Observation of Coherent Spin Waves in a Three-Dimensional Artificial Spin Ice Structure - data

The spin wave (SW) dynamics of the 3D array were measured by using conventional Brillouin light scattering (BLS) technique. The 3D-ASI was fabricated by using a combination of TPL and thermal evaporation. BLS is a popular tool to measure SW dynamics of magnetic thin films and patterned nanostructures. It is a non-contact and thus non-invasive tool to measure thermally excited SWs at room temperature without any external excitation and under ambient conditions. This technique relies upon inelastic scattering of light from the sample. The mechanism of inelastic scattering can be quantum mechanically described as a photon–magnon collision, where the creation (Stokes process) and annihilation (anti-Stokes process) of a magnon of wave vector (k) and angular frequency (ω) is detected. A continuous wave of monochromatic laser light (wavelength λ = 532 nm, power = 60 mW) was focused on the sample to a spot size of around 40 µm, which is close to the lateral dimensions of the sample. As a result, the SWs were measured from almost the entire sample volume. The cross polarization between the inelastically backscattered beam and incident beam was exploited to supress the phonon contribution. A Sandercock-type six-pass tandem Fabry–Perot interferometer was used to analyse the frequencies of the scattered beam, in order to extract the SW frequencies. In our experiment, we applied a bias magnetic field (H) parallel to the substrate plane, along a principal axis (x-direction) of the lattice. A high magnetic field was first applied to completely saturate the sample magnetization, which was then gradually decreased to each bias field value for the BLS measurement. In order to study the SW frequency variation with H, the BLS spectra were measured for the k  ≈  0 in the Damon-Eschbach (DE) geometry corresponding to scattering of photon by a surface magnon, for different H values in 0.6 ≤ H ≤ 2.0 kOe. Two clear SW modes were observed in the BLS spectra, each of which showed a systematic variation with the applied magnetic field. These experimental results have been understood in the context of 3D micromagnetic simulations, which show the observed modes can be reproduced in the simulation. The simulated mode profiles revealed complex quantized characters with its power distributed over the entire structure.

Here, we provide experimental and simulated data of 3D-ASI sample.

Files –

HysteresisLoop.txt

In the above file, the 1^st column presents magnetic field in Oe and 2^nd column presents normalized Kerr rotation in arb. units.

BLS_Spectra_1.0kOe.txt

BLS_Spectra_1.4kOe.txt

BLS_Spectra_1.8kOe.txt

LorentzianFitting_BLS_Spectra_1.0kOe.txt

LorentzianFitting_BLS_Spectra_1.4kOe.txt

LorentzianFitting_BLS_Spectra_1.8kOe.txt

ElasticPeak_of_BLS_spectra.txt

GaussianFitting_elasticPeak.txt

In the above files, the 1^st column presents frequency in GHz and 2^nd column presents spectra intensity in arb. Units.

simulated_SW_spectra_1.0kOe.txt

simulated_SW_spectra_1.2kOe.txt

simulated_SW_spectra_1.6kOe.txt

simulated_SW_spectra_one_3D-ASI_at_1.6kOe.txt

simulated_SW_spectra_one_tetrapod_element_at_1.6kOe.txt

simulated_SW_spectra_single_nanowire_leg_at_1.6kOe.txt

In the above files, the 1^st column presents frequency in Hz and 2^nd column presents spectra intensity in arb. Units.

Field dependence Plot_of_expt_data_with_error_bar.txt

Field_dependence_Plot_of_simulated_data.txt

Kittel_fitting_of_highest_frequency_Mode_M2.txt

In the above files, 1^st column presents magnetic field in Oe and rest columns presents frequency in GHz.  For “Field dependence Plot_of_expt_data_with_error_bar.txt^“3^rd and 5^th column present error bar of experimentally observed SW frequency.

MuMax3_code_of_unit_cell_of_3D_ASI_Magnetization_Dynamics.go

: MuMax3 code for magnetization dynamics simulation of 3D-ASI sample at 1.22 kOe.

Research results based upon these data are published at https://doi.org/10.1021/acs.nanolett.1c00650