A method and apparatus for measuring the resonant frequency and quality factor of a cantilever

Abstract

The present application provides a kind of cantilever resonance frequency and quality factor measurement method and device, compared with the measurement method based on the PLL technology of existing phase-locked loop, can more comprehensively grasp sample magnetic property, and when responding to cantilever quality factor mutation, there is good measurement stability.The measurement method of the present application includes: cantilever driving step, wherein the driving signal of first frequency is used to drive the cantilever to vibrate, and then stop the driving signal;Free decay signal acquisition step, wherein in response to the stop of the driving signal, the free decay vibration signal of the free end of the cantilever is acquired;And data processing step, wherein the acquired free decay vibration signal is processed to obtain the resonance frequency and quality factor of the cantilever.

Description

Technical Field

[0001] This invention belongs to the field of sensitive force detection research, specifically relating to a method for measuring the resonant frequency and quality factor of a cantilever beam, and more specifically, to a method for simultaneously and in real time measuring the resonant frequency and quality factor of a cantilever beam. Background Technology

[0002] Laser interferometry-based displacement measurement of microcantilever beams (hereinafter referred to as "cantilever beams") is one of the important methods for sensitive force detection. It has important applications in areas such as magnetic torque measurement of nanoscale magnetic samples, measurement of Casimir force, and magnetic resonance force measurement.

[0003] The cantilever beam operates in two modes: static and dynamic. Taking dynamic cantilever magnetometry (DCM) for measuring micro / nano magnetic samples as an example, a low-elasticity nanocantilever beam is used. The magnetic material sample is fixed to the free end of the cantilever beam, and an external magnetic field is applied, causing a torque effect on the sample. This alters the resonant frequency of the cantilever beam (including the sample). Measuring the change in the resonant frequency under different magnetic fields reflects the magnetic properties of the sample. Typically, dynamic cantilever magnetometry only measures the resonant frequency of the cantilever beam. Using phase-locked loop (PLL) technology, the resonant frequency and its changes can be measured in real time.

[0004] With the development of dynamic cantilever magnetic measurement methods, it has been discovered that the magnetic properties of the sample at the free end (vibrating end) of the cantilever beam are altered not only by its resonant frequency but also by its quality factor in a magnetic field. For some samples, observing changes in the quality factor can better reflect the characteristics of their magnetic properties. Therefore, to gain a more comprehensive understanding of the magnetic properties of samples, it is desirable to simultaneously measure the resonant frequency and quality factor of the cantilever beam under different magnetic fields.

[0005] However, when using phase-locked loop (PLL) technology to measure the resonant frequency of a cantilever beam, the quality factor of the cantilever beam cannot be obtained simultaneously; the quality factor needs to be measured separately. Furthermore, when the sample's magnetism changes with the magnetic field, resulting in different magnetization states that significantly alter the quality factor of the cantilever beam (e.g., abrupt changes in the quality factor), the PLL measurement method may lose its locking effect, making the measurement extremely unstable and even forcing it to stop.

[0006] Therefore, a new measurement method needs to be developed that can simultaneously and in real time obtain the resonant frequency and quality factor of the cantilever beam, and make the measurement more stable and reliable. Summary of the Invention

[0007] The technical problem that the invention aims to solve

[0008] As described above, the force detection method based on a cantilever beam operating in a dynamic mode reflects the stress on the sample by measuring the change in the cantilever beam's resonant frequency, thereby reflecting the sample's magnetic properties. Currently, the measurement of the cantilever beam's resonant frequency commonly employs phase-locked loop (PLL) technology. To facilitate understanding of this invention, its basic principles and main problems are explained in detail below.

[0009] Figure 1 The amplitude response curve and frequency response curve of the cantilever beam under a constant magnetic field are schematically shown. Figure 1 In diagram (a), the amplitude response curve is shown. The horizontal axis represents the frequency at which the cantilever beam is driven by the drive unit (e.g., piezoelectric ceramic) at the fixed end, and the vertical axis represents the vibration amplitude at the free end of the cantilever beam at different drive frequencies. Figure 1 As shown in (a), the frequency response curve of the cantilever beam has a prominent peak, the position of which represents the position of the cantilever beam's resonant frequency f0. Figure 1 In diagram (b), the frequency response curve is shown. The horizontal axis represents the frequency driven by the drive unit, and the vertical axis represents the phase shift of the cantilever beam, which is the phase difference (phase lag) between the drive signal and the vibration signal at the free end of the cantilever beam. Figure 1 As shown in (b), the phase response curve of the cantilever beam changes from 0 degrees to 180 degrees near the resonant frequency f0. 90 degrees corresponds exactly to the resonant frequency f0, where the curve slope is the largest and the phase change is the fastest.

[0010] The method of measuring the resonant frequency of a cantilever beam using phase-locked loop (PLL) technology is to control the driving frequency of the cantilever beam driven by the driving unit to lock the measured phase offset of the cantilever beam at the resonant frequency, i.e., 90 degrees. Furthermore, when the resonant frequency of the cantilever beam changes due to the force on the sample, for example, by changing the magnetic field, the driving frequency is changed accordingly to ensure that the measured phase offset of the cantilever beam remains at 90 degrees.

