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Enhancement of the Magneto-Optical Kerr Effect in Permalloy
We examine the longitudinal magneto-optic Kerr effect (MOKE) in thin permalloy films and attempt to enhance the strength of the MOKE signal using a glass prism. A sample placed within a magnetic field was probed using a 635 nm diode laser in order to measure the fractional Kerr signal. The measurement was repeated with a glass prism covering the sample. It was predicted that the prism would have the effect of approximately doubling the maximum strength of the signal. We obtained values that are within 1 standard deviation of what was predicted. The addition of the prism resulted in a smaller enhancement than expected at 49%.
Introduction
The magneto-optic Kerr effect was discovered by physicist John Kerr in 1888 [1]. It causes linearly polarized light that has been reflected off a magnetized surface to experience a rotation in its polarization by the Kerr angle. The MOKE is similar to the Faraday effect, which occurs in light passing through a magnetized medium. There are three different geometries for which the Kerr effect may be observed, each involving a different magnetization direction in the material: longitudinal, transverse, and polar [1]. Here we consider only the longitudinal MOKE. In this geometry, rotation of polarization occurs when the magnetization vector is parallel to both the sample surface and the plane of incidence, which is the plane that contains both the incident and reflected beams of light. Reversing the direction of the magnetization reverses the direction of rotation of the polarization.
The dependence of light polarization on magnetization has made the MOKE a useful tool in numerous applications. Notably it has been used in storage devices such as the magneto-optical (MO) drive, which was introduced in 1985 [2]. Information is encoded in magnetic 'bits', where two opposite magnetization directions represent a zero or a one. These bits are then read via changes in polarization of a reflected probe laser. MOKE is also a powerful technique in physics of studying the magnetic structure of materials [2]. Since Kerr rotation is small, typically on the order of 1/1000 of a degree, enhancing the strength of its signal is desirable and allows it to be detected more easily. This is particularly vital in the study of magnetic nanostructures that are smaller than the diameter of the probing laser; only a very small portion of the beam experiences rotation and must be differentiated from the rest of the beam. It has been found that altering the index of refraction of the incident medium can enhance the strength of the MOKE signal [3].
MOKE Theory
Abstract
In the longitudinal Kerr effect, the magnetization vector of the material under inspection is parallel to both the plane of incidence of the light beam and to the sample itself. Consider the above figure. If linearly polarized light is reflected from a non-magnetized surface, it will retain this initial polarization and no Kerr effect is observed. However, if the material possesses a longitudinal magnetization (shown by
in the diagram), the incident light will experience a rotation in its polarization . This is referred to as the Kerr angle. Flipping the direction of magnetization will flip the direction of the polarization change of the light.
To measure the very small changes in polarization that result from the Kerr effect, a linear polarizer called an analyzer is introduced after reflection that is positioned at an angle , as seen in the figure below.
If the direction of the magnetization is flipped, the light that passes through the analyzer obeys Malus' Law. The intensities I+ and I- of the light at either magnetization direction can thus be expressed as:
The quantity we want to measure is the fractional MOKE signal, which is highly sensitive to any changes in the Kerr angle. To obtain this, we divide the difference of I+ and I- by their average, yielding
Each r is a function of the indices of refraction of both the permalloy sample and the incident medium, the angle of incidence, and several other quantities that may be looked up for a given material [4]. For brevity, these equations will not be given here. However, by increasing the index of refraction of the incident medium, a larger Kerr angle and thus a larger fractional MOKE signal should theoretically be obtained. The figure below [original] shows the fractional MOKE signal
where is a quantity introduced to compensate for imperfections in the optical equipment known as the depolarization fraction.
Enhancement
The Kerr angle can be theoretically predicted using the equation below, where rps and rss are elements of the Fresnel reflection matrix. Each quantity rij represents the ratio of j-polarized light to i-polarized light.
, calculated from the above equations and the relevant physical quantities using Mathematica, plotted vs. analyzer angle
. was estimated to be on the order of . As can be seen, the Kerr signal theoretically should double when the prism is added.
Methods
The design of this experiment is shown below. A 635 nm diode laser was sent through both a neutral density filter and a chopper before being linearly polarized. This polarized, chopped light was then reflected off of a thin permalloy sample, which was magnetized using a helmholtz coil. These coils were powered using a bi-operational power supply (BOP).
