Quantitative Magnetic Force Microscopy Research Articles

Numerical Characterization of Magnetic Vortex Probe Imaging for Magnetic Force Microscopy

We study theoretically the performance and limitations of the magnetic vortex probe for magnetic force microscopy (MFM). In the ideal case, the only magnetically active part of the probe is the magnetic vortex core (VC) existing in the center of a Permalloy (Py) disk located at the apex of a non-magnetic tip. Such VC can be effectively characterized as a point dipole with the magnetic moment of the order of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-17</sup> Am <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> embedded about 20 nm inside the disk, which is similar to the commercial low-momentum MFM probes. In addition to the standard probes, the ideal VC probe offers high durability and a well-controlled magnetic moment suitable for quantitative MFM. However, since the VC probe is made of magnetically soft material its magnetization profile and the resulting MFM image can be deformed by the stray field of the sample. Therefore, the VC probe is suited for imaging the samples with small domain sizes which generate low stray fields. We numerically examine VC imaging of typical magnetic samples, i.e. domain arranged as a single circular dot, stripe patterns, and the chessboard. We determine the limiting dimensions of the domains that can be correctly imaged by the VC tip of optimal parameters. In general, we can conclude that MFM imaging by VC probes gives reasonable results for the samples with domains with lateral dimensions up to 100 nm.

Simultaneous magnetic field and field gradient mapping of hexagonal MnNiGa by quantitative magnetic force microscopy

Magnetic force microscopy (MFM) is a scanning microscopy technique that is commonly employed to probe the sample’s magnetostatic stray fields via their interaction with a magnetic probe tip. In this work, a quantitative, single-pass MFM technique is presented that maps one magnetic stray-field component and its spatial derivative at the same time. This technique uses a special cantilever design and a special high-aspect-ratio magnetic interaction tip that approximates a monopole-like moment. Experimental details, such as the control scheme, the sensor design, which enables simultaneous force and force gradient measurements, as well as the potential and limits of the monopole description of the tip moment are thoroughly discussed. To demonstrate the merit of this technique for studying complex magnetic samples it is applied to the examination of polycrystalline MnNiGa bulk samples. In these experiments, the focus lies on mapping and analyzing the stray-field distribution of individual bubble-like magnetization patterns in a centrosymmetric [001] MnNiGa phase. The experimental data is compared to calculated and simulated stray-field distributions of 3D magnetization textures, and, furthermore, bubble dimensions including diameters are evaluated. The results indicate that the magnetic bubbles have a significant spatial extent in depth and a buried bubble top base.

Size-Specific Magnetic Configurations in Electrodeposited Epitaxial Iron Nanocuboids: From Landau Pattern to Vortex and Single Domain States.

As the size of magnetic devices continuously decreases, the creation of three-dimensional nanomagnets and the understanding of their magnetic configurations become increasingly important for modern applications. Here, by progressive nucleation during epitaxial nanoelectrodeposition, we synthesize single-crystal iron nanocuboids with sizes ranging 10 to 200 nm on one sample. The size-dependent magnetic configurations of these nanocuboids are studied by quantitative magnetic force microscopy and electron holography. In conjunction, a "magnetic configuration versus size" phase diagram is established via micromagnetic simulations. Both experiment and theory reveal a sequential transition from Landau pattern to vortex and finally single domain when decreasing the sizes of the nanocuboids. The combinatorial-like approach leads to a quantitative understanding of the magnetic configurations of the nanomagnets in a broad size range. It can be transferred to other materials and shapes and thereby presents an advanced route to enrich the material library for future nanodevice design.

Uncertainty Propagation in Quantitative Magnetic Force Microscopy Using a Monte-Carlo Method

A Monte-Carlo (MC)-type method is utilized for the propagation of uncertainties in quantitative magnetic force microscopy (qMFM). In qMFM, quantitative magnetic field distributions are inferred from magnetic force microscopy (MFM) raw data using a calibration of the instrument point spread function and a subsequent inversion process. The two stages of calibration and measurement may be subject to a variety of uncertainties that naturally arise in practice. Identifying these sources of uncertainties and quantifying their impact on the reconstruction of the measurand is crucial for reliable quantitative studies of nanomagnetic materials and devices. So far, the propagation of variance method has been applied to determine the uncertainty budget for a complete calibration and measurement process. In this work, we are able to improve the uncertainty description in terms of structure and magnitude by application of an MC method. We demonstrate the importance of correlations and show possible side effects of model linearizations.

