2.0 Magneto Optic Kerr Effect (MOKE)
Magneto Optical effects in magnetic materials arise due to the optical anisotropy of the materials. The source of this optical anisotropy is the magnetisation M within surface domains which can be influenced by external forces such as magnetic fields. The optical anisotropy alters the state of linearly polarised light which is reflected off magnetic materials. These effects are generally known as the Magneto-Optical Kerr Effect (MOKE) which were observed by John Kerr in 1887, and are analogous to the Faraday effect where the polarisation of the light is rotated through a transparent material subjected to a magnetic field as observed by Michael Faraday in 1845.
The magneto optical effects are characterised by the Kerr effect being proportional to the magnetisation. This makes it particularly useful in the study of surface magnetism since it is highly sensitive to the magnetisation within the skin depth region, typically 10-20nm in most metals [Bland et al (1989)]. The effect has been utilised to obtain hysteresis loops or domain images and is a relatively simple technique to implement. It has the ability to probe the magnetisation in very small regions of a material, such as wires or patterns [Shearwood et al (1996)], or in real device applications [Karl et al (1999)]. MOKE has emerged as an important technique in the study of surface magnetism. It has been used extensively to characterise magnetic materials, especially in the field of magnetic thin films. The Kerr effect is also the basis of the commercially available magneto optical drives.
Part of this study has been involved with the construction of a MOKE magnetometer and MOKE imaging system, in order that the amorphous ferromagnetic thin films could be studied. The MOKE magnetometer provided information in the form of hysteresis loops, whereas the imaging system provided magnetic information by means of domain images. The two systems were built to overcome the limitations of the Inductive Magnetometer which was designed primarily for studying amorphous, ribbon based materials. The principles of MOKE are discussed here only qualitatively; this account is not intended to be complete and rigorous, but to provide an overview for the reader.
2.2 Principles of MOKE
Magneto Optical Kerr effects are generally described macroscopically by dielectric tensor theory [Zak et al (1990)], or the effects can also be described microscopically, where the coupling between the electric field of the light and the magnetisation occurs by the spin-orbit interaction [Daalderop et al (1988)]. In the present work the effects are described less formally, in a pictorial fashion, using the idea of a Lorentz force. To understand the magneto optical Kerr effects, one needs to understand the terminologies associated with the effect, how the state of polarisation of reflected light is dependent upon the initial polarisation and the magneto optical geometry in which it is being used.
Light is a transverse electromagnetic wave which can be manipulated optically into plane, circularly or elliptically polarised light (Fig. 2.1). Generally, the plane of polarisation is the plane which contains the electric field E and the direction of propagation. However in some texts [Corson & Lorrain (1970)], the definition of plane of polarisation refers to the plane containing the B field. Any reference to the plane of polarisation in the present work will assume the former definition. If the electric field is polarised in the plane of incidence, it is referred to as p-polarised light as shown in Figure 2.2. Conversely, if the electric field is polarised perpendicular to the plane of incidence, then it is referred to as s-polarised light. The plane of incidence is also known as the scattering plane - the plane which contains the incident and reflected light beam. Circularly polarised light can be further referred to as L-circularly polarised and R-circularly polarised light, where L and R signify the electric field rotating in either a clockwise or an anticlockwise direction with respect to the direction of propagation.
Plane polarised light which is reflected off a metallic surface, is generally elliptically polarised. However if the incident light is either p or s-polarised, then the reflected light will still be plane polarised upon reflection (p or s) [Hecht (1989)]. This is because the reflecting surface is a plane of symmetry for the system. This symmetry is destroyed in the situation where plane polarised light is reflected off a magnetised surface. When p-polarised light is reflected off a magnetic surface, the reflected light has a p-component as in the ordinary metallic reflection but, in addition, a small s-component also appears in the beam. In general, this second electric field component is out of phase with the reflected p-component. This causes the light to become elliptically polarised with its major axis rotated from its initial incident polarisation plane. This magneto optic interaction is shown schematically in Figure 2.3. A similar effect occurs for s-polarised light. The two effects are know as the Kerr ellipticity and the Kerr rotation. As mentioned earlier, the effects are described macroscopically using dielectric tensor theory. In this theory, plane polarised light is viewed as being
Figure 2.1: Polarisation of light.
Figure 2.2: Illustration of p-polarised and s-polarised light.
made up of the superposition of two circular components, L and R-circularly polarised light. The magnetic medium has different refractive indices for these two polarised modes. Therefore the two circular modes travel with different velocities and attenuate differently in the material. Upon reflection from the material, the two modes recombine to produce the Kerr rotation and ellipticity. The macroscopic description of Kerr effects relies on the two modes having different refractive indices within the material. The general form of the dielectric tensor which represents the effects of a magnetic medium is given by [see Zak et al (1990) for details]
where Qx,y,z is the Voigt magneto optic constant which describes the magneto optical effect. This Voigt term is to the first order proportional to the magnetisation of the material. It is this complex Voigt term (the off diagonal terms) which generally modifies the polarisation. Basically, what MOKE measures directly, is the magneto optic response of the medium, which is a change in the incident polarisation of the light. This magneto optic response consists of two parts: a change in the polarisation of the in-phase component of the reflected light which gives rise to the rotation, and a change in the polarisation of the out-of-phase component of the reflected light which gives rise to the ellipticity.
Figure 2.3: Reflection of p-polarised light of a magnetic sample.
Figure 2.4: Longitudinal, transverse and polar Kerr effects.
