Nonlinear magnetoimpedance and parametric excitation of standing spin waves in a glass-covered microwire

Abstract

The giant magnetoimpedance of an 8.5 m glass-covered amorphous microwire was investigated in the frequency range of 10 MHz-3.5 GHz. It was found that when the exciting microwave current exceeds some threshold value, a periodic fine structure appears in the frequency dependence of the complex impedance. The appearance of this nonlinear phenomenon is interpreted to be a consequence of the parametric excitation of standing spin waves. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3079659͔ Nonlinear magnetization dynamics, which is one of the fundamental issues in applied magnetism, has recently received increasing attention in connection with the advances in magnetic storage technologies and spintronics. 1 Materials and devices used in these areas typically have nanoscale dimensions and operate in the gigahertz range. The understanding of magnetization dynamics is of great importance for these technologies. The nonlinear behavior of ferrites and garnets was systematically investigated during the 1950s and 1960s, particularly in connection with the development of radar and microwave techniques. With increasing interest in metallic ferromagnets, nowadays, new experimental methods are desirable for investigation of the nonlinear magnetic phenomena in these materials. One such technique is the giant magnetoimpedance ͑GMI͒.GMI comes from the dependence of electromagnetic skin depth in soft magnetic metals on the external dc magnetic field. 2 It has been shown by Yelon et al. 3 that the theoretical description of GMI, which is based on the simultaneous solution of Maxwell equations and the LandauLifshitz ͑LL͒ equation of motion is similar to the theory of ferromagnetic resonance ͑FMR͒ in metals. The LL is generally a nonlinear equation. In the small signal limit ͑low ac excitation current͒, where the LL equation can be linearized, this theoretical approach provides a very good explanation for the observed GMI behavior. 4 Nevertheless, at high excitation current, where the nonlinearity of LL equation must be taken into account, nonlinear effects should appear. Considering the correspondence between GMI and FMR one can expect that various nonlinear effects, similar to those observed in FMR, 5 also take place in the GMI. Because of the large damping of magnetization motion, the standard nonlinear FMR experiments in ferromagnetic metals require high power microwave sources. 6 In GMI measurements, however, the conditions for nonlinear behavior can already be achieved with exciting currents of a few milliampere. 7 Among various nonlinear phenomena, "frequency multiplication" ͑higher order harmonics of GMI signal͒ has already been investigated. [8][9][10][11][12][13][14][15] Although the similarity between the experimental configurations for transverse GMI in metallic ribbons and parallel pumping experiments in ferromagnetic insulators has already been pointed out by Yelon et al., 7 the parametric excitation of spin waves, 16 and other known nonlinear phenomena have not been reported so far.The aim of this paper is to ...

Circular domains nucleation in magnetic microwires

“…3) to Eq. (3), assuming the following set of parameters for the wire and defects: E a /k B T ¼ 10; r ¼ 0.2E a ; the mean defect size, r 0 $ 20-50 nm; and 4pM S ¼ 5400 G. 24 The results shown in Fig. 3 demonstrate good agreement between the measured (points) and the fitted (solid lines) data.…”

Magnetoimpedance dependence on width in Co66.5Fe3.5Si12.0B18.0 amorphous alloy ribbons

“…As shown in Fig. 6(a), the resonance frequencies f satisfy rather well the Kittel resonance condition for a uniaxial thin film magnetized along the plane, which can also be applied to the ribbons, and can be written as 16,17 …”

Ferromagnetic resonance in individual wires

“…The dependence of characteristic frequency o m,n on the longitudinal propagation constant b is schematically shown in Figure 15.25. The increasing complexity of the nonlinear spectrum with increasing power level may be explained by the parametric excitation of the dipole-exchange modes with higher radial numbers m. Fine structure has been also found on NA-FMR resonance curves measured on an 8.5-mm-thick amorphous microwire Co 67 Fe 4 Cr 7 Si 8 B 14 (Kraus et al, 2009). To get the numbers x m,n the boundary condition problem must be solved numerically.…”

“…The most commonly used method is the network-analyzer ferromagnetic resonance (NA-FMR). The second one is a two-port DUT consisting of an interrupted microstrip line with the wire bridging the gap (Kraus et al, 2009). One-port or two-port fixtures can be used.…”