  We are reporting a new type of synchronization, termed dancing
synchronization, between two spin-torque nano-oscillators (STNOs) coupled
through spin waves. Different from the known synchronizations in which two
STNOs are locked with various fixed relative phases, in this new synchronized
state two STNOs have the same frequency, but their relative phase varies
periodically within the common period, resulting in a dynamic waving pattern.
The amplitude of the oscillating relative phase depends on the coupling
strength of two STNOs, as well as the driven currents. The dancing
synchronization turns out to be universal, and can exist in two nonlinear Van
der Pol oscillators coupled both reactively and dissipativly. Our findings open
doors for new functional STNO-based devices.
