# 3D Magnonic Conduits by Direct Write Nanofabrication

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Fabrication

_{3}(CO)

_{12}. The precursor was prepared according to the method reported previously [50]. The beam voltage, current, and dwell time were 5 keV, 1.6 nA, and 1 μs, respectively. The pitch for the plank conduit was 26 nm, and for the bumped conduit 20 nm.

#### 2.2. Characterisation

## 3. Results

#### 3.1. Thermal FMR

#### 3.2. Microwave Excitation

#### 3.3. Area Scan

## 4. Discussion

^{−1}, in consideration of literature values [57]. The other parameters were freely varying, resulting in $\gamma $ = $3.04$ $\mathrm{M}$$\mathrm{Hz}$ Oe

^{−1}, ${\mathrm{H}}_{\mathrm{ani}}$ = $-110$ $\mathrm{Oe}$, ${\mathrm{M}}_{\mathrm{s}}$ = 1159 $\mathrm{k}$$\mathrm{A}$ m

^{−1}. The magnetisation value is close to previously reported values for Co

_{3}Fe-FEBID nanostructures [21]. With a ca. 80 at.% of Co-Fe in the FEBID deposit, the corrected ${\mathrm{M}}_{\mathrm{s}}$ for the Co-Fe deposit amounts to 1449 $\mathrm{k}$$\mathrm{A}$ m

^{−1}. This estimate is in line with the ${\mathrm{M}}_{\mathrm{s}}$ value resulting from the expected Co

_{3}Fe composition with reference values of magnetisation for cobalt of 1400 $\mathrm{k}$$\mathrm{A}$ m

^{−1}and iron 1700 $\mathrm{k}$$\mathrm{A}$ m

^{−1}, which corresponds to a net magnetisation of 1475 $\mathrm{k}$$\mathrm{A}$ m

^{−1}.