There are principally three Kerr effects which are classified depending upon the magneto optic geometry being employed. These are shown in Figure 2.4. The effects are dependent on the orientation of the magnetisation with respect to the incident and sample planes. In the longitudinal Kerr effect, the magnetisation is in the plane of the sample and parallel to the incident plane. In the transverse Kerr effect, the magnetisation is also in the plane of the sample, but is perpendicular to the incident plane. In the polar Kerr effect, the magnetisation is perpendicular to the sample plane and is parallel to the plane of incidence. It should be noted the Kerr effect will occur for any arbitrary direction of magnetisation within the sample. Consideration of these three magneto optic geometries simplifies the understanding of the Kerr effect. The longitudinal and transverse Kerr effects are generally used to study the in-plane magnetic anisotropy, whereas the polar configuration is used to study thin films, which exhibit perpendicular anisotropy. The thin films investigated in this study on the whole only exhibited an in-plane magnetic anisotropy and therefore the polar effect was not used. Upon refection the longitudinal and polar Kerr effects, generally, alter the polarisation of the incident light from plane to elliptically polarised with the major axis rotated (Kerr rotation). In the transverse effect there is no change in the polarisation of the incident light. This is more clearly illustrated in Figure 2.5, where a vector representation using the idea of a Lorentz force indicates how p and s-polarised light interact in the three magneto optic geometries. The electric field of the plane polarised light which is incident upon the material, can be thought of as exciting the electrons so that they oscillate parallel to the incident polarisation. This gives rise to the normal component (EN) of light in the reflected light. The additional Kerr component, EK, arises because of the Lorentz force. The Lorentz force induces a small component which is perpendicular to both the primary motion (normal component) and the direction of the magnetisation. Generally, the two components are not in-phase and it is the superposition of these two components which gives rise to a magnetisation dependent rotation of the polarisation. In the longitudinal and polar Kerr effects (Fig. 2.5a,b), p or s-polarised light will generally become elliptically polarised with its major axis rotated (Kerr rotation). This is a consequence of an orthogonal electric field component being induced because of the Lorentz force. The directions of the Lorentz force, and therefore the induced components, are shown by the dashed arrows (EK). The Kerr effect diminishes as the angle of incident approaches the normal to the sample plane in the longitudinal effect because either the Lorentz force vanishes (p-polarised) or points along the direction of the light (s-polarised). This is not the case for the polar Kerr effect because the magnetisation is out of the sample plane and a Lorentz force always exists at normal incidence. The polar effect is independent of the incident polarisation at normal incidence. The angle of incidence generally tends to be independent of the incident polarisation
Figure 2.5: A schematic representation of the Magneto Optic interaction using the idea of a Lorentz force. The normal component (EN) of light is indicated by the solid lines, the Kerr component (EK) and the direction of the Lorentz force is indicated by the broken lines.
at normal incidence. The angle of incidence generally tends to vary in the range 5-600 depending on the experimental arrangement for the longitudinal and transverse modes. In most instances the angle of incidence is fixed by the constraints of the experimental layout. It has been shown experimentally [Deeter & Sarid (1988)] that the angle of incidence does have a small effect on the magnitude of the Kerr rotation. The polar Kerr effect is usually an order of magnitude larger than the longitudinal Kerr effect. The transverse effect involves no change in polarisation, since there is either no Lorentz force present (s-polarised) or the induced component (p-polarised) has the same polarisation as the incident polarisation (Fig. 2.5c). The transverse effect involves a change in the intensity of the light (Kerr reflectivity). The intensity changes are dependent upon the component of magnetisation perpendicular to the plane of incidence. There is no Kerr ellipticity since M´E induces a component which is in the plane of incidence. The induced Kerr component and the normal component give rise to a change in the amplitude. One only sees a Kerr rotation if a Lorentz force is present. In general either s or p-polarised light is used. This is because any change in the polarisation of the light will be a result of the magnetisation, since in an ideal situation there will be no change in the polarisation of light for either s or p-polarised light reflected off a non-magnetic surface.
The above explanation is elegantly summarised by the Kerr Fresnel reflection coefficients [Florczak & Dahlberg (1990)] which have been obtained from applying the Maxwell boundary conditions at the surface of the magnetic films [see Zak et al (1990) for details]. The coefficients for the transverse and longitudinal effects have been listed here for completeness. A more detailed analysis is given in the references cited.
Here, q is the angle of incidence, n is the index of refraction of the film, , and . The term represents the reflection coefficient which relates the incident s-wave to the reflected p-wave in the longitudinal effect. From the transverse coefficients, it is clear that the light does not undergo a rotation of its plane of polarisation, since the off-diagonal terms which give rise to the rotation are equal to zero . The only quantity which is dependent on the magnetisation is the reflection coefficient relating the incident and reflected p-polarised light, as shown/explained by Figure 2.5c, whereas the longitudinal coefficients indicate a rotation of the polarisation by the existence of the off diagonal terms .
For simplicity and clarity the author has used a pictorial explanation of the Kerr effect for a more qualitative approach here.
2.3 MOKE Magnetometer
The MOKE magnetometer characterises materials by providing magnetic information in the form of a hysteresis loop. It relates the magnetisation M, to the applied magnetic field, H. The principles of the MOKE magnetometer are based on the Kerr effect as explained in the previous section. Figure 2.6 shows a schematic layout of the MOKE system at Sheffield. The whole system was constructed by the author; this included the computer automation of the equipment and the writing of the associated software. Light was provided by a 15mW He-Ne laser (l=633nm) at an incident angle of 450 to the sample plane. The polarisation of the light beam before reflection was controlled by a Glan Taylor polariser to be either p or s-polarised, which was then focused onto the sample by a lens of focal length 30cm. The sampling area was determined by the size of the laser spot; this was approximately 100mm in diameter. The reflected light beam was passed through an analysing Glan Taylor polariser onto a photo-diode, where the reflected intensity was measured. The output signal from the photo-diode was fed into the signal conditioning unit (see later) before being read by the computer by means of an analogue to digital converter (ADC - 12 bit). The software was also interfaced to a programmable voltage controlled bipolar current source (KEPCO BOP 36-12M), by means of a digital to analogue converter (DAC - 14 bit). The KEPCO was used to provide the driving current for the Helmholtz coils, which produced the sweeping magnetic field. The software simultaneously swept the magnetic field and recorded the transmitted intensity as a function of the applied magnetic field. All components were mounted onto an optical table which had anti-vibration cushioning and the MOKE magnetometer was placed in a Faraday room to screen the apparatus from electromagnetic noise. The Faraday room also doubled as dark room which eliminated the problem of the fluctuating ambient light. The samples were mounted onto a non-magnetic holder either by a high temperature vacuum grease, wax or by double sided tape. The holder could be traversed, and this moved the sample in the xy plane of the magnetic field (Fig. 2.6) by means of two micrometers; it also provided the freedom of rotating the sample through a full 3600 in the plane of the magnetic field.
