Nanotorsional resonator torque magnetometry

Davis, J. P.; Vick, D.; Fortin, D. C.; Burgess, Jacob A. J.; Hiebert, Wayne K.; Freeman, M. R.

doi:10.1063/1.3319502

Cited by 51 publications

(56 citation statements)

References 24 publications

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“…1(a). 27 The 100 µW of optical power impinging on the string causes no significant heating: we have verified that the resonance frequencies do not shift as a function of optical power, 17 a consequence of the low absorption of silicon nitride in the visible. Interferometric detection can be performed with or without a voltage applied to the piezo.…”

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confidence: 71%

Dissipation mechanisms in thermomechanically driven silicon nitride nanostrings

Suhel

Hauer

Biswas

et al. 2012

Applied Physics Letters

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High-stress silicon nitride nanostrings are a promising system for sensing applications because of their ultrahigh mechanical quality factors (Qs). By performing thermomechanical calibration across multiple vibrational modes, we are able to assess the roles of the various dissipation mechanisms in these devices. Specifically, we possess a set of nanostrings in which all measured modes fall upon a single curve of peak displacement versus frequency. This allows us to rule out bulk bending and intrinsic loss mechanisms as dominant sources of dissipation and to conclude that the most significant contribution to dissipation in high-stress nanostrings occurs at the anchor points.The extremely high values of mechanical Q that have been reported in silicon nitride nanostrings 1-3 have generated a great deal of excitement in the nanomechanics community. 4 These devices are ideal for use in mass sensing, 5 temperature sensing, 6 and optomechanics 7-9 and have proved to be an invaluable platform for research into the quantum properties of nanoscale resonators. 10,11 Nanostrings possess all the desired properties for these endeavors, including small mass, high frequency, and high Q, with correspondingly large displacement amplitudes. This combination makes them sensitive to external perturbation yet still within the limits of current detection techniques. 12 In this manuscript, we demonstrate thermomechanically limited detection of up to six mechanical nanostring modes. Furthermore, we present a set of devices in which all harmonics fall upon a single curve of calibrated peak displacement versus frequency. As we discuss below, we are able to infer that the mechanical Q is limited by dissipation processes operating in the vicinity of the anchor points-thus suggesting ways to further engineer the mechanical Q.Silicon nitride nanostrings are devices under extremely high tensile stress (σ = 0.8 GPa for our devices). The accepted understanding is that the tension along their length results in large stored elastic energy and a correspondingly large mechanical Q. 3 Experiments have confirmed that Q increases with mechanical tensioning of non-prestressed (low tension, non-stoichiometric silicon nitride) devices, 13,14 corroborating the tension's central role.In addition to causing the high Q, the tension compels the devices to behave like strings rather than doubly clamped beams, as one would usually expect for this geometry. The harmonics are at integer multiples of the fundamental frequency, 15 ν n = nν 1 , where ν 1 is the fundamental mode frequency and n indicates the mode number; the mode frequency depends only on the length of the string (not on the width or thickness). These features are in contrast to the more complicated harmonics of doubly clamped beams, 16 which are realized in low-stress silicon nitride devices of the same geometry. 17 Furthermore, it has now been shown that very high mechanical Qs exist for nanostrings under tension in a variety of other materials, including the polymer SU-8, 18 aluminum, 6,19 and AuPd...

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confidence: 71%

Dissipation mechanisms in thermomechanically driven silicon nitride nanostrings

Suhel

Hauer

Biswas

et al. 2012

Applied Physics Letters

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“…Nanomechanical resonators were studied by Davis et al, 13 and a quality factor of 2000 was reported for a torsional mode with effective mass of 0.1 pg at frequency 21 MHz. Measurements were performed at room temperature and pressure of $10 À7 Pa. A pattern of 3 "paddles" (rectangular elements) along a rod of width 100 nm was used to isolate the vibration of the central paddle from vibrations of the surrounding silicon nitride membrane.…”

Section: Introductionmentioning

confidence: 99%

High quality factor mg-scale silicon mechanical resonators for 3-mode optoacoustic parametric amplifiers

