The Gallium Nitride (GaN) devices have been attractive due to their low loss and high switching speed. With the soft switching, for example critical mode operation, the GaN converter can be further pushed over the MHz range. How to design the critical mode inductor at such switching frequency is a challenge, because the loss on the inductor is a big concern for the converter efficiency. This paper experimentally and numerically evaluates different core materials, structures and winding types. The best candidate can reduce the inductor loss below 3 W for a 1 kW critical mode converter operating at 1 MHz.