Study of The Magneto-Optical Kerr Effect in Thick and Ultrathin Composite Layers

Hameedullah Zahin; Ahad Khan Pyawarai; Fazalullah Marufi

doi:10.62810/jnsr.v3i4.309

Authors

Hameedullah Zahin Department of Physics, Faculty of Education, Urozgan University, Kabul, Afghanistan
Ahad Khan Pyawarai Department of Physics, Faculty of Electromechanics Kabul Polytechnics University, Kabul, Afghanistan
Fazalullah Marufi Department of Physics, Faculty of Electromechanics Kabul Polytechnics University, Kabul, Afghanistan

DOI:

https://doi.org/10.62810/jnsr.v3i4.309

Keywords:

Electric field, Linear and angular polarized light, Magneto-optical Kerr effect, Spin-orbit interaction, Thick and ultra-thin layers

Abstract

When a transparent isotropic material is subjected to an electric field, birefringence occurs, and the material acquires the properties of a uniaxial crystal. The difference in refractive indices parallel and perpendicular to the field is proportional to the square of the field intensity and the Kerr constant. The importance of this topic lies in investigating how magnetic fields affect the optical properties of thick and ultrathin composite layers, which are crucial for enhancing the performance and design of magneto-optical memories and advanced sensors. The goal of this research is to determine the exact relationships between the thickness of composite layers and their magneto-optical sensitivity to optimize composite materials. Also, the angle of polarization rotation of light due to the Kerr effect is quantitatively measured and optimized to achieve maximum magneto-optical response. In this research, simplified analytical expressions for the magneto-optical Kerr effect in composite layers are presented, and the MOKE formulas for and layers are investigated, accounting for the second-order nonlinear refractive index. , the time rotation constant , and the phase difference of the incoming light. The results show that the longitudinal and polar Kerr rotation angles in thick and ultra-thin layers exhibit a systematic dependence on the angle of incidence and agree well with theoretical calculations at specific angles. This research shows that by combining materials and controlling the thickness of the composite layers, the polarization rotation angle due to the Kerr effect can be significantly improved.

Downloads

Download data is not yet available.

References

Bader, S. D., Moog, E. R., & Grünberg, P. (1986). Magnetic hysteresis of epitaxially-deposited iron in the monolayer range: A Kerr effect experiment in surface magnetism. In Journal of Magnetism and Magnetic Materials (Vol. 53, Issue 4). https://doi.org/10.1016/0304-8853(86)90172-1

Brajpuriya, R. (2014). Thickness and Interface-Dependent Structural, Magnetic, and Transport Properties of Cu/Co Thin Film and Multilayer Structures. Journal of Experimental Physics, 2014, 1–5. https://doi.org/10.1155/2014/569691

Brée, C., Demircan, A., & Steinmeyer, G. (2011). Saturation of the all-optical kerr effect. Physical Review Letters, 106(18). https://doi.org/10.1103/PhysRevLett.106.183902

Chen, J., Wu, G., Gu, P., Tang, Y., Yang, C., Yan, Z., Tang, C., Liu, Z., Gao, F., & Cai, P. (2021). Theoretical study on metasurfaces for transverse magneto-optical kerr effect enhancement of ultra-thin magnetic dielectric films. Nanomaterials, 11(11). https://doi.org/10.3390/nano11112825

Ferreiro-Vila, E., Iglesias, M., Paz, E., Palomares, F. J., Cebollada, F., González, J. M., Armelles, G., García-Martín, J. M., & Cebollada, A. (2011). Magneto-optical and magnetoplasmonic properties of epitaxial and polycrystalline Au/Fe/Au trilayers. Physical Review B - Condensed Matter and Materials Physics, 83(20). https://doi.org/10.1103/PhysRevB.83.205120

Fleischer, K., Thiyagarajah, N., Lau, Y.-C., Betto, D., Borisov, K., Smith, C. C., Shvets, I. V., Coey, J. M. D., & Rode, K. (2018). Magneto-optic Kerr effect in a spin-polarized zero-moment ferrimagnet. https://doi.org/10.1103/PhysRevB.98.134445

Hecht, J. (2017). Understanding Fiber Optics. In Understanding Fiber Optics. Laser Light Press. https://doi.org/10.1117/3.1445658

Heintzmann, R., & Kubitscheck, U. (2017). Introduction to Optics. In Fluorescence Microscopy: From Principles to Biological Applications: Second Edition. Cambridge University Press. https://doi.org/10.1002/9783527687732.ch1

Huang, D., Lattery, D., & Wang, X. (2021). Materials Engineering Enabled by Time-Resolved Magneto-Optical Kerr Effect for Spintronic Applications. ACS Applied Electronic Materials, 3(1), 119–127. https://doi.org/10.1021/acsaelm.0c00961

Jeppson, S. (2022). Understanding ultrafast magnetization dynamics in magnetic thin films. University of California, Davis.

