  By generating a Brillouin laser in an optical microresonator, we realize a
soliton Kerr microcomb through exciting the Kerr frequency comb using the
generated Brillouin laser in the same cavity. The intracavity Brillouin laser
pumping scheme enables us to access the soliton states with a blue-detuned
input pump. Due to the ultra-narrow linewidth and the low-noise properties of
the generated Brillouin laser, the observed soliton microcomb exhibits
narrow-linewidth comb lines and stable repetition rate even by using a diode
laser with relatively broad linewidth. Also, we demonstrate a low-noise
microwave signal with phase noise levels of -24 dBc/Hz at 10 Hz, -111 dBc/Hz at
10 kHz, and -147 dBc/Hz at 1 MHz offsets for a 11.14 GHz carrier with only a
free-running input pump. The easy operation of the Brillouin-Kerr soliton
microcomb with excellent performance makes our scheme promising for practical
applications.