[0011] Phase-locked loop (PLL) technology applied to cantilever beam force detection can only measure changes in the resonant frequency of the cantilever beam, but cannot reflect changes in its quality factor. Here, the quality factor Q is an indicator of the cantilever beam's vibration characteristics, and its physical meaning can be expressed, for example, as Q = f0 / Δf, where Δf is the resonant bandwidth. Therefore, for a fixed resonant frequency f0, the quality factor Q is inversely proportional to the resonant bandwidth Δf; that is, if Q decreases, the resonant bandwidth Δf increases, and the maximum amplitude at resonance decreases, while if Q increases, the resonant bandwidth Δf decreases, and the maximum amplitude at resonance increases. Furthermore, when the drive unit stops and the cantilever beam undergoes free decay vibration, the quality factor Q characterizes the energy dissipation effect of the cantilever beam, determining the rate of vibration signal decay.

[0012] When a phase-locked loop (PLL) is working, a voltage signal of a certain frequency is output to the drive unit via a lock-in amplifier to drive the cantilever beam to vibrate. Simultaneously, the amplitude and phase of the cantilever beam vibration are measured and fed back, thereby controlling the amplitude and frequency output of the lock-in amplifier to lock the amplitude and phase of the cantilever beam vibration. However, for example, when measuring the magnetism of a sample at the vibrating end of the cantilever beam, changes in the magnetic field can cause drastic changes in the cantilever beam's quality factor. As mentioned above, this leads to huge variations in the cantilever beam's vibration amplitude. When the cantilever beam vibration cannot maintain a stable value, the measurement of all parameters of the entire cantilever beam becomes extremely unstable, causing large fluctuations in the measured amplitude and phase values. The originally locked state may be disrupted, forcing the measurement to stop.

[0013] In summary, when using a cantilever beam in dynamic working mode to measure the magnetic properties of a sample, if the phase-locked loop (PLL) technology is used to measure the resonant frequency of the cantilever beam and its changes, the quality factor of the cantilever beam cannot be measured simultaneously. For some samples, the characteristics of their magnetic properties cannot be fully understood. In addition, for example, when the quality factor changes abruptly, the locking state may be broken, and the measurement may be forced to stop.

[0014] In response, this invention proposes a technique that can simultaneously measure the resonant frequency and quality factor of a cantilever beam in real time under dynamic working mode. This technique can solve the problems existing in the prior art, provide a more comprehensive understanding of the magnetic properties of the sample, and has good measurement stability when dealing with sudden changes in the quality factor of the cantilever beam.

[0015] Technical means to solve the problem

[0016] The first technical solution of the present invention is a method for measuring the resonant frequency and quality factor of a cantilever beam. In a cantilever beam force measuring device in dynamic working mode, the resonant frequency and quality factor of a cantilever beam carrying a sample are measured in real time and simultaneously under an applied current magnetic field. The method includes: a cantilever beam driving step, wherein the cantilever beam is driven to vibrate using a driving signal of a first frequency, and then the driving signal is stopped; a free decay signal acquisition step, wherein in response to the cessation of the driving signal, a free decay vibration signal at the free end of the cantilever beam is acquired; and a data processing step, wherein the acquired free decay vibration signal is processed to obtain the resonant frequency and quality factor of the cantilever beam. In the data processing step, the resonant frequency is obtained by performing a Fourier transform on the free decay vibration signal and then determining the peak position. Furthermore, the quality factor is obtained by taking the outer envelope of the free decay vibration signal and fitting the outer envelope.

[0017] The second technical solution of the present invention is a method for measuring the resonant frequency and quality factor of a cantilever beam. In the first technical solution, during the cantilever beam driving step, the frequency spectrum of the cantilever beam is first swept to obtain the swept resonant frequency, and the swept resonant frequency is used as the first frequency.

[0018] The third technical solution of the present invention is a method for measuring the resonant frequency and quality factor of a cantilever beam. In the first technical solution, the cantilever beam force measuring device sequentially applies multiple different magnetic fields. When the current magnetic field is the first applied magnetic field, in the cantilever beam driving step, the frequency spectrum of the cantilever beam is first swept to obtain the swept frequency resonant frequency, and the swept frequency resonant frequency is used as the first frequency. When the current magnetic field is not the first applied magnetic field, in the cantilever beam driving step, the resonant frequency obtained in the data processing step under the previously applied magnetic field is used as the first frequency.

[0019] The fourth technical solution of the present invention is a method for measuring the resonant frequency and quality factor of a cantilever beam. In any of the first to third technical solutions, in the data processing step, a Fourier transform is performed on the free decaying vibration signal, and the resulting spectrum curve is fitted using the Lorentz curve shape of the following formula. The fitted x-value is used as the resonant frequency.

[0020]

[0021] In the formula, a, b, and c are fitting parameters, and y(f) represents the change in amplitude of the resonance peak of the spectral curve with frequency.

[0022] The fifth technical solution of the present invention is a method for measuring the resonant frequency and quality factor of a cantilever beam. In the fourth technical solution, during the data processing step, the outer envelope is fitted using the following formula, and the Q value obtained from the fitting is used as the quality factor.