## 5. Conclusions

_{3}Fe nanostructures by direct write using FEBID which show a significant change in the supported magnon spectra. The richness of the magnon spectra is attributed to field non-uniformity induced effects which are derived solely from the 3D geometry of the structures. Our observations stimulate further investigations into the use of geometric engineering in magnetic structures to deliberately tune the supported mode spectra of magnonic conduits. Further investigations of 3D geometry and curvature effects in conduit structures from a theoretical or numeric approach would guide the direction of further experimental studies of complex-shaped magnonic conduits.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Barman, A.; Gubbiotti, G.; Ladak, S.; Adeyeye, A.O.; Krawczyk, M.; Grafe, J.; Adelmann, C.; Cotofana, S.; Naeemi, A.; Vasyuchka, V.I.; et al. The 2021 Magnonics Roadmap. J. Physics Condens. Matter
**2021**, 33, 413001. [Google Scholar] [CrossRef] [PubMed] - Chumak, A.V.; Kabos, P.; Wu, M.; Abert, C.; Adelmann, C.; Adeyeye, A.O.; Akerman, J.; Aliev, F.G.; Anane, A.; Awad, A.; et al. Advances in Magnetics Roadmap on Spin-Wave Computing. IEEE Trans. Magn.
**2022**, 58, 3149664. [Google Scholar] [CrossRef] - Wang, Q.; Kewenig, M.; Schneider, M.; Verba, R.; Kohl, F.; Heinz, B.; Geilen, M.; Mohseni, M.; Lägel, B.; Ciubotaru, F.; et al. A magnonic directional coupler for integrated magnonic half-adders. Nat. Electron.
**2020**, 3, 765–774. [Google Scholar] [CrossRef] - Zakeri, K. Terahertz magnonics: Feasibility of using terahertz magnons for information processing. Phys. C Supercond. Appl.
**2018**, 549, 164–170. [Google Scholar] [CrossRef] - Chumak, A.V.; Serga, A.A.; Hillebrands, B. Magnon transistor for all-magnon data processing. Nat. Commun.
**2014**, 5, 5700. [Google Scholar] [CrossRef] [PubMed] - Dobrovolskiy, O.V.; Sachser, R.; Bunyaev, S.A.; Navas, D.; Bevz, V.M.; Zelent, M.; Śmigaj, W.; Rychły, J.; Krawczyk, M.; Vovk, R.V.; et al. Spin-Wave Phase Inverter upon a Single Nanodefect. ACS Appl. Mater. Interfaces
**2019**, 11, 17654–17662. [Google Scholar] [CrossRef] [PubMed] - Fischer, T.; Kewenig, M.; Bozhko, D.A.; Serga, A.A.; Syvorotka, I.I.; Ciubotaru, F.; Adelmann, C.; Hillebrands, B.; Chumak, A.V. Experimental prototype of a spin-wave majority gate. Appl. Phys. Lett.
**2017**, 110, 152401. [Google Scholar] [CrossRef] - Qin, H.; Holländer, R.B.; Flajšman, L.; Hermann, F.; Dreyer, R.; Woltersdorf, G.; van Dijken, S. Nanoscale magnonic Fabry-Pérot resonator for low-loss spin-wave manipulation. Nat. Commun.
**2021**, 12, 2293. [Google Scholar] [CrossRef] - Yuan, H.Y.; Cao, Y.; Kamra, A.; Duine, R.A.; Yan, P. Quantum magnonics: When magnon spintronics meets quantum information science. Phys. Rep.
**2022**, 965, 1–74. [Google Scholar] [CrossRef] - Mohseni, M.; Vasyuchka, V.I.; L’vov, V.S.; Serga, A.A.; Hillebrands, B. Classical analog of qubit logic based on a magnon Bose–Einstein condensate. Commun. Phys.
**2022**, 5, 196. [Google Scholar] [CrossRef] - Andrianov, S.N.; Moiseev, S.A. Magnon qubit and quantum computing on magnon Bose–Einstein condensates. Phys. Rev. A At. Mol. Opt. Phys.
**2014**, 90, 042303. [Google Scholar] [CrossRef] - Grollier, J.; Querlioz, D.; Camsari, K.Y.; Everschor-Sitte, K.; Fukami, S.; Stiles, M.D. Neuromorphic spintronics. Nat. Electron.
**2020**, 3, 360–370. [Google Scholar] [CrossRef] [PubMed] - Demokritov, S.O.; Demidov, V.E.; Dzyapko, O.; Melkov, G.A.; Serga, A.A.; Hillebrands, B.; Slavin, A.N. Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping. Nature
**2006**, 443, 430–433. [Google Scholar] [CrossRef] [PubMed] - Schneider, M.; Breitbach, D.; Serha, R.O.; Wang, Q.; Serga, A.A.; Slavin, A.N.; Tiberkevich, V.S.; Heinz, B.; Lägel, B.; Brächer, T.; et al. Control of the Bose–Einstein Condensation of Magnons by the Spin Hall Effect. Phys. Rev. Lett.
**2021**, 127, 237203. [Google Scholar] [CrossRef] [PubMed] - Wang, Q.; Chumak, A.V.; Pirro, P. Inverse-design magnonic devices. Nat. Commun.
**2021**, 12, 2636. [Google Scholar] [CrossRef] [PubMed] - Papp, A.; Porod, W.; Csaba, G. Nanoscale neural network using non-linear spin-wave interference. Nat. Commun.
**2021**, 12, 6422. [Google Scholar] [CrossRef] [PubMed] - Vogel, M.; Chumak, A.V.; Waller, E.H.; Langner, T.; Vasyuchka, V.I.; Hillebrands, B.; Von Freymann, G. Optically reconfigurable magnetic materials. Nat. Phys.
**2015**, 11, 487–491. [Google Scholar] [CrossRef] - Dobrovolskiy, O.V.; Sachser, R.; Brächer, T.; Böttcher, T.; Kruglyak, V.V.; Vovk, R.V.; Shklovskij, V.A.; Huth, M.; Hillebrands, B.; Chumak, A.V. Magnon–fluxon interaction in a ferromagnet/superconductor heterostructure. Nat. Phys.
**2019**, 15, 477–482. [Google Scholar] [CrossRef] - Xu, M.; Yamamoto, K.; Puebla, J.; Baumgaertl, K.; Rana, B.; Miura, K.; Takahashi, H.; Grundler, D.; Maekawa, S.; Otani, Y. Nonreciprocal surface acoustic wave propagation via magneto-rotation coupling. Sci. Adv.
**2020**, 6, 1724. [Google Scholar] [CrossRef] - Papp, A.; Kiechle, M.; Mendisch, S.; Ahrens, V.; Sahin, L.; Seitner, L.; Porod, W.; Csaba, G.; Becherer, M. Experimental demonstration of a concave grating for spin waves in the Rowland arrangement. Sci. Rep.
**2021**, 11, 14239. [Google Scholar] [CrossRef] - Dobrovolskiy, O.V.; Vovk, N.R.; Bondarenko, A.V.; Bunyaev, S.A.; Lamb-Camarena, S.; Zenbaa, N.; Sachser, R.; Barth, S.; Guslienko, K.Y.; Chumak, A.V.; et al. Spin-wave eigenmodes in direct-write 3D nanovolcanoes. Appl. Phys. Lett.
**2021**, 118, 132405. [Google Scholar] [CrossRef] - Körber, L.; Zimmermann, M.; Wintz, S.; Finizio, S.; Kronseder, M.; Bougeard, D.; Dirnberger, F.; Weigand, M.; Raabe, J.; Otálora, J.A.; et al. Symmetry and curvature effects on spin waves in vortex-state hexagonal nanotubes. Phys. Rev. B
**2021**, 104, 184429. [Google Scholar] [CrossRef] - Li, X.; Labanowski, D.; Salahuddin, S.; Lynch, C.S. Spin wave generation by surface acoustic waves. J. Appl. Phys.
**2017**, 122, 043904. [Google Scholar] [CrossRef] - Heinz, B.; Brächer, T.; Schneider, M.; Wang, Q.; Lägel, B.; Friedel, A.M.; Breitbach, D.; Steinert, S.; Meyer, T.; Kewenig, M.; et al. Propagation of Spin-Wave Packets in Individual Nanosized Yttrium Iron Garnet Magnonic Conduits. Nano Lett.
**2020**, 20, 4220–4227. [Google Scholar] [CrossRef] [PubMed] - Wang, Q.; Heinz, B.; Verba, R.; Kewenig, M.; Pirro, P.; Schneider, M.; Meyer, T.; Lägel, B.; Dubs, C.; Brächer, T.; et al. Spin Pinning and Spin-Wave Dispersion in Nanoscopic Ferromagnetic Waveguides. Phys. Rev. Lett.
**2019**, 122, 247202. [Google Scholar] [CrossRef] [PubMed] - Gubbiotti, G. (Ed.) Three-Dimensional Magnonics; Jenny Stanford Publishing: New York, NY, USA, 2019. [Google Scholar] [CrossRef]
- Garlando, U.; Wang, Q.; Dobrovolskiy, O.V.; Chumak, A.V.; Riente, F. Numerical Model for 32-bit Magnonic Ripple Carry Adder. arXiv
