Magnetic stray fields of periodically arranged Co-Crmicro strips

Research was carried out on magnetic stray fields of Co-Cr micro strips. This investigation was motivated by the search for increasing bit density and miniaturisation in magnetic data storage and magnetic sensor devices. In these devices the magnetisation is patterned, i.e. by writing bits or etching micro structures in a magnetic material. As a result magnetic stray fields exist outside the material which determine the actual information in these applications. The magnetisation pattern is however influenced by its shape and therefore, in turn, also the magnetic stray field. In this thesis this relation between shape and magnetic (stray) fields of magnetic micro strips was studied. The basic question was: 'how do parameters such as shape, geometry, magnetisation and anisotropy of the micro strips influence the actual shape of the stray field?'. The strips were obtained by patterning as-sputtered Co-Cr into periodic micron-sized strips with conventional lithographic processes. This process leaves intrinsic magnetic properties, like Ms and K1, unaffected but influences the magnetic behaviour inside and stray field outside the material. The relation was investigated both theoretically and experimentally and principal agreement was obtained. The theoretical investigation is based on magneto-static calculations and includes actual shape and geometry of the micro structures. The experimental investigation was carried out by SEM and X-ray diffraction for micro-structural investigation, and by VSM, torque magnetometer, magnetic force and Lorentz microscopy for the magnetic characterisation. This chapter is organised in the following manner. The major findings of chapters 2, 4, 5 and 6 are shortly discussed in succeeding paragraphs. The final paragraph of this chapter contains a general conclusion which characterises the contents of this thesis. In chapter 2 a theoretical description was given of demagnetisation and stray field calculations. These are magneto-static calculations based on literature, however here it is applied to periodically arranged strips which exhibit the schematic shape of the experimentally investigated micro-strips. The magnetisation is assumed to be uniform in magnitude and the magnetic anisotropy is perpendicular. In the calculations two approaches are considered, i.e. the magnetisation is assumed to be parallel (§ 2.2) and the magnetisation is allowed to relax micro-magnetically towards its equilibrium direction (§ 2.3). In particular the first approach proved to be a relative simple description of the magneto-static problem, by application of a Fourier approximation to the magnetic pole densities. Therefore, and because both sections result in approximately the same magneto-static behaviour, the first approach is applied to the calculations in the succeeding chapters. A general solution of the magneto-static potential, from which the stray and demagnetising fields can be easily derived, was given. In appendixes A and B several newly derived applications are listed, such as strips with tilted side flanks and rectangular strips exhibiting a domain structure. The major results of these calculations were that patterning a sample into rectangular strips will hardly affect the equilibrium value of domain period. That the influence of these domains on the stray field confirms that for distances to the sample which exceeds the dimensions of the domain structure no influence can be seen on the shape of the stray fields. And that a tilting of the side flanks was found to hardly influence the stray field, but can have a considerable effect on the demagnetising field. The Fourier description is helpful in understanding stray field and demagnetisation behaviour, and is therefore of practical use in device design. Two examples were given for bit stabilisation in VBLM (§ 2.4) and bit geometry considerations in perpendicular digital magnetic recording (§ 2.5). The former example benefits from a simple description because an optimum bit stabilisation must be designed in correlation with other requirements of a VBLM. The latter was found to predict square bits as the best possible bit shape for high bit density in perpendicular digital recording. The findings of chapter 2 result in a better understanding of magneto-static considerations regarding artificially shaped magnetic micro strips. The general question is, however, whether this theory applies to real materials which do not meet the assumption of uniform magnetisation. This was investigated in the experimental chapters 4 to 6. In chapter 4 the demagnetising influence on magnetic properties was investigated. This had its practical motivation in finding the relation between the shape of the micro-strip and the remanent perpendicular magnetisation (and thus its stray field amplitude!). However it can also be regarded as a measurement method which investigates the influence of demagnetisation without changing the intrinsic properties, and is therefore also of fundamental interest. The influence of the shape and geometry of the micro structures were related to an average demagnetisation factor. A method was developed to derive this demagnetisation factor