Magnetoelectric Behavior from $S=1/2$ Asymmetric Square Cupolas

Abstract

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 above the saturation field, and several anomalies are observed depending on the field directions. We propose a $S$=1/2 spin model with Dzyaloshinskii-Moriya interactions, which well reproduces the full magnetization curves. 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 experiments. The results elucidate the crucial role of the in-plane component of Dzyaloshinskii-Moriya interactions, which is induced by the noncoplanar buckling of square cupola. We also predict a `hidden' phase and another magnetoelectric response both of which appear in nonzero magnetic field.

arXiv comment5 pages, 5 figures

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• $A$-cation control of magnetoelectric quadrupole order in $A$(TiO)Cu${}_4$(PO${}_4$)${}_4$ ($A$ = Ba, Sr, and Pb)
• Frustration of square cupola in Sr(TiO)Cu${}_4$(PO${}_4$)${}_4$
• Spin-orbital-momentum locking under odd-parity magnetic quadrupole ordering
• Magnetoelectric behavior from cluster multipoles in square cupolas: Study of Sr(TiO)Cu${}_4$(PO${}_4$)${}_4$ in comparison with Ba and Pb isostructurals
• Magnetic structure of Ba(TiO)Cu${}_4$(PO${}_4$)${}_4$ probed using spherical neutron polarimetry
• Magnetic Structural Unit with Convex Geometry: a Building Block Hosting an Exchange-striction-driven Magnetoelectric Coupling
• Magnetoelectric spectroscopy of spin excitations in LiCoPO4
• Spin-1/2 $XXZ$ Heisenberg cupolae: magnetization process and related enhanced magnetocaloric effect
• Optical Hall response in spin-orbit coupled metals: Comparative study of magnetic cluster monopole, quadrupole, and toroidal orders
• The spin-1/2 coupled tetramer system Ba(TiO)Cu${}_4$(PO${}_4$)${}_4$ probed by magnetization, specific heat, and ${}^{31}$P-NMR
• High-field phase diagram of the chiral-lattice antiferromagnet Sr(TiO)Cu4(PO4)4
• Spin dynamics in the square-lattice cupola system Ba(TiO)Cu${}_4$(PO${}_4$)${}_4$