Fields From a Magnetized Conical Shell and Quantitative Magnetic Force Microscopy

Fields From a Magnetized Conical Shell and Quantitative Magnetic Force Microscopy

A Ti/Pt/Co Multilayer Stack for Transfer Function Based Magnetic Force Microscopy Calibrations

Magnetic force microscopy (MFM) is a widespread technique for imaging magnetic structures with a resolution of some 10 nanometers. MFM can be calibrated to obtain quantitative (qMFM) spatially resolved magnetization data in units of A/m by determining the calibrated point spread function of the instrument, its instrument calibration function (ICF), from a measurement of a well-known reference sample. Beyond quantifying the MFM data, a deconvolution of the MFM image data with the ICF also corrects the smearing caused by the finite width of the MFM tip stray field distribution. However, the quality of the calibration depends critically on the calculability of the magnetization distribution of the reference sample. Here, we discuss a Ti/Pt/Co multilayer stack that shows a stripe domain pattern as a suitable reference material. A precise control of the fabrication process, combined with a characterization of the sample micromagnetic parameters, allows reliable calculation of the sample’s magnetic stray field, proven by a very good agreement between micromagnetic simulations and qMFM measurements. A calibrated qMFM measurement using the Ti/Pt/Co stack as a reference sample is shown and validated, and the application area for quantitative MFM measurements calibrated with the Ti/Pt/Co stack is discussed.

Comparison and Validation of Different Magnetic Force Microscopy Calibration Schemes.

The future of consumer electronics depends on the capability to reliably fabricate nanostructures with given physical properties. Therefore, techniques to characterize materials and devices with nanoscale resolution are crucial. Among these is magnetic force microscopy (MFM), which transduces the magnetic force between the sample and a magnetic oscillating probe into a phase shift, enabling the locally resolved study of magnetic field patterns down to 10 nm. Here, the progress done toward making quantitative MFM a common tool in nanocharacterization laboratories is shown. The reliability and ease of use of the calibration method based on a magnetic reference sample, with a calculable stray field, and a deconvolution algorithm is demonstrated. This is achieved by comparing two calibration approaches combined with numerical modeling as a quantitative link: measuring the probe's effect on the voltage signal when scanning above a nanosized graphene Hall sensor, and recording the MFM phase shift signal when the probe scans across magnetic fields produced by metallic microcoils. Furthermore, in the case of the deconvolution algorithm, it is shown how it can be applied using the open-source software package Gwyddion. The estimated magnetic dipole approximation for the most common probes currently in the market is also reported.

Uncertainty Analysis of Stray Field Measurements by Quantitative Magnetic Force Microscopy

Magnetic force microscopy (MFM) measurements generally provide phase images which represent the signature of domain structures on the surface of nanomaterials. To quantitatively determine magnetic stray fields based on an MFM image requires calibrated properties of the magnetic tip. In this work, an approach is presented for calibrating a magnetic tip using a Co/Pt multilayered film as a reference sample which shows stable well-known magnetic properties and well-defined perpendicular band domains. The approach is based on a regularized deconvolution process in Fourier domain with a Wiener filter and the L-curve method for determining a suitable regularization parameter to get a physically reasonable result. The calibrated tip is applied for a traceable quantitative determination of the stray fields of a test sample which has a patial frequency spectrum covered by that of the reference sample. According to the "Guide to the expression of uncertainty in measurement", uncertainties of the processing algorithm are estimated considering the fact that the regularization influences significantly the quantitative analysis. We discuss relevant uncertainty components and their propagations between real domain and Fourier domain for both, the tip calibration procedure and the stray field calculation, and propose an uncertainty evaluation procedure for quantitative magnetic force microscopy.

Quantitative magnetic force microscopy using calibration on superconducting flux quanta

We present a new procedure that takes advantage of the magnetic flux quantization of superconducting vortices to calibrate the magnetic properties of tips for magnetic force microscopy (MFM). Indeed, a superconducting vortex, whose quantized flux is dependent upon Plank constant, speed of light and electron charge, behaves as a very well defined magnetic reference object. The proposed calibration procedure has been tested on new and worn tips and shows that the monopole point-like approximation of the probe is a reliable model. This procedure has been then applied to perform quantitative MFM experiments on a soft ferromagnetic thin film of permalloy, leading to the determination of the local out-of-plane component of the canted magnetization, together with its spatial variations across a few μm2 scan area.

