Microscopic toy model for magnetoelectric effect in polar Fe2Mo3O8

Abstract

The kamiokite, Fe2Mo3O8, is regarded as a promising material exhibiting giant magnetoelectric (ME) effect at the relatively high temperature T . Here, we explore this phenomenon on the basis of first-principles electronic structure calculations. For this purpose we construct a realistic model describing the behavior of magnetic Fe 3d electrons and further map it onto the isotropic spin model. Our analysis suggests two possible scenaria for Fe2Mo3O8. The first one is based on the homogeneous charge distribution of the Fe 2+ ions amongst tetrahedral (t) and octahedral (o) sites, which tends to low the crystallographic P63mc symmetry through the formation of an orbitally ordered state. Nevertheless, the effect of the orbital ordering on interatomic exchange interactions does not seem to be strong, so that the magnetic properties can be described reasonably well by averaged interactions obeying the P63mc symmetry. The second scenario, which is supported by obtained parameters of on-site Coulomb repulsion and respects the P63mc symmetry, implies the charge disproportionation involving somewhat exotic 1+ ionization state of the t-Fe sites (and 3+ state of the o-Fe sites). Somewhat surprisingly, these scenarios are practically indistinguishable from the viewpoint of exchange interactions, which are practically identical in these two cases. However, the spin-dependent properties of the electric polarization are expected to be different due to the strong difference in the polarity of the Fe 2+ -Fe 2+ and Fe 1+ -Fe 3+ bonds. Our analysis uncovers the basic aspects of the ME effect in Fe2Mo3O8. Nevertheless, the quantitative description should involve other ingredients, apparently related to the lattice and orbitals degrees of freedom. I.J t J ô J 1 J ij (meV) J || J 2 3 4 5 6 7 8 9 10 11 -6 -4 -2 0 J t J ô J || J

Structure, phonons, and orbital degrees of freedom in Fe2Mo3O8

“…These values are somewhat lower than o = 1.13 eV and t = 0.50 eV reported in Ref. [12]. We repeated calculations for the crystal structure used in that work, but obtained the same values as for the 1.7 K crystal structure from Table I.…”

“…[11], symmetry lowering was inferred from the additional, presumably phonon modes appearing at low temperatures, whereas the authors of Ref. [12] speculated on the possibility of an orbital ordering, which should also lead to a symmetry lowering. Alternatively, they put forward charge separation between the octahedral and tetrahedral sites as a microscopic mechanism that does not require symmetry lowering [12].…”

“…[12] speculated on the possibility of an orbital ordering, which should also lead to a symmetry lowering. Alternatively, they put forward charge separation between the octahedral and tetrahedral sites as a microscopic mechanism that does not require symmetry lowering [12]. Our low-temperature structural data exclude all these possibilities.…”

“…However, a recent spectroscopic study pinpointed additional IR-and Raman-active, presumably phonon modes appearing below T N , and interpreted them as a signature of symmetry lowering [11], although no direct measurement of the low-temperature crystal structure was attempted. Moreover, an ab initio study [12] led to a ground-state spin configuration different from the experimental collinear and commensurate antiferromagnetic order (Fig. 1).…”

“…1). Taken together, these observations raise the question whether the hexagonal room-temperature crystal structure is the right starting point for modeling the interesting physics of Fe 2 Mo 3 O 8 , or effects like charge separation and Jahn-Teller distortions on Fe sites with tetra-and octahedral coordination should be taken into account [12].…”