Fig. 1: The detection principle of nonlinear magnons using NV centers in diamond.

a The configuration of the magnon-spin qubit hybrid system. The bulk diamond with implanted NV centers is closed to the magnetic film on the waveguide. The bias field is parallel to the waveguide. The two microwave signals show the delivery of the microwaves, referred to as Figs. 3 and 4. b The energy level of the NV center. Left panel: a 520 nm green laser is used to initialize the spin states, and the red photoluminescence (PL) is detected for the read-out of spin states. The denoted excited state electron spin resonance (ES-ESR) and ground state electron spin resonance (GS-ESR) correspond to the zero-field condition. Right panel: under a bias field aligned with the NV-axis, the frequencies of GS-ESR will shift with the bias field due to the Zeeman effect. c. The conversion principle of the hybrid system. The microwave photons will stimulate the magnon (spin-wave) in the CoFeB film, and the presence of magnetic domain walls leads to strong nonlinear magnetic effects due to the nonlinear susceptibilities \({\chi }^{\left(2\right)},{\chi }^{\left(3\right)},\cdots \,\), generating multi-wave mixing. Violet arrow line: the NV center can detect the stray fields generated by converted magnons when their frequency is resonant with the ESR frequencies f_ESR± of NV centers.