We present a theoretical description of a quantum phase transition in a dimerized antiferromagnet, induced by an external magnetic field. The description of such transitions is constructed by determining the minimum of the Lagrange function which depends on the parameters of the ground-state crystal wavefunction. We determine that during a crystal transition from the singlet state of the dimer to the state with a noncollinear spin orientation, an order-order type phase transition occurs. We show that in the case of a single-axis character of the exchange anisotropy, the location of the quantum phase transition critical point is affected by the spin-spin interactions inside the dimer. Additionally, analogous to the classical Néele antiferromagnets, single-axis type anisotropic spin-spin interactions between dimers, shift the point of the spin-flip transition from the noncollinear antiferromagnetic phase to the ferromagnetic phase.
Quantum phase transitions induced by an external magnetic field in a Van Vleck paramagnet with ion spin S = 1, competition of an easy-plane single-particle anisotropy and Ising spin-spin interactions have been investigated. Phase transformations have been described using the Lagrange function, minimization of which is performed by the coefficients of linear combination of the spin wave functions that determine the magnet ground state. It was shown that such an approach is consistent with the Landau theory of phase transitions of the 1st kind. The result obtained showed that the transition from the Van Vleck paramagnetic (singlet) phase to the ferromagnetic phase occurs by forming an intermediate state with only one magnetized spin sublattice.
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