  In this paper, we study typical nonlinear phenomenon of phase-locking or
synchronization in spin-torque nano oscillators (STNOs). To start with the
oscillators are considered as uncoupled but interlinked through either a common
microwave current or a microwave field. We identify the phase locking of an
array of STNOs (first for two and then for 100 oscillators) by means of
injection locking which represents locking the oscillations to a common
alternating spin current or a common microwave magnetic field. We characterize
the locking of STNOs through both first and second harmonic lockings in an
array. We find that second harmonic lockings takes lesser value of microwave
current and field when compared with the first harmonic lockings. Our results
also show that oscillating microwave current can induce integer harmonic
locking while microwave field can induce both integer and several fractional
harmonic lockings. We also extend our analysis to study locking behavior of two
STNOs by introducing time delay feedback and coupling through a current
injection and bring out the associated locking characteristics. Finally, we
have also analyzed the stability of synchronization of identical array of STNOs
with current coupling by using master stability function formalism.
