Weak ferromagnetism and domain effects in multiferroic LiNbO${}_3$-type MnTiO${}_3$-II

Magnetic order consistent with multiferroism has been observed in the acentric LiNbO${}_3$-type, high pressure form II of MnTiO${}_3$ using neutron diffraction and magnetization measurements. Spin order below the 28 K magnetic transition has propagation vector (0 0 0), and spins lie in the $ab$ plane. Representation symmetry analysis shows that the antiferromagnetic Mn${}^{2+}$ spin component observed by neutron scattering, of magnitude 3.9(1) μ${}_B$ at 2 K, coexists with a weak ferromagnetic component of magnitude 0.0014 μ${}_B$. This magnetization is perpendicular to the electrical polarization resulting from cation displacements in this acentric structure, permitting coupled switches of the two ferroic orders. The spin order is stable to fields of at least 5 T; however, facile domain reorientation within the $ab$ plane enhances the antiferromagnetic susceptibility and a constant magnetization/field ($M$/$H$) is observed in field strengths greater than ∼1.5 T. Suppression of the {101} neutron intensity with field follows the same Brillouin-dependence as $M$/$H$ and enables the antiferromagnetic easy axes to be identified as parallel to the $ab$ plane hexagonal axes.

Figure 1

(a) Evolution of the direct and inverse magnetic susceptibilities of MnTiO${}_3$-II with temperature under a 0.5 T field showing the 28 K spin-ordering transition (open/filled points are FC/ZFC data). The inset displays the temperature variation of the ordered Mn moment from neutron diffraction, showing the critical law fit described in the text. (b) $M$-$H$ loop from cycling between ±7 T fields at 2 K. Inset displays the low field hysteresis with a superimposed line showing the high field constant $M$/$H$ limit. (c) Normalized variations of $M$/$H$ from the initial magnetization experiment and of the {101} magnetic neutron intensity with the fit of the $S$ $=$ ½ Brillouin function.

Figure 2

Powder neutron diffraction data for MnTiO${}_3$-II. (a) Fit of the nuclear structure to the 30 K profile. (b) Scattering intensity plots (dark/light shading shows low/high neutron counts) between 20 and 30 K, showing the appearance of magnetic diffraction peaks below 28 K. (c) Fit of the nuclear and magnetic structures (upper and lower tick marks, respectively) to the 2 K profile.

Figure 3

Crystal and magnetic structures of MnTiO${}_3$-II. (a) Mn spin order in the $ac$ plane. (b) (001) projection of the magnetic structure with antiferromagnetic components shown parallel to the $a$ axis, and the perpendicular weak ferromagnetic component (not to scale) parallel to the [120] direction. (c) The possible perpendicular-switching mechanism proposed in Ref. 8, where inversion of the Mn and Ti displacements as electrical polarization is changed from the $+$c direction (upper image) to −c (lower image), switches the magnetization in (b) from [120] to the [$\overline{1}$$\overline{2}$0] direction.

Figure 4

(a) Magnetic powder neutron diffraction intensities of MnTiO${}_3$-II as a function of applied field at 2 K. The inset shows {101} intensity in zero field before and after a 2 T field was applied, demonstrating that no sample texturing occurs. (b) Normalized variation of the {101} intensity with field. (c) Rietveld fits of the crystal and magnetic structures of MnTiO${}_3$-II to the zero field and 5 T diffraction profiles as described in the text, with a parasitic scattering contribution from aluminum shown by the lower Bragg markers.

Figure 5

(a) Scheme for the magnetic neutron diffraction experiment on MnTiO${}_3$-II showing a Mn spin at the intersection of the (hkl) scattering plane and the $ab$ plane of the crystal structure. Scattering vector $\mathit{\varepsilon }$ is normal to the vertical magnetic field H and to p which is defined as the horizontal vector in the scattering plane. Vectors relevant to the $ab$ plane are shown as broken lines; unit cell vector c is normal to this plane. Perpendicular antiferromagnetic ${\mathbf{S}}_{\mathrm{AF}}$ and weak ferromagnetic ${\mathbf{S}}_{\mathrm{WF}}$ spin components lie in the $ab$ plane, and the offset of ${\mathbf{S}}_{\mathrm{AF}}$ from unit cell vector a is represented by angle ϕ. Magnetic neutron intensities are determined by antiferromagnetic spin component in the scattering plane ${\mathbf{S}}_{{\mathrm{AF}}^{\perp },}$ which makes acute angle ${\alpha }_{\mathrm{AF}}$ to ${\mathbf{S}}_{\mathrm{AF}}$. Domain switching rotates ${\mathbf{S}}_{\mathrm{AF}}$ and ${\mathbf{S}}_{\mathrm{WF}}$ by ±120° in the $ab$ plane, which changes the magnitude of ${\mathbf{S}}_{{\mathrm{AF}}^{\perp }}$ for some reflections. (b) Calculated variation of cos${}^2$${\alpha }_{\mathrm{AF}}$ with $ab$ plane rotation angle ϕ for the {101} family of scattering planes.