The quest for faster and more energy-efficient memory technologies has driven considerable advancements in magnetic materials, with magnetic random-access memory (MRAM) emerging as a promising next-generation solution. MRAM’s non-volatility, and scalability potential make it a competitive alternative to conventional memory. Key challenges remain, however, in optimizing its switching speed, minimizing power consumption, and achieving more scalable designs. Spin-orbit torque (SOT) offers a robust mechanism for electrically controlling magnetization, providing a foundation for the next-generation SOT-MRAM.While most MRAM designs rely on ferromagnetic materials, recent research has shifted focus to antiferromagnets and the newly discovered altermagnets. Antiferromagnets, with their net-zero magnetization, offer ultrafast switching speeds, high scalability, and resilience to external magnetic fields. Altermagnets combine this stability with unique spin-splitting properties, enhancing MRAM devices with potential improvements in tunneling magnetoresistance ratios. Despite these benefits, practical applications of antiferromagnetic and altermagnetic materials remain limited due to challenges in characterizing and controlling their ultrafast spin dynamics. This dissertation addresses these challenges by employing the magneto-optical Kerr effect (MOKE) technique, especially time-resolved quadratic MOKE (TR-QMOKE), to characterize spin dynamics in advanced magnetic materials. Optical methods like TR-QMOKE provide sub-picosecond temporal resolution, enabling precise measurements of ultrafast dynamics beyond the reach of traditional electrical methods. TR-QMOKE also allows non-invasive, localized measurements that bypass the constraints of material conductivity, making it ideal for studying insulating antiferromagnets that can improve the energy efficiency of MRAM further. This dissertation also demonstrates that optical techniques can effectively characterize spin-orbit torque in a range of magnetic materials from ferromagnets to antiferromagnets. Additionally, TR-QMOKE reveals unique wavelength-dependent spin dynamics in altermagnet α-MnTe and long-lived coherent magnon in insulating antiferromagnets LaFeO3. These findings highlight the feasibility of all-magnonic antiferromagnetic MRAM and provide insights that may drive further advances in high-density, high-speed, energy-efficient memory solutions. Overall, this dissertation advances the understanding of ultrafast spin dynamics, positioning optical methods as critical tools in the development of future MRAM technologies.