摘要： Realizing the precise measurement of the magnetic field is of great significance in many fields, including optics, metrology, bioscience, and engineering technology. With the development of nanophotonics, optomechanical systems have provided an on-chip platform to explore new availability for high-sensitivity measurement due to its extreme sensitivity on weak force [Ref. Nat. Nanotechnol. 7, 509 (2012)]. In this paper, a theoretical scheme for precision measurement of magnetic field based on a nonlinear optomechanical effect: second-order sideband generation in a hybrid electromagnetic-optomechanical system is proposed. We find that the system exhibits a kenspeckle magnetic-field-dependent generation of the frequency component at the second-order sideband, which is more sensitive than the previous paper based on optomechanically induced transparency. Numerical calculations show that the measurement accuracy of the magnetic field in our scheme may reach the order of nT or even smaller, so our findings will provide a more accurate solution for the precise measurement of magnetic fields.