Calculation of coercivity of magnetic nanostructures at finite temperatures

Abstract

We report a finite temperature micromagnetic method (FTM) that allows for the calculation of the coercive field of arbitrary shaped magnetic nanostructures at time scales of nanoseconds to years.Instead of directly solving the Landau-Lifshitz-Gilbert equation, the coercive field is obtained without any free parameter by solving a non linear equation, which arises from the transition state theory. The method is applicable to magnetic structures where coercivity is determined by one thermally activated reversal or nucleation process. The method shows excellent agreement with experimentally obtained coercive fields of magnetic nanostructures and provides a deeper understanding of the mechanism of coercivity.

Fabrication and high-resolution electron microscopy study of FePt L10 /A1 graded exchange spring media

“…In this study the exchange coefficients A L10 and A A1 are supposed to have same value, 10 pJ m −1 . From the thermal‐fluctuation‐induced deviation between the switching fields of FePt L1 0 single phase obtained experimentally (32.2 kOe) and theoretically (2 K U,L10 / J S,L10 = 79.5 kOe), the experimental switching field of the FePt L1 0 /A1 bilayer with a sharp flat interphase boundary is supposed to be 9.76 kOe . The value is very close to the switching field of the specimen C (9.36 kOe), which has an adequately thick graded layer and small interphase boundary roughness.…”

Qualitative insight and quantitative analysis of the effect of temperature on the coercivity of a magnetic system

“…The preparation of a magnetic system in a particular state can be destroyed by thermally activated transitions to other available states, contributing to the temperature dependence of various properties of magnetic materials, including hysteresis loops [2][3][4][5][6][7][8][9][10]. If the energy barrier separating stable states is large compared to thermal energy, the thermally activated transition become a rare event and special techniques are required for the long time scale spin dynamics simulations [5,[11][12][13]. According to statistical rate theories, the rate of a thermally activated, over-the-barrier transition typically follows Arrhenius law [14,15], which contains two parameters: an energy barrier for the transition and a pre-exponential factor.…”

“…The system will remain in the spiral state until the applied field has lowered the energy barrier sufficiently and, thereby, decreased the lifetime of the spiral state sufficiently for the transition to the collinear state to occur on the time scale of the experiment. This approach is similar to the finite temperature micromagnetic method which has been used to calculate angular and thickness dependence of the coercive field for graded perpendicular recording media [5] . The expression for the lifetime obtained from HTST is of Arrhenius form, (see Supplemental Material),…”

Porous silicon/Ni composites of high coercivity due to magnetic field-assisted etching

“…The achieved coercivity is still far less than the theoretically obtained value of the coercivity of a monocrystalline individual nanowire with H C = 3,400 Oe. Reasons for the reduction of the coercivity H C are the still-occurring weak dipolar coupling between Ni-wires of adjacent pores, an imperfect cylindrical shape of the nanowires (due to the roughness of the pore walls) and, especially, the end of the wires showing an arbitrary geometry (not flat), which strongly influences the stray fields of the Ni-wires [ 11 ]. Further enhancement of the coercivity to come closer to the theoretical value of a single wire could be reached by improving the nanowire growth (cylindrical shape with less roughness and monocrystallinity) and further decreasing the magnetostatic interactions between wires by increasing the distance between the pores.…”