Analytic expression of the temperature increment in a spin transfer torque nanopillar structure

TL;DR

This paper derives an analytical, time-dependent solution for temperature increase due to Joule heating in spin transfer torque nanopillars, extending Holm's steady-state equation to dynamic scenarios and validating with simulations.

Contribution

It provides the first analytical time-dependent heat conduction solution for nanopillar spin transfer torque structures, applicable to magnetic tunneling junctions with insulator barriers.

Findings

Analytic solution matches finite element simulations.

Solution extends Holm's equation to time-dependent cases.

Applicable to magnetic tunneling junctions with insulators.

Abstract

The temperature increment due to the Joule heating in a nanopillar spin transfer torque system is investigated. We obtain a time dependent analytic solution of the heat conduction equation in nanopillar geometry by using the Green's function method after some simplifications of the problem. While Holm's equation is applicable only to steady states in metallic systems, our solution describes the time dependence and is also applicable to a nanopillar-shaped magnetic tunneling junction with an insulator barrier layer. The validity of the analytic solution is confirmed by numerical finite element method simulations and by the comparison with Holm's equation.