Spin-localized model for the Lifshitz point in MnP

We present a theoretical interpretation for the occurrence of a Lifshitz point (LP) in the field-temperature ($H-T$) phase diagram of MnP. On the basis of a simple spin-localized model, with the assumption that the exchange constants depend on $H$ and $T$, we calculate the thermodynamic properties of MnP asymptotically close to the LP. In particular, we determine asymptotic expressions for the transition lines which meet tangentially at the LP. The predictions of the model concerning the behavior of the uniform transverse and longitudinal susceptibilities, and some other thermodynamic quantities, are in agreement with the reported experimental data. Finally, a renormalization-group analysis of the model shows that near the LP the Hamiltonian assumes essentially the form of the uniaxial ($m=1\mathrm{}$), one component ($n=1\mathrm{}$), Landau-Ginzburg-Wilson Hamiltonian suitable to describe a LP in magnetic systems with uniaxial symmetry. All of these results are in agreement with the suggestion that MnP has a triple point, where paramagnetic, ferromagnetic, and helicoidal (fan) phases meet, with the characteristic properties of a uniaxial one-component LP.