# Harnessing Multi-Photon Absorption to Produce Three-Dimensional Magnetic Structures at the Nanoscale

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}particles (particle size: 1.5–7.5 nm) which could self-assemble into complex 3D colloidal crystals [19]. In the same year, 3D cobalt nanocrystals were produced by application of a ferrofluid to oriented pyrolytic graphite and applying a magnetic field [20]. Such methods were innovative and provided a first taste of the interesting properties that may arise when nanostructuring magnets in three-dimensions. Perhaps what was lacking was a controlled means to produce nanomagnets of arbitrary 3D geometry.

## 2. Experimental Setup and Physics of Two-Photon Lithography

_{th}, the exposed area is polymerised. The exposure dose is approximately proportional to the generated free radicals and therefore to the excited photoinitiator molecules and thus to the number of absorbed photons. In order to write arbitrary structures, it is necessary to only expose desired areas. This is trivial to do for 2D fabrication by using a simple optical mask. For more complex 3D geometries, it becomes necessary to focus the light using a high numerical aperture (NA) lens, so that only a limited volume (‘voxel’) of the photoresist around the focal point is exposed with enough intensity to reach the threshold dose.

^{2}∙mol

^{−1}), c is the concentration of photoinitiator (mol∙m

^{−3}) and z is the depth into the photoresist (m). The absorbance A(z) is related to the transmittance T(z) (ratio of transmitted intensity I(z) to incident intensity I

_{0}) by:

_{i}so that Σhν

_{i}≥ ΔE (multi-photon absorption) (Figure 2). In the case of multi-photon absorption, the photons must arrive at the photoinitiator within a small enough time window. It is therefore less likely than 1PA. The probability of absorption (absorption rate) is proportional to I

^{n}where n is the number of absorbed photons (assuming photons of the same frequency ν) and I the intensity of the light at the given frequency ν. Two-photon absorption (2PA) therefore requires much stronger intensities than one-photon absorption to make the process efficient enough for lithography. Table 1 summarises the properties of 1PA and 2PA.

^{2}instead of I, the exposed area is much smaller. In addition, when integrating over the x-y plane, one finds a peak in the focal plane. This allows setting the power so that only the volume enclosed within the focal point (the voxel) receives sufficient exposure to be polymerised, thus enabling the creation of the desired 3D plane or any arbitrary 3D structure.

_{0}is the beam waist (minimum radius of beam at focus), σ

_{2}is the effective two-photon radical absorption cross-section, I

_{0}is the photon flux at the beam centre, τ is the laser pulse width and C is defined as the following equation:

_{0}is the density of free radicals at the focal plane and ρ

_{th}is the threshold density of free radicals.

_{R}is the Rayleigh length, which is defined as the following equation:

_{laser}= incident laser power, t = processing time, f = repetition frequency of the laser, τ = pulse width, ν = frequency of light, M

_{0}= initial concentration of photoinitiator in the ground state, M

_{th}= threshold amount of dissolvable photoinitiator. The factor C’ relates the quantum efficiency (Φ), two-photon absorption cross-section (δ), the Einstein coefficient of absorption (A

_{E}) and a rate constant (C

_{0}) as shown below:

**Table 1.**Comparison of optical properties for single photon absorption (1PA) versus two-photon absorption (2PA).

Optical Property | 1PA | 2PA |
---|---|---|

transmitted intensity, I [48] | $I\left(z\right)=\text{}{I}_{0}{e}^{-\mathrm{ln}\left(10\right)\epsilon cz\left(z\right)}$ | $I\left(z\right)=\text{}\frac{{I}_{0}}{1+\beta z{I}_{0}}$ |

$\frac{\mathit{d}\mathit{I}\left(\mathit{z}\right)}{\mathit{d}\mathit{z}}$ [49] | $\frac{dI\left(z\right)}{dz}=\text{}-\mathrm{ln}\left(10\right)\epsilon c\times I\left(z\right)$ | $\frac{dI\left(z\right)}{dz}=\left(-\beta \right)\times I{\left(z\right)}^{2}$ |

transmittance [50] $\mathit{T}\left(\mathit{z}\right)=\text{}\frac{\mathit{I}\left(\mathit{z}\right)}{{\mathit{I}}_{0}}=\text{}{10}^{-\mathit{A}\left(\mathit{z}\right)}$ | $T\left(z\right)=\text{}{e}^{-\mathrm{ln}\left(10\right)\epsilon cz\left(z\right)}$ | $T\left(z\right)=\text{}\frac{1}{1+\beta z{I}_{0}}$ |

decadic absorbance [51,52] $\mathit{A}\left(\mathit{z}\right)=\text{}\frac{-\mathrm{ln}\left(\mathit{T}\right)}{\mathrm{ln}\left(10\right)}$ | $A\left(z\right)=\text{}\epsilon cz$ | $A\left(z\right)=\text{}\frac{\mathrm{ln}\left(1+\beta z{I}_{0}\right)}{\mathrm{ln}\left(10\right)}$ $\cong \text{}\frac{\beta z}{\mathrm{ln}\left(10\right)}\times {I}_{0}$ |

absorption probability/rate [44,50] $\mathit{P}\text{}\propto \text{}{\mathit{I}}^{\mathit{n}}$ | $P\text{}\propto \text{}I$ | $P\text{}\propto \text{}{I}^{2}$ |