experimentally from torque measurements and its value was compared to the theory described in chapter 2. Principal agreement is obtained, although a relatively large scatter is present. This scatter is attributed to errors in determining the shape of the strip, which can be rather inhomogeneous over the sample. And also to the value of the anisotropy, which exhibits an anomalous field dependence for these type of materials. Possible reasons for the anomalous field dependence of torque curves were investigated in § 4.2 and described qualitatively. The major new findings are that micro-magnetic simulations show the shape anisotropy to exhibit second order effects. That the inhomogeneous- and low effective anisotropy character of these films are shown to result in an anomaly of the field dependence. And that the measurement method (null position detection and image effects) also influences the anistropy measurements. In two appendixes the theoretical field dependency of various anisotropy sources (app. C) and the influence of an image effect in torque measurements (app. D) were derived. This image effect has up till now been disregarded in literature, but it is found here to have a significant contribution for low effective anisotropy samples. The relation between demagnetisation and magnetic behaviour was investigated in the remainder of chapter 4. Here the interesting result is found that the demagnetising influence on most macroscopic parameters, such as remanence and anisotropy field, can be explained by a simple theory which is based on a change in mean internal field with demagnetisation factor. This indicates that for a number of magnetic properties the (magnetic) micro-structure can be taken as an average property. The relation of the demagnetisation factor with coercivity is however not understood. Magnetic viscosity measurements and domain structure observations were carried out, but did not reveal an unilateral explanation. Further research is therefore recommended because tailoring coercivity is of great interest in many applications. The investigation of the demagnetising influence on time dependent behaviour itself are in agreement with theory. Here measurements were presented which investigated the magnetic viscosity as a function of demagnetisation factor. The results show that perpendicular media exhibit behaviour similar to in-plane media. However the Barbier plot, which is the logarithmic relation of magnetic viscosity with coercivity, is found to exhibit a slope of two. This result has not been investigated before and proved different from what was expected for in-plane media, where a slope of one is obtained. This makes it of fundamental interest for investigating magnetic reversal of perpendicular media. As mentioned previously, the stray field directly determines the application in data storage and magnetic sensor devices. This stray field was investigated with Lorentz- and magnetic force microscopy in chapter 5 and 6, respectively. Both methods resulted in a qualitative confirmation of the magneto-static description of chapter 2 and therefore indicate, as in chapter 4, that the (magnetic) micro-structure can be taken as an average property. At the same time these results display the usefulness of a proper magneto-static description in interpreting stray field measurements (quantitatively). Such an interpretation is needed for development of new stray field measurement techniques like Lorentz tomography and interpretation of MFM observations where the (unknown) micro-magnetics of the tip determines the response to the stray field. Chapter 5 and 6 can be regarded as examples for this, where in the latter a MFM height scan is shown to be a powerful tool in investigating the micro-magnetic behaviour of the tip. In chapter 6 MFM observations were carried out on stray fields of micro strips, bits and domain structure. The micro strips and bits showed a clear resemblance and confirm therefore the magneto-static considerations of chapter 2. The MFM observations on domain structure were related to topography of the sample by scanning the sample also in AFM mode. It was shown that the domain size was considerably larger than the size of the columnar Co-Cr structure and hardly affected by the patterning into micro strips. This indicates that the increase in coercivity can not be directly related to a change in domain structure. As a general conclusion it can be said that the magneto-static calculations in chapter 2, which are derived for uniform magnetisation, do (qualitatively) apply for the investigated Co-Cr micro-strips here. This makes the practical interest of these general applicable magneto-static calculations apparent for device design and interpretation of measurement results. A fundamental interest can be taken in the fact that by patterning media into strips the demagnetising influence can be investigated. For the here investigated micro strips this influence can be well understood from mean demagnetising field considerations. It is however also of great interest to investigate how this tendency evolves when the strips are scaled down to sub-micron (or even nanometer) dimensions. Patterned media can then be used to relate thin film switching behaviour to theory.