Magnetoelectric behavior from cluster multipoles in square cupolas: Study of Sr(TiO)Cu${}_4$(PO${}_4$)${}_4$ in comparison with Ba and Pb isostructurals

Abstract

We report our combined experimental and theoretical study of magnetoelectric properties of an antiferromagnet Sr(TiO)Cu${}_4$(PO${}_4$)${}_4$, in comparison with the isostructurals Ba(TiO)Cu${}_4$(PO${}_4$)${}_4$ and Pb(TiO)Cu${}_4$(PO${}_4$)${}_4$. The family of compounds commonly possesses a low-symmetric magnetic unit called the square cupola, which is a source of magnetoelectric responses associated with the magnetic multipoles activated under simultaneous breaking of spatial inversion and time reversal symmetries. Measuring the full magnetization curves and the magnetic-field profiles of dielectric constant for Sr(TiO)Cu${}_4$(PO${}_4$)${}_4$ and comparing them with the theoretical analyses by the cluster mean-field theory, we find that the effective $S=1/2$ spin model, which was used for the previous studies for Ba(TiO)Cu${}_4$(PO${}_4$)${}_4$ and Pb(TiO)Cu${}_4$(PO${}_4$)${}_4$, well explains the experimental results by tuning the model parameters. Furthermore, elaborating the phase diagram of the model, we find that the square cupolas could host a variety of magnetic multipoles, i.e., monopole, toroidal moment, and quadrupole tensor, depending on the parameters that could be modulated by deformations of the magnetic square cupolas. Our results not only provide a microscopic understanding of the series of the square cupola compounds, but also stimulate further exploration of the magnetoelectric behavior arising from cluster multipoles harboring in low-symmetric magnetic units.

arXiv comment13 pages, 12 figures

References in corpus (8)

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• Magnetodielectric detection of magnetic quadrupole order in Ba(TiO)Cu${}_4$(PO${}_4$)${}_4$ with Cu${}_4$O${}_{12}$ square cupolas
• $A$-cation control of magnetoelectric quadrupole order in $A$(TiO)Cu${}_4$(PO${}_4$)${}_4$ ($A$ = Ba, Sr, and Pb)
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• Magnetoelectric Behavior from $S=1/2$ Asymmetric Square Cupolas
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Cited by in corpus (7)

• Magnetic structure in square cupola compound Ba(TiO)Cu${}_4$(PO${}_4$)${}_4$: a ${}^{31}$P NMR Study
• 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${}_4$)${}_4$
• Microscopic Magnetism of A(TiO)Cu4(PO4)4 (A = Ba, Pb, Sr): 31P and 63,65Cu NMR Study