micromagnetic

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	INESC MN	Microsistemas & Nanotecnologias

Micromagnetic Simulations

Introduction

We want to be able to simulate the dependence of magnetization on applied field of a mesoscopic device. A two dimensional code (J. Appl. Phys. 81, 4847 (1997)) has been in use in the group. We have developed a fully three-dimensional code to simulate devices (J. Appl. Phys. 85, 5810 (1999)) which is now being applied to simulate devices (J. App. Phys. 91, 8296 (2002)).

A good micromagnetic code should be fast for large systems, which means that the CPU time should have a good scaling with system size, it should solve in a stable way the Maxwell equations relevant to micromagnetism, and should be applicable to arbitrarily shaped devices. The time consuming part of the original code is the solution of a Poisson equation, we do it with finite differences with an over-relaxation method, and the boundary conditions are calculated with a multipole expansion. We define the "magnetic charge" and magnetization on two interpenetrating cartesian grids. Our discrete equations satisfy the discrete version of Gauss's law, so we obtain stable solutions. With the use of interpenetrating grids we do not need to consider the surface "magnetic charges" used by other codes, so it is trivial to treat arbitrarily shaped devices.

After an initial period where we simulated "standard problems" and found the importance of being able to use a fine discretization grid, we are now simulating real multi-layer devices and how they react to external applied fields. The multilayers can have arbitrary shapes, and number of layers. The simulations can be static or dynamic.

The original 3D code has been improved significantly since the beginning of 2000 when a new project started and a PhD student and a Post-doc started full-time research on the project.

The Poisson equation can be solved with a multi-grid method, which has a computational cost that scales as NlogN, where N is the number on nodes in the simulation, compared with the N^1.5 scaling of the first version of the 3D code.
The minimization of the magnetic energy can be done by a conjugate gradient method.
For fast transient phenomena, we can simulate the time evolution of the magnetization
We can treat arbitrarily shaped devices

We have since the beginning of 2002 a linux cluster with 8 nodes running in parallel and appearing to the user as a single machine. Each node is a 1.7 GHz pentium-4 PC with 1.5 Gb of RAM. Parts of the code have already been modified to run in parallel.

For more information on this research topic, contact Prof. José Luís Martins.

Main Results

Development of a new code for the simulation of three-dimensional micromagnetic structures.
Simulation of "standard problems" in micromagnetism.
Simulation of magnetic multilayers.