Epitaxial growth and stoichiometry control of pyrochlore ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ thin films

We report on the epitaxial growth of pyrochlore NRO thin films utilizing a reactive off-axis sputtering technique. The growth process employed Ru and Nd metal targets with a repetitive substrate temperature sequence. X-ray diffraction, magnetic susceptibility, and spectroscopic ellipsometry measurements confirm that the structural, magnetic, and electronic properties of near-stoichiometric NRO films match those of the bulk material. Our spin-polarized density functional calculations based on ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ structural parameters accurately describe the optical spectra and assign Hubbard bands to the interband transitions observed above the optical band gap of 0.2 eV. By utilizing the technique's capability to adjust the degree of ruthenium deficiency, we investigated ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ films across a wide range of stoichiometric variations. Decreasing the Ru/Nd ratio results in lattice expansion, an increase in the optical band gap, and the suppression of Ru $4d$ intersite optical transitions. Additionally, this adjustment facilitates the elimination of minor inclusions of a ferromagnetic ${\mathrm{NdO}}_x$ impurity phase, influencing the magnetic properties of stoichiometric films at low temperatures. The successful growth of ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ films opens up promising opportunities for designing and exploring strain- and light-induced states in pyrochlore ruthenates.

Figure 1

(a) Schematic of the off-axis reactive sputtering chamber. (b) Substrate temperature profile applied during the thin film growth process. (c), (d) Projection along the [111] direction for ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ pyrochlore (c) and YSZ fluorite (d) structures, with the unit cell edges depicted by thin solid lines. (e) Corner-sharing Nd (orange balls) and Ru (gray balls) tetrahedra within the pyrochlore lattice. The body diagonal of the cubic unit cell aligns with the film growth [111] direction. (f) Schematic illustration of ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ deposition on YSZ. Gray arrows in (c) and (e) illustrate the strain-induced distortion of the pyrochlore lattice.

Figure 2

(a) X-ray diffraction patterns of ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ films deposited on a YSZ (111) substrate using different power ratios for the Ru and Nd sputtering guns (${\mathrm{Ru}}^{\mathrm{W}}:{\mathrm{Nd}}^{\mathrm{W}}$). The lattice spacing $d_{hkl}=\lambda /2sin\theta$, where $\lambda =1.5406\text{Å}$, and $\theta$ represents the Bragg angle. The vertical dashed lines indicate the positions of (111), (222), (333), and (444) reflections in the $S_1$ film, serving as a reference. (b) Rocking curves of the ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ (222) and YSZ (111) peaks. (c) Out-of-plane lattice spacing, determined from the peak positions in (a), as a function of the Ru/Nd ratio determined by EDX. (d), (e) Reciprocal space maps around the ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ (662) and YSZ (331) peaks of the $S_1$ (d) and $S_2$ (e) films. The black vertical lines indicate the in-plane (${\mathrm{Q}}_{\mathrm{x}}$) position of the YSZ (331) reflection. The reciprocal spacing of strain-free cubic ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ is indicated by the black circles. The dashed-line arrows point toward the origin.

Figure 3

Zero-field-cooled (ZFC) and field-cooled (FC) temperature dependence of magnetic moment $M$ for ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ films (a) $S_1$, (b) $S_1^{*}$, (c) $S_2$, (d) $S_3$. A magnetic field of 1000 Oe was applied in the film plane ($H_{\parallel }$). Color coding of the ZFC curves corresponds to the XRD patterns in Fig. 2. Insets: (b) $M$ of the reference $\text{Nd}{\text{O}}_x$ film, (c) enlargement near the magnetic transition.

Figure 4

(a) Real part of the optical conductivity ${\sigma }_1\left(\omega \right)$ (upper panel) and dielectric permittivity ${\varepsilon }_1\left(\omega \right)$ (bottom panel) of ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ measured on films $S_1$, $S_2$, and $S_3$ at room temperature ($T=293$ K). Color coding of the ${\sigma }_1\left(\omega \right)$ and ${\varepsilon }_1\left(\omega \right)$ curves corresponds to the XRD patterns in Fig. 2. The inset shows the Tauc plot obtained from the infrared absorption spectra. The linear fit (dashed lines) yields direct band gaps of 0.2 eV and 0.45 eV for samples $S_2$ and $S_3$, respectively. (b) Partial densities of the majority spin (spin up, left panel) and minority spin (spin down, right panel) Ru $4d$ states (red lines) and oxygen $\text{O}2p$ states (blue shaded areas) calculated by $\mathrm{DFT}+U$ assuming antiferromagnetic order [37]. The calculations utilize the crystal structure of bulk ${\text{Nd}}_2{\text{Ru}}_2{\text{O}}_7$ [22]. The colors of the vertical arrows indicate the orbital character of the corresponding optical bands. (c) Real part of the optical conductivity ${\sigma }_1\left(\omega \right)$ (upper panel) and dielectric permittivity ${\varepsilon }_1\left(\omega \right)$ (bottom panel) calculated by $\mathrm{DFT}+U$ (thick black lines) with a breakdown into separate orbital contributions (thin colored lines). The colors of the separate bands correspond to the electronic transitions depicted by the arrows in (b). The dashed lines correspond to the experimental $S_2$ spectra in (a).