Spin-spiral state of a Mn monolayer on W(110) studied by soft x-ray absorption spectroscopy at variable temperature

The noncollinear magnetic state of epitaxial Mn monolayers on tungsten (110) crystal surfaces is investigated by means of soft x-ray absorption spectroscopy to complement earlier spin-polarized scanning tunneling microscopy experiments. X-ray absorption spectra (XAS), x-ray linear dichroism (XLD) and field-induced x-ray magnetic circular dichroism (XMCD) Mn $L_{2,3}$-edge spectra were measured in the temperature range from 8 to 300 K and compared to results of fully relativistic ab initio calculations. We show that antiferromagnetic (AFM) helical and cycloidal spirals give rise to significantly different Mn $L_{2,3}$-edge XLD signals, enabling, thus, to distinguish between them. It follows from our results that the magnetic ground state of a Mn monolayer on W(110) is an AFM cycloidal spin spiral. Based on temperature-dependent XAS, XLD, and field-induced XMCD spectra we deduce that magnetic properties of the Mn monolayer on W(110) vary with temperature, but this variation lacks a clear indication of a phase transition in the investigated temperature range up to 300 K—even though a crossover exists around 170 K in the temperature dependence of XAS branching ratios and in XLD profiles.

Figure 1

(a) STM image of the Mn/W(110) surface with a Mn coverage of about 80% of a ML. Yellow arrows indicate W(110) step edges. The LEED image of the W(110) surface taken before Mn growth defines the azimuthal orientation $\varphi =0^{\circ }$ with respect to ${\epsilon }_h$ and ${\epsilon }_v$ incoming photon polarization vectors. (b) Schematic of the surface atomic configuration and respective orientation of ${\epsilon }_h$ and ${\epsilon }_v$ photon polarization vectors for $\varphi =0^{\circ }$. The small dark circles denote Mn atoms, the large light circles denote W atoms in the subsurface layer. Rods at Mn atoms indicate symbolically the directions of magnetic moments for an antiferromagnetic CSS.

Figure 2

(a) Experimental XAS and (b) XLD spectrum recorded at 8 K compared to spectra calculated for AFM cycloidal spin spiral and AFM helical spin spiral states.

Figure 3

(a) Temperature dependence of the XLD signal. The data are shown with a vertical offset for better visibility. The dashed curve on top of the $T=300\text{−}\mathrm{K}$ curve represents a fitted temperature-independent background. (b) Detailed view of temperature-dependent XLD at the $L_3$ edge without the vertical offset. (c) As panel (b) but for the $L_2$ edge. The minus/plus signs indicate features where the temperature dependence of the XLD is most pronounced.

Figure 4

(a) Experimental XAS recorded at 8 and 300 K together with theoretical XAS calculated for a CSS state, for a paramagnetic state, and for a nonmagnetic state. (b) Difference of experimental XLD signals recorded at 300 and 8 K compared to the differences between respective theoretical XLD signals obtained by assuming a paramagnetic or a nonmagnetic state at 300 K and a CSS state at 8 K.

Figure 5

(a) Experimental Mn $L_{2,3}$-edge XMCD spectra of Mn/W(110) for $T=8$, 120, and 300 K, for $\mathrm{\Theta }=0^{\circ }$ (normal incidence) and $\mathrm{\Theta }={70}^{\circ }$ (grazing incidence). An external magnetic field of $B=5\mathrm{T}$ has been applied as indicated in the insets. (b) The temperature dependence of corresponding XMCD asymmetries both for the normal and for the grazing incidence.

Figure 6

(a) Experimental XAS and (b) field-induced XMCD recorded at 8 K compared to theoretical spectra calculated for system: (i) in an uncompensated DLM state, (ii) in a ferromagnetic state, and (iii) in an AFM state with moments nearly in plane but tilted by $5^{\circ }$ in the out-of-plane direction. Note that the XMCD signal for the tilted AFM state was divided by 7, and the XMCD signal for the ferromagnetic state was divided by 70.

Figure 7

Experimental branching ratios $I_{L_3}/(I_{L_2}+I_{L_3})$ for Mn $L_{2,3}$-edge XAS spectra at different temperatures.

Figure 8

In situ sample characterization in the ID8 preparation chamber by scanning tunneling microscopy. (a) Clean W(110) substrate with multiple terraces. (b) Step-flow growth of monolayer Mn stripes on W(110) at Mn coverages of about 0.8 MLs. (b) and (d) show images of respective sample areas on a smaller scale. Tungsten step edges are indicated by yellow arrows.

Figure 9

XAS and XLD signals measured for the polycrystalline MnO reference sample. Top graph: XAS for horizontal and vertical photon polarizations ${\epsilon }_h$ and ${\epsilon }_v$. Bottom graph: XLD signal resulting from the XAS spectra shown above. The constant offset of XLD values reflects the offset in the raw data in the top graph as they are not normalized to 1 at 637 eV.

Figure 10

Scaling of the Mn $L_{2,3}$-edge XLD intensity under azimuthal rotation of the W(110) substrate. All data were measured at $T=300\mathrm{K}$. (a) Mn $L_{2,3}$-edge XAS and XLD for angles $\varphi =0^{\circ }$ and ${48}^{\circ }$ between the $\mathrm{W}\left[1\overline{1}0\right]$ direction and the ${\epsilon }_h$ photon polarization vector. XLD data for $\varphi ={48}^{\circ }$ are shown multiplied by $1/cos\left(2\varphi \right)$. (b) LEED images used for deducing the azimuthal orientation of the crystal.

Figure 11

Theoretical Mn $L_{2,3}$-edge XLD spectra for spin spirals compared to averages of spectra for AFM configurations for two perpendicular magnetization directions. Calculations performed within the ASA without a core hole.

Figure 12

Mn $L_{2,3}$-edge XAS and XLD calculated for the ground-state potential (core hole ignored), for the potential corresponding to the Slater transition state (half core hole) and for the potential obtained by means of the final-state approximation (full core hole). The experimental spectrum is shown for comparison.

Figure 13

DOS at Mn atoms calculated for (a) nonmagnetic and (b) AFM configurations of Mn/W(110). The spin channels are shown separately for the AFM state and summed together for the nonmagnetic state.

Figure 14

Mn $L_{2,3}$-edge XLD for Mn/W(110) in an AFM state with the direction of magnetic moments $\mathit{M}$ oriented along W[001], $\mathrm{W}\left[1\overline{1}0\right]$, and W[110]. A XLD spectrum calculated with SOC suppressed is shown for comparison.