Three-dimensional spin orientation in antiferromagnetic domain walls of NiO studied by x-ray magnetic linear dichroism photoemission electron microscopy

A determination of the three-dimensional spin directions in all types of domain walls (DWs) of antiferromagnetic NiO has been successfully performed by photoemission electron microscopy combined with x-ray magnetic linear dichroism (XMLD), both for $s$- and $p$-polarized light. By comparing the azimuthal angle dependence of the XMLD contrast in the DWs with cluster model calculations which include the crystal symmetry and full-multiplet splitting, we determine the spin structures in the $\left\{001\right\}$ T walls, $\left\{011\right\}$ T walls, 120° S walls, and 180° S walls. In some cases, distinct S walls are not formed between two adjacent S domains, and the spin direction changes gradually over a wide range of the S domain structures. In the S walls, the spin direction is parallel to the magnetic easy $\left\{111\right\}$ plane. These spin configurations arise from the large difference in anisotropy energy between the in-plane and out-of-plane directions. Unexpectedly large widths in the several hundred nanometer range were observed for all the DWs. This also shows that NiO has a small magnetocrystalline anisotropy energy. Together with Monte Carlo simulation results, the qualitative phenomena concerning the wall energies are discussed. We further investigated the difference in wall energy between the $\left\{001\right\}$ T wall and the $\left\{011\right\}$ T wall. From the Monte Carlo simulation and an experimental study of heating effects, it is revealed that the $\left\{001\right\}$ T wall energy is smaller than the $\left\{011\right\}$ T wall energy.

Figure 1

Schematic illustration of the AFM spin structure in NiO. The circles indicate Ni${}^{2+}$ ions with up and down spins. The spin directions are parallel to the $\left[\overline{2}11\right]$ direction. The black circles indicate O${}^{2-}$ ions. The spins couple ferromagnetically within the same $\left\{111\right\}$ plane.

Figure 2

Schematic illustrations of possible types of T walls. (a), (f) $\left\{011\right\}$ T walls, where the walls are formed between T1[111] and T2$\left[\overline{1}11\right]$, and T3$\left[1\overline{1}1\right]$ and T4$\left[11\overline{1}\right]$ domains, respectively. (b)–(e) $\left\{001\right\}$ T walls, where the walls are formed between T1–T3, T1–T4, T2–T3, and T2–T4.

Figure 3

Schematic illustrations of possible types of S walls: (a) 60° S wall, (b) 120° S wall, (c) 180° S wall, and (d) same as in (c) but viewed from the $\left[1\overline{1}0\right]$ direction.

Figure 4

(a) XLD- PEEM image recorded with $p$-polarized light at the O $K$ edge. The T domains of NiO are observed. (010) T walls are located in the areas surrounded by elliptic curves. (b) XMLD image recorded with $s$-polarized light at the Ni $L_2$ edge. The T and S domains of NiO are observed. The observed area is the same as in (a). (010) T walls are located in the areas surrounded by elliptic curves. Along the tick mark, we derived the line profile in Fig. 8. (c) Schematic illustration of (a). (d) Same as in (a) but for a different area, and for $s$-polarized light. (011) T walls are located in the areas surrounded by elliptic curves. (e) Same as in (b) but observed at the same area in (d). (011) T walls are located in the areas surrounded by elliptic curves. (f) Schematic illustration of (d).

Figure 5

(a) XMLD-PEEM image of NiO recorded with $s$-polarized light. The areas marked with a cross and a triangle correspond to S domains with spin axes illustrated in (d). The area surrounded by an elliptic curve is a 180° S wall. The crystallographic axes are also indicated. (b) Same as in (a) but with a different light incidence angle. (c) Schematic illustration of (a) and (b). (d) Schematic illustration of the easy spin axes of the S domains marked by the cross and the triangle S domains in (a)–(c). (e) Same as in (a) but for a different observed area. The areas marked with a circle and a square correspond to S domains with spin axes illustrated in (h). The area surrounded by an elliptic curve is a 120° S wall. (f) Same as in (e) but with a different light incidence angle. (g) Schematic illustration of (e) and (f). (h) Schematic illustration of the easy spin axes of the S domains marked by the cross and the triangle S domains in (e)–(g).

Figure 6

(a) XMLD-PEEM image in a single T domain. Three S domains, S1, S2, and S3, are observed. (b) Line profile of the solid line shown in (a). This corresponds to the contrast along S1 to S2 to S3. (c) Spin structures estimated from the contrast in (a). The spin axes gradually change from S1 to S2 to S3.

Figure 7

AAD of one of the $\left\{001\right\}$ T walls. (a)–(e) XMLD-PEEM images for different azimuthal angles but the same observed area. The cross and the triangle areas are S4 and S5 domains. The image was recorded using $s$-polarized light. (f)–(j) Line profiles for the solid lines shown in (a)–(e). These correspond to the contrast for S4 and S5 domains and DW. (k) Calculated AAD for three kinds of spin axes. These are calculated for the axes which can reproduce the observed AAD above.

Figure 8

(a) Schematic illustration of the spin structures of $\left\{001\right\}$ T walls obtained by a comparison of the theoretical and experimental AADs. (b) The circles are the experimental line profile of Fig. 4b. The solid line corresponds to the XMLD contrast calculated for the spin axes shown in (c). (c) Schematic illustration of the spin structures in the $\left\{001\right\}$ T wall shown in (a). Here the axes are projected onto the (001) plane.

Figure 9

(a) Same as in Fig. 8a but for the $\left\{011\right\}$ T wall. (b) Same as in Fig. 8c but for the $\left\{011\right\}$ T wall.

Figure 10

(a) Schematic illustration of the spin structures in one of the 180° S walls obtained from a comparison of the theoretical and experimental AADs. (b) Same as in (a) but for a different type of 180° S wall.

Figure 11

(a) Same as in Fig. 10 but for one of the 120° S walls. (b) Same as in (a) but for a different type of 120° S wall.

Figure 12

Schematic illustration to explain the difference between the intrinsic DW width and the observed width. This is for a 180° S wall.

Figure 13

Distribution of DW widths obtained from many PEEM images. Histograms (a)–(d) correspond to the width distribution for the $\left\{001\right\}$ T wall, $\left\{011\right\}$ T wall, 180° S wall, and 120°,S wall, respectively.

Figure 14

(a) T and S domain structures of NiO before annealing the sample. The image was recorded using XMLD-PEEM at the Ni $L_2$ edge. Because circularly polarized light is used, the image corresponds to the sum of images for $s$- and $p$-polarized light. (b) Schematic illustration of (a). The thick line indicates a surface crack. The solid and dotted lines indicate $\left\{001\right\}$ and $\left\{011\right\}$ T walls, respectively. (c) As in (a) but after annealing at a temperature above $T_{\mathrm{N}}$ for longer than 25 minutes. (d) Schematic illustration of (c).