Typical films had coercivities of 30-50 A/m. This meant the applied field had to be stable and uniform across the whole of the film in order for this quantity to be determined accurately. The dimensions indicated for the Helmholtz coils in Figure 2.7 insured that a uniform field was produced over a large volume of space. This is shown in Figure 2.8 where the equation for the field produced by the Helmholtz coil [Jiles 1994] was used to generate the curve to illustrate this. The inset shows that the field strength only varies by 1% over a distance of ±3.0 cm from the centre. Measurements taken using a Hall effect magnetometer (Oxford Instruments 5200) indicated no measurable change in the field strength at 100 A/m over a region of ±2.5cm. The Helmholtz coils also provided ample room for a range of sample dimensions, and the flexibility to enable more exotic holders to be used. Limitations imposed on the sample dimensions by the inductive magnetometer, and its inability to investigate any in-plane magnetic anisotropies are alleviated with MOKE magnetometry.
Figure 2.6: Schematic layout of MOKE magnetometer.
Figure 2.7: Schematic of Helmholtz coils.
Figure 2.8: Calculated plot of field uniformity produced by the Helmholtz coils.
The Helmholtz coils were designed to generate fields up to 23 kA/m using the KEPCO bipolar power supply. This was so that direct comparisons could also be made with the inductive magnetometer, which had a similar maximum field. Figure 2.7 is an illustration of the Helmholtz coils which were constructed. The coils were mounted onto a cylindrical plastic tube, which had circular apertures bored out for incident and reflected laser beam to pass through. The mounting of the coils on the cylindrical tube ensured that the magnetic field could be orientated easily in either the transverse or longitudinal modes with respect to the incident plane (Fig. 2.2). Each coil consisted of 300 turns of 1.71 mm diameter copper enamel wire. The coils were carefully designed to ensure that they were load matched with the KEPCO power supply to ensure that if needed, the maximum current could be drawn from the supply. Heating effects of the coils were negligible for two reasons. Firstly, the typical field needed to saturate the majority of the FeSiBC films, were of the order of 5kA/m or less. The coils were over engineered to take account of other magnetic thin film systems. These generally required much larger fields to saturate (20 kA/m), and therefore only a quarter of the maximum available current was generally driven through the coils when investigating the FeSiBC films. Secondly, heating of the coils was further reduced by the implementation of a non-linear field ramp, which reduced the amount of time the coils were subjected to a high current. The non-linear field ramps were essential in the measurement of soft amorphous films. This was because the magnetisation in these materials changed rapidly over a small change in the applied field near the origin. Using a linear field ramp (each field point equally spaced) would have meant the sampling rate would decrease in this region where the rate of change of the magnetisation was at its maximum. Figure 2.9 shows two hysteresis loops, one taken using a linear field ramp, and the other using a non-linear field ramp. In both cases, 128 sample points were taken, and each point was equally spaced in time. The general shapes of the two loops were independent of the field ramp. The loop obtained using the linear field ramp illustrates the problem associated with the sampling rate, by only managing to sample one data point as the magnetisation changes rapidly. However, in loop B, the sampling rate is increased in
Figure 2.9: Loop A is a hysteresis loop taken using a linear field ramp, whereas the loop B was taken using a non-linear ramp.
Figure 2.10: Digital ramps generated using equation 2.8 for a selection of shape factors S.
this critical region, by decreasing the density of data points taken along the two extreme regions of each arm of the hysteresis loop, were the rate of change of magnetisation is at its minimum. The reduction of the number points in this region does not influence the shape of the hysteresis loops and therefore no magnetic information is lost, as shown by Figures 2.9 and 2.11. This also had an added benefit of ensuring that the coils were only subjected to the maximum field applied for short periods of time. The increased sampling rate in this region insured that a number of data points could be sampled as the magnetisation changed rapidly, increasing the resolution of the measurement in the critical region. The form of the function which was used to generate the field ramps was a truncated tangent [Squire et al (1988)]
where n was the data point being taken, N was the total number of data points being taken in one half of the (± H) loop, and S was a user-adjustable shape parameter which determined the shape of the field ramp being generated. Small values of the shape factor S, produced a ramp which was approximately linear, whereas large values of S produced a sharply peaked ramp. The shape factor, S, governed the region of the tangent curve which was used to generate the ramp. Figure 2.10 shows a selection of ramps generated using the tangent function. The second half of the ramp is a mirror image of the first. The ramps were software generated by parameters pre-determined by the user. The software generated ramp in turn produced the corresponding magnetic field ramp via the DAC through the KEPCO power supply; this is shown in Figure 2.6. The use of the potentiometer to control the maximum voltage applied from the DAC to the KEPCO power supply ensured the full scale (all bits) of the DAC was always being utilised. The field ramp was determined by trial and error by varying the shape factor, the total number of points and the maximum field, so that a reasonable number of points were taken in the critical region. This was not always possible for films which were very soft and exhibited very square hysteresis loops. Figure 2.11 shows two hysteresis loops taken from a magnetically soft FeSiBC film. For comparison with Figure 2.9, 128 data points were taken, but this time at a field ramp of 0.9 and a
Figure 2.11: Two loops obtained using a field ramp of 0.1 and 0.9 from a FeSiBC film which exhibits a very square hysteresis loop.
maximum field of 300 A/m. Using these parameters, it was only possible to sample one or two data points as the magnetisation switched. The resolution of the field step is determined by the shape factor, S, the total number of data points, N, the maximum applied field, and the resolution of the DAC. The inset in Figure 2.12 shows the field step between consecutive points using a field ramp of 0.99 and 340 data points, which generates a digital field ramp that approaches the resolution of the 14 bit DAC. The main figure shows the resolution of the field step suffers from bit noise as 5 bits or less is approached. To ensure that the field step did not suffer from any bit noise during the measurements, a maximum shape factor of 0.98 was imposed. This insured that the smallest field step consisted of 7 bits or more. This gave a possible field step resolution of 0.5 A/m at a field of 500 A/m. The field steps were equally spaced in time, and 350ms was allowed for the field to stabilise before each measurement was taken.