[0023]

[0024] In the formula, U(t) is the amount by which the amplitude of the cantilever beam decays with time, U0 is the initial value at the start of decay, and ω is the obtained resonance frequency.

[0025] The sixth technical solution of the present invention is a method for measuring the resonant frequency and quality factor of a cantilever beam. In any of the first to third technical solutions, in the cantilever beam driving step, after the cantilever beam stops vibrating for a period of time after the driving signal is stopped, the cantilever beam is driven again using the driving signal of the first frequency, thereby causing the cantilever beam to be driven and stopped repeatedly. In the free decay signal acquisition step, multiple free decay vibration signals are acquired. In the data processing step, the multiple free decay vibration signals are averaged and then further processed.

[0026] The seventh technical solution of the present invention is a method for measuring the resonant frequency and quality factor of a cantilever beam, wherein in any of the first to third technical solutions, the outer envelope is obtained by taking the positive value of the free decay vibration signal and calculating the average smooth curve.

[0027] The eighth technical solution of the present invention is a measuring device for the resonant frequency and quality factor of a cantilever beam. It is installed in a cantilever beam force measuring device operating in dynamic mode, and measures the resonant frequency and quality factor of a cantilever beam carrying a sample under an applied current magnetic field in real time and simultaneously. The device includes: a drive signal output unit that outputs a drive signal of a first frequency to the drive unit of the cantilever beam force measuring device to drive the cantilever beam to vibrate, and then stops outputting the drive signal; a free decay signal acquisition unit that, in response to the cessation of the drive signal, acquires the free decay vibration signal at the free end of the cantilever beam; and a control unit that processes the free decay vibration signal acquired by the free decay signal acquisition unit to obtain the resonant frequency and quality factor of the cantilever beam. The control unit obtains the resonant frequency by performing a Fourier transform on the free decay vibration signal and determining the peak position, and obtains the quality factor by taking the outer envelope of the free decay vibration signal and fitting the outer envelope.

[0028] The ninth technical solution of the present invention is a device for measuring the resonant frequency and quality factor of a cantilever beam. In the eighth technical solution, the control unit performs a Fourier transform on the free decaying vibration signal and fits the obtained spectrum curve using the Lorentz curve shape of the following formula. The fitted x-value is used as the obtained resonant frequency.

[0029]

[0030] In the formula, a, b, and c are fitting parameters, and y(f) represents the change of the amplitude of the resonance peak with frequency in the frequency domain.

[0031] The tenth technical solution of the present invention is a device for measuring the resonant frequency and quality factor of a cantilever beam. In the eighth technical solution, the control unit fits the outer envelope using the following formula, and uses the fitted Q value as the obtained quality factor.

[0032]

[0033] In the formula, U(t) is the amount by which the amplitude of the cantilever beam decays with time, U0 is the initial value at the start of decay, and ω is the obtained resonance frequency.

[0034] Invention Effects

[0035] The method for measuring the resonant frequency and quality factor of a cantilever beam according to the present invention can simultaneously obtain information on the resonant frequency and quality factor of the cantilever beam by measuring the free decaying vibration signal of the cantilever beam. Moreover, since no feedback control loop is required, the measurement stability is greatly guaranteed. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the amplitude response curve and frequency response curve of a cantilever beam.

[0037] Figure 2 This is a schematic diagram showing the main parts of the cantilever beam force measuring device.

[0038] Figure 3 This is a diagram showing the general measurement process of the cantilever beam force measuring device in dynamic working mode.

[0039] Figure 4 This is a flowchart illustrating the method for measuring the resonant frequency and quality factor of a cantilever beam according to the present invention.

[0040] Figure 5 This is a block diagram illustrating the modular structure of the measuring device for the resonant frequency and quality factor of the cantilever beam according to the present invention.

[0041] Figure 6 This is a sequence diagram of cantilever beam driving and data acquisition in Example 1.

[0042] Figure 7 This is a flowchart of the process for obtaining the resonant frequency and quality factor of the cantilever beam in Example 1.

[0043] Figure 8 It is the free decay vibration signal of the cantilever beam actually measured in Example 1.

[0044] Figure 9 Example 2 shows the variation of the cantilever beam resonant frequency with the applied magnetic field when measuring MnSi magnetic material.

[0045] Figure 10Example 2 shows the change in the quality factor of a cantilever beam with an applied magnetic field when measuring MnSi magnetic materials. Detailed Implementation

[0046] The specific embodiments of the present invention will now be described with reference to the accompanying drawings.

[0047] In the following embodiments, when referring to numbers or other numerical values ​​(including number, value, quantity, range, etc.) of elements, they are not limited to that specific number, except where specifically stated or where they are clearly limited to a specific number in principle. They may be above or below that specific number.

[0048] Furthermore, in the following embodiments, the structural elements (including step elements, etc.) are not necessarily required except where specifically stated or where they are obviously understood to be necessary in principle, and may also include elements not explicitly mentioned in the specification, which need not be explicitly stated.

[0049] Similarly, in the following embodiments, when referring to the material, shape, positional relationship, etc., of structural elements, this includes elements that are substantially similar or analogous to their shape, except where specifically stated or where it is clearly understood from a principle standpoint that such elements are not feasible. The same applies to the aforementioned values ​​and ranges.