Kampfrath, T., Campen, R. K., Wolf, M., & Sajadi, M. (2018). The Nature of the Dielectric Response of Methanol Revealed by the Terahertz Kerr Effect. Journal of Physical Chemistry Letters, 9(6), 1279–1283. https://doi.org/10.1021/acs.jpclett.7b03281

Kleibert, A., Senz, V., Bansmann, J., & Oppeneer, P. M. (2005). Thickness dependence and magnetocrystalline anisotropy of the x-ray transverse magneto-optical Kerr effect at the Co 2 p edges of ultrathin Co films on W (110). Physical Review B—Condensed Matter and Materials Physics, 72(14), 144404.

Li, T., Wang, Y., Jiang, Y., Zhang, S., Luo, L., & Zhang, Z. (2024). High-precision measurement of the complex magneto-optical Kerr effect using weak measurement. Applied Physics Letters, 124(5).

Lu, Y. F., Przybylski, M., Nývlt, M., Winkelmann, A., Yan, L., Shi, Y., Barthel, J., & Kirschner, J. (2006). Growth and magnetism of Co films on a Pd monolayer on Cu(001). Physical Review B - Condensed Matter and Materials Physics, 73(3). https://doi.org/10.1103/PhysRevB.73.035429

Mistrik, J., Krishnan, R., Visnovsky, S., Keller, N., Biondo, A., Franca De Souza, A., Mello, A. A., & Baggio-Saitovitch, E. M. (2002). Effect of Cu thickness in Co/Cu multilayers on polar and longitudinal magneto-optical Kerr spectra. Journal of Magnetism and Magnetic Materials, 240(1–3), 523–525. https://doi.org/10.1016/S0304-8853(01)00836-8

Okabayashi, J., Miura, Y., & Munekata, H. (2018). Anatomy of interfacial spin-orbit coupling in Co/Pd multilayers using X-ray magnetic circular dichroism and first-principles calculations. Scientific Reports, 8(1). https://doi.org/10.1038/s41598-018-26195-w

Qiu, Z. Q., & Bader, S. D. (2000). Surface magneto-optic Kerr effect.

Robertson, S. (2019). Optical Kerr effect in vacuum. https://doi.org/10.1103/PhysRevA.100.063831

Sato, K., & Ishibashi, T. (2022). Fundamentals of Magneto-Optical Spectroscopy. In Frontiers in Physics (Vol. 10). Frontiers Media SA. https://doi.org/10.3389/fphy.2022.946515

Shin, Y., & Kim, J.-W. (2024). Fundamental basics on measurement instruments and techniques for ultrafast magnetism dynamics. Current Applied Physics, 61, 34–46.

Silva, A. S., Sá, S. P., Bunyaev, S. A., Garcia, C., Sola, I. J., Kakazei, G. N., Crespo, H., & Navas, D. (2021). Dynamical behaviour of ultrathin [CoFeB (tCoFeB)/Pd] films with perpendicular magnetic anisotropy. Scientific Reports, 11(1). https://doi.org/10.1038/s41598-020-79632-0

Stejskal, O., Veis, M., & Hamrle, J. (2021). Band structure analysis of the magneto-optical effect in bcc Fe. Scientific Reports, 11(1). https://doi.org/10.1038/s41598-021-00478-1

Sun, Y., Wu, L., Yang, M., Xia, M., Gao, W., Luo, D., Huo, N., & Li, J. (2022). Anomalous Hall Effect and Magneto-Optic Kerr Effect in Pt/Co/Pt Heterostructure. Magnetochemistry, 8(5). https://doi.org/10.3390/magnetochemistry8050056

Suzuki, D. H., & Beach, G. S. D. (2024). Measurement of Kerr rotation and ellipticity in magnetic thin films by MOKE magnetometry. Journal of Applied Physics, 135(6). https://doi.org/10.1063/5.0185341

Tan, Y., Zhao, H., Zhang, R., Zhang, C., Zhao, Y., & Zhang, L. (2020). Ultrafast optical pulse polarization modulation based on the terahertz-induced Kerr effect in low-density polyethylene. Optics Express, 28(23), 35330. https://doi.org/10.1364/oe.408555

Tudu, B., Tian, K., & Tiwari, A. (2017). Effect of composition and thickness on the perpendicular magnetic anisotropy of (Co/Pd) multilayers. Sensors (Switzerland), 17(12). https://doi.org/10.3390/s17122743

You, C. Y., & Shin, S. C. (1996). Derivation of simplified analytic formulae for magneto-optical Kerr effects. Applied Physics Letters, 69(9), 1315–1317. https://doi.org/10.1063/1.117579

You, C. Y., & Shin, S. C. (1998). Generalized analytic formulae for magneto-optical Kerr effects. Journal of Applied Physics, 84(1), 541–546. https://doi.org/10.1063/1.368058

Zak, J., Moog, E. R., Liu, C., & Bader, S. D. (1990). UNIVERSAL APPROACH TO MAGNETO-OPTICS. In Journal of Magnetism and Magnetic Materials (Vol. 89).

Zhou, S., Chen, L., Su, Y., & Qian, Y. (1993). The Magneto‐Optical Kerr Effect in Co‐Based Multilayered Structures. Physica Status Solidi (B), 179(2), 557–562.