Thermal relaxation rates of magnetic nanoparticles in the presence of magnetic fields and spin-transfer effects

Abstract

We have measured the relaxation time of a thermally unstable ferromagnetic nanoparticle incorporated into a magnetic tunnel junction (MTJ) as a function of applied magnetic field, voltage $V$ (\ensuremath{-}0.38 V $V$ $+$ 0.26 V), and temperature (283 K $T$ 363 K). By analyzing the results within the framework of a modified N\'eel-Brown formalism, we determine the effective attempt time of the nanoparticle and also the bias dependences of the in-plane and out-of-plane spin-transfer torques. There is a significant linear modification of the effective temperature with voltage due to the in-plane torque and a significant contribution of a ``field-like'' torque that is quadratic with voltage. The methods presented here do not require complicated models for device heating or calibration procedures but instead directly measure how temperature, field, and voltage influence the energy landscape and thermal fluctuations of a two-state system. These results should have significant implications for designs of future nanometer-scale magnetic random access memory elements and provide a straightforward methodology to determine these parameters in other MTJ device structures.