Strain-driven domain wall network with chiral junctions in an antiferromagnet

Abstract

Materials with antiferromagnetic order have recently emerged as promising candidates in spintronics based on their beneficial characteristics such as vanishing stray fields and ultra-fast dynamics. At the same time more complex localized non-coplanar magnetic states as for instance skyrmions are in the focus of applications due to their intriguing properties such as the topological Hall effect. Recently a conceptual shift has occurred to envision the use of such magnetic defects not only in one-dimensional race track devices but to exploit their unique properties in two-dimensional networks. Here we use local strain in a collinear antiferromagnet to induce non-coplanar domain wall junctions, which connect in a very specific way to form extended networks. We combine spin-polarized scanning tunneling microscopy with density functional theory to characterize the different building blocks of the network, and unravel the origin of the handedness of triple-junctions and the size of the arising topological orbital moments.

Figures (9)

• Figure 1: Strain-induced domain wall network in a collinear antiferromagnet.a, Constant-current STM image of a Mn double-layer film on Ir(111); the bright spots correspond to Ar bubbles below the Ir surface; bright lines indicate domain walls between orientational antiferromagnetic domains ($\Delta z=60$ pm); cyan boxes indicate sample areas which are shown again in Figs. \ref{['fig:walls']}c,d. b, d$I$/d$U$ map acquired simultaneously with (a), labels refer to the types of triple-junction. c, SP-STM constant-current image of a domain wall between two orientational antiferromagnetic domains ($\Delta z=15$ pm). d, Spin model of a superposition wall between orientational antiferromagnetic domains (see methods). (Measurement parameters: a,b: $U = +10$ mV, $I = 5$ nA; c: $U = +10$ mV, $I = 3$ nA; all: $T=4$ K).
• Figure 2: Domain wall triple-junctions.a,b, Schematics of the two different types of triple junctions, i.e. Y and T, respectively; numbers refer to the three possible orientational antiferromagnetic domains, green lines indicate the favorable $120^\circ$ domain walls. c,d, SP-STM constant-current images of a Y- and a T-junction, respectively ($\Delta z=36$ pm and $\Delta z=25$ pm), see boxes in Fig. \ref{['fig:network']}a for their positions within the network. The insets show a magnified view of the central area of the junction exhibiting the hexagonal magnetic pattern characteristic for the 3Q state; for better visibility of the magnetic pattern here high frequency noise has been removed by a lowpass filter with a cut-off frequency corresponding to a wavelength of $0.4$ nm. ($U = +10$ mV, $I = 5$ nA, $T=4$ K). e,f, Spin models of the two types of junctions (see methods).
• Figure 3: Competing spin configurations of the Mn double-layer on Ir(111).a,b, Top view of the 3Q state for a net AFM ($\rightleftarrows$) and FM ($\rightrightarrows$) coupling between the moments of the Mn layers. The top layer atoms are represented by larger spheres, see also insets for perspective views. c,d, Top view of the corresponding RW-AFM states; each of them represents one orientation of the 1Q states that lead to the 3Q superposition states in (a,b); blue triangles indicate the triangular lattice of the lower Mn layer. e,f Laterally relaxed RW-AFM states, where the displacement of the Mn atoms in the top layer relative to the hollow sites is indicated by cyan arrows. The total energies of each magnetic structure are given with respect to the RW-AFM$\rightleftarrows$ state.
• Figure 4: Magnetism-driven structural shift.a, STM image calculated via DFT for the 3Q$\rightleftarrows$ state (Fig. \ref{['fig:RWAFM_shift']}a). Large (small) spheres indicate atoms of the top (bottom) Mn layer. b, STM image calculated via DFT for the shifted RW-AFM$\rightleftarrows$ state (Fig. \ref{['fig:RWAFM_shift']}e). c, Atomic resolution constant-current STM image of a Y$^*$-junction; the black line is placed across an atomic row (dark spots) in the right domain, and extrapolation to the top domain confirms the different relative shifts for the top Mn layer, as indicated by cyan arrows ($U = +10$ mV, $I = 5$ nA, $T = 4$ K). d, Atomistic model of a Y$^*$-junction where the atom positions vary from hollow-site in the center (3Q) to bridge site in the RW-AFM domains; the color code illustrates the size of the shift, which leads to a structural handedness with compressive strain on one side and tensile strain on the other side of each domain wall.
• Figure 5: Chirality of the triple-junctions. SP-STM constant-current image of several triple-junctions, the different types are labelled; cyan arrows indicate the shift direction of the top Mn layer for the different orientational domains ($\Delta z=50$ pm). Drawing lines along the $120^\circ$ domain walls in different junctions results in an asymmetric intersection (see sketches) of the three domain walls due to the structural shift. Sketches show all possible triple-junctions that can occur with $120^\circ$ domain walls, the T/T$^*$-junctions occur in three orientations. To form a network, a pair of empty (Y/Y$^*$-junction) and filled same color triangles (T/T$^*$-junction) need to be connected, i.e., any straight wall must have a Y/Y$^*$-junction at one end and a T/T$^*$-junction at the other end respectively which is the only possible way of forming the network. (Measurement parameters: $U = +10$ mV, $I = 5$ nA, $T=4$ K).