Figure 2.12: Resolution of the Digital to Analogue Converter.
Two polarisers are used to detect the changes in the polarisation of the light as shown in Figure 2.6. The system is a low cost arrangement, which is adequately suited for measuring hysteresis loops of thin films by detecting the Kerr rotation. The polariser is used to control the polarisation of the incident light, whereas the analyser is used to produce an intensity variation at the photo detector from changes in the polarisation. The magnitude of the Kerr rotation is typically a fraction of a degree, and this only produces a very small change in the intensity. The analyser is generally set one or two degrees from extinction to detect the Kerr rotation. It may initially seem illogical to operate the analyser at extinction, but we are only interested in the relative change in the intensity due to the Kerr rotation. This will be a maximum when the normal component of reflection is screened out. The intensity of the light after passing through the analyser is given by equation 2.9 where I0 is the intensity of the reflected light, and q is the angle between the polarisation of I0 and the pass plane of the analyser.
The maximum change in the intensity with respect to q, is obtained by differentiation, and this is a maximum when q=450.
Any changes in the intensity due to the Kerr rotation can be approximated as
since the Kerr rotation Kr is very small compared to q. The relative change in the intensity due to the Kerr rotation can be expressed as
Figure 2.13: The dependence of the analyser setting on the Kerr sensitivity as from equation 2.14.
Figure 2.14: The dependence of the analyser setting on the Kerr sensitivity for s and p-polarised incident light. The solid circles represent the measurements taken in the longitudinal mode and the open circles represent measurements in the transverse mode. s-polarised is equivalent to 00, and p-polarised is equal to 900.
Figure 2.15: The dependence of the Kerr sensitivity on the polariser setting for transverse mode with no analyser present. s-polarised is equivalent to 00 degrees, and p-polarised is equal to 900 degrees.
Equation 2.14 shows that the maximum relative change in the Kerr intensity, or the Kerr sensitivity, occurs as q approaches 900 as shown in Figure 2.13. The Kerr sensitivity is defined [Moog et al (1989)] as the difference in the intensity for a sample magnetised in opposite directions and normalised to the maximum intensity (Eq. 2.15).
It should be noted that setting the analyser close to extinction is only applicable to the longitudinal and polar Kerr configurations, where the light undergoes a Kerr rotation. The transverse effect involves a change in the intensity of the light, and one would assume from equation 2.10 that the analyser should be set to 450 to maximise any changes in the intensity. A number of experiments were carried out to experimentally verify how the analyser settings effected the Kerr intensity in both the longitudinal and transverse Kerr modes. Figure 2.14 shows the Kerr sensitivity, as defined in equation 2.15, for s and p-polarised incident light for varying analyser settings. As predicted by equation 2.14, the maximum Kerr sensitivity occurs as the analyser approaches 900 from the incident polarisation for either s or p-polarised light in the longitudinal mode. The curves obtained have the form of the tangent function as obtained in Figure 2.13. In contrast, the Kerr sensitivity for s-polarised light in the transverse mode is zero for all angles of the analyser setting. This was as expected, since no Kerr effect is seen using s-polarised light as shown in Figure 2.5c. There is a slight signal at extinction, but this may be due to the incident polarisation not being perfectly s-polarised and therefore some Kerr rotation may be present. The use of p-polarised light in the transverse mode (Fig. 2.14b), indicates that the Kerr sensitivity is independent of the analyser setting and is approximately constant. This is because there is no Kerr rotation involved, just a change in the intensity (Fig. 2.5c) and therefore the analyser is not needed for the transverse effect. This is shown in Figure 2.15 where the analyser was removed and the incident polarisation was varied in the transverse mode. The Kerr effect increases from zero to 1% as the polarisation of the incident light changes from s to p-polarised. The Kerr rotation is much larger in magnitude than the Kerr reflectivity and therefore it is utilised in most MOKE magnetometers. The analyser setting is usually set a few degrees from extinction to compensate for various sources of noise which are present in the system. A detailed theoretical evaluation of the signal to noise ratio for such systems has been carried out by Bland et al (1989). Figure 2.16 shows four hysteresis loops obtained from a sample for different analyser settings. In each case, the loops have been normalised so direct comparisons can be made. As the analyser setting is increased from extinction, the slopes of the loops increase and it seems that an extra signal is appearing. The MOKE loop, taken at an analyser setting of 300, is totally different to the loop obtained at 30, which is similar to a loop obtained by the inductive magnetometer. It is important that the analyser is set as close as possible to extinction as high-lighted by these loops, so that only the Kerr rotation is detected. Florczak & Dahlberg (1990) have shown that the
Figure 2.16: Hysteresis loops obtained for various analyser settings qa from extinction. (a) qa=30; (b) qa=100; (c) qa=200; (d) qa=300.
