Deeply nonlinear excitation of self-normalised exchange spin waves

Abstract

Spin waves are ideal candidates for wave-based computing, but the construction of magnetic circuits is blocked by a lack of an efficient mechanism to excite long-running exchange spin waves with normalised amplitudes. Here, we solve the challenge by exploiting the deeply nonlinear phenomena of forward-volume spin waves in 200 nm wide nanoscale waveguides and validate our concept with microfocused Brillouin light scattering spectroscopy. An unprecedented nonlinear frequency shift of >2 GHz is achieved, corresponding to a magnetisation precession angle of 55° and enabling the excitation of exchange spin waves with a wavelength of down to ten nanometres with an efficiency of >80%. The amplitude of the excited spin waves is constant and independent of the input microwave power due to the self-locking nonlinear shift, enabling robust adjustment of the spin wave amplitudes in future on-chip magnonic integrated circuits.

All-magnonic repeater based on bistability

“…The frequency step is small enough so that magnon state evolves from a preceding one. As a result, the up and down frequency sweep curves do not overlap and show a hysteretic response resulting in a large bistable frequency window of ~1.1 GHz which is similar to our previous study [14]. The nature of this bistable window is similar to those observed in a common nonlinear oscillator (e.g., Duffing oscillator) when the foldover effect takes place, although there are certain differences (see Supplementary Materials).…”

“…where fk,0 is the linear (small-amplitude) spin-wave frequency, Tk > 0 is the nonlinear frequency shift coefficient, and ck is canonic spin wave amplitude. In our case of forward spin waves, 𝑐 𝑘 2 ≈ 1 − cos 𝜃 ̅̅̅̅̅̅̅ , where θ is the precession angle and overbar means averaging over the waveguide width [14]. The nonlinear frequency shift coefficient in the range from k = 0 to k ≈ 20μm -1 , which is the wavenumber of spin waves excited by the CPW antenna, weakly depends on k. Then, the effect of the incident spin waves can be imagined as a shift of the whole spin wave spectrum by the value Δ𝑓 = 𝑇 𝑘 𝑐 𝑘 2 [31].…”

“…In the presented case, the low-frequency edge of the bistability window is located at approximately 5.7 GHz, thus, 200 MHz below the working frequency of 5.9 GHz. The nonlinear frequency shift coefficient for k ≈ 20μm -1 is Tk ≈ 6.35 GHz (see calculation method in [14]). In the simulations, a little above the switching threshold, the propagating spin waves arriving at the pump antenna have the width-averaged precession angle of 𝜃 ̅ = 12.3°, which corresponds to canonic spin wave amplitude ck ≈ 0.185.…”

“…Recently, spin waves have attracted much attention in the field of conventional and unconventional computing [4][5][6] due to their nanoscale wavelengths [7][8][9][10], controllable nonlinear phenomena [11][12][13][14], energy efficiency [15] and the abundant interaction with other quasi-/particle [16][17][18]. Several individual magnon-based computing devices have been demonstrated including spin-wave logic gates [19], majority gates [20], magnon transistors [21][22][23][24], magnonic directional couplers [25], and neuromorphic computing elements [26].…”

“…Here, based on the recently discovered bistability of the deeply nonlinear forward volume spin waves excitation in nanoscale waveguides [14], we demonstrate an elegant way to switch between the two magnon states using a propagating spin wave, thus realizing a magnonic repeater. The repeater is a simple 2 m wide strip antenna placed on top of a magnonic waveguide as shown in Fig.…”