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Superconducting phase transition of Sr2RuO4 in magnetic field

The superconducting state formed due to direct intra-orbital pairing in tetragonal multi-band superconductor Sr$_2$RuO$_4$ has different properties than the state formed due to intra-band pairing. In particular, the theory operating with direct intra-orbital pairing successfully explains the Kerr rotation of reflected light polarization observed several years ago. Here we apply intra-orbital approach to the problem of Ginzburg-Landau description of basal plane upper critical field in this material. It is shown that typical for two component superconducting state additional phase transition in the vortex state at $H<H_{c2}$ for all four crystallographic directions of magnetic field in the basal plane and the basal plane upper critical field anisotropy still are inevitable properties even in case of direct intra-orbital pairing.