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Nanomechanical torque magnetometry of permalloy cantilevers
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View: Figures


Image of FIG. 1.
FIG. 1.

(a) Magnetic actuation schematic of a magnetic nanocantilever. The magnetization along the cantilever, , is mediated by the external field while the sinusoidal torquing field, , drives the flexural torque. For the simple case of magnetization reversal, a straight domain wall propagates across the cantilever, represented by the black line perpendicular to the length. A twisting torque, , is induced if a component of magnetization is oriented perpendicular to the cantilever length. (b) First vibrational mode shape calculated using the magnetic actuation model. The dotted line represents the equilibrium position. (c) Calculated deflection profile for the first vibrational mode at the free end of the cantilever as the straight domain wall was swept across the cantilever to switch the magnetization from to .

Image of FIG. 2.
FIG. 2.

Instrumentation for optical interferometric detection and magnetic actuation scheme (, splitter, lens). The bias magnet is rotatable and situated on an automated translation rail. A “dither” coil provides the ac magnetic field transverse to the direction of magnetization and the resulting mechanical torque is detected interferometrically. The devices are driven at the cantilever flexural resonance frequency, referenced to a lock-in amplifier. A SEM image of a long, 300 nm wide cantilever is shown in the inset. The scale bar represents 500 nm.

Image of FIG. 3.
FIG. 3.

Fundamental resonance frequencies of the set of permalloy cantilevers. The solid line is a linear least-squares fit to the data (solid circles) and the dashed line is the expectation based on the ideal design geometry and using the mechanical parameters (Young’s modulus, density) of bulk nickel. A frequency spectrum for a long cantilever is shown in the inset, fitted to a Lorentzian lineshape. The quality factor of 880 was extracted from the fit.

Image of FIG. 4.
FIG. 4.

Spatial imaging on the resonance frequency of a cantilever (a) Raster scanned image of the reflected optical intensity (scale ). [(b) and (c)] In-phase lock-in signals acquired at −12 kA/m and , respectively. The color bar scale is in arbitrary units.

Image of FIG. 5.
FIG. 5.

Lock-in (a) magnitude and (b) phase signals acquired during the magnetization sweep of a long cantilever while driven at its resonance frequency. The symbols represent each quarter of the hysteresis loop (in order: square, star, triangle, and circle). (c) Amplitude through the combination of the phase and magnitude signals

Image of FIG. 6.
FIG. 6.

Mechanical transformation of the LLG micromagnetics simulation representing the final quarter of a cantilever hysteresis loop. The magnetization was equilibrated at a high positive field with free boundary conditions on five of the cantilever faces and an artificially pinned boundary in the direction on the face at the base of the cantilever . The field was then swept down to negative field. At −400 A/m, the magnetization at the base of the cantilever was reversed while the sweep continued in steps of −400 A/m. The deflection profile was calculated using Eq. (1). In the inset are selected spatial distributions of the -components of magnetization during the loop. The color bar represents the normalized .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nanomechanical torque magnetometry of permalloy cantilevers