Torres

Meng

et al. 2013

Journal of Applied Physics

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A contour-mode film bulk acoustic resonator of high quality factor in a liquid environment for biosensing applications Appl. Phys. Lett. 96, 053703 (2010) Milligram-scale resonators have been shown to be suitable for the creation of 3-mode optoacoustic parametric amplifiers, based on a phenomena first predicted for advanced gravitational-wave detectors. To achieve practical optoacoustic parametric devices, high quality factor resonators are required. We present millimetre-scale silicon resonators designed to exhibit a torsional vibration mode with a frequency in the 10 5 -10 6 Hz range, for observation of 3-mode optoacoustic interactions in a compact table-top system. Our design incorporates an isolation stage and minimizes the acoustic loss from optical coating. We observe a quality factor of 7.5 Â 10 5 for a mode frequency of 401.5 kHz, at room temperature and pressure of 10 -3 Pa. We confirmed the mode shape by mapping the amplitude response across the resonator and comparing to finite element modelling. This study contributes to the development of 3-mode optoacoustic parametric amplifiers for use in novel high-sensitivity signal transducers and quantum measurement experiments. V C 2013 AIP Publishing LLC. [http://dx

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“…The dynamic range of the moment sensitivities ranges from ∼ 2×10 10 µ B at the thermo-mechanical limit to ∼ 4 × 10 6 µ B at the maximum driving field (600A/m) of our instrumentation. This is approximately an orderof-magnitude improvement in sensitivity to comparable torque magnetometry studies at room temperature using low applied fields [6,13,14].…”

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confidence: 88%

Thermo-mechanical sensitivity calibration of nanotorsional magnetometers

Losby

Burgess

Diao

et al. 2012

Journal of Applied Physics

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We report on the fabrication of sensitive nanotorsional resonators, which can be utilized as magnetometers for investigating the magnetization dynamics in small magnetic elements. The thermo-mechanical noise is calibrated with the resonator displacement in order to determine the ultimate mechanical torque sensitivity of the magnetometer. The combination of improving nanofabrication and detection techniques, along with technological demand, are providing the means and impetus for further understanding of the micromagnetic structure and dynamics of small magnetic elements. The exquisite sensitivities of nanoand micromechanical resonators have recently been utilized for detecting quantum-limited displacements [1,2] and ultra-sensitive atomic-scale mass detection [3,4]. Nanomechanical torque magnetometry allows for direct measurements of single elements [5,6], offering complementary information to other magnetometry methods, while also allowing for the investigation of details that are often indistinguishable when examining arrays of small elements or larger-scale thin films. Such events can be correlated to surface inhomogeneities and edge defects of the magnetic element, which play a dominant role on the overall magnetization configuration at smaller size scales. For understanding of the local energy landscapes of small magnetic elements, it is necessary to further increase the sensitivities of mechanical resonators.The thermo-mechanical noise sets a fundamental limit for the sensitivity of resonant mechanical measurements. This Brownian motion is the result of the coupling of the mechanical subsystem to that of a dissipative reservoir (the 'vacuum'), and is generalized as the fluctuationdissipation theorem [7,8]. This coupling causes the resonator to experience position fluctuations at its modes of mechanical resonance. Following equipartition, the observed mechanical resonance power spectrum must be proportional to the effective temperature of the mechanical mode. This relationship provides a method for torque sensitivity calibration of torsional resonators.Here, we briefly present the fabrication procedure of a doubly-clamped nanomechanical resonator with a permalloy (Ni 80 Fe 20 ) disk selectively deposited on a center paddle. A magnetic driving scheme, where the actuation of the resonator's torsional resonance modes are favored, is described and magnetometry measurements are presented. Using observations of the thermo-mechanical noise in the un-driven paddle resonators, we offer a cali- bration method to determine the mechanical torque sensitivity and consequently the magnetic moment sensitivity of the magnetometer, given the strength of the torquing field.The completed torsional resonator is shown in Fig. 1a. The paddle resonators were fabricated from silicon-oninsulator (SOI) wafers with a 300 nm thick Si device layer and a buried silicon oxide (BOx) layer with a thickness of 1 µm. The geometry of an array of paddles was defined via electron beam lithography (EBL) using a negative tone resist (hydrogen sils...

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Nanotorsional resonator torque magnetometry

Cited by 51 publications

References 24 publications

Dissipation mechanisms in thermomechanically driven silicon nitride nanostrings

Dissipation mechanisms in thermomechanically driven silicon nitride nanostrings

High quality factor mg-scale silicon mechanical resonators for 3-mode optoacoustic parametric amplifiers

Thermo-mechanical sensitivity calibration of nanotorsional magnetometers

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