A theoretical analysis of the features of structural and magnetostructural first-order phase transitions in magnetocaloric helimagnetic alloys of the Mn_{1-x}Cr_{x}NiGe system has been carried out. To describe the observed displacive structural transitions hex(P6_{3}/mmc)<->orth(P_{nma}), we used the local soft mode model in the approximation of a biased harmonic oscillator. In the absence of a magnetic field, the emergence of a helimagnetic order as a structurally induced second-order transition was described in the framework of the Heisenberg model, taking into account the dependence of the exchange integrals on the structural order parameters and elastic strains. In the presence of a magnetic field, it was found that the approximation of the characteristic temperatures for the helimagnetic HM(P_{nma}) and lability temperatures of the hexagonal paramagnetic PM(P6_{3}/mmc) states, due to the influence of the magnetic field, leads to the appearance of previously unexplored peripheral magnetostructural first-order phase transitions with insignificant magnetization jumps that increase with increasing magnetic induction.In this case, as the pressure increases to 4 kbar with constant induction of the magnetic field, the peripheral transitions transform into reversible first-order magnetostructural transitions, and at even higher pressures (10-14 kbar) into full-fledged first-order magnetostructural transitions with magnetization jumps comparable with maximum value of magnetization. Experimental pressure studies of the temperature dependences of magnetization in static magnetic fields with an induction of up to 1 T and a pressure of up to 14 kbar confirm the theoretical results.
Within the framework of the model of interacting parameters of magnetic and structural orders, a theoretical analysis of magnetostructural reversible first-order phase transitions is carried out. Reversible phase transitions are characterized by a jump-like appearance of magnetic order with decreasing temperature (as in a first-order phase transition), and with a reverse increase in temperature, the magnetic order gradually disappears (as in a second-order phase transition). Such transitions are observed in some alloys of the Mn_{1-x}Cr_{x}NiGe magnetocaloric system under pressure (x = 0.11) and without (x = 0.18) and are accompanied by specific magnetic and magnetocaloric features. A phenomenological description of these features is carried out within the concept of a soft mode for the structural subsystem undergoing first-order structural phase transition (P6_{3}/mmc-P_{nma}) and the Heisenberg model for the spin subsystem. For systems with magnetostructural instability within the molecular field approximation for the spin subsystem and the shifted harmonic oscillator approximation for the lattice subsystem, it is shown that the reversible phase transitions arise when the temperature of magnetic disordering is in the temperature hysteresis region of the 1st order structural phase transition P6_{3}/mmc-P_{nma}. It is also shown that the two-peak form of the isothermal entropy, which is characteristic of reversible transitions, is due to the separation of the structural and magnetic entropy contributions.
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