  The main limitation in order to exploit spin torque nano-oscillators (STNOs)
in various potential applications is their large phase noise. In this work, we
demonstrate its efficient reduction by a highly reconfigurable, compact,
specifically on-chip designed PLL based on custom integrated circuits. First,
we thoroughly study the parameter space of the PLL+STNO system experimentally.
Second, we present a theory which describes the locking of a STNO to an
external signal in a general sense. In our developed theory, we do not restrict
ourselves to the case of a perfect phase locking but also consider phase slips
and the corresponding low offset frequency $1/f^2$ noise, so far the main
drawback in such systems. Combining experiment and theory allows us to reveal
complex parameter dependences of the system's phase noise. The results provide
an important step for the optimization of noise properties and thus leverage
the exploitation of STNOs in prospective real applications.
