Frequency shift of spin waves in tunnel-junction spin-transfer nano-oscillators

The excitations of microwave spin waves in magnetic tunnel junctions are theoretically investigated. An analytical approach which describes the dependence of the microwave precession frequency on the applied voltage is developed. It is shown that the spin-wave frequency is directly related to both the in-plane and perpendicular spin-transfer torques. In the low field regime the perpendicular torque can induce changes in the slope of the oscillation frequency versus applied voltage (df/dv) from negative (redshift) to positive (blueshift) values