Frontiers of magnetic force microscopy

Since it was first demonstrated in 1987, magnetic force microscopy (MFM) has become a truly widespread and commonly used characterization technique that has been applied to a variety of research and industrial applications. Some of the main advantages of the method includes its high spatial resolution (typically ∼50 nm), ability to work in variable temperature and applied magnetic fields, versatility, and simplicity in operation, all without almost any need for sample preparation. However, for most commercial systems, the technique has historically provided only qualitative information, and the number of available modes was typically limited, thus not reflecting the experimental demands. Additionally, the range of samples under study was largely restricted to “classic” ferromagnetic samples (typically, thin films or patterned nanostructures). Throughout this Perspective article, the recent progress and development of MFM is described, followed by a summary of the current state-of-the-art techniques and objects for study. Finally, the future of this fascinating field is discussed in the context of emerging instrumental and material developments. Aspects including quantitative MFM, the accurate interpretation of the MFM images, new instrumentation, probe-engineering alternatives, and applications of MFM to new (often interdisciplinary) areas of the materials science, physics, and biology will be discussed. We first describe the physical principles of MFM, specifically paying attention to common artifacts frequently occurring in MFM measurements; then, we present a comprehensive review of the recent developments in the MFM modes, instrumentation, and the main application areas; finally, the importance of the technique is speculated upon for emerging or anticipated to emerge fields including skyrmions, 2D-materials, and topological insulators.

Magnetic charge distribution and stray field landscape of asymmetric néel walls in a magnetically patterned exchange bias layer system

The 3D stray field landscape above an exchange bias layer system with engineered domain walls has been fully characterized by quantitative magnetic force microscopy (qMFM) measurements. This method is based on a complete quantification of the MFM tip’s imaging properties and the subtraction of its contribution from the measured MFM data by deconvolution in Fourier space. The magnetically patterned Ir17Mn83/Co70Fe30-exchange-bias-multilayers have been designed to contain asymmetric head-to-head (hh)/tail-to-tail (tt) Néel walls between domains of different magnetic anisotropies for potential use in guided particle transport. In the current application, qMFM reveals the effective magnetic charge profile on the surface of the sample—with high spatial resolution and in an absolute quantitative manner. These data enable to calculate the magnetostatic potential and the full stray field landscape above the sample surface. It has been successfully tested against: (i) micromagnetic simulations of the magnetization structure of a comparable exchange-bias layer system, (ii) measurements of the magnetization profile across the domain boundary with x-ray photoemission electron microscopy, and (iii) direct stray field measurements obtained by scanning Hall probe microscopy at elevated scan heights. This approach results in a quantitative determination of the stray field landscape at close distances to the sample surface, which will be of importance for remote magnetic particle transport applications in lab-on-a-chip devices. Furthermore, the highly resolving and quantitative MFM approach reveals details of the domain transition across the artificially structured phase boundary, which have to be attributed to a continuous change in the materials parameters across this boundary, rather than an abrupt one.

Magnetic vortex observation in FeCo nanowires by quantitative magnetic force microscopy

An approach is presented that allows quantifying the three dimensional magnetization pattern of a magnetic nanoobject from measured two dimensional Magnetic Force Microscopy (MFM) data. This is based on a MFM deconvolution approach, which quantitatively determines the effective surface charges, on a micromagnetic calculation of the total magnetic charges at and below the sample surface, and on a projection of the lower lying charges onto the sample surface for a comparison of the such obtained effective surface charges with the experimentally determined ones. Thus, by making use of the depth sensitivity of MFM and by applying a quantitative contrast analysis, we are able to reconstruct the inhomogeneous magnetization state at the end of individual cylindrical Fe52Co48 nanowires arranged in a triangular array. As a result, we prove the existence of a magnetic vortex state at their ends.

Single core–shell nanoparticle probes for non-invasive magnetic force microscopy

We present an easy, fast and reliable method for the preparation of magnetic force microscopy (MFM) probes based on single Co nanoparticles (NPs). Due to their dipolar character, these magnetic probes open up a new approach for quantitative and non-invasive MFM measurements on the nanometer length scale. To guarantee long-term stability of these tips under ambient conditions, an ultrathin protecting Au shell was grown around the Co NPs through photochemical deposition. Single magnetic particles were firmly attached to standard silicon AFM tips using bifunctional self-assembling molecules. Such probes were tested on longitudinal magnetic recording media and compared to the results as recorded with conventional thin-film MFM tips. Easy data interpretation of the magnetic nanoparticle probes in a point dipole model is shown. Our nanoparticle tips provide excellent endurance for MFM recording, enable non-invasive probing while maintaining a high sensitivity, resolution, and reproducibility.

