Magnetization switching by microwaves synchronized in the vicinity of precession frequency

We propose a theoretical framework of a magnetization switching induced solely by a microwave. The microwave frequency is always close to but slightly different from the oscillation frequency of the magnetization. By efficiently absorbing energy from the microwave, the magnetization climbs up the energy landscape to synchronize the precession with the microwave. We introduced a dimensionless parameter $\epsilon$ determining the difference between the microwave frequency and the instant oscillation frequency of the magnetization. We analytically derived the condition of $\epsilon$ to switch the magnetization, and confirmed its validity by the comparison with numerical simulations.