  Chromium dioxide (CrO2) offers a rare example of metallic ferromagnetism
among stoichiometric transition-metal oxides. What makes it even more
remarkable is the half-metallic electronic structure. Today, CrO2 is widely
used in magnetorecording and regarded as a promising spintronic material.
Nevertheless, the key question "Why is it ferromagnetic?" remains largely
unanswered, despite general interest to the problem and practical importance of
CrO2. In the present work we challenge this question by combining
first-principles electronic structure calculations with the model Hamiltonian
approach and modern many-body methods for treating electron correlations. Our
analysis demonstrates that the problem is indeed highly nontrivial: at the
first glance, the ferromagnetism in CrO2 can be easily explained by Hund's rule
related exchange processes in the narrow t2g band. However, the electron
correlations, rigorously treated in the frameworks of dynamical mean-field
theory, tend to destabilize this state. The ferromagnetism reemerges if,
besides conventional kinetic energy changes in the t2g band, to consider other
mechanism, involving direct exchange and magnetic polarization of the oxygen
band. We show how all these contributions can be evaluated using
first-principles electronic structure calculations. Our results explain the
overall stability of the ferromagnetic state and provide the firm microscopic
basis for understanding the magnetism of CrO2.
