Exchange Interactions in CrO$_2$ studied with density functional theory

We report a study of exchange interactions in bulk CrO$_2$ calculated from first principles. We considered three near neighbor Cr-Cr exchange interactions: the interaction between corner and body center atoms mediated through a single oxygen atom; the interaction between a Cr and the Cr directly "above" it in the (001) direction, also mediated by a single O atom; and the interaction between a Cr and its neighbor in the (100) direction, mediated by two intervening oxygen atoms. The interactions were calculated by rotating the moments of one or more of the Cr ions while constraining the others to remain parallel. We then fit the resulting energy vs. angle data to the Heisenberg model and extracted exchange energy parameters with a least-squares method. We also calculated the exchange interactions using a "spin-spiral" technique, in which a relative angular displacement was imposed upon Cr moments in adjacent cells. Similar results were obtained with both approaches. The calculated T=0 K exchange interactions were subsequently used to determine the magnetization as a function of temperature via low-T spin-wave dispersion and a Monte-Carlo method. Reasonable agreement with experiment was obtained.