= Ba, Sr, Pb)

We study the magnetoelectric properties in a newly synthesized series of quasi-two-dimensional magnets A(TiO)Cu₄(PO₄)₄ (A = Ba, Sr, Pb), by the cluster mean-field theory for a minimal quantum spin model [1,2]. The important building block of these compounds is Cu₄O₁₂ forming antiferromagnetic square cupolas where the local inversion symmetry is absent, and the Dzyaloshinskii-Moriya interaction is activated. By this antisymmetric interaction, the so-called quadrupole type spin configuration is stabilized at zero magnetic field. For nonzero magnetic fields, the magnetization curves are experimentally obtained up to above the saturation field for all A, and several anomalies are observed depending on the magnetic field directions. Our analysis well reproduces the full magnetization curves by tuning model parameters. Elaborating the phase diagram of the model, we show that the anomalies are explained by magnetoelectric phase transitions. Our theory also accounts for the dielectric anomaly observed in experiments. Furthermore, we show that the magnetoelectric behavior is well explained by the cluster multipole decomposition of complex spin configurations stabilized under the magnetic field.

[1] Y. Kato et al., Phys. Rev. Lett. 118, 107601 (2017).
[2] K. Kimura et al., arXiv:1807.10457.