[0050] Furthermore, the figures shown are merely examples, and the relative sizes of the components and the proportions of the constituent parts are not limited to the examples in the figures. The descriptions of some figures use directional terms such as "left" and "right," which may be changed according to the specific implementation.

[0051] The embodiments described in this specification are merely examples of a complete description and do not limit the scope of protection of this invention. All other embodiments that can be obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0052] [Cantilever Beam Force Measurement Device]

[0053] The method for measuring the resonant frequency and quality factor of a cantilever beam according to the present invention can be applied to a cantilever beam force measuring device operating in dynamic mode. First, a general description of the cantilever beam force measuring device will be given.

[0054] Figure 2 This is a schematic diagram showing the main parts of the cantilever beam force measuring device 200.

[0055] like Figure 2As shown, the cantilever beam force measuring device 200 includes a nano cantilever beam (hereinafter referred to as "cantilever beam") 201, a drive unit 202, an interferometric optical system 203, a laser source 204, a detection unit 205, a data acquisition unit 206, and a calculation and control system 207. Solid lines connecting the parts in the figure represent electrical connections, and dashed lines represent optical connections (optical paths).

[0056] The cantilever beam 201 can be, for example, a silicon-based cantilever beam fabricated by an etching process, and its shape can be any common shape, such as rectangular, T-shaped, U-shaped, triangular beam, etc. When using optical interferometry to measure the vibration displacement of the free end, it is preferable to configure it as a T-shape to increase the reflective area. The fixed end (right end in the figure) of the cantilever beam 201 is fixed to a drive part 202, for example, made of piezoelectric ceramic, etc., and a magnetic sample 210 is transferred to the free end (left end in the figure), and a light-reflecting surface is formed at the free end to reflect incident light from the optical system (described later).

[0057] The cantilever beam 201 and the drive unit 202 are located in a vacuum chamber 209. During operation, various magnetic fields are applied to the chamber 209. The magnetic sample 210 is affected by the magnetic field, which changes the resonant frequency f0 of the cantilever beam 201 and also changes the quality factor Q of the cantilever beam 201.

[0058] The interferometric optical system 203 measures the displacement of the free end of the cantilever beam 201. It uses a laser emitted from a laser source 204 as its light source, directing one path of light in the interferometric optical path to the free end of the cantilever beam 201. After reflection at the free end, the light couples back to the interferometric optical system 203, interfering with the other path of light to produce interference light. This interference light is detected by a detection unit 205 composed of a photodetector. The signal detected by the detection unit 205 is input to the computational control system 207 via a data acquisition unit 206 composed of a data acquisition card.

[0059] The computational control system 207 has signal calculation / processing functions, signal generation functions, and data output / storage functions. For example, it can receive user settings and output a voltage signal of a specified frequency to the drive unit via a built-in signal generator, causing the drive unit 202 to vibrate, thereby driving the cantilever beam 201 to vibrate. It can also perform calculations based on the input signals and set parameters, outputting / storing various calculated parameters, or further processing the parameters to output visualized tables, curves, etc. As a variation, the functions of the acquisition unit 206 can also be integrated into the computational control system 207. Of course, the computational control system 207 can also integrate magnetic field application and control functions, but since this is not directly related to the present invention, it will not be described further. The computational control system 207 can be implemented by a general-purpose computer connected to a signal generator, but the present invention does not limit this.

[0060] When using the existing phase-locked loop (PLL) technology to measure the resonant frequency of a cantilever beam, the computational control system 207 can calculate the change in displacement of the free end of the cantilever beam over time, i.e., the cantilever beam vibration signal, based on the detection results of the interference light by the detection unit 205. Then, it can obtain the frequency and phase of the cantilever beam and adjust the frequency of the voltage signal output to the drive unit 202 through feedback control to ensure that the measured phase offset of the cantilever beam is maintained at 90 degrees.

[0061] When the cantilever beam resonance frequency and quality factor measurement method of the present invention is applied, as described below, the operation control system 207 can obtain the cantilever beam free decay vibration signal based on the detection result of the interference light by the detection unit 205, and further calculate the resonance frequency f0 and quality factor Q of the cantilever beam 201 (described below).

[0062] Next, the general measurement process of the cantilever beam force measuring device 200 will be explained.

[0063] The measurement method of the present invention is applied to the cantilever beam force measuring device 200 in dynamic working mode. Figure 3 This is a diagram showing the general measurement process of the cantilever beam force measuring device 200 in dynamic working mode.

[0064] In step S301, the sample 210 is transferred to the free end of the cantilever beam 201 and the chamber 209 is evacuated. Then, in step S302, the magnetic field to be applied is set for the calculation control system 207.

[0065] When measuring the magnetic properties of a sample, it is necessary to measure the change in the resonant frequency of the cantilever beam with the magnetic field. Therefore, it is necessary to continuously change the magnetic field and measure the resonant frequency after each change. Thus, multiple magnetic fields B1 to B2 need to be set according to the sample to be measured, with specified magnetic field magnitude and / or directional steps. n When step S302 is executed for the first time, the first magnetic field B1 to be applied is set.

