Magnetic resonance study of rare-earth titanates

We present an electron spin resonance (ESR) and nuclear magnetic resonance (NMR) study of rare-earth titanates derived from the spin-1/2 Mott insulator ${\mathrm{YTiO}}_3$. Measurements of single-crystalline samples of (Y, Ca, La)${\mathrm{TiO}}_3$ in a wide range of isovalent substitution (La) and hole doping (Ca) reveal several unusual features in the paramagnetic state of these materials. ESR of the unpaired Ti electron shows broad resonance lines at all temperatures and substitution/doping levels, which we find to be caused by short electronic spin-lattice relaxation times. We model the relaxation as an Orbach process that involves a low-lying electronic excited state, which enables the determination of the excited-state gap from the temperature dependence of the ESR linewidths. We ascribe the small gap to Jahn-Teller splitting of the two lower Ti $t_{2g}$ orbitals. The value of the gap closely follows the Curie temperature $T_C$. ${}^{89}\mathrm{Y}$ NMR demonstrates a clear discrepancy between the static and dynamic local magnetic susceptibilities, with deviations from Curie-Weiss behavior at temperatures far above $T_C$, consistent with the electronic gap detected with ESR. No significant changes are observed by NMR close to $T_C$, but suppression of fluctuations is detected in the NMR spin-lattice relaxation time at temperatures of about $3\times T_C$. Additionally, the nuclear spin-spin relaxation rate shows an unusual peak in dependence on temperature for all samples. These results provide insight into the interplay between orbital and spin degrees of freedom in rare-earth titanates and indicate that full orbital degeneracy lifting is associated with ferromagnetic order.

Figure 1

Schematic phase diagram of rare-earth titanates, including the solid solution systems ${\mathrm{Y}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3, {\mathrm{Y}}_{1-y}{\mathrm{Ca}}_y{\mathrm{TiO}}_3$, and ${\mathrm{La}}_{1-y}{\mathrm{Sr}}_y{\mathrm{TiO}}_3$. Compounds studied with NMR and ESR in this paper are marked with symbols. $T_C$ and $T_N$ correspond to the Curie and Néel temperatures, respectively, and MI marks the metal-insulator transition.

Figure 2

(a) Sketch of the magnetic field direction and sample orientation relative to the goniometer angle scale. (b) Magnetic field derivative of the absorbed microwave power at 60 K for the ${\mathrm{YTiO}}_3$ sample. Results obtained for different orientations are shifted upwards for easier comparison. (c) Angular dependence of the resonant field and width of the ESR absorption line for ${\mathrm{YTiO}}_3$ at 40 K, 60 K, and 80 K obtained from Lorentizan fits.

Figure 3

Magnetic field derivative of the absorbed microwave power measured for ${\mathrm{YTiO}}_3$ at different temperatures, with the external field perpendicular to the crystallographic $c$ axis. A strong increase of the signal is observed with decreasing temperature, as expected for a system with FM spin fluctuations. We show measurements at all temperatures in (a), whereas (b) shows spectra at higher temperatures with the vertical scale adjusted for clarity.

Figure 4

Resonance field $H_{\mathrm{res}}$ of the ESR signal obtained from Lorentzian fits. Temperature and doping dependence of $H_{\mathrm{res}}$ with the external field: (a) parallel to the $c$ axis; (b) perpendicular to the $c$ axis.

Figure 5

Lorentzian linewidths of the ESR absorption lines vs temperature, with the $c$ axis parallel (full symbols) and perpendicular (half-empty symbols) to the external field. Error bars from fits are smaller than the symbol size, but we note that systematic errors are possible when the widths become comparable to the experimental magnetic field of $\sim 1$ T. The linewidths are significantly broader than the static dipole-dipole estimate (see text), and are instead determined by fast spin-lattice relaxation. Lines are best fits to Eq. (2).

Figure 6

(a) Schematic depiction of the splitting of the triply degenerate crystal field levels by Jahn-Teller distortions of the ${\mathrm{TiO}}_6$ octahedra. Octahedral elongation along the $c$ axis creates a doubly degenerate ground state, while additional distortions in the basal plane lift the orbital degeneracy completely. Energy splitting values were taken from [2]. (b) Schematic of the resonant phonon (Orbach) relaxation process of the electronic spins, that involves a real electronic excited-state spin doublet separated by the ground-state spin doublet by ${\mathrm{\Delta }}_{Orb}$. The external magnetic field $H$ lifts the remaining twofold spin degeneracy of the orbital levels. Note that this Zeeman splitting is much smaller than ${\mathrm{\Delta }}_{Orb}$ in our case.

