Electronic structure of EuN: Growth, spectroscopy, and theory

We present a detailed study of the electronic structure of europium nitride (EuN), comparing spectroscopic data to the results of advanced electronic structure calculations. We demonstrate the epitaxial growth of EuN films, and show that in contrast to other rare-earth nitrides successful growth of EuN requires an activated nitrogen source. Synchrotron-based x-ray spectroscopy shows that the samples contain predominantly Eu${}^{3+}$, but with a small and varying quantity of Eu${}^{2+}$ that we associate with defects, most likely nitrogen vacancies. X-ray absorption and x-ray emission spectroscopies (XAS and XES) at the nitrogen K edge are compared to several different theoretical models, namely, local spin density functional theory with Hubbard $U$ corrections ($\text{LSDA}+U$), dynamic mean field theory (DMFT) in the Hubbard-I approximation, and quasiparticle self-consistent $GW$ (QS$GW$) calculations. The DMFT and QS$GW$ models capture the density of conduction band states better than does $\text{LSDA}+U$. Only the Hubbard-I model contains a correct description of the Eu $4f$ atomic multiplets and locates their energies relative to the band states, and we see some evidence in XAS for hybridization between the conduction band and the lowest-lying ${}^{8}S$ multiplet. The Hubbard-I model is also in good agreement with purely atomic multiplet calculations for the Eu M-edge XAS. $\text{LSDA}+U$ and DMFT calculations find a metallic ground state, while QS$GW$ results predict a direct band gap at X for EuN of about 0.9 eV that matches closely an absorption edge seen in optical transmittance at 0.9 eV, and a smaller indirect gap. Overall, the combination of theoretical methods and spectroscopies provides insights into the complex nature of the electronic structure of this material. The results imply that EuN is a narrow-band-gap semiconductor that lies close to the metal-insulator boundary, where the close proximity to the Fermi level of an empty Eu $4f$ multiplet raises the possibility of tuning both the magnetic and electronic states in this system.

Figure 1

RHEED images from a 75-nm-thick epitaxial EuN film taken along (a) the $\langle 100\rangle$ and (b) the $\langle 110\rangle$ YSZ substrate azimuths. The film was grown at 590 ${}^{\circ }$C, using 125 V N${}_2$ ions from an ion source. The N${}_2$ partial pressure was 3.7$\times {10}^{-4}$ mbar. The inset to (b) shows a line scan across the $\langle 110\rangle$ pattern, emphasizing the weak streaks that suggest a surface reconstruction.

Figure 2

X-ray diffraction from an epitaxial EuN film grown using activated nitrogen from an ion source and from a film grown under similar conditions but without activated nitrogen. The latter contains only Eu metal.

Figure 3

Normalized XAS taken over the Eu M${}_{4,5}$ edges, compared to atomic multiplet calculations for Eu${}^{2+}$ and Eu${}^{3+}$ ions. Samples EuN${}_{\mathrm{thin}}^{\mathrm{AS}}$, EuN${}_{\mathrm{bulk}}^{\mathrm{AS}}$, and EuN${}_{\mathrm{bulk}}^{\mathrm{NSLS}}$ were grown using excited nitrogen, sample EuN${}_{\mathrm{N}}^{\mathrm{AS}}2$ under a nonexcited nitrogen partial pressure, and sample Eu${}^{\mathrm{AS}}$ without nitrogen. Only EuN${}_{\mathrm{thin}}^{\mathrm{AS}}$, EuN${}_{\mathrm{bulk}}^{\mathrm{AS}}$, and EuN${}_{\mathrm{bulk}}^{\mathrm{NSLS}}$ contain predominantly Eu${}^{3+}$ corresponding to EuN, while EuN${}_{\mathrm{N}}^{\mathrm{AS}}2$ and Eu${}^{\mathrm{AS}}$ are largely metallic Eu. Spectra are offset for clarity.

Figure 4

Normalized nitrogen K-edge XAS from a series of EuN samples grown under different conditions, along with the spectrum from GdN for comparison. The most nearly stoichiometric films are sample EuN${}_{\mathrm{bulk}}^{\mathrm{NSLS}}$ and sample EuN${}_{\mathrm{bulk}}^{\mathrm{AS}}$, and these bear the most resemblance to the GdN spectrum. Note, however, the shoulder at about 397 eV that does not appear in GdN, and which is likely related to the presence of an Eu $4f$ multiplet near the conduction band minimum. Spectra are offset for clarity.

Figure 5

Various theoretical models of the N $p$ projected density of states, compared with normalized nitrogen K-edge XAS and XES from sample EuN${}_{\mathrm{bulk}}^{\mathrm{NSLS}}$. Thick black solid line, experimental data; green dash-dotted line and purple dashed line, $\mathrm{LSDA}+U$ for the cubic symmetry (Eu${}^{3+}$) and Hund's rule (Eu${}^{2+}$) solutions obtained by Larson et al. (Ref.3); red solid line, QS$GW$ results; blue dash-dotted line, DMFT calculation; turquoise thin solid line, Eu $f$ PDOS in DMFT.

Figure 6

Partial density of states correlation in QS$GW$ (upper panel) and DMFT (lower panel) calculations. For QS$GW$ the Eu-$f$ PDOS is resolved into spin-up (solid red line) and spin-down (dashed red line) components, whereas for DMFT a multiplet description is more appropriate.

Figure 7

Comparison of Eu M${}_4$ and M${}_5$ XAS with DMFT and purely atomic multiplet spectra. Some of the main lines are labeled in spectroscopic notation.

Figure 8

Comparison of XPS and XES measurements of the EuN valence band PDOS with various theories. Solid black line, XPS; thin light blue line, N K-edge XES; solid red line with labels, DMFT of Eu $f^5$ multiplet PDOS; blue dashed line, N $2s$ PDOS; pink dash-dotted line, N $2p$ PDOS; purple dotted line, Eu $4f$ in $\mathrm{LSDA}+U$. The XES energy scale has been shifted by $-396.6$ eV.

Figure 9

Experimental optical transmittance of an epitaxial EuN film. The data show a clear absorption edge near 0.9 eV.

Figure 10

QS$GW$ calculation showing a semiconducting band structure of EuN. The states are divided into majority (solid lines) and minority (dashed lines) spin states. The minimum gap at $\Gamma$-X is 0.31 eV, while the minimum direct gap at X is 0.94 eV.