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In this paper relativistic-invariant phenomenological Lagrangians of interaction between spin-1 particles and electromagnetic field were obtained in the Duffin-Kemmer-Petiau formalism on the basis of the covariant model that takes into account both spin polarizabilities and gyrations of the above-mentioned particles. It was shown that in the suggested covariant model with regard to the crossing symmetry, spatial parity and gauge invariance conservation laws, definite spin polarizabilities and gyrations of spin-1 particles contribute to the expansion of Compton scattering amplitude, starting from the corresponding orders on energy of pfotons that is in the agreement with low-energy theorems for that process.

In this work, the amplitude of the interaction of an electromagnetic field with π-mesons has been determined in the context of a relativistic gauge-invariant approach by solving electrodynamic equations with the use of the covariant Green's function method. Based on this approach, the effective Lagrangian of the two-photon interaction with spin-0 hadrons taking into account the electric and magnetic polarizabilities has been obtained.

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