Figure 2.17: Hysteresis loop obtained for analyser setting of qa=600 from extinction. A number of points have been labelled to help visualise not only the crossing of the curve, but also the direction of the magnetisation.
difference in the transverse and longitudinal effects can be utilised to detect specific components of the magnetisation. For analyser angles approaching extinction, the component of magnetisation parallel to the plane of incidence is detected, whereas for analyser angles approaching 900 from extinction, the component of magnetisation perpendicular to the plane of incidence is detected. For intermediate analyser angles, both components are simultaneously detected to varying degrees (Kerr rotation and reflectivity). This can lead to unconventional hysteresis loops as shown in Figure 2.17. For a more detailed analysis one should review the paper by Florczak & Dahlberg (1990) were the technique is extensively discussed. Here we were only concerned with obtaining conventional hysteresis loops for the purposes for characterisation, and the optimum setting for the analyser was found to be 2.00 for the system built in this study.
A silicon photo diode with an active area of 35mm2 with a low noise amplifier was used to measure the reflected intensity. The large active area of the photo diode removed the need for any precise focusing optics. Typical intensities would correspond to a third of volt, and changes in the intensity due to the Kerr rotation would be approximately 50mV (15%). In order to enhance the detection of these small changes in voltages from the photo diode, the signal was initially conditioned before being read by ADC by the software. The signal conditioning unit consisted of a DC off-set, an amplifier with a number of gain settings, and a number of time constant settings. The amplifier was used to amplify the small signal from the photo diode to approximately three to four volts, ensuring the full resolution of the 12 bit ADC was being utilised by the software when reading the measurements. The signal was electronically cleaned which removed any low frequency signals, any background noise from the photo diode and ambient light. A number of experiments were performed by examining the hysteresis loops at a number of amplifier and time constant settings to ensure that they had no other influence on the magnetic signal being measured. It was established that the drift from the HeNe laser was negligible over the time period required to obtain a hysteresis loop (1 min), once the laser was allowed sufficient time to reach thermal equilibrium with its surrounding environment.
The software which was written by the author to automate the system was user friendly and straight forward to use. The sample was mounted onto the relevant holder and placed into position ensuring the reflected laser beam was passing through the analyser. A number of user-adjustable parameters were available on the menu if need. The main ones were:
Shape Factor - Which controlled the distribution of points in the field ramp. (0<S<1)
Upon selection for data acquisition, the software generated the corresponding digital ramp from the parameters set by the user. The first point of the digital ramp was triggered; this set the maximum positive field. The user now has the option of setting the maximum field he/she wishes by adjustment of the potentiometer. The voltage set by the potentiometer was constantly measured by the software and the corresponding field was displayed on-screen for the user. Once the field was set, the software then commenced data acquisition by stepping the field ramp, allowing 350ms for the field to stabilise before each measurement was taken. If a number of loops were being taken, the data for each loop was stored until all the required loops were obtained. This was so that each loop could be examined to determine whether the loop had closed, in some instances the loops would fail to close because of drift due to the electronics, especially when the whole system had recently been first turned on. The drift was measured to be small (0.1%) and was found to be linear with time. In this situation, a linear drift correction routine was executed whereby the difference in the initial and final points was divided by the total number of points in the loop and then added/subtracted to each point respectively. This was possible since each point was equally spaced in time. If the loops displayed a visible drift on-screen as the loops were being taken, this implied the sample was moving in the applied field and had to be secured more
Figure 2.18: Hysteresis loops obtained from an aluminium thin film for three different field settings. The loops show no artificial signal which may influence the shape of a hysteresis loop.
firmly. The loops were then normalised before being averaged, and then re normalised between ±1. It was important that the loops were initially normalised before averaging, since any drift in the system would displace each loop, and the averaging would be invalid. The data was displayed on-screen giving the user the option to save the data after examining the loop. The data for the first loop was saved in its measured state along with the averaged/normalised data. The software also calculated a number of magnetic terms, the coercive field Hc, the anisotropy field Hk, and the remanence Rm; these were also saved.
To ensure the system was measuring a magnetic signal and that no artificial signal was being added to the magnetic signal, a number of measurements were taken using an aluminium thin film which eliminated the magnetic signal from the system. Figure 2.18 shows the data for three loops taken at different fields. From the loops it is clear there is no artificial signal present, just random noise in the system. The Kerr sensitivity is also shown, and can be directly compared to Figures 2.14 and 2.15. The sensitivity to the non-magnetic signal can be assumed to be negligible (Ikerr<0.4%) compared to the sensitivity to the magnetic signal, which is approximately 15%. There was a very small dependence of the electronics on the applied field but this had no real influence, since the effect was only seen at high fields and is negligible. To confirm the reliability of the measurements, a number of samples were measured at York University under the guidance of G. Matauous, where a similar MOKE system existed. The measurements taken at York were comparable to those taken at Sheffield and are shown in Figure 2.19. The signal to noise ratio of the measurements taken at York were not as good, but the general shape of the hysteresis loops were comparable, considering that it was not possible to sample the exact same spot of each sample on the two respective systems.
MOKE is only sensitive to the penetration depth (10-20 nm) and the sampling area of the laser spot of 100mm in diameter, it was therefore important to complement these measurements, by taking bulk measurements using the inductive magnetometer. This ensured that the magnetisation process at the surface region of the sample was representative of the entire film. This was found not to be the case with the as-deposited FeSiBC films, since they exhibited a unique but peculiar magnetic anisotropy (discussed in more detail in Chapter 5) which influenced both the bulk and surface magnetic measurements. Figure 2.20 shows a number of loops obtained by the two respective systems. It should be remembered that the bulk MH-loops are sensitive to the average magnetisation process over the entire sample, whereas MOKE is only sensitive to the magnetisation process sampled by the laser spot. For these reasons alone, one would not expect identical hysteresis loops from the two systems. The bulk
Figure 2.19: Comparison of MOKE hysteresis loops taken at York University with those taken at Sheffield. (a) Loops taken at Sheffield. (b) Loops measured at York. The two sets of data obtained indicate that the measurements are comparable and presumably reliable.
