Triplet supercurrents in clean and disordered half-metallic ferromagnets

Interfaces between materials with differently ordered phases present unique opportunities to study fundamental problems in physics. One example is the interface between a singlet superconductor and a half-metallic ferromagnet, where Cooper pairing occurs between electrons with opposite spin on the superconducting side, whereas the other exhibits 100% spin polarization. The recent surprising observation of a supercurrent through half-metallic CrO2 therefore requires a mechanism for conversion between unpolarized and completely spin-polarized supercurrents. Here, we suggest a conversion mechanism based on electron spin precession together with triplet-pair rotation at interfaces with broken spin-rotation symmetry. In the diffusive limit (short mean free path), the triplet supercurrent is dominated by inter-related odd-frequency s-wave and even-frequency p-wave pairs. In the crossover to the ballistic limit, further symmetry components become relevant. The interface region exhibits a superconducting state of mixed-spin pairs with highly unusual symmetry properties that open up new perspectives for exotic Josephson devices.