Frequency- and magnetic-field-dependent properties of ordered magnetic nanoparticle arrangements

Nils Neugebauer, Toni Hache, Matthias T. Elm, Detlev M. Hofmann, Christian Heiliger, Helmut Schultheiss, and Peter J. Klar

Phys. Rev. B 103, 094438 – Published 24 March 2021

Abstract

We present investigations of the frequency and magnetic field dependent properties of ordered magnetic nanoparticles (MNPs) arrangements consisting of magnetite ( ${Fe}_{3} O_{4}$ ) nanoparticles with an average diameter of 20 nm by employing micro Brillouin light scattering microscopy. We utilized electron beam lithography to prepare hexagonally arranged, circularly shaped MNP assemblies consisting of a single layer of MNPs using a variant of the Langmuir-Blodgett technique. By comparing the results with nonstructured, layered superlattices of MNPs, further insight into the influence of size and geometry of the arrangement on the collective magnetic properties is obtained. We show that at low static external field strengths, two signals occur in frequency dependent measurements for both nonstructured and structured assemblies. Increasing the static external field strength results in a sharpening of the main signal, while the satellite signal decreases in its intensity and increases in its linewidth. The occurrence of multiple signals at low external field strengths is also confirmed by sweeping the static external field and keeping the excitation frequency constant. Furthermore, two-dimensional spatial mapping of the resonances reveals that the main and the satellite signal originate from the center and the edge, respectively, of a single circular MNP assembly. Micromagnetic simulations confirm these assignments and the dependence of the two signals on the static external field strength, justifying an interpretation of the observed characteristics in terms of different local environments of MNPs forming the MNP assembly.

Received 5 November 2020
Revised 16 February 2021
Accepted 15 March 2021

DOI:https://doi.org/10.1103/PhysRevB.103.094438

Physics Subject Headings (PhySH)

Dipolar interaction Magnetic coupling Magnetization dynamics Micromagnetism Spin dynamics

2-dimensional systems Honeycomb lattice Magnetic nanoparticles

Brillouin scattering & spectroscopy Landau-Lifschitz-Gilbert equation Langmuir-Blodgett deposition Lithography Micromagnetic modeling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Nils Neugebauer^1,*, Toni Hache ^2,3, Matthias T. Elm^1,4,5, Detlev M. Hofmann^1,4, Christian Heiliger^4,6, Helmut Schultheiss ^2,7, and Peter J. Klar^1,4

¹Institute of Experimental Physics I, Justus Liebig University Giessen, Heinrich-Buff-Ring 16, 35392 Giessen, Germany
²Helmholtz-Center Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research, Bautzner Landstraße 400, 01328 Dresden, Germany
³Institute for Physics, Technische University Chemnitz, 09107 Chemnitz, Germany
⁴Center for Materials Research (ZfM/LaMa), Justus Liebig University Giessen, Heinrich-Buff-Ring 16, 35392 Giessen, Germany
⁵Institute of Physical Chemistry, Justus Liebig University Giessen, Heinrich-Buff-Ring 17, 35392 Giessen, Germany
⁶Institute for Theoretical Physics, Justus Liebig University Giessen, Heinrich-Buff-Ring 16, 35392 Giessen, Germany
⁷Technische Universität Dresden, 01062 Dresden, Germany

^*Nils.Neugebauer@physik.uni-giessen.de

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Vol. 103, Iss. 9 — 1 March 2021

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Images

Figure 1
(a) Using a variant of the Langmuir-Blodgett technique, a mixture of MNPs suspended in toluene and PMMA is pipetted onto a water subphase. During the evaporation of the solvent, a self-assembling process takes place leading to a hexagonal arrangement of a single layer of MNPs which can be transferred to a silicon wafer substrate. (b) After the EBL exposure with high doses and a subsequent development process, patterned MNP arrangements are synthesized.
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Figure 2
(a) $μ BLS$ intensity of the circularly structured MNP arrangement shown in Fig. 1 detected in an microwave excitation frequency range between $f_{ext} = 0 GHz$ and 15 GHz as a function of the external excitation frequency $f_{ext}$ . The data were recorded at an external field strength of $B_{ext} = 230 mT$ . Integrating the data for each $f_{ext}$ leads to an accumulated spectrum as shown in (b) (black dashed curve). It is clearly visible that one main signal is present at $f_{ext} = 9.1 GHz$ , accompanied by a satellite signal located at $f_{ext} = 6.6 GHz$ . Keeping the excitation frequency constant at $f_{ext} = 9 GHz$ and sweeping the external field strength yields the corresponding accumulated field-dependent spectrum which also exhibits two signals (blue dashed curve). The continuous curves represent fits with two Lorentzian curves to the corresponding data. (c) Simulated $f_{ext}$ - (black curve) and $B_{ext}$ -dependent spectra (blue curve) of a hexagonally arranged, circularly shaped MNP assembly. The assembly has a diameter of 300 nm. The frequency-dependent spectrum was calculated for $B_{ext} = 200 mT$ , while the external field strength dependent spectrum was simulated for $f_{ext} = 9.75 GHz$ . Both spectra show a main peak accompanied by a satellite peak of lower intensity in agreement with the experimental results.
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Figure 3
Top: Spatial maps of the scattered light intensity at the frequency of the satellite peak (left) and the main peak (right) obtained at constant $B_{ext}$ of a circular MNP assembly with a diameter of 450 nm. The white circle indicates the boundary of the MNP assembly and each pixel is 20 nm wide. Bottom: Line scans of the scattered light intensity at the two resonances along the red line $[1]$ and the purple line $[2]$ shown in the top image.
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Figure 4
(a) Integrated $μ BLS$ spectra recorded at a nonstructured, layered MNP arrangement at different external field strengths $B_{ext}$ . As $f_{ext}$ increases, the resonance positions are shifted according to the resonance condition [see Eq. (1)]. The linewidths $σ_{S/M}$ of the two resonances and the ratio of their intensities $A_{S} / A_{M}$ show distinct field dependencies, which are shown in (c). (b) Simulated frequency dependence of nonstructured, layered MNP assemblies at different $B_{ext}$ . While at low $B_{ext}$ of 100 mT a satellite peak can be recognized, at large $B_{ext}$ of 300 mT its presence is only noticeable as an asymmetry in the low frequency range of the spectrum.
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Figure 5
(a) Simulated $f_{ext}$ -dependent $μ BLS$ spectra of a circularly shaped monolayer of MNPs with a radius of 150 nm. The spectra were calculated at $B_{ext} = 200 mT$ (black curve) and 500 mT (blue curve). Increasing $B_{ext}$ results in a shift of the resonance position according to the resonance condition [Eq. (1)]. In addition, a decrease of the intensity of the satellite peak with increasing $B_{ext}$ is visible. (b) Performing 2D-Fourier analyses unveils the active regions of the two resonances. As $B_{ext}$ increases, the active areas of the satellite resonance decrease resulting in a reduction of its relative intensity, compared with the main resonance. The arrows indicate the direction of the external field pointing in the plane of the structure in the $x$ direction. (c) Averaged dipole field ${\vec{B}}_{dd,z}$ in the direction perpendicular to the sample plane ( $z$ axis) over one period $T = 1 / f_{ext}$ with $f_{ext} = 7.5 GHz$ and 15.6 GHz (S-200 mT and S-500 mT). The vertical axis is normalized to the strength of the microwave field $B_{mw} = 2 mT$ .
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