Enhanced triplet Andreev reflection off a domain wall in a lateral geometry

We find that the triplet Andreev reflection amplitude at the interface between a half-metal and an $s$-wave superconductor in the presence of a domain wall is significantly enhanced if the half-metal is coupled laterally to the superconductor. Whereas triplet Andreev reflection is absent at the Fermi energy in the case of serial coupling, it is nonzero in a lateral contact geometry. We also find that in the lateral case domain walls cause (Andreev) backscattering even in the adiabatic limit of long domain walls, contrary to adiabatic domain walls in ordinary magnetic systems. For a lateral contact, domain walls can thus be an effective source of the triplet proximity effect.

Figure 1

Superconductor–half-metal junction with a domain wall and serial (a) and lateral (b) contacts.

Figure 2

(Color online) Half-metal superconductor interface with a domain wall. An electron (e) incident on the interface is either normally reflected, or Andreev reflected as a hole (h). The Andreev reflection amplitude $r_{\text{he}}$ for this situation given by Eq. (14) of the main text.

Figure 3

(a) Ballistic and (b) disordered half-metallic film of thickness $d$ laterally coupled to a superconductor. The Andreev reflection amplitude in the presence of a slowly varying magnetization direction is enhanced by multiple scattering at the superconductor interface.

Figure 4

Superconductor–half-metal–superconductor junction with a domain walls and lateral contacts.