Calculation of Current-driven Switching rates
P. B. Visscher and D. M. Apalkov
At present, high density non-volatile information storage in a computer is accomplished by magnetic storage on a hard disk (but is relatively slow); fast memory is generally accomplished with integrated-circuit transistor electronics, and is volatile, i.e, the information is lost when the computer is turned off. An appealing prospective technology is current-switched MRAM (magnetic random-access memory), which has the speed of electronic storage (and may even exceed its density) but the nonvolatility of magnetic storage. It has recently [ref. 1] been shown that the passage of a current from a pinned ferromagnet produces a “spin torque” that can switch the magnetization of a nanometer-sized free ferromagnet. Although various theories of this effect have been proposed, testing them against experimental results has been difficult because most experiments are on a long time scale that is hard to simulate directly. In the absence of spin torque, long-time thermal effects such as switching rates have historically been calculated by statistical methods, using the Fokker-Planck equation, which leads [Brown, 1963] to a switching rate proportional to exp(-E/kT), referred to as the Arrhenius-Neel law. The problem with generalizing this approach is that spin torque is not conservative, so we cannot define a potential energy barrier E. We have shown for the first time that it is possible to include non-conservative torques in the Fokker-Planck equation and still solve it for the switching rate. In the limit of small oscillations about the energy minimum, the result has approximately the form of the Arrhenius-Neel law, but with an elevated effective temperature Teff. However, the “effective temperature” picture fails for large oscillations — our method can be used to calculate the spectra of microwave oscillations that have recently been observed in these systems. The graph shows a fit (lines) of our results to “telegraph-noise” data (symbols), in which the average time spent in each state (parallel or antiparallel magnetization) is measured. A preprint describing this work in detail is on the cond-mat archive, at arXiv.org/abs/cond-mat/0405305.
1. F. J. Albert, J. A. Katine, R A. Buhrman, and D. C. Ralph, ”Spin-Polarized Current switching of a Co thin film nanomagnet”, Appl. Phys. Lett. 77, 3809 (2000).
2. S. Urazhdin, N.O. Birge, W.P. Pratt, and J. Bass, ”Current-Driven Magnetic Exciations in Permalloy-Based Multilayer Nanopillars”, Phys. Rev. Lett. 91, 146803(2003).