Characterisation of MFM Tip Stray Fields using Lorentz Electron Tomography

The work presented in this thesis is a study of the magnetic properties of various magnetic force microscopy (MFM) tips using Lorentz electron microscopy and tomography. The implementation of tomography and differential phase contrast (DPC) microscopy allows the stray field distribution in the half space in front of MFM tips to be measured with a spatial resolution of <30 nm and a field resolution of <2 mT. This information will allow the development of better models for MFM imaging performance and, potentially, the quantification of MFM images.
In Chapter 1 the properties of ferromagnetic materials are reviewed. The various energy contributions that govern magnetism in these materials are reviewed, leading on to the formulation of the micromagnetic equations. The use of these equations in numerical simulations of magnetic elements is discussed. Finally, the type of magnetic domain structure specific to thin films is discussed, with particular focus on domain walls in thin films and the behaviour of small magnetic elements.

In Chapter 2 the general principles of electron microscopy are briefly reviewed, and the main methods of observing phase contrast in samples are covered. Special attention is given to the DPC imaging mode, and it's implementation on the Philips CM20 field emission gun (FEG) electron microscope at Glasgow. It is shown that DPC imaging by itself only yields the projection of the MFM tip stray field distribution, and so to obtain the three-dimensional field distribution a tomographic method must be used. The collection and calibration of the tomographic data series is discussed, including the special sample mounting methods required.

To understand the principles behind MFM, the theory behind atomic force microscopy (AFM) is discussed at length in Chapter 3. The extension of AFM to MFM is covered, and the simple point charge analysis of the MFM imaging process is reviewed. A more sophisticated analysis is then presented, based on the knowledge of the MFM point-response function. It is demonstrated that in some cases, the magnetic charge distribution of a samples can be extracted provided that the response function of the MFM tip (related directly to the stray field distribution from the tip) is known. Finally, some specialised MFM techniques are briefly reviewed.

In Chapter 4, prototype tips (produced at Sheffield University) coated with a low-coercivity amorphous ferromagnetic alloy (METGLAS®2605SC) are characterised by Lorentz tomography. Planar thin films of the same alloy are also characterised by Fresnel imaging, and the response of both the planar films and the coated tips to external fields is shown. The results indicate that these tips, while possessing finite coercivity, can be considered as very 'soft' tips when coated with >50 nm of METGLAS alloy. Thus these tips are shown to be well suited for imaging samples with very strong stray fields, where the use of a normal (CoCr) tip would result in hysteretic attefacts in the MFM image.

In Chapter 5 other special purpose MFM tips are investigated using Lorentz tomography. The tips investigated comprise two examples modified by focused ion beam (FIB) milling to form 'spike' tips, a tip intended to measure magnetic moments several orders of magnitude smaller than is currently possible with MFM, and a tip coated with a high-coercivity coating for imaging samples with strong stray fields. Tomographic reconstructions for all of these tips are presented, and the effects of the various tip modifications on the character of the tip stray fields are discussed.

One of the problems that arises when performing DPC imaging of MFM tips is the electrostatic charging of the tips by the electron beam. In Chapter 6 the effects of electrostatic charging on the tomographic field reconstructions are simulated numerically, and it is demonstrated that the effect on the reconstruction is a characteristic smearing of the field distribution. A method for separating the magnetic and electrostatic effects is proposed, and is shown to work in an experimental case study. The effect of DPC detector misalignment is also investigated, and is found not to be a critical problem.

In Chapter 7 the future of MFM tip design and MFM operation is considered in the light of the results in this thesis, and some improved tip designs are suggested. The separation of the electrostatic (arising from the inner potential) and magnetic effects from DPC images of thin-film samples is also considered, as is a possible improved design of DPC detector.