Abstract
We present a rotating field method to separate the linear and quadratic magneto-optical Kerr effects (LMOKE and QMOKE) in Fe/GaAs(001) films. The LMOKE is isotropic in crystal orientation, while the QMOKE has both isotropic and anisotropic contributions. The experimental observation is well explained by Yeh's 4×4 matrix formalism. We also report the incident angle and the thickness dependences of the LMOKE and QMOKE, and extract the material's index of refraction n and the magneto-optical coupling constant K and G. The study gives a full description of the Kerr effect in Fe films, and the proposed method can be applied to other magneto-optical coupling systems.
Highlights
The magneto-optical Kerr effect (MOKE) was discovered by John Kerr [1, 2] and first applied to study surface magnetism by Moog and Bader in 1985 [3]
The quadratic magneto-optical Kerr effect (QMOKE) analysis is important in the following considerations: (i) for materials with a huge QMOKE [4,5,6], this higher-order contribution must be considered to quantitatively calibrate the magnetization measurements; (ii) because the quadratic magneto-optical (MO) coupling is caused by second-order spin-orbit coupling terms [4], the MO coupling parameters related to the QMOKE can be used as a probe for fundamental electronic interactions in ferromagnetic materials; and (iii) optical effects quadratic in magnetization have recently been determined to be important, including magnetization-dependent second-harmonic generation [7], the quadratic X-ray magneto-optical effect [8], and the closely related X-ray Voigt effect [9]
The linear magneto-optical Kerr effect (LMOKE) signals are always independent of the crystalline orientation, and the two QMOKE terms oscillate with similar amplitudes
Summary
The magneto-optical Kerr effect (MOKE) was discovered by John Kerr [1, 2] and first applied to study surface magnetism by Moog and Bader in 1985 [3]. The eight-field method has been used to separate ΦL , ΦLT and ΦTT contributions [4,5,6, 15] on magnetic films with separated thicknesses. It is crucial to propose a better method to quantitatively separate the QMOKE terms and systematically study it. We quantitatively separated the linear and quadratic Kerr terms in Fe thin films using a rotating field method. By measuring the Kerr signal as a function of the field orientation, we separated ΦL , ΦLT and ΦTT contributions from the total Kerr signal. The film thickness dependences of the LMOKE and QMOKE’s isotropic and anisotropic contributions were studied in a wedge-type sample, and the results indicate that the MOKE is primarily due to bulk-type MO coupling. All the experimental observations can be quantitatively explained by a 4 × 4 transfer matrix method, and all the MO coupling parameters can be determined through the theoretical fitting
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