The reflected beam, with its induced MOKE signal, was then passed through a quarter wave plate to remove ellipticity. While the Kerr effect induces a slight ellipticity to the polarization, this effect is unimportant to this experiment and can be easily eliminated. The light then passed through a half wave plate, which was rotated with a stepper motor to simulate the rotation of the analyzer angle. The half wave plate was rotated through 10 degrees in 0.2 degree increments, with a data point taken each increment. The beam then passed through a Glan-Thompson analyzer, which split the light into its polarization components. These components were then each passed through a 50 mm lens to focus them and collected by a photo-diode.
The photo-diodes were each read by a lock-in amplifier, which was controlled using LabVIEW programming. This programming was also used to control the magnetic field and the stepper motor.
The first step in this experiment, after aligning the optics, was to take a measurement of the general Kerr angle. This was done through a hysteresis loop, which was produced by balancing the photo-diodes and sweeping the magnetic field of the sample while holding all other variables constant.
Once this was accomplished, the second step of the experiment was to obtain data for the non-enhanced MOKE signal. This data was obtained in the fashion described above, and was plotted as the fractional MOKE as a function of analyzer angle. The third step of this experiment was to take a similar data set enhanced with a glass prism.
The glass prism was attached to the sample using an index matching gel. This gel also assured that there was no air in between the sample and the prism. Once this was completed, the data collection process was the same as that for the un-enhanced runs. The data was plotted in the same way, and was then compared with both the un-enhanced data and the theoretical curves.
Results
First, a hysteresis loop was obtained for the permalloy sample in order to establish that it has a low coercivity and thus has a magnetization that is easy to flip. This property is vital to obtaining the fractional MOKE signal. This was done by keeping the analyzer angle constant and sweeping the magnetic field from -15 to +15 oersted. It is clear that the coercivity is low, and that there are two flat plateaus on either side that indicate a saturated magnetization in the sample.There is some asymmetry about the x-axis present, but this is minimal and is likely the result of an exchange bias in the sample.
The data obtained both with and without the prism are shown in the plot below along with their fits. Instead of the doubling that was expected, the signal only increased by approximately 50%. However, as shown in the table below, values for the Kerr angle both with and without the prism were obtained that agree with the experimentally predicted values to within one standard deviation. The lower enhancement is believed to likely be due to the differing values obtained for the depolarization fraction
with and without the prism; the prediction was made assuming one value for both situations. It is not clear why these values are so different, but since the results for the Kerr angle were accurate it is thought that there are some other underlying physics behind this discrepancy.
Acknowledgements
PI - Paul Crowell
Gordon Stecklein
References
[1] M. Mansuripur, Classical Optics and Its Applications. (Cambridge, 2002), pp. 139-145.
[2] Wikipedia. https://en.wikipedia.org/wiki/Magneto-optic_Kerr_effect.
[3] L.F. Holiday and U.J. Gibson. 25 December 2006. Improved longitudinal magneto-optic Kerr effect signal contrast from nanomagnets with dielectric coatings. Optics Express. 14(26)
[4] Chun-Yeol You and Sung-Chul Shin. 1998. Generalized analytic formulae for magneto-optical Kerr effects. Journal of Applied Physics. 84(1):541-546
[5] D. A. Allwood, Gang Xiong, M. D. Cooke and R. P. Cowburn. 3 September 2003. Magneto-optical Kerr effect analysis of magnetic nanostructures. Journal of Physics D: Applied Physics. 36:2175-2182
[6] Shun-ichi Tanaka. 1963. Longitudinal Kerr Magneto-Optic Effect in Permalloy Film. Japanese Journal of Applied Physics. Vol. 2, No. 9, September 1963.
[7] N. Qureshi and H. Schmidt. 19 July 2004. Cavity enhancement of the magneto-optic Kerr effect for optical studies of magnetic nanostructures. Applied Physics Letters. 85(3):431-433
[8] Scott A. Crooker. September 1997. Ultrafast Optical Studies of Coherent Spin Dynamics in Magnetic Quantum Structures. Thesis, University of California Santa Barbara.
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