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Rutile CrO$_2$ is an important half-metallic ferromagnetic material, which isalso widely used in magnetic recording. In an attempt to find the conditions,which lead to the increase the Curie temperature ($T_{\rm C}$), we studytheoretically the band-filling dependence of interatomic exchange interactionsin the rutile compounds. For these purposes, we use the effective low-energymodel for the magnetic $t_{2g}$ bands, derived from the first-principleselectronic structure calculations in the Wannier basis, which is solved bymeans of dynamical mean-field theory. After the solution, we calculate theinteratomic exchange interactions, by using the theory of infinitesimal spinrotations, and evaluate $T_{\rm C}$. We argue that, as far as the Curietemperature is concerned, the band filling realized in CrO$_2$ is far frombeing the optimal one and much higher $T_{\rm C}$ can be obtained by decreasingthe number of $t_{2g}$ electrons ($n$) via the hole doping. We find that theoptimal $n$ is close to $1$, which should correspond to the case of VO$_2$,provided that it is crystallized in the rutile structure. This finding wasconfirmed by using the experimental rutile structure for both CrO$_2$ andVO$_2$ and reflects the general tendency towards ferromagnetism for thenarrow-band compounds at the beginning of the band filling. In particular, ourresults suggest that the strong ferromagnetism can be achieved in the thinfilms of VO$_2$, whose crystal structure is controlled by the substrate.

Band filling dependence of the Curie temperature in CrO2