Stacking-Dependent Spin Interactions in $\mathrm{Pd}/\mathrm{Fe}$ Bilayers on Re(0001)

Using spin-polarized scanning tunneling microscopy and density functional theory, we have studied the magnetic properties of $\mathrm{Pd}/\mathrm{Fe}$ atomic bilayers on Re(0001). Two kinds of magnetic ground states are discovered due to different types of stacking of the Pd adlayer on $\mathrm{Fe}/\mathrm{Re}(0001)$. For fcc stacking of Pd on $\mathrm{Fe}/\mathrm{Re}(0001)$, it is a spin spiral propagating along the close-packed ($\overline{\mathrm{\Gamma }K}$) direction with a period of about 0.9 nm, driven by frustrated exchange and Dzyaloshinskii-Moriya interactions. For the hcp stacking, the four-site four-spin interaction stabilizes an up-up-down-down state propagating perpendicular to the close-packed direction (along $\overline{\mathrm{\Gamma }M}$) with a period of about 1.0 nm. Our work shows how higher-order exchange interactions can be tuned at interfaces.

Figure 1

(a) STM topography of a pseudomorphic Fe monolayer (ML) on Re(0001). The coverage is about 0.3 ML ($U=100\mathrm{mV}$, $I=1\mathrm{nA}$). The inset is a closer view of both the Re(0001) substrate and the Fe monolayer close to a Re(0001) step edge (marked by a yellow dashed line), indicating an hcp stacking of Fe on Re(0001) ($U=5\mathrm{mV}$, $I=20\mathrm{nA}$). (b) STM topography of Pd on $\mathrm{Fe}/\mathrm{Re}(0001)$. The Fe coverage is about 0.3 ML, and the Pd coverage is about 1 ML ($U=200\mathrm{mV}$, $I=2\mathrm{nA}$). The inset is a closer view of a Pd island on $\mathrm{Fe}/\mathrm{Re}(0001)$ ($U=20\mathrm{mV}$, $I=2\mathrm{nA}$). (c) Simultaneously recorded $dI/dU$ map of (b) allowing the distinction between different layers exposed. (d) Point $dI/dU$ spectra of the different layers.

Figure 2

(a) STM topography and (b) simultaneously recorded $dI/dU$ map ($U=-100\mathrm{mV}$, $I=2\mathrm{nA}$, 0 T, Cr bulk tip). The monolayer Pd islands on $\mathrm{Fe}/\mathrm{Re}(0001)$ are marked in (a). The $\mathrm{Pd}/\mathrm{Fe}/\mathrm{Re}(0001)$ islands show two different contrast levels in the $dI/dU$ map at $U=-100\mathrm{mV}$. This is attributed to two different stacking types, i.e., fcc and hcp of Pd on $\mathrm{Fe}/\mathrm{Re}(0001)$. (c)–(e) Spin-polarized $dI/dU$ maps at 0T, 5T, and 9T out-of-plane magnetic field. ($U=15–20\mathrm{mV}$, $I=2\mathrm{nA}$, Cr bulk tip.) Periodic stripes can be observed on the $\mathrm{Pd}/\mathrm{Fe}/\mathrm{Re}(0001)$ islands in the spin-polarized $dI/dU$ maps with a different contrast for fcc- and hcp-stacked islands: The stripe period for fcc islands is about 0.9 nm, and the stripe directions are perpendicular to the close-packed directions of the islands. For hcp islands, the observed period is about 1.0 nm, and the stripe directions are along the close-packed directions of the islands. (f),(g) line profiles of the periodic stripes in fcc- and hcp-stacked $\mathrm{Pd}/\mathrm{Fe}/\mathrm{Re}(0001)$ islands [marked in (e)], respectively.

Figure 3

Energy dispersion $E(\mathbf{q})$ of flat spin spirals along two high-symmetry directions ($\overline{\mathrm{\Gamma }KM}$ and $\overline{\mathrm{\Gamma }M}$) for $\text{fcc}\text{−}\mathrm{Pd}/\mathrm{Fe}/\mathrm{Re}(0001)$ (purple) and $\mathrm{hcp}\text{−}\mathrm{Pd}/\mathrm{Fe}/\mathrm{Re}(0001)$ (green). The light (dark) color is used for spin spirals without SOC (with SOC). The filled circles represent DFT data and the solid lines are the fit to the spin model. The filled diamonds represent the 3Q and $uudd$ states at the $\mathbf{q}$ points corresponding to the single-$Q$ states.

Figure 4

Spin-polarized local density of states (LDOS) of (a) $4d$ Pd, (b) $3d$ Fe, and (c) $5d$ Re in the FM state. Filled LDOS represent hcp-$\mathrm{Pd}/\text{hcp-}\mathrm{Fe}/\mathrm{Re}(0001)$ and solid lines represent fcc-$\mathrm{Pd}/\text{hcp-}\mathrm{Fe}/\mathrm{Re}(0001)$.