[0066] Then, in step S303, the set magnetic field is applied. Next, in step S304, the resonant frequency is measured. Here, the resonant frequency can be obtained using existing phase-locked loop (PLL) technology, or the resonant frequency and quality factor can be obtained simultaneously using the cantilever beam resonant frequency and quality factor measurement method of this invention. Then, in step S305, the calculation control system 207 determines whether it is necessary to switch to the next magnetic field to continue the measurement. If the determination is yes, the process returns to step S302 to set the next magnetic field to be applied. If it is determined in step S305 that it is not necessary to switch to the next magnetic field, it is considered that all magnetic fields have been measured, the measurement process ends, and then in step S306, the calculation control system 207 outputs the measurement results of multiple magnetic fields.

[0067] As described above, the method for measuring the resonant frequency and quality factor of a cantilever beam according to the present invention is applied to... Figure 3 Step S304, or in other words, is applied to the calculation and control system 207 of the cantilever beam force measuring device 200. This will be explained in detail below.

[0068] [Methods for measuring the resonant frequency and quality factor of a cantilever beam]

[0069] Figure 4 This is a flowchart illustrating the method for measuring the resonant frequency and quality factor of a cantilever beam according to the present invention. This flowchart corresponds to step S304 described above. Figure 3 In the general measurement process of the cantilever beam force measuring device 200, each applied magnetic field is performed once.

[0070] The inventors discovered that the resonant frequency and quality factor of a cantilever beam can be calculated simultaneously and in one go based on its free decaying vibration signal. Therefore, in this invention, the resonant frequency and quality factor of the cantilever beam are calculated using its free decaying vibration signal. Compared with existing technologies, this method provides a more comprehensive understanding of the magnetic properties of the sample and improves measurement stability.

[0071] like Figure 4 As shown, the method for measuring the resonant frequency and quality factor of a cantilever beam according to the present invention generally includes three steps: a cantilever beam driving step S401, wherein the cantilever beam is driven to vibrate at a relatively large amplitude, and the cantilever beam driving is stopped after a period of time; a free decay signal acquisition step S402, wherein the free decay vibration signal at the free end of the cantilever beam is acquired; and a data processing step S403, wherein the acquired free decay vibration signal is processed to obtain the resonant frequency and quality factor of the cantilever beam.

[0072] (Step S401)

[0073] Specifically, in the cantilever beam driving step S401, a driving signal of a predetermined frequency (first frequency) is output to the driving unit 202 based on a predetermined trigger signal from, for example, a signal generator in the calculation control system 207, causing the driving unit 202 (i.e., piezoelectric ceramic) to vibrate, thereby driving the cantilever beam 201 to vibrate.

[0074] The driving signal can be, for example, but not limited to, a voltage signal, and it must satisfy the condition that it enables the cantilever beam 201 to vibrate with a large amplitude to facilitate subsequent measurements. Therefore, the frequency of the driving signal is preferably near the current resonant frequency f0 of the cantilever beam, for example, within the resonant bandwidth Δf.

[0075] Therefore, for example, if the current magnetic field is the first applied magnetic field described in step S302 above, since there is no information about the resonant frequency of the cantilever beam at this time, in the cantilever beam driving step S401, it is preferable to roughly sweep the frequency spectrum of the cantilever beam to determine the approximate location of its current resonant frequency before formally driving the cantilever beam. The result of the frequency sweep depends on the resolution of the frequency sweep, etc., and is a relatively coarse result. In this specification, the frequency at this approximate location is referred to as the "sweep resonant frequency".

[0076] Next, by using the sweep frequency resonance frequency as the frequency of the driving signal during formal driving, the cantilever beam can be easily driven and made to vibrate with a large amplitude.

[0077] Then, after a certain period of vibration (ensuring the cantilever beam has vibrated), the output drive signal is stopped.

[0078] (Step S402)

[0079] In the free decay signal acquisition step S402, in response to the cessation of the driving signal, the free decay vibration signal of the cantilever beam when it is no longer driven and undergoes free decay vibration is acquired.

[0080] After the output stops, the drive signal immediately decreases to zero, and the drive unit 202 (piezoelectric ceramic) stops vibrating. However, the vibration of the cantilever beam 201 does not stop immediately, but undergoes free decay vibration, gradually decaying to zero. The vibration frequency during the decay process is the resonant frequency f0 of the cantilever beam 201 under the current magnetic field, while the curve of vibration amplitude decaying with time is related to the quality factor Q.

[0081] After the output drive signal is stopped, the signal obtained by the acquisition unit 206 from the interference light output by the interference optical system 203 detected by the detection unit 205 is then acquired; that is, the acquired free decay vibration signal is acquired and awaits further processing in the calculation control system 207. Here, the acquired signal is a signal of a certain duration, preferably acquired from the start of stopping the output drive signal until the cantilever beam 201 stops vibrating. Of course, the signal can also be continuously acquired without interruption, and the calculation control system 207 can select a signal of an appropriate duration (e.g., a certain period after the drive stops) that can characterize the decay process of the cantilever beam 201 as the free decay vibration signal.

