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Band filling dependence of the Curie temperature in CrO2

Rutile CrO$_2$ is an important half-metallic ferromagnetic material, which is also widely used in magnetic recording. In an attempt to find the conditions, which lead to the increase the Curie temperature ($T_{\rm C}$), we study theoretically the band-filling dependence of interatomic exchange interactions in the rutile compounds. For these purposes, we use the effective low-energy model for the magnetic $t_{2g}$ bands, derived from the first-principles electronic structure calculations in the Wannier basis, which is solved by means of dynamical mean-field theory. After the solution, we calculate the interatomic exchange interactions, by using the theory of infinitesimal spin rotations, and evaluate $T_{\rm C}$. We argue that, as far as the Curie temperature is concerned, the band filling realized in CrO$_2$ is far from being the optimal one and much higher $T_{\rm C}$ can be obtained by decreasing the number of $t_{2g}$ electrons ($n$) via the hole doping. We find that the optimal $n$ is close to $1$, which should correspond to the case of VO$_2$, provided that it is crystallized in the rutile structure. This finding was confirmed by using the experimental rutile structure for both CrO$_2$ and VO$_2$ and reflects the general tendency towards ferromagnetism for the narrow-band compounds at the beginning of the band filling. In particular, our results suggest that the strong ferromagnetism can be achieved in the thin films of VO$_2$, whose crystal structure is controlled by the substrate.