Magnetic charges and magnetoelectricity in hexagonal rare-earth manganites and ferrites

Magnetoelectric (ME) materials are of fundamental interest and show broad potential for technological applications. The common dominant contribution to the ME response is the lattice-mediated one, which is proportional to both the Born electric charge $Z^{\mathrm{e}}$ and its analog, the dynamical magnetic charge $Z^{\mathrm{m}}$. Our previous study has shown that exchange striction acting on noncollinear spins induces much larger magnetic charges than those that depend on spin-orbit coupling. The hexagonal manganites $R{\mathrm{MnO}}_3$ and ferrites $R{\mathrm{FeO}}_3$ ($R=\text{Sc}$, Y, In, Ho-Lu) exhibit strong couplings between electric, magnetic, and structural degrees of freedom. The transition-metal ions in the basal plane antiferromagnetically coupled through super-exchange so as to form a ${120}^{\circ }$ noncollinear spin arrangement. In this paper, we present a theoretical study of the magnetic charges, and of the spin-lattice and spin-electronic ME constants, in these hexagonal manganites and ferrites. We clarify the conditions under which exchange striction leads to enhanced $Z^{\mathrm{m}}$ values and anomalously large in-plane spin-lattice ME effects.

Figure 1

Structure of ferroelectric hexagonal $R{\mathrm{MnO}}_3$ (6 f.u. per primitive cell). (a) Side view from [110]. (b) Plan view from [001]; dashed (solid) triangle indicates three ${\mathrm{Mn}}^{3+}$ connected via ${\mathrm{Op}}_1$ to form a triangular sublattice at $z=0\left(z=1/2\right)$.

Figure 2

Magnetic phases of hexagonal $R{\mathrm{MnO}}_3$ and $R{\mathrm{FeO}}_3$. ${\mathrm{Mn}}^{3+}$ ions form triangular sublattices at $z=0$ (dash line) and $z=1/2$ (solid line). (a) ${\mathrm{A}}_2$ phase with magnetic symmetry $\mathrm{P}{6}_3{\mathrm{c}}^{\prime }{\mathrm{m}}^{\prime }$; spins on a given ${\mathrm{Mn}}^{3+}$ layer point all in or all out. (b) ${\mathrm{A}}_1$ phase with the magnetic symmetry $\mathrm{P}{6}_3\mathrm{cm}$, with ${\mathrm{Mn}}^{3+}$ spins pointing tangentially to form a vortex pattern. The ${\mathrm{A}}_1$ and ${\mathrm{A}}_2$ phases differ by a ${90}^{\circ }$ global rotation of the spins. The ${\mathrm{B}}_1$ and ${\mathrm{B}}_2$ phases can be obtained from ${\mathrm{A}}_2$ and ${\mathrm{A}}_1$ by reversing the spins on the dashed triangles.

Figure 3

Transverse MECs for $R{\mathrm{MnO}}_3$ and ${\mathrm{LuFeO}}_3$. ${\alpha }_{xx}$ (ps/m) in the ${\mathrm{A}}_2$ phase and ${\alpha }_{yx}$ in the ${\mathrm{A}}_1$ phase. (a) Spin-lattice, (b) spin-electronic, and (c) total spin couplings.