Five years later, he obtained the Candidate of Science (PhD) degree; thesis "Features of the infrared spectra of antiferromagnetic Co compounds" (scientific advisers: B.I.

[4][5] In 1974 he has obtained the Doctor of Science (Physics and Mathematics) degree, thesis "Features of the energy spectrum and phase transitions in magnets with the low symmetry of crystal lattice".

In 1991 he has obtained the State Prize of Ukraine in Science and Technology (for the detection and investigations of the new type of resonances, structures and magneto-elastic anomalies in low-dimensional antiferromagnets).

From 1988 till 4 May 1991 (died from the heart attack) he was the director of the Institute for Low Temperature Physics and Engineering of the Academy of Sciences of Ukrainian SSR.

His works, devoted to the investigations of the low-frequency branches of spectra of highly anisotropic magnets and layered ferroelectric elastics, are widely known.

Zvyagin and co-workers in studies of magnetic properties of undoped cuprates, which manifest the high-temperature superconductivity at the optimal doping.