Imaging Topological Defects in a Noncollinear Antiferromagnet

We report on the formation of topological defects emerging from the cycloidal antiferromagnetic order at the surface of bulk ${\mathrm{BiFeO}}_3$ crystals. Combining reciprocal and real-space magnetic imaging techniques, we first observe, in a single ferroelectric domain, the coexistence of antiferromagnetic domains in which the antiferromagnetic cycloid propagates along different wave vectors. We then show that the direction of these wave vectors is not strictly locked to the preferred crystallographic axes as continuous rotations bridge different wave vectors. At the junctions between the magnetic domains, we observe topological line defects identical to those found in a broad variety of lamellar physical systems with rotational symmetries. Our work establishes the presence of these magnetic objects at room temperature in the multiferroic antiferromagnet ${\mathrm{BiFeO}}_3$, offering new possibilities for their use in spintronics.

Figure 1

(a) Sketch of the pseudocubic cell of ${\mathrm{BiFeO}}_3$ showing the three possible propagation directions of the antiferromagnetic cycloid for a given ferroelectric variant. Here $\mathbf{P}$ is pointing along the [111] axis, so that ${\mathbf{k}}_{\mathbf{1}}\parallel [\overline{1}10]$, ${\mathbf{k}}_{\mathbf{2}}\parallel [0\overline{1}1]$, and ${\mathbf{k}}_{\mathbf{3}}\parallel [10\overline{1}]$. (b) Schematic representation of the cycloid propagating with a wave vector ${\mathbf{k}}_{\mathbf{i}}$ perpendicular to $\mathbf{P}$. The zoom illustrates the canting of the spins out of the cycloidal plane, leading to a spin density wave (SDW) characterized by the modulated uncompensated moment ${\mathbf{m}}_{\mathrm{DM}}$. (c)–(e) Expected magnetic field maps produced by the SDW above a (001)-oriented ${\mathrm{BiFeO}}_3$ sample, showing a modulated field amplitude whose direction and period is tied to the cycloid wave vector.

Figure 2

(a) Out-of-plane PFM phase image recorded above the (001)-oriented bulk ${\mathrm{BiFeO}}_3$ crystal. Inset: corresponding in-plane PFM phase image. The black arrow indicates the projection of the ferroelectric polarization $\mathbf{P}$ on the (001) sample surface. (b) Magnetic field image recorded with the scanning-NV magnetometer operating in dual-iso-B imaging mode. The red dashed line indicates the propagation direction of the cycloid along ${\mathbf{k}}_{\mathbf{3}}$. The period of the modulation is ${\mathrm{\Lambda }}_3=92\pm 2\mathrm{nm}$. (c) Sketch indicating the orientation of $\mathbf{P}$ and ${\mathbf{k}}_{\mathbf{3}}$ on the images shown in (a) and (b).

Figure 3

NV magnetometry image recorded in dual-iso-B mode showing the coexistence of the three propagation directions of the cycloid (red dashed arrows) in a single ferroelectric domain of the bulk ${\mathrm{BiFeO}}_3$ crystal.

Figure 4

(a) NV magnetometry image recorded in dual-iso-B mode showing a continuous rotation of the cycloid propagation direction. (b) Fourier transform of the magnetic image (a). The red dashed arrows indicate the three expected cycloid wave vectors. (c) Polar diagram of the in-plane projection of the wave vector obtained by measuring the period of the magnetic field modulation and its orientation with respect to $\mathbf{P}$ in different regions of the sample. The red ellipse is the projection on the surface plane of the circle with radius $2\pi /{\lambda }_b$ in the (111) plane. The shaded area of the diagram is reconstructed by symmetry. (d) Resonant elastic x-ray scattering (REXS) at the Fe $L$ edge (708.78 eV). (e)–(g) Sketches and corresponding NV magnetometry close views of the different topological defects found in bulk ${\mathrm{BiFeO}}_3$: $\pm \pi$ disclinations and edge dislocations. The scale bars correspond to 100 nm, the perturbation of the lamellar state induced by the defects is typically enclosed in a circle of radius $2{\lambda }_b$ [26].