Exact Activation Energy of Magnetic Single Domain Particles.pdf

a r X i v : 0 7 0 5 .3 7 6 1 v 1 [ c o n d - m a t .m e s - h a l l ] 2 5 M a y 2 0 0 7 Exact Activation Energy of Magnetic Single Domain Particles Daniel Braun? Infineon Technologies, 2070 State Route 52, Hopewell Junction, NY, 12533 MRAM Developement Alliance, IBM/Infineon Technologies, IBM Semiconductor Research and Developement Center, 2070 State Route 52, Hopewell Junction, NY, 12533 I present the exact analytical expression for the activation energy as a function of externally applied magnetic fields for a single–domain magnetic particle with uniaxial anisotropy (Stoner–Wohlfahrt model), and investigate the scaling behavior of the activation energy close to the switching boundary. PACS numbers: 75.75.+a, 75.45.+j, 75.10.-b I. INTRODUCTION A lot of effort has been spent over the last few years to understand the magnetization reversal of small magnetic particles1,2,3,4,5,6,7. At sufficiently low temperatures, macroscopic quantum tunneling has been observed8,9,10,11, while for higher temperatures thermally activated behavior may switch the magnetization of the particle12. For the anlaysis of the experiments one needs to know the activation energy. Moreover, with the advancing developement of integrated magnetoresistive memory devices (MRAM) the dependence of the energy barrier on the magnetic field has become of crucial technological importance as well. In a typical MRAM array, magnetic memory cells are written by a coincident field technique, where both a selected bitline (BL) and a selected wordline (WL) create magnetic fields, the sum of which are strong enough to switch the memory cell, whereas the fields from either BL or WL alone are not sufficient to switch the cell. Nevertheless, these fields do destabilize the non–selected cells to some extent, i.e. they reduce the energy barrier against thermally activated switching. Also, even for the selected cells the switching at finite temperatures happens before the actual zero temperature boundary of stab