**2023**, arXiv:2109.12973. [Google Scholar] [CrossRef] - May, A.; Saccone, M.; van den Berg, A.; Askey, J.; Hunt, M.; Ladak, S. Magnetic charge propagation upon a 3D artificial spin-ice. Nat. Commun.
**2021**, 12, 3217. [Google Scholar] [CrossRef] [PubMed] - Ho, P.; Tan, A.K.; Goolaup, S.; Oyarce, A.L.; Raju, M.; Huang, L.S.; Soumyanarayanan, A.; Panagopoulos, C. Geometrically tailored skyrmions at zero magnetic field in multilayered nanostructures. Phys. Rev. Appl.
**2019**, 11, 024064. [Google Scholar] [CrossRef] - Sheka, D.D. A perspective on curvilinear magnetism. Appl. Phys. Lett.
**2021**, 118, 230502. [Google Scholar] [CrossRef] - Makarov, D.; Volkov, O.M.; Kákay, A.; Pylypovskyi, O.V.; Budinská, B.; Dobrovolskiy, O.V.; Makarov, D.; Volkov, O.M.; Kákay, A.; Pylypovskyi, O.V.; et al. New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures. Adv. Mater.
**2022**, 34, 2101758. [Google Scholar] [CrossRef] [PubMed] - Fernández-Pacheco, A.; Streubel, R.; Fruchart, O.; Hertel, R.; Fischer, P.; Cowburn, R.P. Three-dimensional nanomagnetism. Nat. Commun.
**2017**, 8, 15756. [Google Scholar] [CrossRef] [PubMed] - Smith, E.J.; Makarov, D.; Sanchez, S.; Fomin, V.M.; Schmidt, O.G. Magnetic microhelix coil structures. Phys. Rev. Lett.
**2011**, 107, 097204. [Google Scholar] [CrossRef] [PubMed] - Sanz-Hernández, D.; Hamans, R.F.; Osterrieth, J.; Liao, J.W.; Skoric, L.; Fowlkes, J.D.; Rack, P.D.; Lippert, A.; Lee, S.F.; Lavrijsen, R.; et al. Fabrication of Scaffold-Based 3D Magnetic Nanowires for Domain Wall Applications. Nanomaterials
**2018**, 8, 483. [Google Scholar] [CrossRef] [PubMed] - Harinarayana, V.; Shin, Y.C. Two-photon lithography for three-dimensional fabrication in micro/nanoscale regime: A comprehensive review. Opt. Laser Technol.
**2021**, 142, 107180. [Google Scholar] [CrossRef] - Fernández-Pacheco, A.; Skoric, L.; De Teresa, J.M.; Pablo-Navarro, J.; Huth, M.; Dobrovolskiy, O.V. Writing 3D Nanomagnets Using Focused Electron Beams. Materials
**2020**, 13, 3774. [Google Scholar] [CrossRef] [PubMed] - Höflich, K.; Hobler, G.; Allen, F.I.; Wirtz, T.; Rius, G.; Krasheninnikov, A.V.; Schmidt, M.; Utke, I.; Klingner, N.; Osenberg, M. Roadmap for focused ion beam technologies. arXiv
**2023**, arXiv:2305.19631. [Google Scholar] - Weitzer, A.; Huth, M.; Kothleitner, G.; Plank, H. Expanding FEBID-Based 3D-Nanoprinting toward Closed High-Fidelity Nanoarchitectures. ACS Appl. Electron. Mater.
**2022**, 4, 744–754. [Google Scholar] [CrossRef] - Córdoba, R.; Orús, P.; Strohauer, S.; Torres, T.E.; De Teresa, J.M. Ultra-fast direct growth of metallic micro- and nano-structures by focused ion beam irradiation. Sci. Rep. X
**2019**, 9, 14076. [Google Scholar] [CrossRef] - Dobrovolskiy, O.V.; Begun, E.; Bevz, V.M.; Sachser, R.; Huth, M. Upper Frequency Limits for Vortex Guiding and Ratchet Effects. Phys. Rev. Appl.
**2020**, 13, 024012. [Google Scholar] [CrossRef] - Heil, T.; Waldow, M.; Capelli, R.; Schneider, H.; Ahmels, L.; Tu, F.; Schoneberg, J.; Marbach, H. Pushing the limits of EUV mask repair: Addressing sub-10 nm defects with the next generation e-beam-based mask repair tool. J. Micro/Nanopatterning Mater. Metrol.
**2021**, 20, 031013. [Google Scholar] [CrossRef] - Bunyaev, S.A.; Budinska, B.; Sachser, R.; Wang, Q.; Levchenko, K.; Knauer, S.; Bondarenko, A.V.; Urbánek, M.; Guslienko, K.Y.; Chumak, A.V.; et al. Engineered magnetization and exchange stiffness in direct-write Co–Fe nanoelements. Appl. Phys. Lett.
**2021**, 118, 022408. [Google Scholar] [CrossRef] - Urbánek, M.; Flajšman, L.; Křiáková, V.; Gloss, J.; Horký, M.; Schmid, M.; Varga, P. Research Update: Focused ion beam direct writing of magnetic patterns with controlled structural and magnetic properties. APL Mater.
**2018**, 6, 060701. [Google Scholar] [CrossRef] - Davies, C.S.; Francis, A.; Sadovnikov, A.V.; Chertopalov, S.V.; Bryan, M.T.; Grishin, S.V.; Allwood, D.A.; Sharaevskii, Y.P.; Nikitov, S.A.; Kruglyak, V.V. Towards graded-index magnonics: Steering spin waves in magnonic networks. Phys. Rev. B Condens. Matter Mater. Phys.