[0082] Furthermore, in step S401, the drive signal can be repeatedly output and stopped. That is, the drive signal is first output to make the cantilever beam vibrate, then the output is stopped, and after the cantilever beam stops vibrating, the drive signal is output again, thereby repeatedly causing the cantilever beam to undergo free decaying vibration. In this case, step S402 can obtain free decaying vibration signals of multiple cycles.

[0083] (Step S403)

[0084] Then, the free decay vibration signal acquired in step S402 is processed in the calculation control system 207 to obtain the resonant frequency f0 and quality factor Q of the cantilever beam.

[0085] In detail, since the vibration frequency during the free decay vibration of the cantilever beam is the resonance frequency f0 of the cantilever beam under the current magnetic field, the position of the peak in the spectrum when the free decay vibration signal is Fourier transformed can be regarded as the resonance frequency f0.

[0086] That is, the resonance frequency f0 can be obtained by performing a Fourier transform on the free decay vibration signal.

[0087] However, for higher accuracy, when determining the resonant frequency position in the spectrum obtained from the Fourier transform, the Lorentz curve can be further fitted to the spectrum curve, as shown in formula (1). The fitted x value is the more accurate resonant frequency f0.

[0088]

[0089] In the formula, a, b, and c are fitting parameters, and y(f) represents the change of the amplitude of the resonance peak with frequency in the frequency domain.

[0090] Furthermore, the outer envelope of the free decaying vibration signal and the quality factor Q have the relationship shown in Equation (2).

[0091]

[0092] In the formula, U(t) is the amount by which the amplitude of the cantilever beam decays with time, U0 is the initial value at the start of decay, and ω is the vibration frequency that is a constant, which is the resonant frequency f0 obtained above.

[0093] The quality factor Q reflects the rate of signal decay, and its value can be obtained by fitting Equation 2. The envelope of a free decaying vibration signal can be obtained by taking the signal as positive and calculating the average smooth curve.

[0094] In addition, if the drive signal is repeatedly output and stopped in step S401 and multiple cycles of free decay vibration signal are obtained in step S402, the above processing is performed after averaging the multiple free decay vibration signals in step S403.

[0095] Therefore, through the above steps S401 to S403, the resonant frequency f0 and quality factor Q of the cantilever beam under the current magnetic field are obtained simultaneously in one go.

[0096] The above describes the procedure for measuring the resonant frequency f0 and quality factor Q of a cantilever beam when the current magnetic field is the first applied magnetic field B1.

[0097] The current magnetic field is the i-th applied magnetic field B. i In the case of the previous magnetic field B, i-1 The resonant frequency f0 at that time has already been measured, so as a preferred approach, the previous magnetic field B can be used in step S401. i-1 The measured resonant frequency f0 is used for driving. Magnetic field B i-1 and B i The resonant frequencies of the cantilever beams are different under different conditions; however, in order to obtain an accurate magnetic property curve of the sample, the magnetic field B... i-1 and B i The difference is small, therefore the resonant frequencies under the two magnetic fields are quite similar, i.e., using magnetic field B... i-1 By using the measured resonant frequency for driving, the cantilever beam can vibrate significantly with a very low driving voltage, achieving a good driving effect.

[0098] Of course, the above is only a preferred method. Alternatively, the frequency sweep resonant frequency can be obtained by frequency sweeping in the same way as in magnetic field B1, which is also included in the scope of this invention.

[0099] According to the method for measuring the resonant frequency and quality factor of the cantilever beam of the present invention, since it is only necessary to measure the free decay vibration signal of the cantilever beam and obtain the two parameters of resonant frequency and quality factor through simple fitting calculation, it has the advantages of simple operation and low hardware and software cost. In addition, in addition to obtaining the resonant frequency, the quality factor is also obtained at the same time, which can more comprehensively reflect the magnetic properties of the sample.

[0100] Furthermore, unlike the measurement of resonant frequency based on phase-locked loop (PLL) technology, the measurement method of this invention does not require feedback control to lock the phase and amplitude of the cantilever beam vibration. It is well known that cantilever beams are highly sensitive to vibration; external floor vibrations, sound vibrations, and even vibrations from sources such as the magnets in the refrigerator can all cause unnecessary vibrations in the cantilever beam. When such interference affects signal stability, the PLL's locking mechanism is prone to failure. However, the measurement method of this invention can operate stably without forced interruptions to the measurement.

[0101] [Measuring device for resonant frequency and quality factor of cantilever beam]

[0102] Next, the measuring device for the resonant frequency and quality factor of the cantilever beam of the present invention will be described.

[0103] As described above, the measurement method of the present invention can be said to be applied to the calculation control system 207 of the cantilever beam force measuring device 200. Therefore, the calculation control system 207 that applies this measurement method essentially constitutes the measurement device of the present invention.

[0104] Figure 5 This is a block diagram illustrating the modular structure of the measuring device 500 for measuring the resonant frequency and quality factor of the cantilever beam according to the present invention.

[0105] like Figure 5 As shown, the measuring device 500 includes a drive signal output unit 501, a control unit 502, and a free attenuation signal acquisition unit 503.

