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 ..... MAGNETO-OPTICAL EFFECTS

The Magneto-Optical effects described here were first discovered by Michael Faraday, THE FARADAY EFFECT (an effect observed in transmission through a material) and the reverend J C Kerr THE KERR EFFECT (an effect observed on reflection from a material)

Often there is some confusion in referring to the Kerr effect in reflection from materials that are not optically opaque and where radiation may travel through the material and back again several times; eventually appearing on the side of reflection as a multiply reflected beam.The material properties that give rise to MO effects are simple and intrinsic and give rise to both Kerr and Faraday effects. It is convention to refer to effects in reflection as Kerr effects and in transmission as Faraday effects.
 

Magneto-optical effects may be observed in non-magnetic media such as glass when a Magnetic field is applied. Indeed, Faraday first discovered his effect in a glass rod with a magnetic field applied along the direction of propagation of an optical beam. However, the intrinsic effects are usually small in such cases.

In magnetic media (ferro-magnetic or ferri-magnetic) the effects are much larger, although still small and often difficult to detect. In these cases it is usual and convenient to refer to three principal orientations. These are:
 

• The Polar Orientation
• The Longitudinal Orientation
• The Transverse Orientation

These are best illustrated by means of three diagrams shown below.
 
 
 
 

In the longitudinal case the magnetisation vector is in the plane of the surface and parallel to the plane of incidence. The effect is simple and occurs for radiation incident in the P-plane (E-vector parallel to the plane of incidence) or the S-Plane (E-vector perpendicular to the plane of incidence). The effect is that radiation incident in either of these linearly polarised states is, on reflection, converted to elliptically polarised light. The major axis of the ellipse is often rotated slightly with respect to the principal plane and this is referred to as the Kerr rotation. There is an associated ellipticity and this is called the Kerr ellipticity. Similar effects also occur in transmission though one usually needs to have a thin film to see these since most magnetic materials are opaque in regions where they are magneto-optically active. The sign and magnitude of these effects are proportional to M and its direction.
 
 

In the Polar case the magnetisation vector is perpendicular to the plane of the surface. Like the longitudinal case  the effect is simple and occurs for radiation incident in the P-plane (E-vector parallel to the plane of incidence) or the S-Plane (E-vector perpendicular to the plane of incidence). The effect is that radiation incident in either of these linearly polarised states is, on reflection, converted to elliptically polarised light. The major axis of the ellipse is often rotated slightly with respect to the principal plane and this is referred to as the Kerr rotation. There is an associated ellipticity and this is called the Kerr ellipticity. Similar effects also occur in transmission though one usually needs to have a thin film to see these since most magnetic materials are opaque in regions where they are magneto-optically active. The sign and magnitude of these effects are proportional to M and its direction.
 
 

The transverse case is quite different from the previous two. First there is only an effect for radiation polarised in the P-plane (E-vector as show above). Second, in such a case, the reflected radiation remains linearly polarised and there is only a change in reflected (or transmitted) amplitude such that as M changes sign from +M to -M the reflectivity changes from R+DR to R-DR.
 

To continue. We now look at this in a little more detail. Putting in the E-vectors etc. Readers might like to note that it is the interaction of E with M (indirectly through Spin-orbit coupling) that gives rise to the MO effect. The H -vector plays no part at optical frequencies.

The diagram below shows the longitudinal case but it also applies to the polar case too. Here you can see the specific case of the E-vector incident in the S-plane (WHY? - I couldn't get the perspective right for the other case - yeh yeh and me a bit of an artist too!). The incident amplitude we take as unity (or one for those who can count). To a very good approximation (FIRST-ORDER EFFECTS) the reflected beam will consist of two orthogonal E-vectors. One is big and is the usual Fresnel amplitude reflection coefficient r. The other is small, and I mean small, and is called the Kerr Coefficient k. Now have a look at the diagram.
 

NOTE.

• If we flip M though 180 degrees. The k-vector will do the same.
• The M vector may point up for the polar case, but the effects are the same.

The problem is that r and k need not necessarily be in phase. Remember these are vectors representing oscillating EM waves. Let's look at these END-ON after reflection - looking along the beam!
 

The combination of the two orthogonal vectors r and k, in general, give rise to elliptically polarised light. The major axis of the ellipse is rotated slightly by the small Kerr angle known as the Kerr rotation and the associate ellipticity is the Kerr Ellipticity. Try to work out what happens when the M -vector is reversed.

The Complex Kerr rotation can be written as follows, since k<<r;
 

One could repeat this analysis for the Faraday effect where we operate in transmission and replace r by the transmission coefficient t and the Kerr coefficient k by the Faraday coefficient f. Then we have:-
 

In this case the incident radiation must be polarised in the P-plane. The result is two vectors the normal amplitude reflectance r and a small Kerr vector k whose magnitude and direction depends on M.

Now we have two intensity reflectances R-plus and R-minus corresponding to a switch between the two magnetisation states +M and -M.

APPLICATIONS
 

• Magnetic  Domain Imaging
• Hysteresis loop plotting
• Magneto-Optic Recording

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