Magnetic elements for switching magnetization magnetic force microscopy tips

Using combination of micromagnetic calculations and magnetic force microscopy (MFM) imaging we find optimal parameters for novel magnetic tips suitable for switching magnetization MFM. Switching magnetization MFM is based on two-pass scanning atomic force microscopy with reversed tip magnetization between the scans. Within the technique the sum of the scanned data with reversed tip magnetization depicts local atomic forces, while their difference maps the local magnetic forces. Here we propose the design and calculate the magnetic properties of tips suitable for this scanning probe technique. We find that for best performance the spin-polarized tips must exhibit low magnetic moment, low switching fields, and single-domain state at remanence. The switching field of such tips is calculated and optimum shape of the Permalloy elements for the tips is found. We show excellent correspondence between calculated and experimental results for Py elements.     

Study on magnetization reversal of cobalt nanowire arrays by magnetic force microscopy

The magnetic properties of self-assembly cobalt nanowire arrays formed in anodic porous alumina template were investigated by nanosize imaging method and macroscopic magnetic measurement. We have successfully made a wire-by-wire observation of magnetization reversal of a cobalt nanowire array using magnetic force microscopy with a home-made FePt tip. The nanowires in this medium have uniaxial anisotropy with easy axis along the wire due to the large aspect ratio of the wires (30 nm in diameter and 300 nm in length). Considering the nanowires as single-domain structures, we can obtain the average DC demagnetization curve from nanosize images by calculating the number of wires in each magnetized direction, and the results agreed well with the DC demagnetization curve measured by macroscopic measurement. The magnetostatic field between wires was evaluated by a new nanosize imaging method. Macroscopic measurement shows that reversible magnetization occurs in this medium. Nanosize images of the remanent and saturated states prove that the reversible magnetization processes mainly take place inside individual wires and reversed wires induced by magnetostatic field just give a little contribution to the reversible magnetization.     

Quantitative analysis of magnetization reversal in patterned strip wire by magnetic force microscopy

Magnetic force microscopy (MFM) was used to investigate the magnetization reversal process in a patterned strip wire of permalloy thin film. The magnitude of the phase-shift of tapping mode MFM changed with the varying interactive magnetic force between the magnetic tip and the sample. By analyzing the change in values of the phase-shift, the behaviors of magnetization reversal of different local regions in a patterned strip wire can be quantitatively analyzed. The intensity of the phase-shift in the wider end is stronger than that in the narrower one. In contrast, due to a strong anisotropic effect, the coercive force in the narrower end (9 Oe) is larger than that in the wider one (8 Oe). Therefore, the H_c in the neck section could become strongly affected by the competition of the head-to-tail magnetic configurations in the two parts of the strip wire, and this results in a small H_c in the neck section. In addition, in a simple neck shape connection in a strip NiFe wire, a single domain configuration can be easily changed to a two single domain magnetic configuration.     

Micromagnetic properties and magnetization switching of single domain Co dots studied by magnetic force microscopy

Magnetic force microscopy was applied to study the magnetic properties of Co dot microstructures. The high density magnetic dot arrays were fabricated using nanolithographic techniques on GaAs substrates. The ferromagnetic Co dots were found to be in a single domain state for Co film thicknesses of 7 nm and 17 nm. The magnetization of the as-prepared Co dot array was found to be in a non-uniform state. After applying a magnetic field the Co dots are in a uniform magnetization state. Induced switching of the magnetization of single Co dots by the stray field of the probing tip using an additionally applied in-situ magnetic field has been demonstrated.     

Effect of the probe field in a magnetic force microscope on the magnetization distribution in samples

The effect of the probe field in a magnetic force microscope on the magnetization distribution in objects under study has been theoretically investigated. The perturbation of uniform magnetization state in thin ferromagnetic samples under the probe field was analyzed in the linear approximation. The additional contribution to the magnetic force microscope contrast caused by a local magnetic bias of the sample was calculated.     

Computer simulation of magnetization flop in magnetic tunnel junctions exchange-biased by synthetic antiferromagnets

Computer simulation in a single domain multilayer model is used to investigate magnetization flop in magnetic tunnel junctions, exchange-biased by pinned synthetic antiferromagnets with the multilayer structure NiFe/AlO_x/Co/Ru/Co/FeMn. The resistance to magnetization flop increases with decreasing cell size due to increased shape anisotropy and hence increased coercivity of the Co layers in the synthetic antiferromagnet. However, when the synthetic antiferromagnet is not or weakly pinned, the magnetization directions of the two layers sandwiching AlO_x, which mainly determine the magnetoresistance, are aligned antiparallel due to a strong magnetostatic interaction, resulting in an abnormal MR change from the high MR state to zero, irrespective of the direction of the free layer switching. This emphasizes an importance of a strong pinning of the synthetic antiferromagnet at small cell dimensions. The threshold field for magnetization flop is found to increase linearly with increasing antiferromagnetic exchange coupling between the two Co layers in the synthetic antiferromagnet. The restoring force from magnetization flop to the normal synthetic antiferromagnetic structure is roughly proportional to the resistance to magnetization flop. Irrespective of the magnetic parameters and cell sizes, the state of magnetization flop does not exist near H_a=0, indicating that magnetization flop is driven by the Zeeman energy.     