Figure 2.20: Comparison of hysteresis loops taken by the inductive magnetometer (MH-bulk) with those obtained by the MOKE magnetometer (Surface). The bulk measurements are sensitive to the average magnetisation process, whereas MOKE is sensitive to the local magnetisation process. (a) Measurements taken from a film which has significant growth induced stresses. The MOKE measurement is sensitive to the local stress induced by the growth. (b) Measurements taken of the sample in (a) after being thermally treated to relieve the stress. The loops are now comparable, indicating that the magnetisation on a local scale are comparable to the entire film. (c) and (d) are further examples of how comparable the loops can be from the two systems. In (d) loops taken at orthogonal directions are shown.
hysteresis loop shown in Figure 2.20a indicates the coercive field is 150 A/m, were as the MOKE loop indicates a significantly higher value. In this sample the differences were attributed to the growth induced stresses which were simply averaged out by the bulk measurement and not by the MOKE measurement. It highlights how misleading the bulk hysteresis loops could have been if no MOKE hysteresis loops were available for comparison. Figure 2.20b is the sample in 2.20a after it has undergone a thermal treatment to relieve the growth induced stresses. Here the bulk and surface loops are now comparable, indicating the surface magnetisation is representative of the entire film. Figures 2.20c and 2.20d are other examples of how comparable the bulk and surface measurements can be.
The MOKE system was capable of measuring the magnetic properties of thin films down to film thickness of 10nm, and there was no minimum sample size restrictions. As long as the laser could be positioned on the magnetic material, it could be investigated. The lower sample volumes do not effect the signal to noise ratio, as they do with inductive magnetometer. The system was not calibrated to give absolute magnetisation values, since the Kerr signal is very sensitive to the precise settings of the polariser/analyser, and also to the surface conditions. Therefore the magnetisation scale was normalised.
2.4 MOKE Imaging
The Kerr effect has been used to observe domain structures for many years now, but it was initially considered to be a weak effect and it was thus difficult to obtain satisfactory images, especially from the surface of samples which were not flat and smooth. This led to the magnetic contrast of the images being quite poor for the majority of materials. The arrival of microcomputers, along with digital imaging, overcame such problems by the introduction of digital techniques, where the contrast from the non-magnetic background is digitally subtracted to enhance the magnetic contrast of the domains. The Kerr effect technique allows one to observe the domain magnetisation directly without any ambiguity, and the technique itself does not influence the magnetisation process. It is a non-invasive/destructive technique, compared to the Bitter pattern technique, which tends to spoil (dirty) the surface of the samples. Depending upon the experimental arrangement, there are generally no constraints on the sample dimensions or shape. Most importantly of all, the technique allows the magnetisation process to be observed under the influences of external forces, predominantly magnetic fields.
The experimental layout which was built is shown in Figure 2.21 and is similar to the MOKE magnetometer shown in Figure 2.6. It is a relatively low cost and simple arrangement, but was ideal for obtaining domain images off large areas of thin films. The white light source was provided by a halogen slide projector fitted with an infra red filter, which illuminated an area of 4x4cm. The detection system was an Electrim EDC1000 CCD camera, with a standard 50mm camera lens. The images from the CCD were relayed to a computer through a video card. An additional zoom lens was also available, which allowed imaging of domain structures of fabricated devices as small as 100mm. The resolution of the system allowed domain sizes as small as 100mm to be resolved. Two sets of Helmholtz coils were used to apply a transverse and/or longitudinal field in the plane of the sample, so that one could observe how the domain structure behaved under the influence of the two orthogonal fields. The outer set of coils were of the same specification as those of the MOKE magnetometer which applied the transverse field,
Figure 2.21: Schematic layout of MOKE imaging system. Note computer and KEPCO power supply are not shown.
whereas the inner set were designed to provide a longitudinal field of 2kA/m, which was sufficient to saturate the samples along the easy axis. All optical components were mounted onto two optical rails which were housed in a Faraday room to remove the ambient light from the system which was important to maximise the contrast of the images and screen the apparatus from electromagnetic noise. The white light imaging system was configured to detect the changes in the polarisation of the light due to the longitudinal and transverse Kerr Effect, as in the MOKE magnetometer at an incident angle of 300. The digital imaging of the domains was computer controlled by software written by Dr Richard Watts and the software for controlling the applied fields was written by the author. The samples were mounted onto a non-magnetic holder which provided the freedom to tilt the sample for the purposes of alignment. The samples were secured to the holder either using vacuum grease or double-sided tape depending on the size and nature of the sample.
The Kerr images obtained appear essentially as different shades of grey, which represent the differently magnetised domains. The direction of the magnetisation within the domains governs the direction in which the plane of polarisation of the incident light is rotated. This is shown in Figure 2.22a, where a simple domain structure is shown. The incident light which falls upon the oppositely magnetised domains, is rotated in opposite directions (the rotation is exaggerated). The analyser is adjusted so as to extinguish light being transmitted from domains magnetised to the right, for example. This has the effect of the domain appearing dark on the Kerr image. The light which is reflected off the domain, which is magnetised to the left, is therefore not extinguished and hence appears lighter. Figure 2.22b shows a Kerr image obtained from a FeSiBC film which possesses a uniaxial domain structure.
A digital differencing technique was employed to overcome the problems with the background light, surface imperfections and irregularities which produced a strong non-magnetic contrast which generally masked the magnetic contrast. The process [Schmidt et al (1985)] involved taking a digital reference image of the film in its saturated state, which was then the subtracted digitally from the subsequent images which contained the magnetic contrast. Figure 2.23 shows how the digital differencing technique vastly improved the magnetic contrast. The domain structures in Figure 2.23a are just visible
Figure 2.22: (a) Domain observation by the Kerr effect. (b) Kerr image obtained from a section of a FeSiBC film which has uniaxial anisotropy.