[0106] The control unit 502 controls the drive signal output unit 501 and the free decay signal acquisition unit 503, and acquires signals from the free decay signal acquisition unit 503 for calculation. In addition, it can output the calculation results to an external user, and can also receive user settings and parameters from the user.

[0107] Specifically, the drive signal output unit 501 is connected to the drive unit 202 and outputs a drive signal to the drive unit 202 under the control of the control unit 502, driving the cantilever beam to vibrate at a relatively large amplitude. After a period of time, the drive signal output from the drive signal output unit 501 stops. In response to the cessation of drive signal output, the free decay signal acquisition unit 503, under the control of the control unit 502, acquires the free decay vibration signal of the free end of the cantilever beam from the acquisition unit 206 and outputs it to the control unit 502. The control unit 502 processes the free decay vibration signal obtained from the free decay signal acquisition unit 503 to obtain the resonant frequency and quality factor of the cantilever beam.

[0108] The processing details performed in the drive signal output unit 501, the free attenuation signal acquisition unit 503, and the control unit 502 are essentially the same as the steps S401 to S403 described above, and will not be repeated here.

[0109] in addition, Figure 5 The measuring device 500 of the present invention is represented in the form of a hardware module, but this is only a module derived from the function of the measuring device. It can be implemented by a combination of hardware circuits or by a software program stored in a computer-readable medium, as long as it can execute the aforementioned measuring method under the operation of a processor.

[0110] The following describes an example.

[0111] Example 1

[0112] In this embodiment 1, the displacement of the cantilever beam is measured using fiber optic interferometric ranging, that is, the above-mentioned Figure 2The interference optical system 203 includes an optical fiber coupler, an optical fiber, a lens, etc., which leads the laser from the laser source 204 through the optical fiber to the free end of the cantilever beam and couples the reflected light back into the optical fiber.

[0113] The data acquisition unit 206 uses a National Instruments NI-6221 data acquisition card. In the computational control system 207, data processing is performed through a LabVIEW program, and the drive signal source uses an Agilent 33500B waveform generator.

[0114] This embodiment uses a triggering method to generate drive signals and acquire data. The triggering sequence is as follows: Figure 6 As shown, the output of the 33500B waveform generator is set to trigger the output on the rising edge of the square wave, and the NI-6221 acquisition signal is set to acquire data on the falling edge of the square wave. The square wave used for triggering and acquisition is provided by the output of the NI-6221.

[0115] Figure 7 This indicates that a data processing program written in LabVIEW is used, corresponding to step S403 above. The acquired free decay vibration signal is processed in parallel through two paths. In the upper path, the signal is subjected to Fourier transform and then fitted using the Lorentz curve formula (1) to obtain the magnitude of the resonance frequency f0, which is then output to the lower path. In the lower path, the signal is positively charged, and then the points within 5 periods are averaged to obtain the decay envelope. Then, the resonance frequency f0 output from the upper path is used together with the signal to fit using formula (2) to obtain the magnitude of the quality factor Q.

[0116] Figure 8 This represents the free decay vibration signal of the cantilever beam actually collected under a specific magnetic field in Example 1. After data processing, the resonant frequency was found to be 3974.56 Hz and the quality factor was 7582.97.

[0117] Example 2

[0118] Using the apparatus of Example 1, the magnetization of a MnSi magnetic sample was measured, and the characteristics of the resonant frequency and quality factor of the cantilever beam as a function of the magnetic field were obtained.

[0119] like Figure 9 and 10 As shown, the changes in resonant frequency and quality factor both reflect the magnetization characteristics of the magnetic sample. With the increase of the external magnetic field, the changes in resonant frequency and quality factor both reflect the corresponding magnetization states of the MnSi sample, while the changes in magnetization state corresponding to the quality factor are more refined and obvious.

[0120] Specifically, with increasing magnetic field, MnSi exhibits helical, conical, and ferromagnetic magnetization states. Among these, the conical state includes the Skyrming state, and according to measurements, the conical state causes significantly higher losses in the cantilever beam compared to other magnetization states, resulting in a lower Q-value for the cantilever beam. Figure 10 In the cantilever beam, MnSi is in a helical state when the magnetic field is zero. As the magnetic field increases, it transforms into a cone shape, and the Q value decreases significantly. When a Skyrming state appears in the cone shape, the Q value increases. When the Skyrming state disappears, it returns to a cone shape, and the Q value decreases again. Finally, as the magnetic field becomes sufficiently strong, it enters a ferromagnetic state, and the Q value increases. Therefore, based on the changes in the quality factor of the cantilever beam, the magnetic properties of the sample can be analyzed and understood in greater detail.

[0121] Therefore, by employing the method for measuring the resonance frequency and quality factor of the present invention, the resonance frequency of a cantilever beam can be measured simply and stably, and the quality factor can be measured simultaneously, enabling a more comprehensive and detailed understanding of the magnetic properties of the sample.

[0122] The various embodiments and examples of the present invention have been briefly described above. It should be understood that the present invention is not limited to the above description and various variations are possible.

[0123] Industrial applicability

[0124] This invention can be applied to cantilever beam force measuring devices for measuring the magnetic properties of samples, and is especially suitable for measuring the magnetic properties of samples in dynamic working mode.

