Enhanced Sm spin projection in ${\mathrm{Gd}}_x{\mathrm{Sm}}_{1-x}\mathrm{N}$

The rare-earth nitrides form a series of structurally simple intrinsic ferromagnetic semiconductors, a rare class of both fundamental interest and application potential. Within the series there is a wide range of magnetic properties relating to the spin/orbit contributions to the ferromagnetic ground states. We report an x-ray magnetic circular dichroism investigation of the spin/orbit magnetic dipole alignments of Sm and Gd ions in epitaxial ${\mathrm{Gd}}_x{\mathrm{Sm}}_{1-x}\mathrm{N}$ films. The Sm spin-alignment expectation value $\langle S_z\rangle$ is seen to be strengthened by the Gd/Sm exchange interaction, providing guidance that the composition for an angular momentum compensation point, where the volume-averaged total angular momentum of a film is zero, lies near $x=0.24$.

Figure 1

Schematic showing the alignment of the magnetic moments of ${\mathrm{Sm}}^{3+}$ and ${\mathrm{Gd}}^{3+}$ in (a) the parent materials where the Sm-Gd exchange is absent and (b) the solid solution ${\mathrm{Gd}}_x{\mathrm{Sm}}_{1-x}\mathrm{N}$ where the Sm-Gd exchange dominates the Zeeman interaction and aligns the spins. Panel (c) shows the net (low-temperature, volume averaged) values of the magnetization ($\overline{M}$) and angular momentum ($\overline{J}$) as the composition ($x$) interpolates between the parent materials. This schematic refers to to the most simple model and is shown in Fig. 8, adapted in light of our XMCD results.

Figure 2

X-ray diffraction data for the ${\mathrm{Gd}}_{0.76}{\mathrm{Sm}}_{0.24}\mathrm{N}$ film. The XRD peak around ${31}^{\circ }$, corresponding to the ${\mathrm{Gd}}_x{\mathrm{Sm}}_{1-x}\mathrm{N}$ (111) crystal direction, is typical of these thin films. The exact location of this peak is dependent on both the Gd/Sm ratio and the incidence of nitrogen vacancies in the crystal. The inset shows a rocking curve of the same ${\mathrm{Gd}}_x{\mathrm{Sm}}_{1-x}\mathrm{N}$ crystallites; the intensity scale is linear. The two peaks on the right of the $2\theta$ scan show peaks corresponding to the AlN buffer layer and the GaN cap.

Figure 3

(a) Hysteresis loops of the three ${\mathrm{Gd}}_x{\mathrm{Sm}}_{1-x}\mathrm{N}$ films taken at 5 K. The inset shows a zoom of the region close to zero, emphasising the different coercivities of the films. (b) The inverse susceptibility of the three films with fits included to show the different Curie temperatures extracted from the measurements.

Figure 4

Comparison of XMCD spectra for the three ${\mathrm{Gd}}_x{\mathrm{Sm}}_{1-x}\mathrm{N}$ films at the Gd $L_2$ edge at 5 K. All measurements were cooled to 5 K in an applied field of 6 T. Panel (a) shows the average of the x-ray absorption measurements for left- and right-circularly-polarized light, normalized to the continuum edge jump. Each subsequent dataset is offset by 0.5. Panel (b) shows the XMCD, defined as the difference between the left- and right-circularly-polarized absorption. Each subsequent dataset is offset by $10\%$.

Figure 5

Comparison of XMCD spectra for the three ${\mathrm{Gd}}_x{\mathrm{Sm}}_{1-x}\mathrm{N}$ films at the Sm $L_3$ edge at 5 K. All measurements were cooled to 5 K in an applied field of 6 T. Panel (a) shows the average of the x-ray absorption measurements for left- and right-circularly-polarized light, normalized to the continuum edge jump. Each subsequent dataset is offset by 0.5. Panel (b) shows the XMCD, defined as the difference between the left- and right-circularly-polarized absorptions. Each subsequent dataset is offset by $2\%$. Data taken for a SmN film in a previous study by Anton et al. [10] are included.

Figure 6

Magnitude of the Sm $L_3$ absorption features as a function of the Gd fraction, $x$. Panel (a) shows the magnitude for the conventional ${\mathrm{Sm}}^{3+}$ absorption channel. Panel (b) shows the magnitude of the electric quadrupole absorption. The star marker represents the data taken from Anton et al. [10].

Figure 7

Strengths of the (a) ${\mathrm{Gd}}^{3+}{L}_2$-edge and (b) ${\mathrm{Sm}}^{3+}{L}_3$-edge features measured using XMCD as a function of temperature. Error bars are smaller than the markers where not visible.

Figure 8

Model of the net (volume-averaged) angular momentum, $\overline{J}$, as a function of Gd fraction, $x$. The simple model is a linear interpolation of total angular momentum between $\langle J_z\rangle =-1$ ($\hslash$ per $R$ ion) for SmN (where $\langle L_z\rangle =-2\hslash$ and $\langle S_z\rangle =\hslash$) and $\langle J_z\rangle =J=7/2$ for GdN. Taking into account the variation of $\alpha \left(x\right)$ implied by Fig. 6 alters the net angular momentum, shifting the compensation point.