Slit Length Dependence of rf-SQUID Resonant Frequency

An rf-SQUID is operated at high frequency around its resonant frequency to obtain the magnetic signal. The resonant frequency of the rf-SQUID depends on the shape of the superconducting films. The resonant frequency of the rf-SQUID having the outer diameter of 3.5 mm with the straight slit was 1100 MHz when it was excited without a substrate resonator. It was too high to operate for our using electronics. It was desirable to reduce the resonant frequency while keeping the size of the rf-SQUID small. In this paper, the slit length in the rf-SQUID was focused on. The relation between the resonant frequency and the slit length was investigated by the electromagnetic simulations and the experiments. The meandered slit was proposed as the design of the slit in the rf-SQUID. This design made the slit length longer than that with the straight slit, while the outer diameter of the rf-SQUID was fixed at 3.5 mm. The rf-SQUID having the longer slit length showed the lower resonant frequency. The rf-SQUID with the meandered slit, of which length was 5.1 mm, could be operated at 550 MHz around its resonant frequency. In addition, the low-frequency noise of the rf-SQUID with the meandered slit was smaller than that with the straight slit due to smaller effective area.