Observation of anomalous Hanle spin precession line shapes resulting from interaction with localized states

It has been shown recently that in spin precession experiments, the interaction of spins with localized states can change the response to a magnetic field, leading to a modified, effective spin relaxation time and precession frequency. Here, we show that also the shape of the Hanle curve can change, so that it cannot be fitted with the solutions of the conventional Bloch equation. We present experimental data that show such an effect arising at low temperatures in epitaxial graphene on silicon carbide with localized states in the carbon buffer layer. We compare the effect between materials made with different growth methods, epitaxial growth by sublimation and by chemical vapor deposition. The presented analysis gives information about the density of localized states and their coupling to the graphene states, which is inaccessible by charge transport measurements and can be applied to any spin transport channel that is coupled to localized states.

Figure 1

A spin transport channel coupled to localized states with a coupling rate $\Gamma$. Spins can reside in the localized states for some time, where they pick up extra relaxation and precession, thus strongly effecting the measured Hanle signal.

Figure 2

(a) Device schematics of an EG on SiC nonlocal spin valve with four spin contacts made of a ${\mathrm{TiO}}_2$ tunnel barrier, Co, and an Al capping layer. The inset shows a colored microscopic image of the real device (type I) with a microscopic image of the etch lines (dark brown) superimposed. Additional lines were etched away in between the Co contacts to ensure there were no current paths outside the strip. (b), (c) RT spin valve measurements of EG by sublimation (type I) and CVD (type II). The distance $L$ between the inner electrodes is $1\mu \mathrm{m}$ for both devices. The horizontal arrows represent the sweeping direction of the magnetic field. Vertical arrows show parallel or antiparallel orientation of the inner electrodes. The extra level in (c) is caused by the switching of one of the outer electrodes. The lines between measurement points are a guide to the eye. (d), (e) Hanle precession measurements at RT of type I and II in the parallel (black circles) and antiparallel (red circles) configuration. Note the large difference in the $x$-axis scales. The best fits are performed on a plot of $(R_{\text{nl}}^{\uparrow \uparrow }-R_{\text{nl}}^{\uparrow \downarrow })/2$ and inserted in this figure as black and red lines. Because of a small asymmetry in (e), the fit is performed only in the positive range of $B_z$. $\tau$ and $D$ are obtained by fitting with the solution to Eq. (1) (see text).

Figure 3

Temperature dependent evolution of the Hanle curve. (a) EG by sublimation (type I). The typical RT Hanle line shape (dark red line) develops into a broader curve without zero crossings in $R_{\text{nl}}$ and with a narrow peak around zero magnetic field at temperatures of 30 K and lower. (b) EG by CVD (type II). The Hanle line shapes change already at 160 K and also the amplitude decreases in the temperature range 293–30 K and increases again at 30–4.1 K.

Figure 4

Simulated curves for Hanle precession including the effect of localized states. The figures show the evolution of the Hanle line shape when changing the coupling rate $\Gamma$. For both plots we used $D=200{\mathrm{cm}}^2{\mathrm{s}}^{-1},{\tau }_S=150$ ps, and $g=2$. The blue curves show the weak coupling limit which is not influenced by the localized states and is therefore the same in both figures. (a) uses the estimated quantities ${\tau }_S^{*}$ and $\eta$ of type I and (b) uses ${\tau }_S^{*}$ and $\eta$ of type II.