  We report on our design of a scanning gate microscope housed in a
cryogen-free dilution refrigerator with a base temperature of 15 mK. The recent
increase in efficiency of pulse tube cryocoolers has made cryogen-free systems
popular in recent years. However, this new style of cryostat presents
challenges for performing scanning probe measurements, mainly as a result of
the vibrations introduced by the cryocooler. We demonstrate scanning with
root-mean-square vibrations of 0.8 nm at 3 K and 2.1 nm at 15 mK in a 1 kHz
bandwidth with our design.