Figure 7

Values of the ${\mathrm{\Delta }}_{\text{Orb}}$ gap in Kelvin, obtained from fits of the Orbach relaxation temperature dependence to ESR linewidths. The line is a linear fit to the data with the magnetic field parallel to the crystallographic $c$ axis (full symbols).

Figure 8

Temperature dependence of ${}^{89}\mathrm{Y}$ NMR spectra in a 12-T field for different samples. The individual spectra are scaled and shifted vertically for comparison. The stoichiometric compound ${\mathrm{YTiO}}_3$ shows a large shift above the Curie temperature, whereas doping decreases the shift significantly and increases the low-temperature linewidths.

Figure 9

Temperature dependence of ${}^{89}\mathrm{Y}$ spectra peak frequencies for ${\mathrm{YTiO}}_3, {\mathrm{Y}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3$ ($x=0.1$, 0.3), and ${\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x{\mathrm{TiO}}_3$ ($x=0.1$, 0.25, 0.35, 0.4), obtained from Gaussian fits. (a) Full frequency range and (b) expanded view. All lines are guides to the eye.

Figure 10

Temperature dependence of the dynamic spin susceptibility $1/\left(T_{1}T\right)$ for the ${}^{89}\mathrm{Y}$ nucleus. The lines are best fits to the Curie-Weiss form at high temperatures (for fit range, see Table 1). (a) A clear downward deviation from Curie-Weiss behavior is seen in the undoped parent compound ${\mathrm{YTiO}}_3$ below $\sim 120\mathrm{K}$. Similar, but weaker effects are found for some of the nonstoichiometric compositions. (b) Data for La-substituted, and (c) for Ca-doped samples.

Figure 11

High-temperature spin fluctuations quantified through $1/\left(T_{1}T\right)$ at 300 K (normalized to the value for ${\mathrm{YTiO}}_3$; full symbols) and Curie constants obtained from Curie-Weiss fits ($\times$ symbols; see Table 1 for fit ranges). The line is the ${(1-x)}^2$ dependence based on the assumption that substitution/doping effects are captured by simple dilution.

Figure 12

(a) Raw spin-echo decay data used to determine $T_2$ relaxation times for ${\mathrm{Y}}_{0.7}{\mathrm{La}}_{0.3}{\mathrm{TiO}}_3$ at several temperatures. Lines are best fits to the compressed exponential dependence, Eq. (5). Inset shows the compression parameter $b$ at different temperatures, demonstrating the transition from nearly Gaussian, $b=2$, to exponential relaxation, $b=1$, in cooling. (b) Alternative analysis of the data in (a), using the product of an exponential and Gaussian decay as a fit function. The corresponding values of $T_{2g}$ and $T_{2e}$ are shown, with the left and right axis referring to $1/T_{2e}$ and $1/T_{2g}$, respectively. As in (a), a crossover from Gaussian to exponential relaxation is observed in cooling, with a strong peak in $T_{2e}$. (c) Temperature dependence of the compression parameter $b$, obtained from fits of Eq. (5) to the raw spin echo decay data in ${\mathrm{YTiO}}_3$ and nonstoichiometric samples. The crossover from Gaussian to exponential echo decay is not as clear as in ${\mathrm{Y}}_{0.7}{\mathrm{La}}_{0.3}{\mathrm{TiO}}_3$, but a similar trend is seen in all samples. We note that the relaxation becomes indistinguishable from exponential at temperatures below $\sim 100$ K. Purely exponential fits were therefore performed at lower temperatures to minimize the number of free parameters, except for ${\mathrm{YTiO}}_3$, where the relaxation is slower and it was possible to collect more data for each spin echo decay.

Figure 13

$1/T_2$ values obtained from fits to a compressed exponential form, Eq. (5), above $\sim 100$ K, and purely exponential relaxation at lower temperatures. Peaks are observed close to the temperatures where $1/T_{1}T$ starts to deviate from Curie-Weiss behavior, and the peak heights increase with increasing Ca/La concentrations. The low-temperature increase in ${\mathrm{YTiO}}_3$ is likely due to fluctuations in the vicinity of $T_C=30$ K, whereas for other samples the peak might be too close to $T_C$ for the additional increase to be resolved. Lines are guides to the eye.