Spin-sensitive shape asymmetry of adatoms on noncollinear magnetic substrates

The spin-resolved density of states of Co atoms on a noncollinear magnetic support displays a distinct shape contrast, which is superimposed on the regular height contrast in spin-polarized scanning tunneling microscopy. The apparent atom height follows the well-known cosine dependence on the angle formed by the tip and adatom local magnetization directions, whereas the shape contrast exhibits a sine dependence. We explain this effect in terms of a noncollinear spin density induced by the substrate, which in our case is the spin spiral of the Mn monolayer on W(110). The two independent contrast channels, apparent height and shape, are identified with the Co magnetization projections onto two orthogonal axes. As a result, all components of the overall atom magnetic moment vector can be determined with a single spin-sensitive tip in the absence of an external magnetic field. This result should be general for any atom deposited on noncollinear magnetic layers.

Figure 1

SP-STM images (8 mV, 1 nA) of Co atoms on the SS, showing the reversal of the magnetic contrast as the tip magnetization is switched by an external magnetic field of (a) +2 and (b) $-2$ tesla. Note that the overall surface magnetization is zero, and therefore the external magnetic field does not affect the sample magnetic state, but only controls the tip magnetization, as indicated in the insets. Red (bright Mn row) and green (dark Mn row) dashed lines highlight the half unit cell shift of the magnetic periodicity upon tip magnetization reversal. (c) Sketch of the spin spiral structure, where the red and green color levels of the arrows represent the spin-up and spin-down components, respectively. (d) Experimental spin-resolved profile along the $\left[1\overline{10}\right]$ direction of the spin spiral together with a fit to Eq. (2).

Figure 2

(a) Set of Co atoms separated by one lattice parameter (10 mV, 2 nA, 2.5 T), showing the gradual increase of the shape asymmetry. This image demonstrates an overall spin direction sensitivity better than $\alpha \simeq {14}^{\circ }$. (b) Atom profiles for several tip-atom magnetization angles showing the gradual development of shape asymmetry, defined as the imbalance between the light and dark gray areas enclosed by the atom profile, Eq. (3). (c)–(d) Comparison of constant-current (c) and constant-height (d) modes (0 T, 1.1 K, the set point for scanning or feedback opening is 10 mV and 2 nA). Note that the color scale is adapted in each image to highlight that the atoms have the same shape in spite of having enhanced magnetic contrast in constant-height mode. (e) Profiles extracted from (c) and (d) illustrating that the spin-dependent shape in closed feedback (i.e., constant-current mode, black line) is identical to constant-height LDOS slices (pale blue line). Atomic profiles are vertically offset.

Figure 3

(a) Topographic spin-polarized height contrast and its corresponding $cos\theta +\eta {cos}^2\theta$ fit with $\eta =0$ (thin dashed line) and $\eta =0.37$ (thick red line). (b) Experimental shape asymmetry of the atoms with a fit to Eq. (4), yielding $\varphi =-123\pm 3^{\circ }$ (red). Error bars are derived from the uncertainty in the atom's center position of $\pm 0.2$ Å. The inset illustrates the spin density across the atom introduced by the linear dependence of $\theta \left(x\right)$ (see text), and the corresponding asymmetric height profile from which ShA is retrieved.

Figure 4

(a) Spin-resolved constant-current map and (b) $dI/dV$ conductance map of Co atoms positioned every $3w$ along the spin spiral, leading to $\mathrm{\Delta }{\theta }_{\mathrm{Co}}\simeq -{42}^{\circ }$ (2 nA, sample bias $-100$ mV, lock-in modulation 5 mV and +2.5 T). (c) Constant-current and $dI/dV$ map over two atoms with opposite spin (that is, separated by $w/2$ in the horizontal axis) scanned with a nonmagnetic W tip (left panel) and two atoms with almost opposite spin scanned with a Fe-coated W tip (right panel). This set of images shows that at $-100$ meV the vacuum LDOS of Co atoms exhibits a strong $d_{xz}$ orbital contribution and is dominated by the minority spin channel. Since $dI/dV$ mapping is energy selective, at $-100$ meV, the distinct nonspherical orbital symmetry contrasts with the round-shaped atom topography responding to the total tunneling current. (d) Enhanced spin-shape asymmetry in atoms' profiles along $\left[1\overline{1}0\right]$ from $dI/dV$ conductance maps at $-100$ mV.