Tunable intrinsic phase shift between a spin torque nano-oscillator and an AC current

Abstract

We present magnetodynamic simulations, based on the Landau-Lifshitz-Gilbert-Slonczewski equations, of the interaction between a spin torque oscillator (STO) and an ac current (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ac</sub> ). To avoide any extrinsic phase shift we inject the ac current at the intrinsic frequency (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">STO</sub> ) of the STO. We nevertheless find an unexpected intrinsic preferred phase shift Δϕ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> between the STO and I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ac</sub> In the in-plane precession mode (IP) the STO adjusts to a state where its resistance (or voltage) lags I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ac</sub> about a quarter of a wave length (Δϕ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> =87-94°). In this regime Δϕ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> increases somewhat with the dc current. However, as the precession changes into the Out-Of-Plane (OOP) mode, Δϕ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> exhibits a dramatic jump by about 180°, i.e. the STO resistance now precedes I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ac</sub> about a quarter of a wave length (|Δϕ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> |=86°). Δϕ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> can furthermore be tuned by changing one or more of the anisotropy field, the demagnetizing field or the applied field. At the IP/OOP boundary, the ac current mixes the two oscillation modes and both chaotic and periodic mixing is observed. We argue that the intrinsic Δϕ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> will impact any circuit design based on STO technology and will e.g. have direct consequences for phase locking in networks of serially connected STOs.