Effect of magnon-magnon interaction on ferromagnetism in hexagonal manganese pnictide monolayers

We have studied the finite-temperature magnetic phase transition using a combination of first-principles calculations and the second-order Holstein-Primakoff approximation of the anisotropic Heisenberg model for hexagonal MnX (X = N, P, As, and Sb) monolayers. The MnX monolayers are all half-metal with dynamically and thermally stable atomic structures at T = 300 K. The hexagonal MnN is an out-of-plane easy-axis ferro-magnetically ordered monolayer with the Curie temperature close to the room temperature. However, the other three MnX (X = P, As, and Sb) monolayers have an easy axis inside the plane with Curie temperature close to zero. The ab initio energy difference between spin configurations is mapped into an anisotropic Heisenberg spin Hamiltonian which is solved using the second-order Holstein-Primakoff approximation. The anharmonic (magnon-magnon) interaction softens the magnetic excitation energy and reduces the magnon energy gap at the I' point, which is crucial for the finite-temperature long-range magnetic order in two dimensions. As a result, the inclusion of magnon-magnon interaction dramatically reduces the Curie temperature of hexagonal MnX monolayers. Although the magnon-magnon interaction is a perturbation in energy dispersion, it has an important effect on the finite-temperature long-range magnetic order in two-dimensional monolayers.

Automated summary

We studied the magnetic phase transition at finite temperatures in hexagonal MnX (X = N, P, As, and Sb) monolayers using first-principles calculations and the second-order Holstein-Primakoff approximation of the anisotropic Heisenberg model. The Curie temperature of MnX monolayers depends on their atomic structures, with the MnN monolayer having a magnetic easy axis out of the plane and the other three (MnP, MnAs, and MnSb) monolayers having an in-plane easy axis with a close-to-zero Curie temperature. The inclusion of magnon-magnon interaction decreases the Curie temperature by softening the magnetic excitation energy and reducing the magnon energy gap at the I' point, which is crucial for the long-range magnetic order at finite temperatures in two-dimensional monolayers.