Figure 1

The simulations shown illustrate the key physics underlying spin-precession imaging; the inhomogeneous magnetic field of a probe (sphere with black arrow, indicating the magnetization direction) generates a well-understood spatially varying dephasing of spins. Spins that are injected into a semiconducting sample reach a steady-state density resulting from a combination of the local spin properties, the injected density, and the probe’s field. The arrows in all figures represent the steady-state spin density vectors $\mathbf{S}$. The color scale represents the $\widehat{\mathbf{z}}$ component (parallel to the orientation of the injected spin) of the spins. (a) Demonstrates the case of a spatially uniform injection density and highlights the full spatial extent of the influence of the probe’s field $B_P$. The left-hand corner shows our coordinate system (black arrows) and the various components of $B_P$ (shorter blue arrows). Strong perpendicular fields from the probe dephase spins in an annular disk centered beneath the probe. Parallel fields immediately below the probe protect spins from dephasing. (b) and (c) show simulations identical to panel (a) except for the case of a Gaussian injection profile, corresponding to two different positions of the probe. Panels (b) and (c) correspond to the blue dot and red cross in Fig. 2d, respectively.Reuse & Permissions

Figure 2

(a) Schematic of the sample with pump laser and detected PL on one side, and a micromagnetic probe glued on the other side. The pump beam is scanned relative to the probe using an objective mounted on translation stages, but is equivalent to scanning the probe for our homogeneous sample. (b) Experimental optical image showing the PL spot created by the pump beam in a $1\mu \mathrm{m}$ thick GaAs membrane and the NdFeB probe. (c) Camera image of PL that corresponds to (and is proportional to) injection profile ${\rho }_c$. (d) The measured spin signal ${\Sigma }_c$ (color bar) corresponding to the injection profile from panel (c), at $B_t=0$. The location of each pixel corresponds to the relative position between the probe and the pump beam; a blue dot and red cross are included to provide two example cases. The location of the blue dot corresponds to a probe position directly above the injection beam; this configuration results in a spin density mostly pointing along the $\widehat{\mathbf{z}}$ direction [Fig. 1b] and gives a large signal. The red cross corresponds to a probe position $8\mu \mathrm{m}$ away from the center of the beam; spins precess away from the $\widehat{\mathbf{z}}$ direction due to large fields perpendicular to the injected spin direction [Fig. 1c] and thereby reduce the signal. (e) ${\Sigma }_c$ for a large $B_t=0.145\mathrm{T}$.Reuse & Permissions

Figure 3

Spin signal ${\Sigma }_c$ (corresponding to ${\rho }_c$), for various $B_t$ plotted as a function of the relative position between the pump and the probe along the $\widehat{\mathbf{y}}$ (left) and the $\widehat{\mathbf{x}}$ (right) directions. The data at various $B_t$ are offset vertically for clarity. The open circles are experimental data while the solid lines represent fits obtained from Eq. (1) using $m_z=2\times {10}^{-9}\mathrm{J}/\mathrm{T}$, $z_p=8\mu \mathrm{m}$, and ${\tau }_s=2.33\mathrm{ns}$. The spin lifetime ${\tau }_s$ is obtained from Hanle measurements (see Supplemental Material [20]). The peaks marked by the green dashed lines result when the peak in ${\rho }_c$ lies directly under the probe. The net parallel field directly under the probe is mostly due to $B_{pz}$ (the $\widehat{z}$ component of the probe’s field) and exceeds the net transverse field (mostly given by $B_t$); this results in a large $\Sigma$ [Eq. (1)]. The second set of peaks seen in scans along the $\widehat{\mathbf{x}}$ direction (blue dashed line) occur when $B_{px}=-B_t$ ($B_{px}$ is the $\widehat{\mathbf{x}}$ component of probe’s field). The resolution of our technique can be estimated by noise and slope that is seen in these line scans. For the bottom right black curve we obtain a resolution of $1.2\mu \mathrm{m}$.Reuse & Permissions

Figure 4

(a) Precessional response function $H_B$, obtained through Wiener deconvolution of ${\rho }_c$ [Fig. 2c] from ${\Sigma }_c(B_t=0)$ [Fig. 2d]. (b) Experimental $H_B$ for $B_t=0.145\mathrm{T}$. (c) and (d) Theoretically derived $H_B$ obtained from Eq. (1), using the dipole moment from the fits in Fig. 3 for $B_t=0\mathrm{T}$ and $B_t=0.145\mathrm{T}$, respectively. The experimental $H_B$ data have been normalized and offset to highlight the match between theory and experiment.Reuse & Permissions

Figure 5

Obtaining the spatial variation of an unknown spin density from the measured signal $\Sigma$: (a) Spin signal ${\Sigma }_u$ measured for a spin density profile ${\rho }_u$ (more information on how it was produced is given in the Supplemental Material [20]), with $B_t=0\mathrm{T}$. (b) An image of ${\rho }_u$ extracted from the Wiener deconvolution of ${\Sigma }_u$ [panel (a)] using the experimental $H_B(B_t=0)$ [Fig. 4a] as the deconvolution kernel. (c) and (d) Similarly measured ${\Sigma }_u$ and extracted ${\rho }_u$, respectively, for $B_t=0.145\mathrm{T}$. (e) Line cuts of ${\rho }_u$ taken along the dashed lines in panels (b) (dotted blue) and (d) (dashed green). Also shown in solid red is a line cut from an independent camera image of ${\rho }_u$ shown in panel (f).Reuse & Permissions