Tunneling anisotropic magnetoresistance via molecular $\pi$ orbitals of Pb dimers

Pb dimers on a ferromagnetic surface are shown to exhibit large tunneling anisotropic magnetoresistance (TAMR) due to molecular $\pi$ orbitals. Dimers oriented differently with respect to the magnetization directions of a ferromagnetic Fe double layer on W(110) were made with a scanning tunneling microscope. Depending on the dimer orientations, TAMR is absent or as large as 20% at the Fermi level. General arguments and first-principles calculations show that mixing of molecular orbitals due to spin-orbit coupling, which leads to TAMR, is maximal when the magnetization is oriented parallel to the dimer axis.

Figure 1

(a) Constant-current topograph of six single Pb atoms (protrusions) on double-layer Fe on W(110) ($6.6\times 9{\mathrm{nm}}^2,100\mathrm{mV}$). Depressions are due to defects. Pb atoms were manipulated with the STM tip at a resistance of $25\mathrm{k}\mathrm{\Omega }(100\mathrm{mV},4\mu \mathrm{A}$) as indicated by the arrows. (b) Dimers with two orientations were obtained ($7\times 9{\mathrm{nm}}^2,1\mathrm{V}$). (c) Atomically resolved topograph of the substrate lattice ($4.7\times 1.9{\mathrm{nm}}^2,70\mathrm{mV},5\mu \mathrm{A}$). (d) Substrate lattice superimposed onto dimers assuming adsorption to hollow sites ($3.8\times 4{\mathrm{nm}}^2,1\mathrm{V}$). (e) Resulting geometries of dimers oriented along the [001] and ($\left[1\overline{1}1\right]$) directions.

Figure 2

(a) Topograph and (b) simultaneously recorded $dI/dV$ map of six dimers ($13\times 19{\mathrm{nm}}^2,70\mathrm{mV}$). The upper (lower) three dimers are adsorbed on a domain (domain wall) with an out-of-plane (in-plane) magnetization. (c) This leads to four angular configurations of spin quantization and coordination axes. (d) Averaged $dI/dV$ spectra of $\left[1\overline{1}1\right]$ dimers on a domain (the dotted curves) and a domain wall (the solid curves) (feedback opened at 1 V, 500 pA) are similar. (e) Spectra of [001] dimers show significant differences at $V<0\mathrm{V}$. The spread between curves with the same style indicates uncertainties (standard deviation of the averaged data). Different tips were used in (d) and (e). A $\left[1\overline{1}1\right]$-dimer spectrum (the orange curve) is shown for comparison. Modification of the tip affects the spectra. However, the characteristics discussed here were present in all spectra.

Figure 3

(a) Detailed [001]-dimer spectra. (b) TAMR of the spectra in (a). The dashed curves represent uncertainty margins. The gray areas mark the peak positions of the $dI/dV$ spectra. (c) Spin-polarized $dI/dV$ spectra of [001] dimers and Fe domains. The dashed and solid curves correspond to oppositely polarized domains and dimers adsorbed on them. (d) Asymmetry of the spectra in (c) defined by $(d{I}_{\alpha }/dV-d{I}_{\beta }/dV)/(d{I}_{\alpha }/dV+d{I}_{\beta }/dV)$ where $\alpha$ and $\beta$ denote the spectra of oppositely polarized domains.

Figure 4

(a) Total and spin-resolved vacuum LDOS 6.8 Å above a $\left[1\overline{1}1\right]$ dimer on Fe/W(110) for out-of-plane (the dashed curve) and in-plane (the solid curve) magnetizations. (b) TAMR obtained from the LDOS. (c) and (d) LDOS and TAMR for the [001] dimer as in (a) and (b). (e) and (f) Orbital decomposition of the LDOS of the [001] dimer for majority and minority channels. The blue, green, and gold colors indicate $p_z,p_y$, and $p_x$ orbitals at the Pb atoms. The solid and dashed curves denote in-plane and out-of-plane magnetizations, respectively.

Figure 5

Spin-resolved charge-density maps of the [001] dimer. The upper panels show a cross-sectional plot through the Pb dimers parallel to the surface, whereas the lower panels show a cross section through the dimers perpendicular to the film. The top Fe layer defines zero on the $z$ axis. The Pb dimer atoms are located $\approx 2\AA$ above the Fe layer. (a) Majority density in the energy interval $[E_F+0.85,E_F+0.95\mathrm{eV}]$. (b) Minority density in the range of $[E_F-0.2,E_F-0.1\mathrm{eV}]$. Majority and minority refer to the spin directions of the Fe film.