**2015**, 92, 020408. [Google Scholar] [CrossRef] - Gruszecki, P.; Krawczyk, M. Spin-wave beam propagation in ferromagnetic thin films with graded refractive index: Mirage effect and prospective applications. Phys. Rev. B
**2018**, 97, 094424. [Google Scholar] [CrossRef] - Kiechle, M.; Papp, A.; Mendisch, S.; Ahrens, V.; Golibrzuch, M.; Bernstein, G.H.; Porod, W.; Csaba, G.; Becherer, M.; Kiechle, M.; et al. Spin-Wave Optics in YIG Realized by Ion-Beam Irradiation. Small
**2023**, 19, e2207293. [Google Scholar] [CrossRef] - Lara, A.; Dobrovolskiy, O.V.; Prieto, J.L.; Huth, M.; Aliev, F.G. Magnetization reversal assisted by half antivortex states in nanostructured circular cobalt disks. Appl. Phys. Lett.
**2014**, 105, 182402. [Google Scholar] [CrossRef] - Khitun, A.; Bao, M.; Wang, K.L. Magnonic logic circuits. J. Phys. D Appl. Phys.
**2010**, 43, 264005. [Google Scholar] [CrossRef] - Vaňatka, M.; Szulc, K.; Wojewoda, O.; Dubs, C.; Chumak, A.V.; Krawczyk, M.; Dobrovolskiy, O.V.; Kłos, J.W.; Urbánek, M. Spin-Wave Dispersion Measurement by Variable-Gap Propagating Spin-Wave Spectroscopy. Phys. Rev. Appl.
**2021**, 16, 54033. [Google Scholar] [CrossRef] - Porrati, F.; Pohlit, M.; Müller, J.; Barth, S.; Biegger, F.; Gspan, C.; Plank, H.; Huth, M. Direct writing of CoFe alloy nanostructures by focused electron beam induced deposition from a heteronuclear precursor. Nanotechnology
**2015**, 26, 475701. [Google Scholar] [CrossRef] [PubMed] - Sebastian, T.; Schultheiss, K.; Obry, B.; Hillebrands, B.; Schultheiss, H. Micro-focused Brillouin light scattering: Imaging spin waves at the nanoscale. Front. Phys.
**2015**, 3, 35. [Google Scholar] [CrossRef] - Kakazel, G.N.; Wigen, P.E.; Guslienko, K.Y.; Chantrell, R.W.; Lesnik, N.A.; Metlushko, V.; Shima, H.; Fukamichi, K.; Otani, Y.; Novosad, V. In-plane and out-of-plane uniaxial anisotropies in rectangular arrays of circular dots studied by ferromagnetic resonance. J. Appl. Phys.
**2003**, 93, 8418–8420. [Google Scholar] [CrossRef] - Lendinez, S.; Taghipour Kaffash, M.; Jungfleisch, M.B. Observation of mode splitting in artificial spin ice: A comparative ferromagnetic resonance and Brillouin light scattering study. Appl. Phys. Lett.
**2021**, 118, 162407. [Google Scholar] [CrossRef] - Kittel, C. Excitation of Spin Waves in a Ferromagnet by a Uniform rf Field. Phys. Rev.
**1958**, 110, 1295. [Google Scholar] [CrossRef] - Kalarickal, S.S.; Krivosik, P.; Wu, M.; Patton, C.E.; Schneider, M.L.; Kabos, P.; Silva, T.J.; Nibarger, J.P. Ferromagnetic resonance linewidth in metallic thin films: Comparison of measurement methods. J. Appl. Phys.
**2006**, 99, 093909. [Google Scholar] [CrossRef] - Schreiber, F.; Frait, Z. Spin-wave resonance in high-conductivity films: The Fe-Co alloy system. Phys. Rev. B
**1996**, 54, 6473. [Google Scholar] [CrossRef] [PubMed] - Schoen, M.A.; Lucassen, J.; Nembach, H.T.; Silva, T.J.; Koopmans, B.; Back, C.H.; Shaw, J.M. Magnetic properties of ultrathin 3d transition-metal binary alloys. I. Spin and orbital moments, anisotropy, and confirmation of Slater-Pauling behavior. Phys. Rev. B
**2017**, 95, 134410. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) is a cartoon representation of the employed excitation and detection scheme. Radio frequency (RF) current (black arrows) injected to the CPW (yellow) generates an Oersted field, ${\mathrm{h}}_{\mathrm{rf}}$, around the conductors as indicated by the grey arrows. The Oersted field drives spin–wave dynamics in the magnonic conduit (purple) resulting in spin-wave (green) propagation along the length of the conduit. The BLS laser is indicated by the blue cone. Dimensions of the sample, CPW, and laser focus diameter are to scale. (

