Speaker
Description
The magnetoimpedance effect (MI) is an attractive phenomenon for several applications, such as magnetic field, stress, and temperature measurement, health monitoring and biological detection. To fully exploit the potential of these applications, it would be useful to develop numerical models able to predict the MI response under different conditions, accounting for materials with diverse properties and geometries. The impedance Z of a magnetic sample can be obtained by solving simultaneously Maxwell Equations (ME) and the Landau-Lifshitz-Gilbert (LLG) magnetization equation of motion. Except for highly symmetric and simple situations, obtaining an analytical solution for the impedance is not possible. One usual simplification is to assume a constant value for the magnetic permeability $\mu$. More elaborate approaches determine the value of the permeability as a function of the applied magnetic field using simple magnetization models. None of the models used So far accounts for the dependence of the permeability on the amplitude of the excitation field $h_{ac}$ created by the alternating current used to measure the impedance. This is certainly important, since the amplitude of $h_{ac}$ varies over the material, both the Ampere’s Law itself and the skin effect.
In this work, we model the MI effect from first principles, starting from fundamental magnetic properties. The method combines the numerical solution of the LLG equation using micromagnetic codes, with a finite element method to solve ME. Fig. 1 schematizes the process: Micromagnetic simulations enable us to determine the permeability for each bias field as a function of a wide range of excitation amplitudes and frequencies of $h_{ac}$. These results are then integrated into the finite element description of the ME, which solves the inter-dependency between $\mu$ and $h_{ac}$ in an auto-consistent way by obtaining the optimal values compatible with the solution of ME at each point. Thus, $Z$ is evaluated for different bias fields and frequencies. It is important to note the effect of ferromagnetic resonance is intrinsically included in the model, and its effects are clearly visible in $Z(H)$ curves. This calculation procedure can be used in special situations, such as under the effect of inhomogeneous fields. This is the case, for example, in the detection of magnetotactic bacteria, which generate a non-uniform stray field over the sensor volume. Using this model, a change of some milliohms is predicted in the MI signal by the presence of a single bacterium.
Fig. 1 Schematic representation of the modeling process: a) Permalloy (Ni$_{80}$Fe$_{20}$) thin film. b) Permeability for a frequency of 200 MHz as a function of $h_{ac}$ and $H_{bias}$. c) $Z(H)$ curves at different frequencies.
