Editing Optical Sensor of Magnetic Dynamics: A Balanced-Detection MOKE Magnetometer

==Team Members==
LI Junxiang E1127462@u.nus.edu

Patricia Breanne Tan SY pb.sy82@u.nus.edu

==Idea==
We will use a laser-based magneto-optical Kerr effect setup featuring a high-sensitivity differential photodiode array to measure the Kerr rotation angle induced by surface magnetism. This system serves as a versatile optical platform to investigate how external perturbations such as magnetic fields or radiation source alter the magnetic ordering of materials, allowing for the quantitative extraction of the magneto-optical coupling coefficients of various thin films.

==Introduction==
In 1875. physicist John Kerr discovered the Kerr Effect, a phenomenon wherein the refractive index of a material varies with the application of an electric field. The change in refractive index is described to be directly proportional to the square of the electric field, and may occur either from the initial application of an electric field (Kerr electro-optic effect) or from an electric field proceeding from an incident ray of light (Optical Kerr effect). In addition to these types of Kerr effect, a third exists: the magneto-optical Kerr effect, or MOKE.

In the MOKE, a magnetized surface causes reflected light beams to vary in its polarization and reflected intensity. We may describe this phenomenon with the use of Maxwell's equations from classical electromagnetic theory:

[[File:Maxwellequations.jpeg|400px|thumb|center]]

with the following corresponding boundary conditions:
[[File:Boundaryconditions.jpeg|400px|thumb|center]]
We assume that no free charges or free currents exist at the interface between the two mediums: an ideal ferromagnetic medium with <math>\vec B = \mu \vec H +\mu_{0} \vec M_{0}</math> (Eqn. 1) and a homogeneous linear medium, following the diagram below. With the magnetization <math> \vec M_{0} </math> taken as a constant vector, Equation 1 describes the hysteresis loop of a the ferromagnetic medium, which is simply the sum of a permanent magnet and linear magnetic medium.
[[File:MOKE Diagram EMtheory.png|200px|thumb|center|Coordinate System with Corresponding Media in the MOKE]]

Depending on whether <math> \vec M_{0} </math> is along the polar, longitudinal, or transverse directions, the effects and rotation angles when linearly polarized plane waves (LPPW) of light will vary. The Kerr angle <math> \theta _{k}</math> is the angle by which LPPW rotates after being incident on the sample, and is proportional to the dot product between light propagation and the magnetization  <math> \vec M_{0} </math>. Consequently, the polar Kerr effect is seen most with light that is nearly perpendicularly incident on the material surface. This is also called S-polarization, where the incident electric field is nearly perpendicular to the surface while the incident magnetic field is nearly parallel. On the other hand, the longitudinal Kerr effect is most observed when light is nearly parallel to the material surface, or P-polarized, with the magnetic field perpendicular to the surface and the electric field nearly parallel.
[[File:MOKEgeometries.png|400px|thumb|center]]
Fundamentally, the MOKE may be used as a measure of how strongly a material is magnetized, with applications for the effect ranging from materials characterization to Kerr microscopy, where

==Experimental Setup==
[[File:Moke setup.png|1000px|thumb|center|MOKE Experimental Setup]]
We want to utilize a 658 nm HL6501 red light CW (continuous wavelength) laser (according to the datasheet). Then the laser beam passes through a ND filter to decrease its intensity the first time. Then it will go through a polarizer and a half-wave plate set to make it intensity continuously adjustable and be initially polarized to S polarized or P polarized. Then the incident laser light is focused on the sample by using a lens/objective. Then the reflected signal is detected by using a Wollaston prism as an analyzer to first,  splits the incident signal light beam into two orthogonal, linearly polarized beams that diverge from each other. Then use two detectors (balanced detectors) to detect two orthogonal, linear polarized beam intensities. The small Kerr rotation of the polarization by the material's magnetic properties can be calculated by making a substract of two intensities read from the two detecters.

==Methods==

==Results==

==Conclusion and Discussion==

==Reference==
1. McCord, J. Progress in magnetic domain observation by advanced magneto-optical microscopy. J. Phys. D: Appl. Phys. 48, 333001 (2015).