Modulated phases, magnetic phase diagrams, and the Lifshitz point in MnP from the mean field theory

The axial next-nearest-neighbor Heisenberg (ANNNH) model with orthorhombic magnetocrystalline anisotropy was applied to describe magnetic phases and phase transitions occurring in manganese phosphide in magnetic field H applied along the lattice vectors a, b, and c. The ground state of the Hamiltonian was obtained using analytical methods of Nagamiya's theory, augmented by numerical minimization of the energy with respect to the wave vector q of the modulated magnetic structures (heli, fan, cone). The latter procedure leads to the dependence $q(H)$ for all modulated phases, and explains both the shapes of the magnetization curves for these phases (convex for the fan and concave for the cone phase) and the weakly first-order nature of the cone-fan phase transition. The magnetic phase diagrams for the three principal directions of the applied field, H∥c, H∥b, and H∥a, are calculated under the assumption that the ratio of competing nearest-neighbor and next-nearest-neighbor interactions depends on the temperature. The characteristics of special points in the phase diagrams (Lifshitz points, triple point, critical end point, and terminations of critical lines) remain in a semiquantitative accordance with experiment. For the Lifshitz point the deviation from asymptotic scaling laws was analyzed by calculating the effective (fit-range-dependent) values for the crossover exponent {φ}, the wave vector exponent βₖ, and magnetization discontinuity exponent βₘ. The results provide an explanation of their experimental values.