Spin waves in a simple ferromagnetic cubic lattice using the Heisenberg model with nearest and next-nearest neighbor interactions

<div>We study the combined effect of the nearest and the next-nearest neighbor interactions on the spin wave dispersion of an isotropic cubic ferromagnet in a uniform magnetic field using the Heisenberg model. Near the groundstate, the components of the spin angular momentum perpendicular to the applied field are negligible as compared to the parallel spin component. Hence, the dispersion relation and the ground state energy estimate of the system are obtained by considering the spin fluctuations along the plane normal to the magnetic field.