Finite-size effects in the nuclear magnetic resonance of epitaxial palladium thin films

We have measured the NMR of ${}^8$Li${}^{+}$ implanted in a set of thin epitaxial films of Pd. We find a large, negative, strongly temperature-dependent Knight shift $K$ consistent with previous measurements on polycrystalline films. The temperature dependence of the shift exhibits a characteristic deviation from the susceptibility $\chi \left(T\right)$. In particular, at low temperature, $K\left(T\right)$ continues to follow a simple Curie-Weiss dependence. This result provides important insight into the origin of the low-temperature behavior of $\chi \left(T\right)$ in strongly paramagnetic metals. In addition, we find the room temperature shift depends on film thickness, with changes on the order of 20% between films 100 nm and 30 nm thick. We also observe a surface-related resonance in both Au-capped and uncapped films with a small positive shift. These features bear a striking similarity to the Pt NMR line shapes in much smaller Pt particles. However, they seem to originate, not from adsorbed species, but rather in confinement effects on the highly exhange-enhanced Pd $d$ band.

Figure 1

Predicted implantation profile of ${}^8$Li${}^{+}$ in sample IV for several representative energies from the Monte Carlo code trim.sp. The vertical lines indicate heterointerfaces.

Figure 2

CW resonance spectra at selected temperatures in sample IV at 4.1 T using an ${}^8$Li${}^{+}$ implantation energy of 13 keV. The high-frequency line to the right is from the Au-capping layer as well as the Pd near the surface, while the lower-frequency line is that of Pd deeper in the film. The vertical dashed line marks the resonance frequency in MgO, which we use conventionally as the zero of the shift scale.

Figure 3

Comparison of pulsed and CW resonance spectra at 270 K in sample IV at 4.1 Tesla using an ${}^8$Li${}^{+}$ implantation energy of 13 keV. The signal to noise is much lower in the pulsed case, but the resolution is much higher yielding a more clearly defined value for the shifts. The long high-frequency tail in the CW spectrum is highly suppressed in the pulsed spectrum. The composite resonance at small positive shift matches very well to the known shifts of ${}^8$Li${}^{+}$ in Au[21] (vertical lines, labeled Au${}_O$ and Au${}_S$), but the corresponding resonance in the CW spectrum (labeled “surface $+$ Au”) is too large and too wide to be due simply to the Au overlayer.

Figure 4

The relative shift of the resonance with respect to MgO as a function of temperature for Pd sample IV at 4.1 T and 13 keV implantation energy (2009 data) and at 2.2 Tesla and 4.5 keV (2012 data). The consistency of the two fields confirms that the shift is magnetic. The temperature dependence is due to the magnetic susceptibility of Pd.

Figure 5

CW ${}^8$Li${}^{+}$ $\beta$-NMR spectra in all four samples at 295 K demonstrating the thickness dependence of the shift of ${}^8$Li${}^{+}$ in Pd films. The high-frequency resonance is present in both capped and uncapped Pd films with a similar amplitude. This line is enhanced when the implantation energy is reduced. The shift of the low-frequency Pd resonance is systematically reduced in the thinner films.

Figure 6

The magnetic susceptibility of Pd from the literature[26] together with a phenomenological fit used in correcting the shift measurements for the demagnetizing field (red curve) and the extrapolated high-temperature Curie-Weiss dependence (blue curve).

Figure 7

The effect of demagnetization correction on the shift in sample IV. The raw shifts from Fig. 4 are replotted, with the demagnetization correction, a scaling of the susceptibility shown in Fig. 6 (blue curve, right scale). The stars are the pulsed and the circles the CW shifts. The correction results in the smaller negative shifts shown. The curvature of the raw shift is largely removed by the correction.

Figure 8

Top: Model depth profiles of the shift for the parameters used in Ref. 32 (red) and for a much larger healing length (blue). The surface layers are substantially different in thickness: 7.5 nm (red), corresponding to the Au capping layer thickness and 22.5 nm (blue), to yield an amplitude comparable to the observed surface resonance. The black curve shows a truncated Gaussian approximation of the 13 keV implantation profile used to generate the corresponding lineshape in the bottom panel, where the colors correspond, and the circles show the experimental data.

Figure 9

The Pd Knight shift in Pd at 295 K and 4.1 Tesla in MBE films of varying thickness in comparison with the polycrystalline film from Parolin et al. 6. The open(closed) circles correspond to the pulsed(CW) RF spectra. The pulsed spectra for samples I-III are all taken at 8 keV. The CW spectra were collected at 8 keV and at 18 keV. For the 50 nm film (sample III) results from two energies are shown. Similarly for sample IV, the results for 13 and 28 keV implantation energies are shown. While the energy dependence, measurement and analysis methods contribute to a scatter of the shift, the trend of a substantial reduction of shift with a reduction in film thickness is robust.

Figure 10

Top: Model depth profiles of the shift for the 30 nm thick film, for symmetric models that treat the surface and substrate interface as equivalent for the parameters used in Ref. 32 (red) and for a much larger healing lengths (blue) and (green) for a asymmetric model that neglects the substrate interface. The surface layers are substantially different in thickness: 2 nm (red, blue) and 7.5 nm (green), to yield a “surface” line comparable in amplitude to the observed spectrum. The black curve shows a truncated Gaussian model of the implantation profile used to generate the corresponding lineshape in the bottom panel, where the colors correspond and the points show experimental data.

Figure 11

The ${}^8$Li Knight shift in Pd at 295 K and 2.2 Tesla in sample IV as a function of the mean range of implantation as varied by the implantation energy. Bottom: The fitted resonance linewidths.

Figure 12

The temperature dependence of the Knight shift of ${}^8$Li in two Au capped 100 nm films of Pd, filled squares the polycrystalline film data of Ref. 6, open circles MBE sample IV. The data are fit to the Curie-Weiss dependence of the high temperature susceptibility of Pd extrapolated to low temperature.