Version 08.04.2016

Advanced Lab Course

MOKE Microscopy M209

Stand: 2016-04-08

Aim: Characterization of magnetization reversal of magnetic bulk and thin film samples by means of magneto-optical Kerr effect and recording of magnetic domain patterns of extended and patterned magnetic materials by Kerr microscopy. Contents:

1 Introduction 1

2 Basics 1 2.1 Ferromagnetic hysteresis 1 2.2 Magnetic domains 2 2.3 Magneto-optical Kerr effect microscopy 4 2.4 Equipment – the MOKE microscope 7 2.5 Electrical steel 7 2.6 Amorphous thin films 8

3 Experiments 9 3.1 Kerr microscope 9 3.2 Analysis of magnetic switching behavior and domains of FeCoBSi thin films 9 3.3 Investigation of influence of patterning on reversal in thin film samples 9 3.4 Investigation of the magnetic domain patterns on electrical steel 9

4 Analysis 10 4.1 Alignment of Kerr contrast in the microscope 10 4.2 Magnetic properties of a FeCoBSi film sample 10 4.3 Magnetic properties and magnetic domains of the patterned FeCoBSi film sample 10 4.4 Magnetic domains of electrical steel 10 4.5 Best image 10

5 References 11

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1 Introduction

Kerr microscopy is one of the most versatile techniques to image magnetic domains and

magnetization processes. The method is based on the magneto-optical Kerr effect (MOKE),

i.e. the rotation of plane polarized light in dependence of the magnetization direction on

reflection from a non-transparent sample. By this an image of the magnetization distribution

of the surface can be recorded. Moreover, magnetic hysteresis curves can be recorded.

2 Basics

2.1 Ferromagnetic hysteresis

The suitability of ferromagnetic materials for particular applications is determined largely

from characteristics shown by their hysteresis loops. Figure 1 displays a typical hysteresis

loop as expected for measuring the magnetization M as a function of the applied magnetic

field H for a ferromagnetic sample.

Fig. 1 Hysteresis loop of a ferromagnetic sample showing the saturation magnetization MS, the remanent magnetization Mr and the coercive field Hc. The applied field H and the plotted magnetization component M are collinear.

The sample is magnetized to the saturation magnetization MS by a strong enough applied

magnetic field. When the applied saturation field is then reduced to zero, the magnetization

decreases to the remanent magnetization Mr. The reversed field required to reduce the

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magnetization to zero is called the coercivity or coercive field Hc. The parameters Mr and Hc

can be used to characterize a ferromagnet.

The energy dissipated by a ferromagnet as it is taken around a circuit of its hysteresis loop is

proportional to the area of the hysteresis loop. If the area is small, the material is said to be

magnetically soft.

2.2 Magnetic domains

In general a non-saturated ferromagnet contains a number of small regions called magnetic

domains, where the local magnetization is homogeneous and reaches the saturation value. The

formation of domains allows a ferromagnetic material to minimize its total magnetic energy,

whereby the magnetostatic energy is the principal driving force for domain formation.

The direction of the magnetization of different domains does not need to be parallel. A

demagnetized sample consists of domains, each ferromagnetically ordered with a vanishing

total magnetization. The boundaries between adjacent domains are called domain walls. In

such domain walls the magnetization rotates continuously.

A classification of domain walls can be given by the angle of the magnetization between two

adjacent domains with the wall as boundary. The energetically most favorable types of

domain walls are those which do not produce magnetic poles within the material, and

therefore do not introduce demagnetizing fields. A 180° domain wall represents the boundary

between two domains with oppositely aligned directions of magnetization (Fig. 2a). Here the

magnetization perpendicular to the boundary does not change across the wall and therefore no

magnetic poles or demagnetizing fields arise. Also stable are 90° tilt boundaries (Fig. 2b),

representing the boundary between two domains with magnetization aligned perpendicular to

each other.

Fig. 2 (a) 180° domain wall and (b) 90° domain wall. The directions of magnetization in the adjacent magnetic domains are indicated by arrows.

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Fig. 3 (a) A common type of 180° domain wall in bulk materials is a Bloch wall, in which the magnetization rotates in a plane parallel to the plane of the wall. (b) In thin films another possible configuration is the Néel wall, in which the magnetization rotates in a plane perpendicular to the plane of the wall in order to reduce magnetic surface charges and thereby avoiding energetically unfavorable stray fields.

