Spatial structure and magnetism of a spin-orbit entangled spin-1 coherent spin center: the manganese neutral acceptor in a III-V semiconductor

Abstract

A Mn dopant in a III-V semiconductor produces a highly-entangled, coherent triplet ground state not fully captured by single-determinant theories of electron structure. We directly construct an analytic form for its ground-state wavefunction, finding surprising spin-charge correlations not revealed by semiclassical calculations. Spin-correlated circulating currents associated with the dopant yield remarkably large magnetic fringe fields of $\sim$1$\,μ$T at distances of $\sim 10$~nm from Mn in GaAs, potentially detectable by NV-diamond magnetometry while the dopant spin coherently precesses.

Figures (4)

• Figure 1: Probability density $|\Psi(\boldsymbol{r})|^{2}$ of a single Mn in GaAs and GaSb hosts within our fully quantum-mechanical description. All planes are 4.95 nm away from the impurity site, along the $[110]$ direction. From (a) to (f) each row has a fixed direction for the core-hole spin $\boldsymbol{F}$ and shows the differences between a Mn in GaAs or in GaSb. (g) and (h) show the isosurface of the probability density $|\Psi|^2$ (scaled by $e^{r/a_B^*}$) at $2.5\times 10^{-3}\,\text{nm}^{-3}$ for a Mn in GaSb with $\boldsymbol{F}\parallel[001]$ and $\boldsymbol{F}\parallel[1\overline{1}0]$, respectively; $a_B^*=$0.77 nm (GaAs) and 2.27 nm (GaSb) (see Supporting Information). Binding energies: Mn in GaAs $E_{F=1}=113$ meV PhysRevB.10.2501madelung2004semiconductors; Mn in GaSb $E_{F=1} =$ 18 meV madelung2004semiconductors. Effective hole masses: GaAs $m_{lh} = 0.074$ and $m_{hh} = 0.559$; GaSb $m_{lh} = 0.041$ and $m_{hh} = 0.40$, from PhysRevB.8.269710.1063/1.1368156.
• Figure 2: Current density $\boldsymbol{j}(\boldsymbol{r})$ for different core-hole spin $\boldsymbol{F}$ directions, for a single Mn in GaAs. All planes are 4.95 nm away from the impurity site, along the [110] direction. (a), (c) and (e) show the absolute values for the current density, while (b), (d) and (f) are the field vectors. The right-hand panels have arrow directions defined by $\boldsymbol{j}(\boldsymbol{r}) \parallel [001]$ and $\boldsymbol{j}(\boldsymbol{r}) \parallel [\overline{1}10]$; arrow colors show the component $\boldsymbol{j}(\boldsymbol{r})_{[110]}$$\equiv \boldsymbol{j}(\boldsymbol{r})\parallel [110]$ and the length of the arrow is given by $|\boldsymbol{j}(\boldsymbol{r})|$, where $|\boldsymbol{j}(\boldsymbol{r})|$ is shown in the left-hand panels.
• Figure 3: Magnetic fringe fields $\boldsymbol{B}(\boldsymbol{r})$ at a plane along the [110] direction and 4.95 nm away from the Mn site in GaAs. Each row corresponds to a different core-hole spin direction $\boldsymbol{F}$. (a), (c) and (e) show the absolute values for the magnetic field, while (b), (d) and (f) are the field vectors. The right-hand panels have arrow directions defined by $\boldsymbol{B}(\boldsymbol{r}) \parallel [001]$ and $\boldsymbol{B}(\boldsymbol{r}) \parallel [\overline{1}10]$; arrow colors show the component $\boldsymbol{B}(\boldsymbol{r})_{[110]}$$\equiv \boldsymbol{B}(\boldsymbol{r})\parallel [110]$ and the length of the arrow is $|\boldsymbol{B}(\boldsymbol{r})|$, which is shown in the left-hand panels.
• Figure 4: Magnetic field profiles along the [001] direction produced by a core-hole spin $\boldsymbol{F}\parallel[1\overline{1}0]$ of a single Mn in (a) GaAs and (b) GaSb. Each line's color corresponds to the indicated (110) plane distance (in nm) from the Mn site. (c) maximum value for the magnetic field max$(|\boldsymbol{B}|)$ at several (110) planes, produced by a single Mn in three different hosts (GaAs, InSb and GaSb) with the core-hole spin $\boldsymbol{F}$ pointing in three different directions. Parameters for InSb: binding energy $E_{F=1}=9$ meV Mauger2015teubert2009influence and effective masses for the light-hole $m_{lh}$=0.014 and heavy-hole $m_{hh}=$0.44PhysRevB.8.269710.1063/1.1368156.