Coexistence of Bloch and Néel walls in a collinear antiferromagnet

We resolve the domain-wall structure of the model antiferromagnet ${\text{Cr}}_2{\text{O}}_3$ using nanoscale scanning diamond magnetometry and second-harmonic-generation microscopy. We find that the ${180}^{\circ }$ domain walls are predominantly Bloch-like, and can coexist with Néel walls in crystals with significant in-plane anisotropy. In the latter case, Néel walls that run perpendicular to a magnetic easy axis acquire a well-defined chirality. We further report quantitative measurement of the domain-wall width and surface magnetization. Our results provide fundamental input and an experimental methodology for the understanding of domain walls in pure, intrinsic antiferromagnets, which is relevant to achieve electrical control of domain-wall motion in antiferromagnetic compounds.

Figure 1

One-dimensional model for an antiferromagnetic ${180}^{\circ }$ domain wall. (a) Sketch of the domain wall separating regions (purple, green) of opposite order parameter. The dashed-dotted line describes the wall profile as given by Eq. (3c). (b) The presence of a residual demagnetizing field favors the formation of Bloch walls ($\chi =\pm \pi /2$). (c) For sufficiently large in-plane anisotropy in a direction orthogonal to the wall, the formation of a Néel wall ($\chi =0,\pi$) or mixed Néel-Bloch wall is favored. Curled arrows indicate the demagnetizing field arising from moments crossing the domain wall perpendicularly.

Figure 2

${\mathrm{Cr}}_2{\mathrm{O}}_3$ crystal structure and experimental arrangement. (a) Side view of the hexagonal unit cell. Blue and green arrows symbolize ${\mathrm{Cr}}^{3+}$ moments of opposite magnetic polarization, and red atoms are ${\mathrm{O}}^{2-}$ ions. (b) Lateral cut through the $c$-oriented ${\mathrm{Cr}}_2{\mathrm{O}}_3$ sample surface. Strong magnetic stray fields (black field lines) are expected at antiferromagnetic domain walls and weak fields at monolayer topographic steps. Blue and green shading indicate regions of opposite order parameter $L^{+}$ and $L^{-}$, defined by the orientation (up or down) of the topmost ${\mathrm{Cr}}^{3+}$ atom in the unit cell [36]. The regions are separated by a domain wall (white) of approximate width $\pi \mathrm{\Delta }$. The diamond scanning tip and NV center are shown in gray and orange, respectively.

Figure 3

Antiferromagnetic domain pattern in $c$-oriented ${\mathrm{Cr}}_2{\mathrm{O}}_3$. (a) SHG image revealing bright and dark domains of opposite order parameter in sample C; corresponding images for samples A and B are given in Figs. S1 and S2 in the Supplemental Material [49]. The order parameter ($L^{+}$ and $L^{-}$) is assigned based on the magnetization map in (c). The image is acquired with right-handed circularly polarized illumination. The twofold axes $a$, $a^{\prime }$, and $b$ (yellow vectors), determined by x-ray crystallography, coincide with the in-plane magnetic easy axes of the spin-flop phase. Dashed lines indicate the in-plane magnetic hard axes. Scale bar: $500\mu \mathrm{m}$.

(b) Magnetometry image of the stray field above a domain wall (white arrow) in sample A. Fainter features are due to surface topography, such as scratch marks from sample polishing (black arrows). The inset shows a high-sensitivity scan above a uniform domain on sample B, revealing weak stray fields due to surface roughness [49]. Dwell time per pixel is $1.5\mathrm{s}$ and total acquisition time is $26\mathrm{h}$. (c) Surface magnetization ${\sigma }_z$ reconstructed from the stray field map of (b), given in units of Bohr magnetons (${\mu }_{\mathrm{B}}$) per ${\mathrm{nm}}^2$. Scale bars for (b) and (c): $2\mu \mathrm{m}$.

Figure 4

Quantitative measurement of domain-wall structure and surface magnetization. (a) Two-dimensional magnetometry scan of a domain wall in sample C. Scale bar: $1\mu \mathrm{m}$. (b) Cross section along the white dashed line in (a), showing the stray field $B_{\mathrm{NV}}\left(x\right)$ as a function of the relative distance $x$ to the domain wall. Dots are the experimental data and the solid line is a fit to the domain-wall model given by Eq. (3). Free fit parameters are the surface magnetization ${\sigma }_z^0$, the domain-wall width $\mathrm{\Delta }$, and the angle $\chi$ [49]. (c) Histograms of ${\sigma }_z^0$ obtained from many line scan fits. Mean and standard deviation (s.d.) are included above the histograms as black dots with horizontal error bars ($\pm 1\mathrm{s}.\mathrm{d}.$). Light gray bars reflect the ${\sigma }_z^0$ values obtained by a secondary analysis (see Supplemental Material [49]; the central bar reflects the step height, and the lower bar reflects the integrated $B_x$ field). The number of line scans per histogram are 2512 for sample A, 726 for sample B, and 1012 for sample C.

Figure 5

Observation of Bloch and Néel walls. (a)–(c) Twist angle $\chi$ plotted against the domain-wall width $\mathrm{\Delta }$ for samples A–C. Each point represents the data from a two-dimensional magnetometry scan. Error bars ($\pm 1\mathrm{s}.\mathrm{d}.$) are obtained by separate fits to each line of the 2D scan and computing the standard deviation (s.d.) of the fit results. Color coding reflects the propagation direction of the domain wall (see right panels). No correlation between chirality and spatial position is evident for samples A and B, whereas a clear correlation is evident for sample C. Mean angle and domain-wall widths are $(\chi ,\mathrm{\Delta })=[106{\left(6\right)}^{\circ },34\left(5\right)\mathrm{nm}]$ for sample A, $[113{\left(11\right)}^{\circ },45\left(8\right)\mathrm{nm}]$ for sample B, $[143{\left(12\right)}^{\circ },42\left(6\right)\mathrm{nm}]$ for sample C with $\alpha <9^{\circ }$, and $[117{\left(7\right)}^{\circ },65\left(4\right)\mathrm{nm}]$ for sample C with $\alpha >9^{\circ }$; brackets denote standard error. (d)–(f) SHG images of the domain-wall regions analyzed in (a)–(c). Colored squares show the scan locations. $\alpha$ is the angle between the local propagation direction of the domain wall (red solid line) and one of the magnetic hard axes [red dashed line, see Fig. 3]. Scale bars: $25\mu \mathrm{m}$.