In order to explain the magnetic domain behavior of ferromagnetic samples one has to

consider the total free energy:

( )3

2 2 2 203sin cos2 2

sample

tot u S SV R

dV A grad K dV mφ l s θ = − ⋅ − − + ∫ ∫E M H M H

In the above equation only the energy terms are included relevant for the soft magnetic

samples investigated. The first term, the exchange energy reflects the fundamental property of

a ferromagnet, which favors a constant equilibrium magnetization direction. Deviations from

this homogenous magnetization invoke an energy penalty, the dependency of which can be

described by the gradient of the magnetization. The second term is called the Zeeman energy.

It describes the interaction of the magnetization with an external magnetic field H. It is

minimal for a parallel alignment of magnetization and magnetic field. The energy of a

ferromagnet in most cases also depends on the direction of the magnetization relative to a

certain axis of the material. This dependence is specified by the magnetic anisotropy energy.

The third term of equation describes the uniaxial case of anisotropy, in which the

magnetization lies preferably parallel or anti-parallel to a single easy axis. Ku is the uniaxial

energy density.

An easy axis of magnetization can also be introduced by straining a magnetic body. For

isotropic material and a uniaxial stress σ, the magneto-elastic coupling energy becomes the

fourth term of equation. The material parameter λS is the saturation magnetostriction.

The last term takes the magnetic stray field energy into account, which is connected with the

magnetic stray field Hs generated by the magnetic sample itself. Sinks and sources of the stray

field are “magnetic charges”, which arise for instance when the magnetization has

components perpendicular to the sample’s edge. The stray field energy in magnetic bodies can

be reduced by forming smaller magnetic domains up to the point where further reduction is

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balanced by the increase of domain wall energy (Fig. 4). A detailed discussion of the

energetic contributions that determine the magnetization distribution of a ferromagnet is given

in [1].

Fig. 4 Stray field energy Es for a cubic sample with different numbers N of domains. The creation of domain walls reduces the stray field energy Es, but increases the domain wall energy Edw.

2.3 Magneto-optical Kerr effect microscopy

Domain observation by magneto-optics is based on a weak dependence of optical constants on

the direction of magnetization M. The magneto optical Kerr effect is the rotation of the plane

of polarization of a light beam during reflection from a magnetized sample. For most

materials the amount of rotation is very small and depends on both the direction and the

magnitude of the magnetization. It may be applied to the characterization of any metallic or

otherwise light-absorbing magnetic material with a sufficiently smooth surface. The Kerr

effect can be rigorously derived from Maxwell’s equations and proper boundary conditions.

The origin of the magneto-optical effects lies in Zeeman exchange splitting together with

spin-orbit interaction. The symmetry of interaction of a plane-polarized electromagnetic light

wave with a magnetic material can be understood assuming a Lorentz force on moving

electrons initiated by the electrical vector E of the wave (this is not the underlying physical

mechanism).

The occurring change of polarization is sketched in Fig. 5a for the so-called longitudinal Kerr

effect. It generates a magnetic contribution to the reflected light amplitude, the so-called Kerr

amplitude K, which is polarized perpendicularly to the normally reflected amplitude N and

causes rotation of the light through interference with N. In the Kerr microscope for domains

with opposite magnetization, a domain contrast is produced if most of the reflected light of

one domain type is blocked by an analyzer (Fig. 5b). If a noticeable phase shift occurs

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between N and K, the result is an elliptical wave that can no longer be detected by the

analyzer. This problem can be eliminated by use of an optical phase shifter (e.g. a quarter-

wave plate – see Fig. 5c), which should be attached in front of the analyzer in such a way that

it can be rotated. It is then possible to eliminate the ellipticity of the darker domains and

thereby to extinguish their light. It should be noted, that the words compensator, retarder

plate, phase shifter and quarter-wave plate all refer to the same device. The longitudinal Kerr

effect occurs with polarization of light in the plane of incidence (so called s-polarization as in

Fig. 5a) and polarization perpendicular to the plane of incidence. The effects have the same

magnitude but differ in sign i.e. black and white contrast in images will be inverted.

