Influence of epitaxial strain on the ferromagnetic semiconductor $\mathrm{EuO}$: First-principles calculations

From first-principles calculations we investigate the electronic structure and the magnetic properties of $\mathrm{EuO}$ under hydrostatic stress and the appropriate biaxial stress for epitaxial films. There is a complex interdependence of the $\mathrm{O}2p$ and $\mathrm{Eu}4f$ and $5d$ bands on the magnetism in $\mathrm{EuO}$, and decreasing lattice parameters is an ideal method to increase the Curie temperature $T_c$. Compared to hydrostatic pressure, the out-of-plane compensation that is available to epitaxial films diminishes this increase in $T_c$, although the $T_c$ increase is nonetheless significant due to the small value of Poisson’s ratio for $\mathrm{EuO}$. We find the semiconducting gap closes at a 6% in-plane lattice compression for epitaxy, at which point a significant conceptual change must occur in the active exchange mechanisms.

Figure 1

(Color online) The spin resolved density of states of bulk $\mathrm{EuO}$ in the FM configuration with optimized bulk lattice parameters, $a=5.1578\mathrm{\AA }$. The bands are labeled and the zero of energy is at the Fermi energy $E_f$. The inset shows the total density of states of the bulk $(a=c=a_0=5.158\mathrm{\AA })$ and the biaxial stress case just prior to the IMT ($a=4.87\mathrm{\AA }$, $c=5.31\mathrm{\AA }$).

Figure 2

(Color online) (a) The nearest neighbor and next-nearest neighbor exchange constants $J_1$ and $J_2$ as a function of the normalized in-plane lattice parameter for the isotropic stress case. (b) The calculated mean field $T_c$ as a function of in-plane lattice parameter for the isotropic stress case and the biaxial stress state of an epitaxial film. Both solid lines change to dashed lines at their respective IMT. Included in the graph is the experimental $T_c$, from susceptibility measurements, of Ref. 25 (circles), and ${\mathrm{T}}_I$—which tracks $T_c$ (Ref. 10)—determined via resistivity measurements in Ref. 10 in combination with the pressure-volume relations from Ref. 26 (triangles). The inset shows the change in the out-of-plane lattice parameters in the biaxial stress case.

Figure 3

(Color online) The mean field $T_c$ as a function of electron doping for bulk $(a=c=a_0=5.158\mathrm{\AA })$, isotropic stress $(a=c=4.92\mathrm{\AA })$, and biaxial stress ($a=4.87\mathrm{\AA }$, $c=5.31\mathrm{\AA }$). $T_c$ of Gd doping from Ref. 6.