Nanoscale Zeeman Localization of Charge Carriers in Diluted Magnetic Semiconductor–Permalloy Hybrids

We investigate the possibility of charge carrier localization in magnetic semiconductors due to the presence of a highly inhomogeneous external magnetic field. As an example, we study in detail the properties of a magnetic semiconductor–permalloy disk hybrid system. We find that the giant Zeeman response of the magnetic semiconductor in conjunction with the highly nonuniform magnetic field created by the vortex state of a permalloy disk can lead to Zeeman localized states at the interface of the two materials. These trapped states are chiral, with chirality controlled by the orientation of the core magnetization of the permalloy disk. We calculate the energy spectrum and the eigenstates of these Zeeman localized states, and discuss their experimental signatures in spectroscopic probes.

Figure 1

$B_z(r,z)$ (left) and $B_r(r,z)$ (right) in units of ${\mu }_0{M}_0\approx 1\mathrm{T}$, plotted as a function of $r$ for several values of $z$, for a disk of height $d=50\mathrm{n}\mathrm{m}$ and a core radius ${\rho }_c=30\mathrm{n}\mathrm{m}$. The discontinuity in the slope of $B_z(r,0)$ at $r={\rho }_c$ is a consequence of the discontinuity of $d{M}_z(r)/dr$ at $r={\rho }_c$ [see Eq. (7)].