Fig. 5 (a) Illustration of elementary magneto-optical interaction using the Lorentz force to demonstrate the symmetry for the longitudinal Kerr effect. The sample is illuminated using plane-polarized light. The electric field E of the incident light, together with the normalized magnetization vector m, generates a Lorentz movement of the electrons ("right-hand rule"). If the resulting Lorentz speed vLor is then projected onto the plane perpendicular to the direction of propagation of the reflected light, the magneto-optical amplitude K that applies to the reflection is obtained. The interference of the normally reflected component N and the Kerr component K results in magnetization-dependent light rotation, which, with the help of an analyzer, leads to the domain contrast (b). The action of the compensator as a phase shifter is illustrated in (c). Appropriate rotation of the quarter-wave plate makes it possible to linearize elliptically polarized light (adapted from [1]).

An appropriate direction of incidence and polarization of the light has to be selected for every

direction of magnetization. As a simple rule, the rotation of the light plane (and consequently

the Kerr signal) is proportional to the magnetization component that is parallel to the reflected

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beam of light. This rule implies that magnetic domains which are magnetized parallel to the

sample surface require oblique light incidence and for maximum contrast the incidence plane

of the light must be parallel to the direction of magnetization (longitudinal Kerr effect). The

longitudinal Kerr signal vanishes for perpendicular incidence. On the other hand, in the case

of perpendicular light incidence maximum contrast is exhibited by domains that are

magnetized perpendicularly to the sample surface (polar Kerr effect).

The main components of a two principle different types of Kerr microscopes are represented

schematically in Fig. 6. As the Kerr effect is weak, a highly intensive light source is used, for

instance a high power LED.

Fig. 6 Symmetrical ray diagram of a Kerr imaging setup for high resolution magnetic domain observations in reflection. (a) Optical path of illumination and (b) simplified path of observation (only the primary image plane is shown). Köhler-type illumination of the specimen is realized by a high power fiber coupled LED light source. Two sets of rays corresponding to two different points in the conjugate sets of aperture planes (AP) are sketched. The locations of rotatable polarizer, retarder plate, and analyzer are shown. The corresponding conjugate sets of field or image planes (IP) are indicated. The image of the AP obtained from a conoscopic image of the back-focal (Fourier) optical plane of the objective lens with insertion of a Bertrand lens in the optical path is shown. (c) Optical ray diagram of a large view magneto-optical Kerr microscope (from [2]).

The domain contrast is optimized by the rotation of analyzer and compensator. For the high

resolution Kerr microscope setup the position of the LED fiber output, controlling the

illumination, has to be adjusted so that angle and plane of incidence can be chosen, allowing

to optimize the Kerr sensitivity to in- or out-of-plane magnetization configurations. The

application of magnetic fields is possible using an electromagnet.

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2.4 Equipment – the MOKE microscope

The Kerr microscope consists of the following components: a polarization microscope, a

control computer, an optical table with vibration isolation, an electromagnet, and a sample

stage. A significant enhancement of magnetic contrast is achieved by digital image

processing. The standard procedure starts with a digitized image of the magnetically

homogenous state, where in an external ac or dc magnetic field all domains are eliminated.

This background (reference) image is subtracted from a state containing domain information.

Non-magnetic contrasts, which do not change, are subtracted during this process. So in the

difference image a clear micrograph of the domain pattern is obtained, which can digitally be

enhanced free of topographic structures. This subtraction process is best carried out in real

time at least video frequency, making it possible to view magnetization processes while

retaining the same reference image.

The same effects that are used for imaging can also be used for the general magnetic

characterization of the material, i.e. local magnetic hysteresis curves may be obtained by just

plotting the average intensity of the Kerr images as a function of applied field.

2.5 Electrical steel

The control of the magnetic reversal in soft magnetic bulk materials is essential for improving

their energy efficiency. Electrical steel is a soft magnetic polycrystalline metallic alloy that is

used as a core material in electrical transformer cores. For grain-oriented electrical steels the

reduction in core losses in recent years are due to two major technological advances,

improved texture control and the control of the magnetic domain structure.

Grain oriented electrical steel or transformer steel has a so-called Goss structure, where a

<100> axis lies in the plane of the material. Ideally a (110)<001> crystal orientation is

obtained due to a discontinuous or abnormal grain growth during a high-temperature

annealing. An image displaying the Goss-texture is displayed in Fig. 8.