Computer simulation of the interaction between two superconducting rings with constant magnetic fluxes

The energy and interaction force of two superconducting rings with constant magnetic fluxes have been calculated by the finite-element method. It is shown that the ring-interaction energy is minimum in the case of unequal codirectional magnetic fluxes.     

A model for quantum jumps in magnetic resonance force microscopy

We propose a simple model which describes the statistical properties of quantum jumps in a single-spin measurement using the oscillating cantilever-driven adiabatic reversals technique in magnetic resonance force microscopy. Our computer simulations based on this model predict the average time interval between two consecutive quantum jumps and the correlation time to be proportional to the characteristic time of the magnetic noise and inversely proportional to the square of the magnetic noise amplitude.     

Variable magnetic field and temperature magnetic force microscopy

Magnetic force microscopy (MFM) studies of epitaxial MnAs films on GaAs(001) have been performed as a function of the applied magnetic field and the sample temperature. For this purpose, we combined a stable variable-temperature sample stage with a compact magnet assembly to fit a commercial magnetic force microscope. In order to keep the thermal drift that affects MFM measurements low, we employed a permanent magnet that can be rotated in a yoke assembly guiding the magnetic flux to the sample. PACS 68.37.Rt; 68.35.Rh; 75.70.-i; 75.70.Kw     

Three dimensional magnetic resonance imaging by magnetic resonance force microscopy with a sharp magnetic needle

An electropolished magnetic needle made of Nd(2)Fe(14)B permanent magnet was used for obtaining better spatial resolution than that achieved in our previous work. We observed the magnetic field gradient |G(Z)|=80.0G/microm and the field strength B=1250G at Z approximately 8.8 microm from the top of the needle. The use of this needle for three dimensional magnetic resonance force microscopy at room temperature allowed us to achieve the voxel resolution to be 0.6 microm x 0.6 microm x 0.7 microm in the reconstructed image of DPPH phantom. The acquisition time spent for the whole data collection over 64 x 64 x 16 points, including an iterative signal average by six times per point, was about 10 days.     

Numerical simulation of random magnetic anisotropy with solid magnetization grains

Random anisotropy model (RAM) was investigated by means of numerical simulation. Magnetization of magnetically interacting grains with randomly oriented uniaxial anisotropy was calculated using the Landau-Lifshitz-Gilbert equation where the magnetization in a particular grain is assumed to align in the same direction (single spin model). Calculations were carried out for 10×10×10 three dimensional cells changing cell sizes from 5 to 25 nm. The relation between coercive forces and grain sizes was obtained to be H_C∼D^5.7 from the simulated magnetization curves. This result fits the primitive theory H_C∼D⁶ and the experimental results.     

Nanoscale Fourier-transform imaging with magnetic resonance force microscopy

We present a versatile method for Fourier encoding the spatial distribution of spins detected by magnetic resonance force microscopy. Shuttling a magnetic particle in synchrony with an rf pulse sequence causes spins in a constant-field slice near the particle to precess at a rate proportional to their x or y coordinate. A two-dimensional spin-density map is recovered by a linear Fourier transform of a set of integrated force signals. Performance of the rf sequence is demonstrated experimentally and numerical simulations show that the method can achieve nanoscale resolution. Our approach offers a new route to manipulating spin wave functions down to the atomic scale.     

Computer simulation of magnetization relaxation in amorphous magnetics with random anisotropy

On the basis of Heisenberg model, the magnetic properties of amorphous terbium were studied by the Monte Carlo method. The temperature dependences of spontaneous magnetization and magnetic susceptibility were plotted as functions of the fraction of the constant of anisotropy to the exchange constant D/J ₀. The behavior of magnetization in an external magnetic field was studied, and the dependence of a coercive field and residual magnetization on the value D/J ₀ was found. The relaxation of magnetization was investigated after the external magnetic field was switched off.     