Figure 2.23: The domain image obtained from a section of an amorphous as-deposited FeSiBC film. See Chapter 5 for a detailed discussion about the domain structure. (a) a direct image of the film with no digital signal processing, (b) image obtained by subtracting a reference image from image (a), (c) the brightness has been digitally optimised for image (b).
in parts of the image, but are too faint to be satisfactory. Subtraction of the saturated reference image removes the majority of the non-magnetic contrast revealing the domain structure. The magnetic contrast of the resulting image is outstandingly sharp and very clear. Surface blemishes (finger-prints deliberately introduced as a test) at the two edges of the film do not appear, indicating that only the non-magnetic contrast has been removed. The digital difference images can be further improved, if necessary, by averaging, and other digital techniques such as brightness and contrast optimisation. Figure 2.23c represents a brightness optimisation of Figure 2.23b, and there is only a slight improvement, indicating the exposure time is neither too long or too short. It was not always possible to obtain images which did not require any digital enhancement (contrast and brightness optimisation) after the subtraction of the non-magnetic contrast. This was because it was difficult, and time consuming, in the early stages to optimise the reflected light and optics to produce the maximum magnetic contrast. Once the conditions were favourable, it took approximately 20 seconds to take an image, depending on the size of the image. Each image consisted of 20 images, which unless otherwise stated were averaged. The maximum image size was limited to 2.5´1.5cm.
As with all techniques, one needs to be aware of artificial effects which can occur, and which can be misinterpreted as being of a magnetic origin. Figure 2.24 shows how the digital difference technique can produce an artificial effect which appears to be magnetic. Figure 2.24a shows a typical domain image obtained from a section of FeSiBC film. At first glance, it would appear that there are two 1800 domain walls producing three domain regions. A more careful inspection reveals that a finer detail domain structure may exist within the main domains. This has been highlighted on both the main image and on the enlarged section of the image (arrows labelled [A]). This apparent fine domain structure only appears in parts of the image and the stripe domains are very uniformly spaced. There are three main reasons why it was thought this fine domain structure was doubtful;
 On repeated measurements the fine domain structure was not reproducible at all. It appeared to occur randomly, and not in the same regions of the film, even though the main domain structure was virtually identical.
 The stripe domains seem unaffected by the main domain walls and do not alter, even on crossing the domain walls. This is high-lighted by the arrow labelled [B] in Figure 2.24a and by Figure 2.24b where this apparently fine domain structure is unaffected by multiple domains and the direction of the walls. The domains always appeared to be vertical and very uniformly spaced, even after the sample had been rotated by 450, so the main domain structure was rotated through 450. This implied that the stripes did
Figure 2.24: Artificial effects which can appear in the magnetic Kerr images. The vertical stripe patterns are non-magnetic in origin and are produced by the CCD camera in conjunction with the subtraction of the reference image (see text). (a) An image obtained from a section of an as-deposited FeSiBC film. Notice the vertical stripe pattern in parts of the image, (b) the pattern is unaffected by multiple domains, (c) represents the image of (a) before the reference image was subtracted. Notice the stripe pattern occurs uniformly across the entire image.
not originate from a magnetic effect, or any surface structural effect of the film. If it were a surface structural effect, then rotating the sample would have also rotated the striped pattern.
 Figure 2.24c is the identical image of Figure 2.24a, but without the reference image being subtracted. Again, notice the dramatic improvement in the contrast. Close examination reveals that a vertical stripe pattern exists across the entire image. This effect has been attributed to the CCD camera, and only seems to occur under certain light illumination of the CCD camera. The stripe patterns which occur on the difference images are a consequence of the non-magnetic contrast being slightly different to the saturated reference image. This is assumed to be a result of the film moving on the application of the saturation field for the reference image. The samples were held in position either with vacuum grease or double sided tape to prevent any clamping stresses from being introduced (Section 5.931). The movement was not detectable by eye, but it was is assumed to be sufficient to cause such an effect. A number of images in this thesis are effected by this effect, and it is important to be aware that this was found to be an artificial effect.
2.5 Interpretation of the Kerr images
The Kerr images were obtained using both the longitudinal and transverse Kerr effects. The polar effect had no influence on the two effects, since the magnetisation was confined to the plane of the film because of the large demagnetising field. The longitudinal effect is only sensitive to the components of magnetisation, which lie parallel to the plane of incidence. This meant that any components of magnetisation perpendicular to the plane of incidence did not show any appreciable magnetic contrast. This is shown if Figure 2.25a where a Kerr image was taken from a sample which possessed a well defined uniaxial anisotropy. The easy axis was oriented perpendicular to the plane of incidence and the image was taken using the optical conditions which favoured the longitudinal effect. The image indicates no magnetic contrast in the horizontal axis. A close examination reveals that there is very faint magnetic contrast in the vertical axis (transverse effect). The positions of the domain walls have been marked in order to help the eye to locate the faint contrast. In order to make the Longitudinal Kerr effect sensitive to the vertical component of magnetisation in the film, the plane of incidence of the light needs to be rotated through 900 with respect to the sample. This was not feasible in this case. The other possibility was the rotation of the sample through 900 so that the longitudinal Kerr effect was sensitive to the magnetisation in this direction. This was also not possible in the current experimental arrangement without physically removing the sample from the holder. This led to two problems; the magnetisation, and therefore domain structure, changed on handling the film because of its magnetostrictive nature, and secondly, it was difficult to image the exact same area of the film upon rotation. Both of these problems made it difficult to correlate the two images precisely. These problems are overcome by use of the transverse Kerr effect, where it is not necessary to disturb the sample. Figure 2.25b is the identical Kerr image obtained of the domain pattern in Figure 2.25a, but using the transverse Kerr effect. The Kerr image shows a domain structure one would expect from a thin film possessing a uniaxial anisotropy. On rotating the sample, so that the easy axis is aligned parallel to the plane of incidence, the opposite effect occurs; the domain structure is only revealed by the longitudinal effect and not the transverse effect. The importance of the two effects is high-lighted by Figure 2.26,
Figure 2.25: Kerr images obtained from a FeSiBC film possessing a well defined uniaxial anisotropy. (a) Kerr image obtained using the longitudinal effect - sensitive to the magnetisation in the horizontal axis (b) Kerr image obtained using the transverse Kerr effect -sensitive to the magnetisation in the vertical axis.
