Electronic and Magnetic Structure of CrO$_2$ and CrO$_2$-RuO$_2$ Interfaces*

CrO$_2$ and RuO$_2$ share the same (rutile) crystal structure and have similar lattice constants. We have used Density Functional Theory within both the generalized gradient and LDA+U approximations to calculate the electronic and magnetic structure of CrO$_2$, RuO$_2$ and their interfaces. Consistent with previous calculations and experiment we find (for both GGA and LDA+U) that the CrO$_2$ Fermi energy lies in a band gap for the minority channel. RuO$_2$, in agreement with experiment, is predicted to be a metal by both types of calculations. We find relatively good matching between the majority energy bands of CrO$_2$ and either channel of RuO$_2$ in the $(100)$, $(110) $ and $(001)$ directions. The nearest neighbor exchange interaction in CrO$_2$ is calculated and used to estimate a Curie temperature of 411K. For $(100)$ interfaces of CrO$_2$ and RuO$_2$, we find that the CrO$_2$ moments remain collinear if the interfaces are abrupt, but our models of intermixed interfaces yielded non-collinear moment configurations with neighboring Cr moments making an angle of approximately $150^\circ{}$ and a small induced Ru moment oriented opposite to that of the sum of the Cr moments. We speculate that non-collinear spins at interfaces may be a common problem in oxides that may be a challenge to overcome to achieve large GMR and TMR effects in some of these materials.