Singularities of the magnetization of a two-dimensional diluted magnetic semiconductor with strong spin-orbit interaction

The properties of the bound states of magnetic impurities and localized carriers in two-dimensional semiconductor systems with strong Rashba spin-orbit interaction have been investigated. The peculiar behavior of the bound states of an electron in such a system leads to the dependence of the ground state of polarons on the external magnetic field. This results in a jump in the dependence of the magnetization on the applied field.     

Self-induced transparency in a resonance medium with the dipole-dipole interaction

Propagation of a pulse of self-induced transparency in a resonance medium is discussed for the case when it is necessary to take into account the direct electric dipole-dipole interaction between atoms. An equation for the envelope of a wave packet—the sine-Gordon equation—is obtained for the case of durations short compared to ω ₀ ^?1 (ω₀ is the transition frequency). The dependence of the velocity and the amplitude of the soliton on the magnitude of the dipole-dipole interaction of atoms is examined in the adiabatic approximation.     

Oscillations of echo amplitude in glasses in a magnetic field induced by nuclear dipole-dipole interaction

The influence of a magnetic field on the dipole echo amplitude in glasses (at temperatures of about 10 mK) induced by the dipole-dipole interaction of nuclear spins has been theoretically studied. It has been shown that a change in the mutual position of nuclear spins at tunneling and the Zeeman energy E _H of their interaction with the external magnetic field lead to a nonmonotonic magnetic-field dependence of the dipole echo amplitude. The approximation that the nuclear dipole-dipole interaction energy E _d is much smaller than the Zeeman energy has been found to be valid in the experimentally important cases. It has been shown that the dipole echo amplitude in this approximation may be described by a simple universal analytic function independent of the microscopic structure of the two-level systems. An excellent agreement of the theory with the experimental data has been obtained without fitting parameters (except for the unknown echo amplitude).     

Local ferromagnetic resonance imaging with magnetic resonance force microscopy

We report nanoscale scanned probe ferromagnetic resonance force microscopy (FMRFM) imaging of individual ferromagnetic microstructures. This reveals the mechanism for high spatial resolution in FMRFM imaging: the strongly inhomogeneous local magnetic field of the cantilever mounted micromagnetic probe magnet used in FMRFM enables selective, local excitation of ferromagnetic resonance (FMR). This approach, demonstrated here in individual permalloy disks, is straightforwardly extended to excitation of localized FMR modes, and hence imaging in extended films.     

Spatial and force resolution of magnetic force microscopy in current imaging

Magnetic force microscopy (MFM) can be used to image current distributions in current leads of sub-micron dimensions. Here we present a systematic study about the spatial and force resolution of such currents. In the case of force resolution, we studied the least measurable magnetic force of MFM for different sample currents. The analysis of images from parallel Al conducting plates are combined with those from force-distance curves and finite element calculations. Several interacting regimes between the magnetic tip and the currents are found and interpreted. It is shown that model calculations are necessary even for qualitative image interpretation. Then spatial resolution in the range of 100nm can well be obtained and quantitative studies of current distribution on widths of 10nm resolution are possible in special cases. The approach is demonstrated in imaging the current distribution in superconducting Bi₂Sr₂CaCu₂O _x single crystals. Presented at the VIII-th Symposium on Surface Physics, Třešt’ Castle, Czech Republic, June 28 – July 2, 1999. This work was supported in part by the Swiss Priority Program on Materials. The authors benefited greatly from discussions with D.A. Bonnell, B. Huey and C. Rüegg.     

Towards a quantitative analysis of magnetic force microscopy data matrices

Fast and efficient software tools previously developed in image processing were adapted to the analysis of raw datasets consisting of multiple stacks of images taken on a sample interacting with a measuring instrument and submitted to the effect of an external parameter. Magnetic force microscopy (MFM), a follow-up of atomic force microscopy (AFM), was selected as a first testbed example. In MFM, a specifically developed ferromagnetic scanning tip probes the stray magnetic field generated from a ferromagnetic specimen. Raw scanning probe images taken on soft patterned magnetic materials and continuous thin films were used, together with synthetic patterns exploited to assess the absolute performance ability of the proposed texture analysis tools. In this case, the parameter affecting the sample-instrument interaction is the applied magnetic field. The application discussed here is just one among the many possible, including, e.g., real-time microscopy images (both optical and electronic) taken during heat treatments, phase transformations and so on. Basically any image exhibiting a texture with a characteristic spatial or angular dependence could be processed by the proposed method. Standard imaging tools such as texture mapping and novel data representation schemes such as texture analysis, feature extraction and classification are discussed. A magnetic texture stability diagram will be presented as an original output of the entropic analysis on MFM datasets.