Mechanical Generation of Radio-Frequency Fields in Nuclear-Magnetic-Resonance Force Microscopy

J. J. T. Wagenaar, A. M. J. den Haan, R. J. Donkersloot, F. Marsman, M. de Wit, L. Bossoni, and T. H. Oosterkamp

Phys. Rev. Applied 7, 024019 – Published 14 February 2017

Abstract

We present a method for magnetic-resonance force microscopy (MRFM) with ultralow dissipation, by using the higher modes of the mechanical detector as a radio-frequency (rf) source. This method allows MRFM on samples without the need to be close to a conventional electrically driven rf source. Furthermore, since conventional electrically driven rf sources require currents that give dissipation, our method enables nuclear-magnetic-resonance experiments at ultralow temperatures. Removing the need for an on-chip rf source is an important step towards an MRFM which can be widely used in condensed matter physics.

Received 20 September 2016

DOI:https://doi.org/10.1103/PhysRevApplied.7.024019

Physics Subject Headings (PhySH)

Spin relaxation

Nanomechanical devices Solid-state detectors

Cryogenics Magnetic force microscopy Nuclear magnetic resonance

General PhysicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

J. J. T. Wagenaar^*, A. M. J. den Haan, R. J. Donkersloot, F. Marsman, M. de Wit, L. Bossoni, and T. H. Oosterkamp

Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands

^*Wagenaar@physics.leidenuniv.nl

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Vol. 7, Iss. 2 — February 2017

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Images

Figure 1
Sketch of a method to mechanically generate rf fields using the higher resonant modes of the cantilever. A higher mode (rainbow beam) of the cantilever causes a rotation of the magnetic particle with an angle $α (t)$ . This rotation effectively results in a magnetic field component $B_{rf} (t)$ perpendicular to the initial magnetic field $B (0)$ . Only spins that are positioned within the resonant slice, for which $B (0) = f_{n} / 2 π γ$ , will be perturbed by this rf field. For the 8th mode, $B (0)$ corresponds to 48 mT and a height $h = 1.54 μ m$ .
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Figure 2
(a) Simulation of the 8th and 9th modes of the cantilever. These two modes are used in the experimental part of this paper. The dynamics of the magnetic particle at higher modes are mainly rotational, which is due to the relatively larger mass of the magnetic particle compared to the bare silicon cantilever. (b) Frequency of the simulated (black) and measured (red) modes of the cantilever. Modes 4 and 6 do not oscillate in the $x$ direction and could therefore not be detected. On the right vertical axis the corresponding magnetic field at resonance [ $f_{n} = (γ / 2 π) B_{0}$ ] for the ${}^{63}{Cu}$ is shown.
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Figure 3
(a) Frequency shift of the cantilever’s first mode at 3 kHz after applying an rf pulse of 0.2 mA and a 1-s length using the rf wire. In blue, the data [11] was measured at a height of $1.54 μ m$ and a temperature of 42 mK. The solid line is numerically calculated [Eq. (6)] using a resonant slice thickness of 38 nm. In red is the simulated signal when the cantilever is positioned 400 nm closer to the surface. The dotted lines indicate the positions of the higher modes $f_{8} = 542 \pm 1 kHz$ and $f_{9} = 759 \pm 1 kHz$ . (b) Frequency shift as a function of time after applying an rf pulse at the frequency of the two higher modes at $T = 77 mK$ . The pulse time of 11 ms is too short to saturate the spins directly with the oscillating magnetic field of the rf line, but the excitation of the higher modes gives a large-enough rf field. As expected from (a), no signal is observed at the mode of 759 kHz, while there is for the mode at 542 kHz. (c) The same as in (b), but the cantilever has been moved 400 nm closer to the sample. The mode at 759 kHz now corresponds to a resonant slice that lies within the sample, resulting in a frequency shift, while the signal at 542 kHz is greatly reduced. Note (b) and (c) are measured at slightly larger temperatures, and have much shorter pulse lengths than (a).
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Figure 4
Exciting the cantilever with the rf line (blue) with a current of 0.2 mA and pulse length of 11 ms, and with the piezoelectric element (green) on the cantilever’s mount stage with a pulse length of 4 ms.
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Figure 5
(a),(b) Exciting the cantilever at its 8th mode, far from the surface, by sweeping the frequency by using the rf wire while recording the SQUID’s signal. Already at a current of $40 μ A$ , a huge nonlinear effect (Duffing) is present. A background signal is subtracted for clarity. (c) The sweeps from right to left at different currents.
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