Spin Pinning and Spin-Wave Dispersion in Nanoscopic Ferromagnetic Waveguides

Abstract

Spin waves are investigated in Yttrium Iron Garnet (YIG) waveguides with a thickness of 39 nm and widths ranging down to 50 nm, i.e., with aspect ratios thickness over width approaching unity, using Brillouin Light Scattering spectroscopy. The experimental results are verified by a semi-analytical theory and micromagnetic simulations. A critical width is found, below which the exchange interaction suppresses the dipolar pinning phenomenon. This changes the quantization criterion for the spin-wave eigenmodes and results in a pronounced modification of the spin-wave characteristics. The presented semi-analytical theory allows for the calculation of spin-wave mode profiles and dispersion relations in nano-structures.Spin waves and their quanta, magnons, typically feature frequencies in the GHz to THz range and wavelengths in the micrometer to nanometer range. They are envisioned for the design of faster and smaller next generational information processing devices where information is carried by magnons instead of electrons [1][2][3][4][5][6][7][8][9]. In the past, spin-wave modes in thin films or rather planar waveguides with thickness-towidth aspect ratios ar = h/w << 1 have been studied. Such thin waveguides demonstrate the effect of "dipolar pinning" at the lateral edges, and for its theoretical description the thin strip approximation was developed, in which only pinning of the much-larger-in-amplitude dynamic in-plane magnetization component is taken into account [10][11][12][13][14][15]. The recent progress in fabrication technology leads to the development of nanoscopic magnetic devices in which the width w and the thickness h become comparable [16][17][18][19][20][21][22][23]. The description of such waveguides is beyond the thin strip model of effective pinning, because the scale of nonuniformity of the dynamic dipolar fields, which is described as "effective dipolar boundary conditions", becomes comparable to the waveguide width. Additionally, both, in-plane and out-of-plane dynamic magnetization components, become involved in the effective dipolar pinning, as they become of comparable amplitude.Thus, a more general model should be developed and verified experimentally. In addition, such nanoscopic feature sizes imply that the spin-wave modes bear a strong exchange character, since the widths of the structures are now comparable to the exchange length [24]. A proper description of the spin-wave eigenmodes in nanoscopic strips which considers the influence of the exchange interaction, as well as the shape of the structure, is fundamental for the field of magnonics.In this Letter, we discuss the evolution of the frequencies and profiles of the spin-wave modes in nanoscopic waveguides where the aspect ratio ar evolves from the thin film case ar → 0 to a rectangular bar with ar → 1. Yttrium Iron Garnet (YIG) waveguides with a thickness of 39 nm and widths ranging down to 50 nm are fabricated and the quasi-ferromagnetic resonance (quasi-FMR) frequencies within them are measured using microfocused Brillouin Ligh...

Efficient wavelength conversion of exchange magnons below 100 nm by magnetic coplanar waveguides

“…4c-e), corresponding to k ≈170 rad μm −1 . We argue that the wavelength conversion based on mCPWs is very versatile and works in both insulting and metallic magnets, in nanoscopic ferromagnetic waveguides 45 and skyrmion-hosting materials 46 . The magnons with k max ¼ 62:4 rad μm −1 reported here possess wavelengths shorter than the minimum ones reported so far for nonmagnetic microwave waveguides 14,15,27 and signals are about three orders of magnitude larger (Fig.…”

Unidirectional Pumping of Phonons by Magnetization Dynamics

“…For GGG at room temperature, ρ ¼ 7080 kg=m 3 , c l ¼ 6545 m=s, and c t ¼ 3531 m=s[53], leading to[42] η ¼ 0.927, c r ¼ ηc t ¼ 3271.8 m=s, and ξ P ¼ 0.537. For YIG[54], γ ¼ 1.82 × 10 11 s −1 T −1 , μ 0 M s ¼ 0.177 T[55], B ⊥ ¼ 6.96 × 10 5 J=m 3…”

Recent Trends in Microwave Magnetism and Superconductivity

“…In particular, low-energy means of the localized magnon excitation, manipulation, and detection on a scale of 10 nm, operations with spin waves of nm-wavelengths and THz frequencies and the development of efficient spin-wave amplifiers belong to the most actual tasks of the modern magnonics. Nevertheless, the fast growth of the field of beyong-CMOS data processing, the recent breakthrough in the miniaturization of lateral sizes of magnonic structures down to 50 nm [275], the decrease in wavelengths down to the same value [276], as well as the progress in the understanding and usage of nonlinear spin-wave physics in nano-sized magnonic circuits [267,270] look very promising. The field of the spin-wave logic is therefore an active, emergent field that could deliver a number of breakthrough developments toward applications in data processing in the middle-term future.…”