Orbital properties of ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ and related ruthenates probed by ${}^{17}\mathrm{O}$ NMR

We report a site-separated ${}^{17}\mathrm{O}$ NMR study of the layered perovskite ruthenate ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, which exhibits nearly two-dimensional transport properties and itinerant metamagnetism at low temperatures. The local hole occupancies and the spin densities in the oxygen $2p$ orbitals are obtained by means of tight-binding analyses of electric field gradients and anisotropic Knight shifts. These quantities are compared with two other layered perovskite ruthenates: the two-dimensional paramagnet ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$ and the three-dimensional ferromagnet $\mathrm{Sr}\mathrm{Ru}{\mathrm{O}}_3$. The hole occupancies at the oxygen sites are very large, about one hole per ruthenium atom. This is due to the strong covalent character of the Ru-O bonding in this compound. The magnitude of the hole occupancy might be related to the rotation or tilt of the $\mathrm{Ru}{\mathrm{O}}_6$ octahedra. The spin densities at the oxygen sites are also large, 20%–40% of the bulk susceptibilities, but in contrast to the hole occupancies, the spin densities strongly depend on the dimensionality. This result suggests that the density of states at the oxygen sites plays an essential role for the understanding of the complex magnetism found in the layered perovskite ruthenates.

Figure 1

(Color online) Crystal structure of the Ruddlesden-Popper series ${\mathrm{Sr}}_{n+1}{\mathrm{Ru}}_n{\mathrm{O}}_{3n+1}$ for ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$ ($n=1$, left), ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ ($n=2$, middle), and $\mathrm{Sr}\mathrm{Ru}{\mathrm{O}}_3$ ($n=\infty$, right). The axes $a$ and $b$ are taken along a Ru-O-Ru bonding. For ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ and $\mathrm{Sr}\mathrm{Ru}{\mathrm{O}}_3$, symmetries are reduced because of a rotation and a tilt of the $\mathrm{Ru}{\mathrm{O}}_6$ octahedra, respectively (Refs. 17, 18). For simplicity, these effects are not shown. There are apical O(2) and in-plane O(1) sites in ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$. ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ has two kinds of apical sites. For ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, we label the inner-apical, outer-apical, and in-plane sites O(1), O(2), and O(3) sites, respectively.

Figure 2

(Color online) (a) ${}^{17}\mathrm{O}$ NMR spectral site notations for ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$. Arrows denote the corresponding field directions $H\Vert c$ and $H\Vert \left[100\right]$. (b) Relevant atomic orbitals at the Fermi surfaces for ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$. We treat interactions of electrons with nuclei by a method of linear combination of atomic orbitals: namely, the tight-binding method. ${\mathrm{Ru}}^{4+}$ ions realize a low-spin configuration, and the resulting $t_{2g}$ $(=4d_{xy},4d_{yz},4d_{zx})$ orbitals hybridize with the oxygen $2p_{\pi }$ $(=2p_x,2p_y,2p_z)$ orbitals.

Figure 3

(Color online) Field-swept ${}^{17}\mathrm{O}$-NMR spectra for ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ with a frequency of $72.5\mathrm{MHz}$ at $1.7\mathrm{K}$. The corresponding ${}^{17}\mathrm{O}$ NMR field for a free atom, ${\mu }_0{H}_0$, is $12.56\mathrm{T}$. $H_{\mathrm{ext}}$ is the external applied field. Lines from each site must consist of five resonances due to the perturbations from the electric quadrupole interaction. The unassigned sites, which exhibit a smaller sample-dependent intensity, are attributed to an impurity phase of ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$.

Figure 4

(Color online) NMR spectral positions as a function of $H_{\mathrm{res}}^{-1}$ for ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ with $H\Vert \left[100\right]$. All data points are taken from the field-swept spectra at $1.7\mathrm{K}$. The arrow denotes the metamagnetic field. At and slightly below the metamagnetic field high transverse relaxation rates $1∕T_2$ prevent observations of signals from the O(1) and $\mathrm{O}{\left(3\right)}^{\perp }$ sites. The plotted lines are based on Eq. (1). The values of EFGs are listed in Sec. 3B. The Knight shifts are evaluated in Sec. 3C.

Figure 5

(Color online) Field-swept NMR spectra with various field orientations for ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ at $1.7\mathrm{K}$ with a frequency of $21.3\mathrm{MHz}—$ i.e., ${\mu }_0{H}_0\sim 3.7\mathrm{T}$. The orientation is varied from [100] (0° in the plot) to the $c$ axis $(\pm 90°)$ by the use of a backlash-free rotator in an $8\text{−}\mathrm{T}$ split-coil magnet. All curves are drawn in the same scheme as in Fig. 4. The $\mathrm{O}{\left(3\right)}^{\perp }$ lines are not observable in this configuration due to a high transverse relaxation rate $1∕T_2$. The narrow dotted curves, which are not attributable to ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, originate from the ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4\text{−}\mathrm{O}\left(1\right)$ site in the impurity phase.

Figure 6

(Color online) ${}^{17}K_{\mathrm{obs}}$ vs $M∕H_{\mathrm{res}}$ plots for ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$. The fitted hyperfine coupling constant for each curve is listed in Table . (a) Temperature varied data points between $1.7\mathrm{K}$ and $100\mathrm{K}$ at low field $\simeq 4\mathrm{T}$ and (b) field varied points between $3\mathrm{T}$ and $13\mathrm{T}$ at $1.7\mathrm{K}$. Below $7\mathrm{T}$ $M$ is measured with a commercial superconducting quantum interference device (SQUID) magnetometer. For higher fields, $M$ is interpolated $(7–8\mathrm{T})$, derived from $2.8\mathrm{K}$ data given in Ref. 8 $(8–11\mathrm{T})$, and extrapolated $(>11\mathrm{T})$.