Investigation of Magnetic Domains in Yttrium Iron Garnet

13th December 1998David.R.Gilson

Abstract

This document is an account on a study of the behaviour of magnetic domains in Yttrium Iron Garnet (YIG). The sample of YIG was in the form a thin film, cut perpendicular to the material's easy axis so that the Faraday effect could be used for observations of the YIG hysterisic behaviour. Other observations made were in the form of photographic data taken from a microscope focused on the sample of YIG. These displayed the change in the domain configuration as a H-Field was applied parallel to the easy axis in varying field strengths. The field was supplied from a coil contained within the casing of the sample (the YIG sample was mounted on a transparent substrate of gadlin gallium garnet within the casing).

A further study of the YIG magnetic domains was that of bubble domains. These are isolated, non-extended domains, the study of such domains demonstrated the elasticity of domain walls and the analogous behaviour with liquid surface tension.

1) Introduction

Magnetic theory has been worked since classical times, back then it was concerned with fields and the bulk properties of magnetic materials. Since then, our attention has turned to the source of magnetic behaviour in materials, down to the constituent units of matter, the atomic level. Modern work has been to determine how the microscopic magnetic properties determine the macroscopic bulk properties.

There are different types of magnetic materials, such as paramagnetics and ferromagnetics. There former class of materials are of a chaotic order. The magnetic moment (which is generated from the spin of electron on each atom) in every atom are randomly aligned, this leads to no microscopic or macroscopic spontaneous magnetisation. The latter is a more cooperative phenomena. Atoms in ferromagnetic materials tend to align themselves with their neighbours, so there are regions of local magnetisation present in ferromagnets. Since YIG is ferromagnetic at room temperature (which is the thermodynamic environment in which the experiment is performed) we shall concentrate our attention on the properties of ferromagnets.

When ferromagnets are heated above a temperature called the Curie temperature it becomes paramagnetic. Langevin produced a theory of paramagnetism based on Boltzmann statistics. Weiss [1] used the Langevin model and added an extra term, the so-called Weiss mean field, which was in effect an inter atomic interaction which caused neighbouring atomic magnetic moments to align parallel, this was favourable for energetic considerations. Weiss's theory held under the assumption that each atomic moment interacts equally with every other atomic moment in the solid. This was a good assumption in the paramagnetic phase because of the homogeneous distribution of magnetic moments. However, in the ferromagnetic phase the magnetisation is locally inhomogeneous, on a scale larger than each domain at least. Subsequently the Weiss mean field model was applied to individual domains only. So we have the situation that in ferromagnets in a demagnetised state, even though there are domains which may have a fairly high magnetisation, the overall magnetisation of the whole crystal is zero when summed over the whole crystal.

The boundaries between magnetic domains are called domain walls. Domain walls are the transition between different alignments of magnetic moments. It should be generally assumed that these walls are of a finite width. If we think of a finite width of domain wall, then we can think of a transition layer where the atoms realigned themselves between domains, with layers of atoms between domains where the atoms belong to neither one domain or the other. This leads us the question of how thick are domain walls ?

Figure 1, Alignment of individual magnetic moments within 180 degree domain wall (source [4]).

The idea of such transition layers between domains, where realignment occurs, was first suggested by Bloch [2]. These layers are sometimes referred to as Bloch walls, however Bloch walls are not the only type of domain wall. The total angular displacement between domain is 180 or 90 degrees, and this change is a gradual one over many atomic layers. For example, the width of 180 degree Bloch walls in iron is 395 Å (or 160 atomic layers) [3].

Because of the trans-aligned state of the atoms in domain walls, it is these atoms that can be most easily aligned to the direction of an applied external field. A simple model to consider domain walls is to consider them as an elastic membrane. Observational data shall of such behaviour shall be seen later. When such magnetic forces act on domain walls, we call this domain wall motion. The walls (and domains) do not actually move, it is just that the atoms which constitute each region are changing. As an

external field is applied, domain wall atoms begin to switch direction and the atoms encompassed by the wall increase in numbers, and so on into the domains. This effect can be seen most effectively in a special type of domain, bubble domains. Bubble domains are isolated, non-extended domains, they could also be considered as self terminating domain walls that encompass, infinitesimally small domains. When an external field is applied in a particular orientation, these bubbles can be forced into changing into fully extended domains. If care is taken with the applied field, the process can be completely reversed (this is seen later).

A good way to represent the behaviour of a ferromagnet is through what is known as the Hysteresis loop. Which is a plot of magnetisation against applied H field. The Hysteresis loop is typically a sigmoid-shaped looped. Hysteresis is given rise by dislocations or impurity elements in the metal cause an increase in the energy lost during the magnetisation process, in the form of a kind of internal friction. It is these imperfections that give rise to hysteresis [5].

