Enhancing Spin Torque Optical Readout with Sagnac Interferometry

Traditional methods for measuring the magneto-optical Kerr effect (MOKE) detect changes in the amplitude of a rotated component of light polarization. In contrast, Sagnac MOKE interferometry measures phase, providing highly sensitive optical readout of out-of-plane magnetization without additional modulation.

In this study, we analyze the Sagnac signal to second order in the magnetization. We demonstrate an additional advantage of Sagnac interferometry: it effectively suppresses the quadratic Kerr effect. Conventional MOKE produces an angular readout defined by θ_conventional = κ m_z + β m_x m_y , where β represents the quadratic coefficient, κ represents the linear coefficient, and m = [m_x,m_y,m_z] represents the magnetization vector. In comparison, the SAGNAC interferometer signal is

θ_sagnac ≈ κ m_z + 2 β m_x m_y sin(κ m_z) [0.71cos(2 κ m_z) - 0.62 cos²(κ m_z)] + O(β²)

Notably, the quadratic term is smaller than the linear term by a factor of β (order 10⁻⁴) , rather than β/κ. Furthermore, a small modification to the interferometer reverses this suppression, to isolate the quadratic effect. Because the quadratic MOKE provides information about two other components of magnetism, this could enable fully vectorial measurements of spin torques.