Magnetic properties ofGaN∕MnxGa1−xNdigital heterostructures: First-principles and Monte Carlo calculations

Abstract

The energetic and magnetic properties of wurtzite $\mathrm{GaN}∕{\mathrm{Mn}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ digital heterostructures are investigated by first-principles total energy calculations, within the spin density-functional theory, and Monte Carlo simulations. In a wurtzite $\mathrm{GaN}$ model sample, periodic in the $c$ axis, we replace a $\mathrm{GaN}$ monolayer (a plane) by a plane with composition ${\mathrm{Mn}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$, and study its properties for varying the $\mathrm{GaN}$ spacer layer thickness and Mn concentration $x$. The 100% $\mathrm{MnN}$ monolayer possesses an antiferromagnetic (AFM) ground state when, in the periodic sample, it is isolated from the other $\mathrm{MnN}$ monolayers by more than four $\mathrm{GaN}$ spacer layers. The case of submonolayers $(x<1)$ is studied by Monte Carlo simulations based on an Ising Hamiltonian, whose parameters are obtained from ab initio calculations on five configurations. At $700\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$, up to the concentration of 8% Mn, the two-dimensional (2D) alloy is stable. However, above this concentration, there is a strong tendency to the formation of $\mathrm{MnN}$ clusters with an AFM ground state defined by ferromagnetic Mn rows coupled antiferromagnetically with other Mn rows. The behavior of the magnetization with the temperature is completely different in these two concentration regimes, with the 2D $\mathrm{MnN}$ cluster being very stable, whereas the 2D alloy presents low magnetic transition temperatures.