## 3. Fabrication of Magnetic Nanostructures with Two-Photon Lithography

#### 3.1. TPL and Electrodeposition

#### 3.2. TPL and Line of Sight Deposition

_{81}Fe

_{19}(permalloy) nanowires with a novel curved cross-section, at a resolution of ~200 nm (Figure 7a–c). With LOS deposition, the permalloy was deposited upon the uppermost unit cell without depositing magnetic material on the lower scaffold layers, thereby minimising dipolar interactions between the magnetic nanowires and the sheet film upon the substrate. Additionally, the buried polymer layers act as optical scattering centres, allowing MOKE measurements to be performed with minimal contribution from the sheet film (Figure 7d). This study reports a first example showing that TPL and LOS deposition can rapidly yield extended arrays of single-domain magnetic nanowires in complex 3D geometries. Standard measurement techniques such as MOKE and magnetic force microscopy (MFM) were used to probe the magnetic properties, providing an exciting new path of investigation for 3D magnetic nanowires and artificial frustrated systems. Utilisation of other imaging techniques such as scanning transmission x-ray microscopy (STXM) [77] and high resolution Hall sensing [78] is expected to yield even more fruitful results.

## 4. Methods to Reduce Feature Size

_{xy}for NA values > 0.7 has been shown to be [81]:

## 5. Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of laser intensity profile for (

**a**) resist with high-concentration photoinitiator; (

**b**) resist with low-concentration photoinitiator; (

**c**) two-photon absorption profile [44].

**Figure 2.**Energy level schematic for single photon absorption and two-photon absorption processes. Dotted line indicates imaginary intermediary state.

**Figure 3.**Use of TPL and electrochemical deposition to fabricate 3D magnetic nanostructures. (

**a**) Spin-coating of a positive resist onto a conductive substrate; (

**b**) Two-photon lithography of a 3D structure into the positive resist; (

**c**) Electrodeposition of magnetic material into the channels; (

**d**) Lift off of the resist.

**Figure 4.**(

**a**) Tilted SEM image of a single Co tetrapod structure; (

**b**) Top-down SEM of a single Co tetrapod structure; (

**c**) SEM micrograph of an individual wire within a tetrapod structure (left) and spin-polarised SEM images showing x and y-components of magnetisation in an as-deposited sample (middle and right); (

**d**) Longitudinal MOKE loop obtained from tetrapod array with field applied along the projection of the lower wires onto the substrate [65].

**Figure 5.**Illustration depicting the fabrication of a 3D arrangement of magnetic nanowires, via TPL and LOS deposition. (

**a**) Exposure of photoresist during TPL; (

**b**) Polymer scaffold after development of unexposed photoresist; (

**c**) Resulting magnetic nanowires and sheet film, following deposition of a thin magnetic film.

**Figure 6.**Physical characterisation of a cobalt-coated buckyball. (

**a**) SEM images displaying the buckyball mounted upon a tomography pin (left) and a magnified image of the fabricated structure (right); (

**b**) 3D rendering of the buckyball composition, obtained by x-ray tomography, cobalt is indicated by orange contrast whilst photoresist is blue; (

**c**) Fluorescence spectra of cobalt deposited upon the polymer scaffold, upon the pillar and cobalt oxide detected in transmission [76].

**Figure 7.**Structural and magnetic characterisation of a 3D N

_{i81}Fe

_{19}nanowire lattice. (

**a,b**) SEM images of the nanowire lattice observed from top view and a 45° tilt respectively; (

**c**) Schematic of the Ni

_{81}Fe

_{19}nanowires (grey) upon a polymer scaffold (yellow), where the effects of shadowing by upper nanowire layers during LOS deposition is evident. Inset: Nanowire cross-sectional geometry; (

**d**) MOKE data captured from the sheet film (blue) and nanowire lattice—this is separated into up-sweep (black) and down-sweep (red) [75].

**Figure 8.**SEM image of a woodpile structure fabricated by TPL with a laser of wavelength 405 nm. Smallest line width is reported to be 68 nm. Reprinted with permission from ref [83] © The Optical Society.

**Figure 9.**Schematic showing the point spread functions in stimulated emission depletion two-photon lithography [82]. Here the excitation beam is red, depletion beam taking the form of a bottle-beam mode is green, and this yields an effective exposure as shown in purple.

**Figure 10.**Illustration of reduction in feature size by separate use of oxygen plasma etching, pyrolysis and then a combination of the two techniques [87].

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## Share and Cite

**MDPI and ACS Style**

Hunt, M.; Taverne, M.; Askey, J.; May, A.; Van Den Berg, A.; Ho, Y.-L.D.; Rarity, J.; Ladak, S.
Harnessing Multi-Photon Absorption to Produce Three-Dimensional Magnetic Structures at the Nanoscale. *Materials* **2020**, *13*, 761.
https://doi.org/10.3390/ma13030761

**AMA Style**

Hunt M, Taverne M, Askey J, May A, Van Den Berg A, Ho Y-LD, Rarity J, Ladak S.
Harnessing Multi-Photon Absorption to Produce Three-Dimensional Magnetic Structures at the Nanoscale. *Materials*. 2020; 13(3):761.
https://doi.org/10.3390/ma13030761

**Chicago/Turabian Style**

Hunt, Matthew, Mike Taverne, Joseph Askey, Andrew May, Arjen Van Den Berg, Ying-Lung Daniel Ho, John Rarity, and Sam Ladak.
2020. "Harnessing Multi-Photon Absorption to Produce Three-Dimensional Magnetic Structures at the Nanoscale" *Materials* 13, no. 3: 761.
https://doi.org/10.3390/ma13030761