where Kerr images were obtained using both effects to reveal the two components of magnetisation. Figure 2.26a shows Kerr images obtained from a FeSiBC film which has been demagnetised and Figure 2.26b are the domain images obtained where an applied field is applied in the direction indicated on the figure. The magneto optical sensitivity has been high-lighted by the arrows for each image. The contrast of the magnetic domains is clearest for the respective magneto optic sensitivity. Together the two images provide a more clear indication of the domain structure, since the individual images do not display all the domain structure. The final image was obtained by the combination of the two images by averaging them. This was a very crude method, but it provided an overall view of the domain structure, even though the grey scale of the averaged image is not quantitative. Quantitative methods have been developed [Rave et al (1987)] to map out the vector magnetisation using the grey (or colour) scale by combination of the two images, but this is a fairly difficult procedure, and requires a very stable system, along with the ability to apply fields in many directions for the purposes of calibration; it is not implemented here.
The domain images obtained using the longitudinal and transverse Kerr effects, provide only an overall view of the domain structure. They do not provide any direct information on the direction of the magnetisation within the domains themselves. For example, the Kerr images obtained in the longitudinal mode, only reveal dark and light regions, which correspond to components of the domain magnetisation magnetised in opposite directions, as shown if Figure 2.26. Any domains which are magnetised in the transverse sense will generally appear equally grey. Thus, we cannot infer directly the direction of the domain magnetisation. Even for simple uniaxial domain structures as shown in Figure 2.22 the dark regions correspond to the magnetisation pointing either to the right or to the left, and therefore the domain images need to be carefully interpreted. For magnetic materials which have a well
Figure 2.26: Domain images obtained from a FeSiBC film possessing a radial anisotropy (Chapter 5). Kerr images obtained using the longitudinal effect (sensitive to the magnetisation in the horizontal axis), and the transverse Kerr effect (sensitive to the magnetisation in the vertical axis). (a) Demagnetised sample. (b) Sample under the influence of an applied field.
defined crystalline structure, the crystalline anisotropy generally dominates the magnetic anisotropy. This simplifies the interpretation of the magnetisation of the domains, since prior knowledge of the magnetisation in such materials allows the determination of the direction of the domain magnetisation for all domains. In materials which do not possess a well defined crystalline structure, such as the amorphous FeSiBC thin films studied here, the interpretation of the resulting domains can be quite complex. In these types of materials the magnetisation is generally determined by random stresses, which tend to vary in magnitude and direction. These stresses are commonly induced during the fabrication process of the material, and therefore the resulting domain structures can be quite complex to interpret. Identification of 1800 domain walls, or closure domains at the edges of these samples, can help to piece the domain structure together, but this is not always the case. To establish the direction of magnetisation in a uniaxial domain structure as shown in Figure 2.22, is relatively straightforward. Here, a small magnetic field of known direction is applied along the direction of the domain walls. The favourable domains will grow in size, from which one can then establish if the dark regions correspond to domain magnetisation pointing to the left or right. In more complicated domain structures such as the radial domain structures shown in Figure 2.23 and discussed in Chapter 5, the domain magnetisation no longer points in the x or y directions. Here, MOKE loops are taken at various points on the sample, from which the direction of the domain magnetisation (easy axis) can be determined accurately. Using this information, one can then apply a small magnetic field whose direction is known, along the easy axis for the domain we are interested in, to determine the direction of the domain magnetisation. By this procedure it is possible to map out the domain magnetisation.
2.6 Magnetic Measurements Through Transparent Substrates
Magnetic films which were deposited on transparent substrates, allowed the magnetic characterisation of the lower surface of the film, or in the case of multi-layered films the bottom layer to be investigated (see MI chapter). It was found that the magnitude of the field strengths being used had no adverse effects on hysteresis or domain images obtained at the fields being used. Figure 2.27 show a number of MOKE hysteresis loops taken from a FeSiBC film. Hysteresis loops (a) and (b) are the respective loops taken from the upper and lower surface of a 500nm film; which are similar. Loops (c) and (d) were taken from the top surface of a film, but with a glass substrate positioned in front. This allowed the glass substrate to be rotated without disturbing the film, to ascertain if the glass substrates being used were altering the polarisation (Faraday effect) of the laser. It appeared that the glass substrates were not affecting the magnetic measurements. Figure 2.27b are domain images taken from a 750nm FeSiBC film, where images of the upper and lower (through the glass substrate) surfaces are similar. It can therefore be assumed that the magnetic measurements performed through the transparent glass substrates used here are reliable.
Figure 2.27: Magnetic measurements through transparent substrates. (a) Loop obtained from top surface, (b) loop obtained from lower surface through glass substrate (Corning®). Loops (c) and (d) were taken from the top surface of the film, but with a glass substrate positioned in front. The glass substrate in (d) was rotated through 900. (e) Domain images obtained from the upper and lower surface of a FeSiBC film. Images taken at H=15 A/m.
A magnetometer and a domain imaging system were constructed by the author to characterise magnetic thin films utilising the Magneto Optical Kerr effect (MOKE). The two systems allowed the possibility to fully investigate the in-plane anisotropy present in the amorphous FeSiBC films deposited in this study. The systems were also used by other colleagues within and external to University of Sheffield. The MOKE system built, was also used by Karl et al (1999) to interrogate the changes in the magnetic properties of a micromachined membrane-type pressure sensor. A very similar MOKE magnetometer system was also built by the author on an invitation by the Universidad Del Pais Vasco in Bilboa, Spain [Castano (1998)]. Comparisons of hysteresis loops with measurements done at York University and with bulk hysteresis loops have shown that results can be taken to be reliable.
The general principles of the Kerr effect have been discussed providing the reader with an insight into the implementation of the Kerr effect, and the interpretation of the domain images obtained and shown in the remainder of this study.