Superconducting Vortices in Half-Metals

When the impurity mean free path is short, only spin-polarized Cooper pairs which are non-locally and antisymmetrically correlated in time may exist in a half-metallic ferromagnet. As a consequence, the half-metal acts as an odd-frequency superconducting condensate. We demonstrate both analytically and numerically that quantum vortices can emerge in half-metals despite the complete absence of conventional superconducting correlations. Because these metals are conducting in only one spin band, we show that a circulating spin supercurrent accompanies these vortices. Moreover, we demonstrate that magnetic disorder at the interfaces with the superconductor influences the position at which the vortices nucleate. This insight can be used to help determine the effective interfacial misalignment angles for the magnetization in hybrid structures, since the vortex position is experimentally observable via STM-measurements. We also give a brief discussion regarding which superconducting order parameter to use for odd-frequency triplet Cooper pairs in the quasiclassical theory.