetodielectric detection of magnetic quadrupole order in Ba(TiO)Cu4(PO4)4 with Cu4O12 square cupolas

A novel phosphate with CoII square planar coordination, BaCo0.5Fe(PO4)2: structural and magnetic features

A novel phosphate containing barium, cobalt, and iron was synthesized in single-crystal and polycrystalline forms. Single crystal-based X-ray measurements revealed that it crystallizes in the monoclinic system with the P21/c space group. The structure is made up of linkages between FeO6 octahedra, CoO4 square planar units, CoO5 square pyramidal units, and PO4 tetrahedra through edges and/or vertices. The interconnection of these polyhedra leads to a three-dimensional framework with tunnels along the a-axis where the Ba2+ cations are located. The polycrystalline form was prepared via the sol-gel method and its XRD pattern was refined by the Le Bail method. Morphological and elemental mapping analyses of this phosphate were performed by scanning electron microscopy. In addition, infrared and Raman spectroscopy provided more insights into chemical bonding. The magnetic behavior was antiferromagnetic below TN ∼ 20 K. Optical measurements revealed a direct bandgap with an energy Eg of 2.83 eV.

Nonreciprocal Directional Dichroism in Magnetoelectric Spin Glass

Optical absorption spectra in the visible and near-infrared light were measured for magnetoelectric spin glass Ni_{0.4}Mn_{0.6}TiO_{3} under various field-cooled conditions. Despite the absence of long-range magnetic-dipole order, this spin-glass system exhibits nonreciprocal directional dichroism (NDD) at zero external field after a magnetoelectric field-cooled procedure. This result is distinct from previous studies on NDD in systems with magnetic toroidal moments induced either by long-range magnetic-dipole order or by applying crossed electric and magnetic fields. The present Letter conclusively demonstrates that the observed NDD originates from magnetoelectrically induced ferroic order of magnetic toroidal moments without conventional magnetic-dipole order.

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.

Magnetoelectric Behavior from S=1/2 Asymmetric Square Cupolas

Magnetoelectric properties are studied by a combined experimental and theoretical study of a quasi-two-dimensional material composed of square cupolas, Ba(TiO)Cu_{4}(PO_{4})_{4}. The magnetization is measured up to the field above the saturation, and several anomalies are observed depending on the field directions. We propose a S=1/2 spin model with Dzyaloshinskii-Moriya interactions, which reproduces the full magnetization curves well. Elaborating the phase diagram of the model, we show that the anomalies are explained by magnetoelectric phase transitions. Our theory also accounts for the scaling of the dielectric anomaly observed in the experiments. The results elucidate the crucial role of the in-plane component of Dzyaloshinskii-Moriya interactions, which is induced by the noncoplanar buckling of a square cupola. We also predict a "hidden" phase and another magnetoelectric response, both of which appear in a nonzero magnetic field.