2) Experimental procedure

The first part of the investigation was to study the demagnetised sample of YIG. The sample of YIG crystal was contained in a metal disk-like casing on a (visibly) transparent substrate of gadolinium gallium garnet. The crystal sample had been cut in a plane perpendicular to the crystal's easy axis, so that changed in the domain structure could be easily observed. Within this casing was a current carrying coil so that an external field could be applied in a sense parallel to the easy axis of the YIG sample. The coil was also capable of heating the sample to the Curie temperature, if desired. The sample casing was placed under a microscope for observations of the domain behaviour. A special "pin-hole" Polaroid camera was used by means of an eye piece adaptor to recorded the image of the domain patterns. The field through the coil was indirectly measured by an Avometer measuring the current through the field coil. The current, and hence the field, was gradually increased up to the magnetic saturation point of the YIG sample (see results), i.e. all the magnetic moment of the atoms of the crystal were aligned in the same direction (along the easy axis in fact).

The current supply to the field coil had the ability to send current pulses. This technique was used in conjunction with the field strength control to generate bubble domains (see introduction). Once such bubbles were formed, they were photographically recorded. To manipulate them the coil current was held constant and an permanent bar magnet (external to the casing) was used to manually manipulate the external field gradient. This entailed the experimenter watching through the microscope while moving the bar magnet around the sample casing and watching for a change in the domain pattern. Once a change had been observed, the resulting pattern was again photographically recorded. The bubble domains could be returned to their original form by repeating the same procedure as before by manually manipulating the external field gradient by the use of a permanent bar magnet.

The last part of the investigation was to obtain a hysteresis loop of the YIG sample. This was done by making use of the Faraday effect, since the sample was thin enough for this technique to be useful. The apparatus used is shown below in Fig. 2.

Figure 2. Experimental set up for observing the hysteresis loop of YIG.

The data for the loop was collected by systematically; increasing from zero to magnetic saturation in one direction from a demagnetised state, decreasing to zero, increasing to saturation in the opposite direction, decreasing to zero again and increasing to saturation in the original direction. To obtain direct information of the magnetic values of the system was beyond the scope of the investigation, so a more qualitative analysis by recording the coil current and the signal from the CCD mounted in line with the laser and YIG sample.

Results

Shown below are copies of photograph taken while taking the YIG from a demagnetised state to a saturated state. All the photographs are of a 100 times magnification. References to current give indication to field strength perpendicular to the plane of the page.

Note to reader. Unfortunately photographs were property of the University of Hull's Physics department and therefore figures 3 to 12 could not be included in this copy

Figure 3. YIG sample with no coil current, demagnetised state.

Figure 4. YIG sample with coil current of (4±1%) Amps.

Figure 5. YIG sample with coil current of (8±1%) Amps.

Figure 6. YIG sample with coil current of (10±1%) Amps.

Figure 7. YIG sample with coil current of (10.8±1%) Amps.

Figure 8. YIG sample with coil current of (12±1%) Amps.

Figure 9. YIG sample at saturation with coil current of (16±1%) Amps.

The exposure of each photograph varied which is the reason for the variation in contrast from photo to photo.

Next we consider the magnetic bubble domains. After varying and send random pulses through the coil, a set of bubble domains were created. These are shown in Fig. 10.

Figure 10. Bubble domains in the YIG thin crystal.

As a uni-axial external field gradient was manually applied to the YIG crystal (with a permanent bar magnet) the bubble patterns changed. They expanded into full domains. This is shown in Fig. 11.

Figure 11. Effect on bubble domains by external field gradient.

By articulating the permanent magnet (outside the casing) in a similar way, the newly formed domains were returned to their original bubble state. This is shown in Fig. 12.

Figure 12. Reformed bubble domains.

The final result obtained is the hysteresis data. This data was obtained from the process described in the last section. The data from the CCD was normalised, information about the CCD signal is not really useful given the lack of other data in this investigation, so we concern ourselves with the shape of the graph only.

Figure 14. Hysteresis plot of the YIG sample.

The error in the coil current was 1%.

Conclusion

From figures 3 to 10, it can easily be seen that the saturation occurs at a field strength corresponding to ±(16±1%) Amps coil current. The behaviour is as expected, an applied field causes the all the atoms to align their magnetic moments, thus destroying any domain patterns. It has also been shown that so called bubble domains can move under the influence of an external field. In moving, we mean that they can stretch their boundaries and expand into full domains and back again. This is supportive of the theory of treating domain walls as elastic membranes.

It has also been shown that the YIG crystal also has a hysteresis loop as general ferromagnets have.

References

[1] Jiles D.C. "Introduction to Magnetism and Magnetic Materials", Chapman and Hall, London, 1991. pp138.

[2] Bloch, F. (1932) Z. Physik, 74, 295.

[3] Jiles D.C. "Introduction to Magnetism and Magnetic Materials", Chapman and Hall, London, 1991. pp162.

[4] Kittel, C (1949) Revs. Mod. Phys., 21, 541.

[5] Jiles D.C. "Introduction to Magnetism and Magnetic Materials", Chapman and Hall, London, 1991. pp114.