Spin-resolved spectra of Shiba multiplets from Mn impurities in ${\text{MgB}}_2$

We study the effect of magnetic Mn ions on the two-band superconductor ${\text{MgB}}_2$, and compute both the total and spin-resolved scanning tunneling spectrum in the vicinity of the magnetic impurity. We show that when the internal structure of the Mn ion’s $d$-shell is taken into account, multiple Shiba states appear in the spectrum. The presence of these multiplets could alter significantly the overall interpretation of local tunneling spectra for a wide range of superconducting hosts and magnetic impurities.

Figure 1

Band structure for ${\text{MgB}}_2$, along the symmetry lines, computed in the framework of tight-binding model described in Appendix . There are six bands: four from $p_{x,y}$ orbitals (solid lines) and two from $p_z$ (dashed lines). Both $p_z$ bands and only two $p_{x,y}$ band cross the Fermi level, which corresponds to zero energy, $E_F=0$.

Figure 2

(Color online) (a) Local environment of an Mn ion in ${\text{MgB}}_2$. The Mn ion is located in a hexagonal cage made of B ions represented by large dots. (b) Level structure and crystal-field splitting of the ${\text{Mn}}^{2+}$ core states. Two levels ($\mu =\pm 2$ and $\mu =\pm 1$) are twofold degenerate and the level $\mu =0$ is nondegenerate.

Figure 3

Diagrammatic expansion for the Green’s function when multiple scattering on the impurity site is considered. The solid line represents the full Green’s function, and the thick line represents the noninteracting part of the Green’s function. Each cross represents a scattering on an impurity site, and the dotted line stands for the impurity scattering potential. $b$ and $b^{\prime }$ stand for band indices.

Figure 4

Position of the quasiparticle poles for separate channels $\mu$. The resonances corresponding to the $\mu =\pm 1$ channels are well resolved for any value of the coupling strength $g$ (solid lines). For large enough $g$ $\left(g>0.6\right)$ the $\mu =0$ resonance moves inside the gap (dotted lines). The couplings corresponding to the $\mu =\pm 2$ channels are much smaller that those in the other channels so the resonances for $\mu =\pm 2$ channels are still merged with the superconducting peaks at energy ${\Delta }_{\pi }$ (dashed lines).

Figure 5

Upper panel: Normalized LDOS at the nearest-neighbor boron sites (labeled A in Fig. 2) for the $p_z$ orbitals, for different coupling constants. Lower panel: Normalized LDOS at the next-nearest neighbor boron sites labeled B in Fig. 2.

Figure 6

Spin polarization (odd part of the spectrum and spin-up density of states for Site A in Fig. 2).

Figure 7

Upper panel: Normalized density of states for site A as function of frequency for different values of $g$ in the geometry when the Mn impurity is below the first B layer. Lower panel: Normalized LDOS at the next-nearest-neighbor boron sites B of Fig. 2, when the Mn impurity is just below the first layer.

Figure 8

Spin polarization and spin-resolved density of states for site A of Fig. 2.

Figure 9

Top: Density of states for $p_{x,y}$ and $p_z$ bands. Bottom: Total density of states. The vertical line represents the position of the Fermi energy.