Probing the Nuclear Spin-Lattice Relaxation Time at the Nanoscale

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Probing the Nuclear Spin-Lattice Relaxation Time at the Nanoscale

J. J. T. Wagenaar, A. M. J. den Haan, J. M. de Voogd, L. Bossoni, T. A. de Jong, M. de Wit, K. M. Bastiaans, D. J. Thoen, A. Endo, T. M. Klapwijk, J. Zaanen, and T. H. Oosterkamp

Phys. Rev. Applied 6, 014007 – Published 15 July 2016

Abstract

Nuclear spin-lattice relaxation times are measured on copper using magnetic-resonance force microscopy performed at temperatures down to 42 mK. The low temperature is verified by comparison with the Korringa relation. Measuring spin-lattice relaxation times locally at very low temperatures opens up the possibility to measure the magnetic properties of inhomogeneous electron systems realized in oxide interfaces, topological insulators, and other strongly correlated electron systems such as high- $T_{c}$ superconductors.

Received 14 March 2016

DOI:https://doi.org/10.1103/PhysRevApplied.6.014007

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Spin relaxation

Strongly correlated systems

Cryogenics Magnetic force microscopy Nuclear magnetic resonance Scanning techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

J. J. T. Wagenaar^1,*, A. M. J. den Haan¹, J. M. de Voogd¹, L. Bossoni¹, T. A. de Jong¹, M. de Wit¹, K. M. Bastiaans¹, D. J. Thoen⁵, A. Endo^2,5, T. M. Klapwijk^2,3, J. Zaanen⁴, and T. H. Oosterkamp¹

¹Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
²Kavli Institute of Nanoscience, Faculty of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands
³Moscow State Pedagogical University, 1 Malaya Pirogovskaya Street, Moscow 119992, Russia
⁴Instituut-Lorentz for Theoretical Physics, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands
⁵Department of Microelectronics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands

^*wagenaar@physics.leidenuniv.nl

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Vol. 6, Iss. 1 — July 2016

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Images

Figure 1
(a) Scanning-electron-microscope image (false color) of the magnetic particle after it is glued to the cantilever using electron-beam-induced deposition from a platinum-containing precursor gas. (b) Optical-microscope image (false colors) of the detection chip. The blue horizontal wire at the top is the (Nb,Ti)N rf wire. The gold-capped copper sample is connected to the mixing chamber for thermalization. The small black dot is where we perform the MRFM experiments. Next to the sample and below the rf wire is the pickup coil for detection of the cantilever’s motion. (c) Schematic drawing of a side view of the local NMR experiment. When the rf frequency meets the resonance condition $f_{rf} = (γ / 2 π) B_{0}$ , copper nuclei at magnetic-field strength $B_{0}$ are in resonance.
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Figure 2
The frequency noise $S_{δ f} (f)$ for two different cantilever heights above the copper sample. The solid line is the expected frequency noise according to Eq. (2) with an added $1 / f$ noise. The $Q$ dependence of the $1 / f$ noise suggests that the additional noise is created by the oscillating currents in the copper, which also cause the drop in the quality factor due to eddy currents.
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Figure 3
(a) The saturating rf pulse results in a direct frequency shift $Δ f_{0}$ of the cantilever’s resonance frequency. The shift relaxes with the nuclear spin’s relaxation time $T_{1}$ . The dashed orange line shows a single measurement of the frequency shift (with a moving average of 1 s); the solid blue line shows 50 averages. The red solid line is an exponential fit according to Eq. (1). From the fit, we extract the direct shift $Δ f_{0}$ , the relaxation time $T_{1}$ , and a residual frequency offset $δ f_{0}$ . (b) The direct frequency shift $Δ f_{0}$ versus the temperature. The linear fit is expected according to Curie’s law $⟨ m ⟩ \propto T^{- 1}$ , which implicitly assumes that the resonant-slice thickness is temperature independent. (c) $Δ f_{0}$ as a function of rf frequency $f_{rf}$ for three different cantilever heights at $T = 42 mK$ . The solid line is the calculated signal with the cantilever height $h$ and resonant-slice width $d$ as parameters. The two resonant slices of the two copper isotopes largely overlap each other. The dashed vertical line at 542 kHz indicates the location of a higher resonance mode, at which the cantilever can be driven using the rf frequency resulting in an amplification of the $B_{1}$ field and, therefore, the spin signal (see the main text).
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Figure 4
The inverse of the relaxation time of the copper nuclei measured by applying saturation pulses versus the temperature. We find the same linear dependence with temperature as is found in bulk copper samples, the so-called Korringa relation. In blue are data measured at a height of $1.54 μ m$ at 542 kHz, where a larger signal is achieved due to amplification of the rf field by a higher cantilever mode. In green are data recorded at $1.31 μ m$ at a frequency of 625 kHz. We find $κ = 1.0 \pm 0.1 sK$ and $κ = 0.9 \pm 0.2 sK$ , respectively, with a linear fit with the error indicating the 95% confidence intervals. Every data point is an average of at least three sets of averaged data. The error bars give the standard deviation of the found relaxation times for the averaged data sets.
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