Surface‐Confined Molecular Coolers for Cryogenics

An excellent molecule-based cryogenic magnetic refrigerant, gadolinium acetate tetrahydrate, is here used to decorate selected portions of silicon substrate. By quantitative magnetic force microscopy for a variable applied magnetic field near liquid-helium temperature, the molecules are demonstrated to hold their magnetic properties intact, and therefore their cooling functionality, after their deposition. These results represent a step forward towards the realization of a molecule-based micro-refrigerating device at very low temperatures.

Performing quantitative MFM measurements on soft magnetic nanostructures

We have extended our previous work (Rawlings et al 2010 Phys. Rev. B 82 085404) on simulating magnetic force microscopy (MFM) images for magnetically soft samples to include an accurate representation of coated MFM tips. We used an array of square 500 nm nanomagnets to evaluate our improved MFM model. A quantitative comparison between model and experiment was performed for lift heights ranging from 20 to 100 nm. No fitting parameters were used in our comparison. For all lift heights the qualitative agreement between model and experiment was significantly improved. At low lift heights, where the magnetic signal was strong, the difference between theory and experiment was less than 30%.

Towards quantitative magnetic force microscopy: theory and experiment

We introduce a simple and effective model of a commercial magnetic thin-film sensor for magnetic force microscopy (MFM), and we test the model employing buried magnetic dipoles. The model can be solved analytically in the half-space in front of the sensor tip, leading to a simple 1/R dependence of the magnetic stray field projected to the symmetry axis. The model resolves the earlier issue as to why the magnetic sensors cannot be described reasonably by a restricted multipole expansion as in the point pole approximation: the point pole model must be extended to incorporate a ‘lower-order’ pole, which we term ‘pseudo-pole’. The near-field dependence (∝R−1) turns into the well-known and frequently used dipole behavior (∝R−3) if the separation, R, exceeds the height of the sensor. Using magnetic nanoparticles (average diameter 18 nm) embedded in a SiO cover as dipolar point probes, we show that the force gradient–distance curves and magnetic images fit almost perfectly to the proposed model. The easy axis of magnetization of single nanoparticles is successfully deduced from these magnetic images. Our model paves the way for quantitative MFM, at least if the sensor and the sample are independent.

Monopolelike probes for quantitative magnetic force microscopy: Calibration and application

A local magnetization measurement was performed by magnetic force microscopy (MFM) to determine magnetization in domains of an exchange coupled [Co/Pt]/Co/Ru multilayer with predominant perpendicular anisotropy. The quantitative MFM measurements were conducted with an iron-filled carbon nanotube tip, which is shown to behave like a monopole. As a result we determined an additional in-plane magnetization component of the multilayer, which is explained by estimating the effective permeability of the sample within the μ∗-method.

Exchange Bias and Domain Evolution at 10 nm Scales

For a fixed 2 μm×2 μm area of a Co/Pt-CoO perpendicular exchange bias system we image the ferromagnetic (FM) domains for various applied fields with 10-nm resolution by magnetic force microscopy (MFM). Using quantitative MFM we measure the local areal density of pinned uncompensated spins (pinUCS) in the antiferromagnetic (AFM) CoO layer and correlate the FM domain structure with the UCS density. Larger applied fields drive the receding domains to areas of proportionally higher pinUCS aligned antiparallel to FM moments. The data confirm that the evolution of the FM domains is determined by the pinUCS in the AFM layer, and also present examples of frustration in the system.

Iron filled carbon nanotubes as novel monopole-like sensors for quantitative magnetic forcemicroscopy

We present a novel ultrahigh stability sensor for quantitative magnetic force microscopy(MFM) based on an iron filled carbon nanotube. In contrast to the complex magneticstructure of conventional MFM probes, this sensor constitutes a nanomagnet with definedproperties. The long iron nanowire can be regarded as an extended dipole of which only themonopole close to the sample surface is involved in the imaging process. We demonstrateits potential for high resolution imaging. Moreover, we present an easy routine to determineits monopole moment and prove that this calibration, unlike other approaches, isuniversally applicable. For the first time this enables straightforward quantitative MFMmeasurements.

A comparative study of write field distribution of trailing-edge shielded and unshielded perpendicular write heads by quantitative magnetic force microscopy

Three-dimensional write field distributions of trailing-edge shielded and unshielded perpendicular write heads with applied direct current write currents were studied by magnetic force microscopy (MFM) measurements. A quantitative MFM approach of two times integrating measured frequency shift at a series of tip scan heights over the perpendicular direction was proposed to measure the magnetic field strength and field gradient. Results indicate shielded heads in addition to smaller saturation write currents, exhibited more than two to three times higher write field gradients over a wide range of moderate field strength over unshielded heads, thus, producing sharper bit transition and improved signal to noise ratio as theoretically predicted.