Angular Dependence of Spin-Torque Critical Currents in CPP-GMR Read   Heads
  This paper derives expressions for the critical current at the onset of spin-transfer-torque (STT) instability in CPP-GMR read heads, as a function of the relative angle (theta) between the free and reference layer magnetizations. Including a general angular dependent STT coefficient B(q=cos(theta)) exclusive of the angular momentum conserving sin(theta) factor, the critical current is found to depend on both B(q) and dB/dq in the non-collinear case |q| < 1. The paper also details the experimental measurement of the angular dependent critical currents on 50-nm sized CPP-GMR devices with synthetic antiferromagnet pinned layers, and fabricated using e-beam lithography. The measurements are consistent with prior theoretical models of the form B(q) ~ 1/[1+cnst*q], and indicate perhaps unanticipated implications for read head operation due to the critical current dependence on dB/dq. 
Neil Smith, J. .A. Katine, Jeffrey R. Childress, and Matthew J. Carey