Research articles
Tracking the Suhl instability versus angle and frequency for the backward volume mode in an yttrium iron garnet film

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Highlights

  • Minimum frequency of the BV spin wave was tracked for a wide range of field angles.

  • Data are compared with a recently developed theory.

  • Disagreement between data and the theory was found at low frequency.

Abstract

Using parametric excitation, we have studied the minimum frequency associated with the backward volume (BV) spin wave branch in a thin film of the ferrimagnetic material yttrium iron garnet (YIG) for the magnetic field lying in plane and parallel to the wave vector as well as for out-of-plane field angles. We find that there is a drastic change in the efficiency of parametric excitation between two different pumping frequency regimes.

Introduction

Parametric excitation of spin waves is a nonlinear magnetic resonance phenomenon first observed in ferromagnetic materials by Damon [1] and by Bloembergen and Wang [2] where they found a broad secondary absorption (subsidiary absorption) lying below the uniform ferromagnetic resonance (FMR) mode. Suhl [3] has provided a macroscopic theory to describe the parametric excitation of spin waves by two different mechanisms, now referred to as the first and second Suhl instabilities. This theory was based on the Landau-Lifshitz equation [4]. Since Suhl’s work, there have been many theoretical and experimental studies of the parametric excitation of spin waves. The theoretical work can be divided into two categories; i) those based on the Landau-Lifshitz equation [5], [6], [7], [8], [9], [10], and those based on a classical Hamiltonian [11], [12], [13], [14], [15], [16], [17]. Recently, theories based on a quantum mechanical Hamiltonian have appeared [18], [19], [20]. Each of these approaches has its strengths and weaknesses [17], [18]. Experimentally much attention has been focused on the so-called butterfly curves [21], [22], [23], [24], [25], [26], [27], [28], [29], [30] which plot the magnitude of the critical dynamic field (or equivalently, the instability threshold) against the static field at a fixed frequency. Apart from the butterfly curves, people also studied fold-over FMR [31], [32], [33], asymmetric FMR [34] and related effects. These studies directly address various characteristics of the nonlinear phenomena itself due associated with parametric excitation. Here we directly study the frequency minimum of two of the BV branches for in-plane and out-of-plane field orientations using characteristics of the parametric excitation and also present a simple way to increase the parametric excitation efficiency.

Section snippets

Experimental techniques

The material studied is a thin film of yttrium iron garnet (YIG), which is a ferrimagnetic material well-known for its low magnetic damping. It was supplied by MTI Corp and was grown by liquid phase epitaxy on a lattice matched (1 1 1) gadolinium gallium garnet (GGG) substrate from which a 5 mm × 10 mm sample was cut. The film thickness was determined to be 2.843 ± 0.002 μm using an M-2000 ellipsometer (J. A. Woollam Corp).

Fig. 1 shows, schematically, the arrangement of the components of our

In-plane analysis

Measurements were first performed for the case where the d.c. magnetic field lies in the plane of the YIG film and perpendicular to the axis of the wire antenna used to excite the sample. Here it is presumed that wavevectors ±kinplane of the spin waves generated in the two magnon decay of the quasi uniform precession excited by the wire lie perpendicular to the wire axis. This corresponds to the so-called backward volume (BV) spin wave geometry. In an independent set of experiments the

Out-of-plane analysis

We have also performed out-of-plane measurements at 2 and 4 GHz. We use the term out-of-plane when the applied field lies in a plane defined by two vectors: the film normal (n) and in-plane wavevector (kin-plane). The field angle θe is that formed by the film normal (n) and external static magnetic field (Hext). The results are given in Fig. 5. The solid lines are generated by the theory of Arias [44]. The Arias theory is based on the Landau-Lifshitz equation and provides an exact analytical

Conclusion

We have developed a technique which exploits the Suhl instability to locate the field dependence of the frequency, ωmin (H), associated with the minimum in the dispersion relation of the backward volume mode in a thin film of the ferrimagnetic material yttrium iron garnet. The associated two-magnon coupling is demonstrated to be enhanced for frequencies ω > 2ωmin. Our in-plane measurements of ωmin are in good agreement with the phenomenological model for the backward volume dispersion relations

CRediT authorship contribution statement

Jinho Lim: Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Writing - review & editing, Visualization. Wonbae Bang: Resources. Jonathan Trossman: Resources, Software. C.C. Tsai: Resources. John B. Ketterson: Conceptualization, Methodology, Writing - review & editing, Visualization, Supervision, Project administration, Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was performed at Northwestern University under support from the U.S. Department of Energy through grant DE-SC0014424.

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  • Cited by (0)

    1

    Current affiliation: Institute of Advanced Materials, LG Chem, Daejeon 34122, South Korea.

    2

    Current affiliation: Department of Green Energy and Environmental Resources, Chang Jung Christian University, Tainan 71101, Taiwan.

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