Direct Visualization of Surface Spin-Flip Transition in ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$

We report direct visualization of spin-flip transition of the surface layer in antiferromagnet ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$, a natural superlattice of alternating ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ layers, using cryogenic magnetic force microscopy (MFM). The observation of magnetic contrast across domain walls and step edges confirms that the antiferromagnetic order persists to the surface layers. The magnetic field dependence of the MFM images reveals that the surface magnetic layer undergoes a first-order spin-flip transition at a magnetic field that is lower than the bulk transition, in excellent agreement with a revised Mills model. Our analysis suggests no reduction of the order parameter in the surface magnetic layer, implying robust ferromagnetism in the single-layer limit. The direct visualization of surface spin-flip transition not only opens up exploration of surface metamagnetic transitions in layered antiferromagnets, but also provides experimental support for realizing quantized transport in ultrathin films of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ and other natural superlattice topological magnets.

Figure 1

(a) Topographical image (5.5 K) measured on a cleaved surface of a ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ single crystal. (b),(c) MFM images (5.5 K, 0 T) measured at the same location with negatively and positively polarized tips, respectively. The domain contrast is reversed as the tip moment is flipped, confirming that the magnetic contrast comes from the sample stray field. A curvilinear domain wall crossing the SL and QL steps is visible in the MFM images. (d),(e) Line profiles of the topographical image (black) and MFM images (red and blue) along the red and blue arrow in (b) and (c). Schematics of crystal and magnetic stacking are sketched under the topographical line profiles. Red and blue layers represent the ferromagnetic SLs with moments pointing down and up, respectively. The gray layers are QLs. The frequency shift line profile is plotted across a SL plus QL step in (d), while it is plotted across the domain wall (DW) on a flat SL layer in (e).

Figure 2

(a)–(f) Selected MFM images taken at 5.5 K with increasing magnetic fields, which are labeled on the corner of each image. The color scales from (a) to (f) are 0.06, 0.11, 0.12, 0.12, 0.26 and 3 Hz, respectively. The AFM domain walls are traced out with dashed lines in (a). The boxed areas $\alpha$ and $\beta$ in (a) corresponds to parallel and antiparallel surfaces, respectively. (g),(h) Magnetic structures of areas $\alpha$ and $\beta$ before and after the surface spin-flip transition, respectively. (i) $H$ dependence of MFM contrast between areas $\alpha$ and $\beta$ and that of forced ferromagnetic (FM) domain population during the BSF transition (between 0.1 and 0.17 T). The colored arrows indicate the field sweeping direction. Above 0.17 T, the system is in the FM state.

Figure 3

(a) Total energy as a function of exchange field, for the four magnetic phases with 12 spin-lattice sites ($N=12$) and reduced surface exchange coupling (${\lambda }_J=0.4$). First-order phase transitions are expected at the crossing points $h_1$, $h_2$, and $h_3$, which are SSF, SLSF, and bulk spin-flip transitions, respectively. (b) The crossing points with respect to the surface exchange coupling ${\lambda }_J$ and the surface spin moment ${\lambda }_S$. The SLSF phase can appear only when the surface parameters are reduced as ${\lambda }_J{\lambda }_S<1$. (c) Schematic illustration of the surface spin-flip states where red and blue represent antiphase domains. Assuming the external field points up, SSF (SLSF) occurs at the first (second) layer of the antiparallel (parallel) surface as highlighted by orange filling.

Figure 4

(a)–(c) MFM images taken at $-0.09\mathrm{T}$ after external magnetic field was increased to the set values labeled at the upper-left corners. The color scale is 0.2 Hz. The field annealing results illustrate partial SLSF transition on the parallel surface. (d) Schematic illustration of SLSF phase. The magnetic moment in the second SL of the $\beta$ domain is partially flipped, which corresponds to the dark patches as highlighted in the white box in (b).