Quantitative magnetic force microscopy on perpendicularly magnetized samples

Abstract

We present a transfer-function approach to calculate the force on a magnetic force microscope tip and the stray field due to a perpendicularly magnetized medium having an arbitrary magnetization pattern. Under certain conditions, it is possible to calculate the magnetization pattern from the measured force data. We apply this transfer function theory to quantitatively simulate magnetic force microscopy data acquired on a CoNi/Pt multilayer and on an epitaxially grown Cu/Ni/Cu/Si͑001͒ magnetic thin film. The method described here serves as an excellent basis for ͑i͒ the definition of the condition for achieving maximum resolution in a specific experiment, ͑ii͒ the differences of force and force z-derivative imaging, ͑iii͒ the artificial distinction between domain and domain wall contrast, and finally ͑iv͒ the influence of various tip shapes on image content.

Quantitative assessment of pinning forces and magnetic penetration depth in NbN thin films from complementary magnetic force microscopy and transport measurements

“…2) can be well approximated to the first order by a magnetic monopole characterized by a "magnetic charge" m located at a distance δ from the sharp end of the tip pyramid. 17 The field distribution from a single flux quantum, φ 0 = 2.07 × 10 −15 T m 2 , measured just above the surface of the superconductor, is also similar to the magnetic field emanated by a magnetic monopole of 2φ 0 , located at the depth λ eff = 1.27λ below the surface, 18 with λ being the magnetic penetration depth. Hence, the magnetic induction of the vortex, B(r, z), taken at a distance z above the surface, can be approximated by…”

“…Taking into account that the shift of the resonance frequency of the cantilever measured by MFM, ∆ f, is proportional to the z-derivative of the normal component of the force that acts between the tip and the sample, 17,19 ∂ z F z (r, z), one obtains the following expression for the measured signal:…”

High resolution magnetic force microscopy of patterned L10-FePt dot arrays by nanosphere lithography

“…By operating a dynamical MFM in the constant height mode, we can achieve high resolution using an ultrasharp tip that does not need to touch the sample surface. The frequency shift measured is commonly assumed to be proportional to the force derivative [11], and can be more easily compared to theoretical simulation. We have shown that the L1 0 -FePt dots contain clearly resolved magnetic fine structures.…”

High resolution MFM: simulation of tip sharpening

“…3(b) do not change due to the character of MFM tip's transfer function [9], [10]. In the spatial frequency domain, the change of is equivalent to multiplying the term of , where is the changed value of [9], [11].…”