Theory of the low-temperature phases in boracites: Latent antiferromagnetism, weak ferromagnetism, and improper magnetostructural couplings

A phenomenological theory of the magnetic and magnetoelectric properties of boracites is developed, using the Landau-Dzialoshinskii approach. An interpretation is proposed for the main distinctive features characterizing eleven members of this family of compounds, namely the symmetry changes, the magnetic and magnetoelectric anomalies, the nature of the order parameter, and its relationship with the relevant macroscopic components arising below $T_c$. Three subclasses of materials are distinguished corresponding to two essentially different physical situations. In Ni-I boracite the simultaneous ferromagnetic-ferroelectric-ferroelastic transition is shown to result from a nonlinear (improper) coupling of the magnetization, polarization, and strain components, to the primary order parameter identified as a "latent" antiferromagnetic ordering. The assumed monoclinic magnetic structure is formed by antiparallel noncompensating average spins of different magnitude, which differs from the usual ferrimagnetic order by the fact that only one type of magnetic ion is involved, which is found in equivalent positions in the cubic paramagnetic phase. Accordingly, Ni-I can be viewed as the first experimental example of a new class of magnetic materials, which should be recognized macroscopically by an $M\sim {(T_c-T)}^{\frac{3}{2}}$ variation law, the existence of a spontaneous structural ordering occurring simultaneously with the magnetic ordering, and a weak value of the magnetization despite its exchange origin. In the two other classes of trigonal and orthorhombic boracites, the transitions are assumed to be purely magnetic, the order parameter having a one- or two-dimensional antiferromagnetic order, bilinearly coupled to a weak magnetization of relativistic origin. The dielectric and elastic anomalies as well as the magnetoelectric properties in these two groups of boracites are explained by secondary couplings of the order parameter with the relevant nonspontaneous polar tensors. The complementarity of the two traditional Landau-type approaches of structural and magnetic transitions is illustrated.