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Fig. 8: Goss texture. The <100>-axes are the easy axes of magnetization.

Magnetic domain observations deliver the scientific fundaments to understand the important

issues of nucleation and annihilation of surface closure domains and pinning processes in the

movement of 180° domain walls and their interaction with defects like grain boundaries.

2.6 Amorphous thin films

Magnetic amorphous alloys obtained by rapid quenching of the melt or by means of

sputtering are excellent soft magnetic materials with a wide range of technological

applications. Despite the absence of a crystalline structure, amorphous materials can possess a

(uniaxial) magnetic anisotropy. The most common compositions for soft magnetic

applications are metal-metalloid based (Fe, Co, Ni)-(Si,B) alloys with a metalloid contents of

about 20%.

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3 Experiments For documentation and for later evaluation store the obtained magnetic hysteresis curves and

images of domain patterns that you have recorded. The experiments will be performed under

supervision. Do not try to operate the Kerr microscope without being first instructed by the

supervisor.

3.1 Kerr microscopes Identify the optical elements as sketched in Fig. 6 at the microscopes. Which elements are

arranged differently?

3.2 Analysis of magnetic switching behavior and domains of FeCoBSi thin films The aim of the investigation is to characterize the magnetic switching behavior of an extended

amorphous FeCoBSi thin film sample. Therefore hysteresis curves are recorded along the

easy axis of magnetization and along the hard axis of magnetization. Obtain typical domain

images at remanent state saturating the samples along and perpendicular to the easy axis of

magnetization.

3.3 Investigation of influence of patterning on reversal in thin film samples The aim of this part is to investigate the switching behavior of FeCoBSi thin film structure.

Record the magnetization loops along both perpendicular edges of the square elements.

Identify the easy axis of magnetization in the patterned sample. Obtain typical domain images

after demagnetization of the sample along and perpendicular to the easy axis of

magnetization. Obtain typical domain images at remanent state saturating the samples along

and perpendicular to the easy axis of magnetization. Compare the obtained magnetic domain

patterns.

3.4 Investigation of the magnetic domain patterns on electrical steel The aim of the investigation is to characterize the different domain patterns in SiFe. Obtain

typical surface domain images after demagnetization of the sample along and perpendicular to

the easy axis of magnetization. Can you identify different grains? How are the domain

patterns changing with the application of a magnetic field along the easy axis and hard axis of

magnetization?

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4 Analysis 4.1 Alignment of Kerr contrast in the microscope Describe the necessary steps in order to achieve longitudinal Kerr contrast in the Kerr

microscopes. How many ways are to obtain longitudinal contrast in the microscopes?

4.2 Magnetic properties of a FeCoBSi film sample Describe the switching behavior in terms of remanent magnetization, coercive field and

saturation field. Is there any hint for a magnetic anisotropy?

4.3 Magnetic properties and magnetic domains of the patterned FeCoBSi film sample Describe the observed domain patterns in terms of domain width and preferential

magnetization directions. Is there any dependency of the magnetic domain width on the

magnetic history? How does the hysteresis loop change with patterning and direction of field

(compare to the non-structured sample)?

4.4 Magnetic domains of electrical steel Describe typical domain patterns obtained at the surface of the electrical steel sheet. What

does it tell you about the crystallographic orientation of the iron sheet? Discuss how the

surface domain patterns obtained with and without the application of a magnetic field

correlate to the bulk domain structure. Is the magnetic flux propagating across the grain

boundaries?

4.5 Best image Which is in your view the nicest domain image that you took? Why?

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5 References [1] A. Hubert, R. Schäfer, Magnetic Domains, Springer-Verlag Berlin, Heidelberg, 1998

[2] J. McCord, Progress in magnetic domain observation by advanced magneto-optical

microscopy, Journal of Physics D: Applied Physics 48, 333001 (2015)

[3] http://magnetism.eu/esm/2005-constanta/abs/mccord-abs.pdf

[4] http://magnetism.eu/esm/2005-constanta/slides/mccord-slides.pdf

[5] N. Spaldin, Magnetic Materials – Fundamentals and applications, Cambridge, 2003