2. Theoretical background
2.1 the Magneto-Optical Kerr Effect
If a beam of plane polarized light, here defined as the plane that contains the E-vector, illuminates a metallic surface the reflected beam will, in general, be elliptically polarized. However in these cases when the plane of polarization of the incident light is either perpendicular or parallel to the plane of incidence then the reflected light is also plane polarized[8]. The reason why this is so is in no way due to any peculiarities of metallic reflection but follows straight-away from the fact that the plane of incidence is a plane of symmetry for the system. Incident light polarized parallel or perpendicularly to this plane is therefore always reflected as plane polarized light.
This symmetry is destroyed by the presence of a magnetic field, for although a uniform magnetic field possesses a plane of symmetry perpendicular to the direction of the field its sign is associated with an unsymmetrical rotation about this direction[9]. Consequently, the reflection of polarized light from the surface of a magnetic material will in general be elliptically polarized even if the incident light is polarized parallel or perpendicular to the plane of incidence, thus carrying information of the magnetization of the material. This phenomenon is known as the magneto-optical (MO) Kerr effect and is used in magneto-optical recording systems. A Scottish physicist, John Kerr [10], discovered this effect in the latter part of the 19th century. The degree of ellipticity imparted to the reflected beam is small and the effect can be regarded as a rotation of the plane of polarization of the light on reflection. The effect is greatest in the ferromagnetic metals, is smaller in ferrites and barely observable in paramagnetic metals. The magneto-optical effects can be shown to be proportional to the magnetization M in ferromagnets or a linear summation of sublattice magnetization?s in ferrimagnets. [11].
There are three different dispositions of the magnetic field with respect to plane of incidence and these give rise to three different effects each governed by slightly different laws.
Fig 2.1a-c Kerr effect
(a) Polar Kerr effect (Figure 2.1a), i.e. magnetization normal to the reflecting surface. The effect is largest in this case and it is the only situation in which an effect exists when the light is incident normally on the surface. Polar Kerr effect is used in magneto-optical recording.
(b) Longitudinal Kerr effect (Figure 2.1b), i.e. magnetization in the plane of the reflecting surface parallel to the plane of incidence. This is often referred to as the meridional effect. The rotation is smaller than for the polar effect usually by a factor of 3 or 4.
(c) Transverse (equatorial) Kerr effect (Figure 2.1c), i.e. magnetization in the plane of the reflecting surface and perpendicular to the plane of incidence This is sometimes referred to as the equatorial effect. Any other situation can easily be seen to be a combination of two or more of these.
In magnetic materials there are certain directions along which the magnetization prefers to orient itself, easy axis, or tries to avoid, hard axis. The magnetic anisotropy constant Ku is the energy density for which the magnetization rotates from the easy axis to the hard axis. As an example Co, HCP structure, has the magnetic anisotropy 5*106 erg/cc [12], with the easy axis aligned along the c-axis. Large values of magnetic anisotropy are required in magnetic recording media in order for the magnetization to remain in the recorded direction. In magneto-optical recording perpendicular anisotropy, easy axis aligned with the film normal, is required whereas media with in-plane anisotropy, easy axis in the film plane, is the material of choice in hard disc fabrication.
The uniaxial magnetic anisotropy constant is proportional to the hysteresis
loss area above the hard axis in the first quadrant of the hysteresis curve.
Fig 2.2 Hysteresis loop with both in-plane and perpendicular
loops
One way to estimate Ku is to extrapolate the initial slope of the hard axis M-H measurement to Ms and thereby gain a value of Hk. The relationship between Ku, Hk and Ms can be written like this[9]:
Trying to estimate Ku by measuring Hk gives large errors. A better method is to use a torque magnetometer[3.3].
2.3 Rare Earth - Transition Metal Amorphous
Alloys
Amorphous rare earth (RE) - transition metal (TM) alloys are at the present time the only commercially available magneto-optical storage media. The heavy rare earth elements like gadolinium and terbium have high magnetic moments but low Curie temperatures. By exchange coupling the rare earth to magnetic transition metals, like cobalt or iron, it is possible to take advantage of the high moments of the RE at room temperature. The heavy RE (Gd to Lu) always couple antiferromagnetically to TM moments and thus the net magnetization is the difference of the subnetwork magnetization?s. The term subnetwork is used in place of sublattice when describing amorphous ferrimagnets.
MNET = MRE - MTM (2.2)
Where MNET is the magnetic moment per formula unit
in Bohr magnetons (
),
MRE is the rare earth subnetwork magnetic moment and MTM
is the transition metal subnetwork magnetic moment.
The light RE generally couples ferromagnetically so they are used in permanent magnets.
The different behavior of the light and heavy rare earth atoms can be explained as a consequence of the nature of the RE-TM exchange interaction combined with Hund's rule. The electron configurations of the RE atoms are 4fn5s25p65d0-16s2, where the 4f shell can have a maximum amount of 14 electrons. The light rare earth has less than half filled 4f shell and the heavy has more than half filled 4f shell. For shells with less than half filled, states with lower J values are lower in energy. Following this J=L-S for the light RE and the heavy RE have J=L+S. The exchange between the rare earth spin and the transition metal moment is always negative. The heavy RE atoms have their J and S in the same direction so therefor their net moments are antiparallel to the TM moment. In the case of the light RE atoms, L is typically greater than S so J becomes antiparallel to S but parallel to the TM moment which means that the net moments of the RE and TM are parallel.
As to the reason for the negative exchange between the RE and the TM, it is likely that the rare earth exchange mainly involves the 6s and 5d that have much greater radial extent than the 4f electrons. The RE 5d and the TM 3d interatomic exchange is probably positive, ferromagnetic, but the 5d-4f intra-atomic exchange is strongly negative. Since most of the RE magnetic moment is associated with the 4f electrons the net result is as described above.
2.3.1 Some of Advantages of RE-TM alloys
When you grow crystalline the orientation of the c-axis fluctuates from crystal to crystal. Since the material has an unisotropic crystal structure its reflectivity for polarized light is a strong function of orientation. Consequently, the medium has a high grain noise even when it is magnetically saturated. The amorphous materials solves this problem immediately, thou they have no grain boundaries. The signal to noise ratio becomes significantly higher.
The amorphous RE-TM alloys have a combination of properties, which make them very suitable for magneto-optical storage media. Some of these properties arise from the fact that they are ferrimagnets. This gives them low saturation magnetization but at the same time have large magneto-optic Kerr rotation. They can be produced with great uniaxial anisotropy under certain deposition conditions and some compositions can be made with very low coercivity, but square loop high coercivity material suitable for storage media can also be obtained. The conditions, which produce good media properties, are also compatible with deposition on polymer substrates.