Robust $A$-Type Order and Spin-Flop Transition on the Surface of the Antiferromagnetic Topological Insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$

Here, we present microscopic evidence of the persistence of uniaxial $A$-type antiferromagnetic order to the surface layers of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ single crystals using magnetic force microscopy. Our results reveal termination-dependent magnetic contrast across both surface step edges and domain walls, which can be screened by thin layers of soft magnetism. The robust surface $A$-type order is further corroborated by the observation of termination-dependent surface spin-flop transitions, which have been theoretically proposed decades ago. Our results not only provide key ingredients for understanding the electronic properties of the antiferromagnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, but also open a new paradigm for exploring intrinsic surface metamagnetic transitions in natural antiferromagnets.

Figure 1

(a) Topographic image (5 K) of one and two septuple layer (SL) steps on an as-grown ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ single crystal. (b),(c) MFM images taken at 0.3 and $-0.3\mathrm{T}$, respectively, after field cooling at 0.6 T, at the same location as in (a). The applied magnetic field is perpendicular to the sample surface. A curvilinear domain wall cuts through the SL step. The domain and SL step contrast were reversed when the tip moment was flipped (dark is attractive and bright is repulsive). (d),(e), Line profiles of the topography (black) and MFM (green and red) data. The frequency shift in (d) was measured across the domain wall over flat topography, while in (e) it was taken across the SLs. The color scale for the topographic (MFM) image(s) is 6 nm (0.3 Hz).

Figure 2

(a),(b) Topographic and MFM images of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ surface covering measured in 1 T at 5 K after 0.425 T field cooling. Magnetic contrast of domains and terraces is visible. (c)–(h) Enlargements of topographic and MFM images outlined by solid white boxes in (a),(b). White arrows (dashed lines) mark the exposed (covered) single SL steps. The bright domain contrast in the region covered by the impurity phase is suppressed, as shown by the white arrow in (h). Domain wall contrast is not suppressed by the impurity phase, as shown in the dotted box in (b). (i) Topographic line profiles [white dotted lines in (a)] of SLs and impurity-phase QLs with schematic of spin configuration. The gray area illustrates a soft magnetic phase that screens the stray fields of the SL edges underneath. The color scales for the topographic and MFM images are 7, 6, 3, and 3 nm (0.2 Hz), respectively.

Figure 3

(a)–(h) MFM images taken at 5 K with increasing field labeled in lower right corners. (i) Domain contrast between red squares, labeled $a$ and $b$ in $A$ versus applied field. Below 1.75 T, the domain contrast is constant. As the applied field is further increased, $a$ domains start to appear rougher and darker near 1.85 T, then the domain contrast quickly reverses above 1.85 T. Similar behavior was observed on $b$ domains around 3.1 T. Above 3.5 T, the system enters the canted AFM phase and the domain contrast disappears. The color scale for MFM images is 0.3 (a)–(d) and 0.8 (e)–(h) Hz.

Figure 4

(a) Theoretical-phase diagram of the spin-flop state in the revised Mills model. Blue and red colored regimes illustrate SSF states for antiparallel and parallel surfaces, respectively. Color code denotes the difference of net spin canting between the two types of surfaces [34]. Black solid line is a phase boundary of the bulk spin-flop state; dashed line is a boundary between AFM and SSF phases for antiparallel (blue) and parallel (red) surfaces. (b) Simulated field dependence of magnetic force gradient differences between antiparallel and parallel surfaces. (c) Schematic illustration of the spin-flop process for surface (upper 4 rows) and bulk (lower) domains. Left blue (right red) represents antiparallel (parallel) surface spins, whereas, left green (right yellow) represents antiparallel (parallel) bulk spins. (d) $H\text{−}T$ phase diagram showing $A$-type AFM phase (red), ${\mathrm{SSF}}_A$ and ${\mathrm{SSF}}_P$ spin-flop phase (pink and light purple), bulk CAFM phase (dark purple), and forced ferromagnetic or paramagnetic (PM) phase (light blue).