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A systematic first-principles study has been performed to understand themagnetism of thin film SrRuO$_3$ which lots of research efforts have beendevoted to but no clear consensus has been reached about its ground stateproperties. The relative t$_{2g}$ level difference, lattice distortion as wellas the layer thickness play together in determining the spin order. Inparticular, it is important to understand the difference between two standardapproximations, namely LDA and GGA, in describing this metallic magnetism.Landau free energy analysis and the magnetization-energy-ratio plot clearlyshow the different tendency of favoring the magnetic moment formation, and itis magnified when applied to the thin film limit where the experimentalinformation is severely limited. As a result, LDA gives a qualitativelydifferent prediction from GGA in the experimentally relevant region of strainwhereas both approximations give reasonable results for the bulk phase. Wediscuss the origin of this difference and the applicability of standard methodsto the correlated oxide and the metallic magnetic systems.

Magnetic ground state of SrRuO$_3$ thin film and applicability of standard first-principles approximations to metallic magnetism