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

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.