Claims

1. A method for measuring the resonance frequency and the quality factor of a cantilever, in a cantilever force measuring device in a dynamic mode of operation, for measuring the resonance frequency and the quality factor of a cantilever on which a sample is placed under the current magnetic field applied, in real time and simultaneously, characterized in that, include: The cantilever beam driving step involves driving the cantilever beam to vibrate using a driving signal of a first frequency, and then stopping the driving signal. The free decay signal acquisition step, wherein in response to the cessation of the drive signal, a free decay vibration signal at the free end of the cantilever beam is acquired; and The data processing steps include processing the acquired free decay vibration signal to obtain the resonant frequency and quality factor of the cantilever beam. In the data processing step, the resonant frequency is obtained by calculating the peak position after performing a Fourier transform on the free decaying vibration signal. Furthermore, the quality factor is obtained by taking the outer envelope of the free decaying vibration signal and fitting the outer envelope. The cantilever beam force measuring device sequentially applies multiple different magnetic fields to determine the resonant frequency and quality factor of the cantilever beam under each magnetic field. When the current magnetic field is the first applied magnetic field, in the cantilever beam driving step, the frequency spectrum of the cantilever beam is first swept to obtain the swept resonant frequency, and the swept resonant frequency is used as the first frequency. If the current magnetic field is not the first applied magnetic field, in the cantilever beam driving step, the resonant frequency obtained in the data processing step under the previously applied magnetic field is used as the first frequency.

2. The method for measuring the resonant frequency and quality factor of a cantilever beam as described in claim 1, characterized in that: In the data processing step, the free decaying vibration signal is subjected to a Fourier transform, and the resulting spectrum curve is fitted using the Lorentz curve shape according to the following formula. The fitted x-value is used as the resonance frequency. In the formula, a, b, and c are fitting parameters, and y(f) represents the change in amplitude of the resonance peak of the spectral curve with frequency.

3. The method for measuring the resonant frequency and quality factor of a cantilever beam as described in claim 2, characterized in that: In the data processing step, the outer envelope is fitted using the following formula, and the Q value obtained from the fitting is used as the quality factor. In the formula, U(t) is the amount by which the amplitude of the cantilever beam decays with time, U0 is the initial value at the start of decay, and ω is the obtained resonance frequency.

4. The method for measuring the resonant frequency and quality factor of a cantilever beam as described in claim 1, characterized in that: In the cantilever beam driving step, after the cantilever beam stops vibrating after a period of time following the stopping of the driving signal, the cantilever beam is driven again using the first frequency driving signal, thereby causing the cantilever beam to be driven and stopped repeatedly. In the step of acquiring the free decay signal, multiple free decay vibration signals are acquired. In the data processing step, the average of the multiple free decay vibration signals is taken and then further processed.

5. The method for measuring the resonant frequency and quality factor of a cantilever beam as described in claim 1, characterized in that: The outer envelope is obtained by taking a positive value for the free decay vibration signal and calculating the average smooth curve.

6. A cantilever resonance frequency and quality factor measuring device, which is provided in a cantilever force measuring device in a dynamic operation mode, measures the resonance frequency and quality factor of a cantilever on which a sample is placed under a current magnetic field applied in real time and simultaneously, characterized in that, include: The drive signal output unit outputs a drive signal of a first frequency to the drive unit of the cantilever beam force measuring device to drive the cantilever beam to vibrate, and then stops outputting the drive signal. The free decay signal acquisition unit acquires the free decay vibration signal of the free end of the cantilever beam in response to the cessation of the drive signal. and The control unit processes the free decay vibration signal acquired by the free decay signal acquisition unit to obtain the resonant frequency and quality factor of the cantilever beam. Specifically, the control unit obtains the resonant frequency by performing a Fourier transform on the free-decaying vibration signal and determining the peak position; and it obtains the quality factor by taking the outer envelope of the free-decaying vibration signal and fitting the outer envelope. The cantilever beam force measuring device sequentially applies multiple different magnetic fields to determine the resonant frequency and quality factor of the cantilever beam under each magnetic field. When the current magnetic field is the first applied magnetic field, the frequency spectrum of the cantilever beam is first swept to obtain the swept resonant frequency. The drive signal output unit uses the swept resonant frequency as the first frequency. If the current magnetic field is not the first applied magnetic field, the drive signal output unit uses the resonant frequency obtained by the control unit under the previously applied magnetic field as the first frequency.

7. The measuring device for the resonant frequency and quality factor of a cantilever beam as described in claim 6, characterized in that: The control unit performs a Fourier transform on the free decaying vibration signal and fits the resulting spectrum curve using the Lorentz curve shape as shown in the following formula. The fitted x-value is then used as the obtained resonance frequency. In the formula, a, b, and c are fitting parameters, and y(f) represents the change of the amplitude of the resonance peak with frequency in the frequency domain.

8. The measuring device for the resonant frequency and quality factor of a cantilever beam as described in claim 7, characterized in that: The control unit fits the outer envelope using the following formula, and uses the Q value obtained from the fitting as the calculated quality factor. In the formula, U(t) is the amount by which the amplitude of the cantilever beam decays with time, U0 is the initial value at the start of decay, and ω is the obtained resonance frequency.

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