**b**) is a schematic representation of the BLS optical path. CW = continuous wave, BS = beam splitter, PBS = polarised beam splitter, MO = microscope objective, FP = Fabry–Pérot pair. Inset is the Feynman diagram for the magnon creation interaction, demonstrating the inelastic scattering of the BLS process. Frequency and wave vector are represented by $\omega $ and

**k**, respectively, for the incident photon (i), signal photon (s), and spin wave (SW).

**Figure 2.**AFM micrographs of both structures. (

**a**) 2D sample (plank conduit) of thickness $0.08$ $\mathsf{\mu}\mathrm{m}$ and width $3.08$ $\mathsf{\mu}$$\mathrm{m}$. (

**b**) 3D sample (bumped conduit), the heights of the shoulders and the bump apex are $0.05$ $\mathsf{\mu}\mathrm{m}$ and $0.21$ $\mathsf{\mu}\mathrm{m}$, respectively. Insets show the cross-sectional height profiles at the positions marked by the dotted lines. Circles (triangles) indicate the BLS laser position for each measurement under thermal (microwave) excitation. A scale dot showing the laser focus spot size is indicated on (

**a**). An area scan over the boxed region of (

**b**) was recorded to investigate the spatial distribution of the propagating spin-wave signal. The external magnetic field is oriented in the substrate plane along the conduits’ long axes, as indicated by the arrows.

**Figure 3.**(

**a**) Design schematic for the bumped conduit with the z dimension stretched for visibility, with simplified BLS operation schematic. Frequency-field plots of the thermally excited BLS-FMR measurements of the flat plank conduit (

**b**), the bumped conduit at the shoulder (

**c**), and the bump apex (

**d**). The constant-frequency intensity peaks at 8.6 GHz and 12.7 GHz are laser side bands, as indicated. Mode number increases with increasing frequency for a given field. The colour scale indicates BLS intensity for all plots, normalised to the highest value in each plot.

**Figure 4.**BLS data for a $\mathbf{k}\ne 0$ mode under local microwave excitation from the CPW for the flat plank conduit (

**a**), and the bumped conduit (

**b**) measured at the bump apex; positions marked by triangles on Figure 2. A fit of the plank conduit peak positions to Equation (1) has been used to plot the dashed line on both panels. The dotted line on panel (

**b**) differs only by the anisotropy field value. The colour scale indicates BLS intensity, normalised to the highest value in each plot.

**Figure 5.**BLS colour map: 2D area plot of the bumped conduit over the region indicated in Figure 2. Signal has been corrected for reflectivity changes due to the surface curvature. Microwave pumping was applied for this measurement though the CPW at the top edge of the figure, with the ground conductor labelled. Colour scale indicates the logarithm of the BLS counts of the integrated signal peak normalised by the reflectivity. Vertical dashed lines show the side edges of the FEBID conduit, the horizontal dashed lines indicate the position of the lower CPW ground conductor.

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## Share and Cite

**MDPI and ACS Style**

Lamb-Camarena, S.; Porrati, F.; Kuprava, A.; Wang, Q.; Urbánek, M.; Barth, S.; Makarov, D.; Huth, M.; Dobrovolskiy, O.V.
3D Magnonic Conduits by Direct Write Nanofabrication. *Nanomaterials* **2023**, *13*, 1926.
https://doi.org/10.3390/nano13131926

**AMA Style**

Lamb-Camarena S, Porrati F, Kuprava A, Wang Q, Urbánek M, Barth S, Makarov D, Huth M, Dobrovolskiy OV.
3D Magnonic Conduits by Direct Write Nanofabrication. *Nanomaterials*. 2023; 13(13):1926.
https://doi.org/10.3390/nano13131926

**Chicago/Turabian Style**

Lamb-Camarena, Sebastian, Fabrizio Porrati, Alexander Kuprava, Qi Wang, Michal Urbánek, Sven Barth, Denys Makarov, Michael Huth, and Oleksandr V. Dobrovolskiy.
2023. "3D Magnonic Conduits by Direct Write Nanofabrication" *Nanomaterials* 13, no. 13: 1926.
https://doi.org/10.3390/nano13131926