... Magnetomotive drive and detection of clamped-clamped mechanical resonators in water W.J. Venstra, H.J.R. Westra, K. Babaei Gavan, and H.S.J. van der Zant Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, The Netherlands (Dated: December 30, 2009) We demonstrate magnetomotive drive and detection of doubly clamped string resonators in water. A compact 1.9 T permanent magnet is used to detect the fundamental and higher flexural modes of 200 µ m long resonators. Good agreement is found between the magnetomotive measurements and optical measurements performed on the same resonator. The magnetomotive detection scheme can be used to simultaneously drive and detect multiple sensors or scanning probes in viscous fluids without alignment of detector beams. PACS numbers: 47.61.Fg, + 85.80.Jm, 85.85.+j, 07.79.-v arXiv:1001.2497v1 [physics.ins-det] 14 Jan 2010 Micro- and nanomechanical resonators have many applications as scanning probes and mass or stress sen- sors. Several techniques have been developed to detect resonator vibrations in vacuum and at atmospheric pres- sure. The natural environment for biological experiments however is an aqueous solution, and detection methods in liquid environments are less numerous. Optical or piezoresistive schemes are commonly used, combined with a separate excitation source, e.g. magnetic [1] or piezoelectric, to drive the strongly damped resonator. linear position sensitive detector, D, and measured on the second input channel of the network analyzer. The resonator is placed in a custom-built tempera- ture controlled flow cell with a volume of 3 µ l, such that the Lorentz force is directed out-of-plane, corresponding to the fundamental resonance mode. In this work we demonstrate that a magnetomotive technique can be used to drive and detect micromechan- ical resonator vibrations in water. The magnetomotive technique allows straightforward resonator geometry, a strong driving force acting directly on the resonator, and it can be scaled towards nanometer dimensions. The technique has been applied in vacuum to characterize resonators up to the GHz-range [2], in mass sensing [3], and to readout resonator arrays driven in the nonlinear regime at atmospheric pressure [4]. A compact and powerful permanent magnet is constructed to drive the strongly damped resonator in the fluid. The magnet is composed of commercially available NdFeB magnets with a remanent induction of B r = 1 . 5 T and a total volume of 213 cm $^{3}$. By configuring the magnets in a Halbach array [5], a field strength up to 2 T is generated in a 6 mm gap between the magnet poles. Figure 1(a) shows the measured field as a function of the position in the gap, x . The inset shows a schematized cross section of the construction, the arrows indicate the polarization of the magnets. The field strength varies less than 5% within a volume of 6 × 6 × 6 mm 3 inside the gap, and is minimum in the center at x = 0, where the resonator is located. Figure 1(b) shows the measurement setup. The alternating voltage from a network analyzer is applied to the resonator via a series resistor, R = 25 Ω. The generated electromotive force is measured via a high impedance buffer, marked A in the figure, on one input channel of the analyzer. As a reference, the deflection of the resonator is probed at the same time by a Helium Neon laser, L. The beam reflection is captured on a FIG. 1: (a) Magnetic field strength as a function of the po- sition in the gap between the magnet poles, x . Inset shows a cross-section of the magnet construction, squares represent the individual magnets, polarized according to the arrows. (b) Schematic of the combined magnetomotive and optical setup. (c) Frequency response functions of the magnetomo- tive driven resonator in air, as measured by magnetomotive and optical techniques, magnitude | H | and phase φ , the black solid lines represent driven harmonic oscillator functions fits. Inset: scanning electron micrograph of two clamped-clamped string resonators, scale bar is 20 µ m. D B network analyzer R A f 100 L x (b) (c) (a)