Theoretical description of magnetic properties of antiferromagnetic state, induced by the longitudinal magnetic field, in the Van Vleck -singlet -magnet with single-ion anisotropy of "easy-plane" type and ion spin S = 1 is proposed. It is shown that the quantum phase transition to the antiferromagnetic state is connected with the spontaneous appearance of spin polarization in the easy plane. Spin polarization of the ground nondegenerated state proves to be the order parameter of such a transition and the Landau thermodynamic approach can be employed for its (transition) description. The magnetic properties which include the field behavior of magnetization and magnetic susceptibility of the antiferromagnetic phase in the fields of different directions are studied. An attempt is made to qualitatively compare the obtained results with the available experimental data.

The description of the collective magnetorheological effect induced by magnetic field in magnetoactive elastomers is proposed. The condition of consistency is used between magnetic and mechanic momenta of forces exerted on magnetically uniaxial ferromagnetic particles in elastomer at their magnetization. The study shows that even in the case of small concentration of particles, the value of magnetically-induced shear can be anomalously large, reaching up to tens of percent. The deformation of magnetoactive elastomer can evolve critically, as a second-order phase transition, if magnetic field is aligned along the easy axis of particles.