Spin precession and inverted Hanle effect in a semiconductor near a finite-roughness ferromagnetic interface

Although the creation of spin polarization in various nonmagnetic media via electrical spin injection from a ferromagnetic tunnel contact has been demonstrated, much of the basic behavior is heavily debated. It is reported here that, for semiconductor/Al${}_2$O${}_3$/ferromagnet tunnel structures based on Si or GaAs, local magnetostatic fields arising from interface roughness dramatically alter and even dominate the accumulation and dynamics of spins in the semiconductor. Spin precession in inhomogeneous magnetic fields is shown to reduce the spin accumulation up to tenfold, and causes it to be inhomogeneous and noncollinear with the injector magnetization. The inverted Hanle effect serves as the experimental signature. This interaction needs to be taken into account in the analysis of experimental data, particularly in extracting the spin lifetime ${\tau }_s$ and its variation with different parameters (temperature, doping concentration). It produces a broadening of the standard Hanle curve and thereby an apparent reduction of ${\tau }_s$. For heavily doped $n$-type Si at room temperature it is shown that ${\tau }_s$ is larger than previously determined, and a new lower bound of 0.29 ns is obtained. The results are expected to be general and to occur for spins near a magnetic interface not only in semiconductors but also in metals and organic and carbon-based materials including graphene, and in various spintronic device structures.

Figure 1

Illustration of local interface magnetic fields and their effect on spin precession in a semiconductor. (a) The inhomogeneous magnetostatic field near a ferromagnetic interface with finite roughness, sketched for a sinusoidal interface profile with period $\lambda$. Field lines are in black; the magnetization of the ferromagnet (black arrows) points strictly along the global interface plane everywhere. Spins are injected into the semiconductor with spin initially aligned with the magnetization of the ferromagnet (solid white arrows). In the local fields, the spins are precessing on different trajectories represented by dotted arrows and white ellipses. Also the strength of the local field and hence the precession frequency is spatially inhomogeneous. (b) Decay of the spin accumulation $\Delta \mu$ as a function of distance $z$ from the oxide/semiconductor interface for (i) a perfectly smooth interface (exponential decay with spin-diffusion length $L_{SD}$) and (ii) an interface with finite roughness. For the latter, the region in which the local magnetostatic fields $B$${}^{ms}$ have an appreciable value is given in pink. Note that tunneling probes the value of $\Delta \mu$ at $z=0$

Figure 2

Spin accumulation and precession in $n$-type silicon near a ferromagnetic interface. Room temperature data for $n$-Si/Al${}_2$O${}_3$/ferromagnet junctions with Ni, Ni${}_{80}$Fe${}_{20}$, Co, or Fe electrode. The vertical axis gives the product of spin resistance and area (the “spin-RA product”), defined as ($\Delta V/I$)$\times$area. The magnetic field is applied perpendicular to the interface plane (open symbols, Hanle), or parallel to the interface (solid symbols, inverted Hanle), with $V_{\mathrm{Si}}-V_{\mathit{FM}}=+172$ mV (electron injection). In the left panel, Hanle curves for different FMs are normalized for better comparison of the linewidth, denoted by an effective time $1/\omega$ representing the half width at half maximum of a fit to a Lorentzian (using $g=2$).

Figure 3

Spin accumulation and precession in $p$-type silicon near a ferromagnetic interface. Room temperature data for $p$-Si/Al${}_2$O${}_3$/ferromagnet junctions with Ni, Ni${}_{80}$Fe${}_{20}$, Co, or Fe electrode. The magnetic field is applied perpendicular to the interface plane (open symbols, Hanle), or parallel to the interface (solid symbols, inverted Hanle), with $V_{\mathrm{Si}}-V_{\mathit{FM}}=-172$ mV (hole injection). In the left panel, Hanle curves for different FMs are normalized for better comparison of the linewidth, denoted by an effective time $1/\omega$ representing the half width at half maximum of a fit to a Lorentzian (using $g=2$).

Figure 4

Spin accumulation and precession in GaAs near a ferromagnetic interface. Experimental data for $n$-type GaAs/Al${}_2$O${}_3$/Co structures at 10 K, for magnetic field applied perpendicular to the interface plane (blue, Hanle), or parallel to the interface (pink, inverted Hanle). Data at $V_{\mathrm{GaAs}}-V_{\mathrm{Co}}=+422$ mV (top panel) and $+$580 mV (bottom panel).

Figure 5

Profiles of magnetostatic fields near a ferromagnetic interface with finite roughness. Calculated $B$${}_x$, $B$${}_y$, and $B$${}_z$ components of the field versus position in the $x$-$y$ plane at 5 nm distance from the interface, represented by a two-dimensional square array of magnetic dipoles pointing along the $x$ axis (period $\lambda =$ 20 nm, central dipole at $x=y=0$). The dipole strength $\mu$ is such that ${\mu }_0\mu /4\pi =$ 2 T nm${}^3$.

Figure 6

Calculated spin accumulation near an interface with local magnetostatic fields. Maps of the $S$${}_x$ component of the spin density in the semiconductor versus position in the $x$-$y$ plane parallel to the interface, for different values of external magnetic field applied along the $z$ axis (Hanle configuration, top row), or along the $x$ axis parallel to the magnetization of the ferromagnetic injector (inverted Hanle configuration, bottom row). Red color corresponds to the maximum spin density (without any precession), blue to zero spin accumulation. The magnetostatic fields were taken at 5 nm distance from a dipole array with $\lambda =$ 20 nm and ${\mu }_0\mu /4\pi =$ 10 T nm${}^3$. The spin lifetime was set to 1 ns. Right panels show the resulting Hanle (blue) and inverted Hanle (pink) curves for external applied magnetic field along the $z$ or $x$ axis, respectively, calculated by averaging the inhomogeneous spin density over the $x$-$y$ plane. The dipole strength is such that ${\mu }_0\mu /4\pi =2$ (top panel) or 10 T nm${}^3$ (bottom panel). Also shown in green are pure Lorentzian line shapes for the same 1 ns spin lifetime, with the peak amplitude scaled for easy comparison.

Figure 7

Hanle (pink) and inverted Hanle (blue) curves for external applied magnetic field $B$${}^{\mathrm{ext}}$ along $z$ or $x$ axis, respectively, calculated using Eq. (A11). Included are magnetostatic fields $B$${}^{ms}$ pointing purely along either the $x$, $y$, or $z$ axis, as indicated, and with a strength that has a simple sinusoidal spatial variation. The spin lifetime ${\tau }_s$ was set to 500 ps. Also shown in green for the same 500 ps spin lifetime are the pure Lorentzian curves, with the amplitude adjusted for easy comparison.

Figure 8

Left panels: Calculated strengths of the $B$${}_x$ (top) and $B$${}_z$ (bottom) components of the local magnetostatic field as a function of lateral $x$ position at different distances $z$ from a ferromagnetic Fe surface with one-dimensional roughness, for $\lambda =20$ nm and roughness amplitude $h=1$ nm. Right panels: The same, but now as a function of distance $z$ at fixed $x$ position, for $\lambda =20$ or 40 nm and roughness amplitude $h=1$ or 0.5 nm.

Figure 9

Top panels: Atomic force image ($500\times 500$ nm${}^2$) of the surface of the Al${}_2$O${}_3$ tunnel barrier on $p$-type Si, prior to metal electrode deposition, and a representative cross-sectional height profile. Bottom panels: The same, but now after deposition of the ferromagnetic metal electrode (Ni,10 nm) and the Au cap layer (10 nm).