Tailoring noncollinear magnetism by misfit dislocation lines

The large epitaxial stress induced by the misfit between a triple atomic layer Fe film and an Ir(111) substrate is relieved by the formation of a dense dislocation line network. Spin-polarized scanning tunneling microscopy investigations show that the strain is locally varying within the Fe film and that this variation affects the magnetic state of the system. Two types of dislocation line regions can be distinguished and both exhibit spin spirals with strain-dependent periods (ranging from 3 to $10\mathrm{nm})$. Using a simple micromagnetic model, we attribute the changes of the period of the spin spirals to variations of the effective exchange coupling in the magnetic film. This assumption is supported by the observed dependence of the saturation magnetic field on the period of the zero-field spin spiral. Moreover, magnetic skyrmions appear in an external magnetic field only in one type of dislocation line area, which we impute to the different pinning properties of the dislocation lines.

Figure 1

(a) Constant-current STM topography map of the triple layer Fe film on Ir(111). Double and single lines are indicated by the arrows. (b),(c) Zoom-in on double line areas. At positive bias, one can see that bright and dark lines alternate and show a double line feature, whereas at negative bias the lines look all very similar. (d),(e) STM topography of single line regions. The single lines have the same appearance at any sample bias voltage. (f) Constant-current STM topography map of a triple layer Fe island on top of a double layer Fe film. The numbers in green circles indicate the local thickness of the film. The color scale was adjusted separately for the two terraces in order to highlight the matching of the dislocation lines. The areas between the bright lines on the double layer are bcc-like. (g) Side view of the triple layer Fe on Ir(111) system, indicating the color code used for the atomic structure models (h) and (i). (h),(i) Proposed atomic structure models (top view) for the triple layer Fe film from the experimental observations presented in (a)–(f). Measurement parameters: $I=1\mathrm{nA}$ and (a) $U=+200\mathrm{mV},T=8\mathrm{K},B=3.5\mathrm{T}$; (b) $T=5\mathrm{K},B=4.5\mathrm{T}$; (c) $T=5\mathrm{K},B=3\mathrm{T}$; (d) $T=8\mathrm{K},B=0\mathrm{T}$; (e) $T=8\mathrm{K},B=2.5\mathrm{T}$; and (f) $U=-700\mathrm{mV},T=153\mathrm{K},B=3\mathrm{T}$.

Figure 2

(a),(b) Spin-resolved constant-current map and spin-resolved differential tunneling conductance map of a triple layer Fe film on Ir(111) measured simultaneously using a Cr bulk tip with out-of-plane spin sensitivity. The magnetic sensitivity of the tip is simply deduced from the magnetic contrast on the spirals, which is identical for all the propagation directions. The magnetic contrast is visible on both the constant-current and differential conductance maps. The ellipses on image (b) mark a zone where the period of the spiral is changing: this can be correlated with the spacing between the dislocation lines indicated in (a). (c) Detail of the spin-resolved differential tunneling conductance map of a double line region. The spin spiral propagates along the lines and its wave front exhibits a zigzag shape. (d),(f) Line profiles taken in the double and single line regions, respectively, at the positions indicated in (b). The displayed profiles are the mean values within the rectangles, each data line was laterally shifted to straighten the wave front, and offsets were applied to the resulting profiles for clarity. The red dashed lines are the results of fits with sine functions, showing that the spirals are homogeneous regardless of the considered region. (e) Spin-resolved differential conductance map of an area with single lines. Spin spirals with various wavelengths are visible and their wave fronts are tilted by about $\pm {62}^{\circ }$ with respect to the lines. Measurement parameters: no external magnetic field, (a),(b) $U=-700\mathrm{mV},I=1\mathrm{nA},T=8\mathrm{K}$; (c) $U=-700\mathrm{mV},I=750\mathrm{pA},T=4\mathrm{K}$; and (e) $U=-700\mathrm{mV},I=1\mathrm{nA},T=8\mathrm{K}$.

Figure 3

Dependence of the spiral period on the spacing of the dislocation lines for the triple layer Fe on Ir(111), both double and single line regions. The SP-STM measurements were performed at low temperature (4 or $8\mathrm{K})$ on several different samples and the spiral periods were extracted using 2D Fourier transformation and fits of the real-space data to sine functions, keeping only points with an error bar below 15%. For the double line regions, the zigzag shape of the wave front was not considered and the period was measured along the lines. The actual wavelength along the direction of the wave vector might be 10% smaller. On the single line regions, the angle of the wave front was taken into account in the determination of the period. It is evident that if the distance between the dislocation lines decreases, the spiral period increases, as observed already in Fig. 2. The insets show the data (both the spin-resolved constant-current map and the differential conductance map as well as their Fourier transforms) used to determine the point marked with the red square. The axis on the right indicates that the effective exchange parameter should vary between 0.6 and $2.2\mathrm{pJ}{\mathrm{m}}^{-1}$ to create spirals with wavelengths between 3 and $10\mathrm{nm}$ from the simple model described in the text.

Figure 4

Spin-resolved differential tunneling conductance maps of a region with single lines surrounded by double lines (left) and of a region with double lines surrounded by single lines (right) in increasing out-of-plane magnetic field, measured with an out-of-plane spin-sensitive Cr bulk tip. When the external field increases, the spin spirals in the double line regions transform into distorted skyrmions whereas those in the areas with single lines become inhomogeneous and can be described as an assembly of independent ${360}^{\circ }$ domain walls. When the width of these walls is similar to the width of the skyrmions in the adjacent areas, they couple to them. Measurement parameters: Left: $U=-700\mathrm{mV},I=1\mathrm{nA},T=8\mathrm{K}$; Right: $U=-500\mathrm{mV},I=1\mathrm{nA},T=4\mathrm{K}$.

Figure 5

(a)–(h) Spin-polarized differential tunneling conductance maps of an ultrathin Fe film on Ir(111). The numbers in green circles in (a) indicate the local Fe coverage. An external out-of-plane magnetic field was applied, increased in 0.5-T steps up to $4\mathrm{T}$ (at this field the sample is completely polarized, i.e., ferromagnetic) and then decreased again to zero. Comparison between scans taken at the same field value shows a hysteretic behavior for the triple layer Fe, both in the regions with the double and single lines. (i) Plot of the magnetic state during the field sweep of the four areas marked in blue in (a). Areas I and II are double line regions; III and IV are single line regions. Measurement parameters: $U=-500\mathrm{mV},I=1\mathrm{nA},T=4\mathrm{K}$, out-of-plane spin-sensitive Cr bulk tip.

Figure 6

Effect of the spiral period on the magnetic fields needed to reach the ferromagnetic state during an increasing field sweep. The correlation between the spiral period and the spacing of the dislocation lines in the Fe layer shown in Fig. 3 leads also to a dependence of the transition field on the strain relief. A trend that higher external fields are required to destroy noncollinear spin structures with smaller spatial period appears. The calculated transition fields were obtained from the phase diagram detailed by Bogdanov and Hubert [17] with the parameters from Fig. 3: $D=2.8\mathrm{mJ}{\mathrm{m}}^{-2}$ and $K_{\mathrm{eff}}=0$. The magnetic moment used is $\mu =2.7{\mu }_{\mathrm{B}}$ per Fe atom [11]. Because of the metastability of the magnetic states revealed by the hysteresis, the experimental field values are upper estimates of the transition fields. The SP-STM measurements were performed at $4\mathrm{K}$ on three different samples and the external magnetic field was increased in steps of 0.25 or $0.5\mathrm{T}$. The error bars correspond to the height of the steps as indicated in Fig. 5.