# Magneto-Transport in Flexible 3D Networks Made of Interconnected Magnetic Nanowires and Nanotubes

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Fabrication

## 3. Results

#### 3.1. Anisotropic Magnetoresistance Networks

**I**restricted along the NW segment and its magnetization

**M**, that is,

**M**and

**I**can be determined from Equations (2) and (3) as

#### 3.2. Giant Magnetoresistance Networks

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Rauber, M.; Alber, I.; Müller, S.; Neumann, R.; Picht, O.; Roth, C.; Schökel, A.; Toimil-Molares, M.E.; Ensinger, W. Highly-Ordered Supportless Three-Dimensional Nanowire Networks with Tunable Complexity and Interwire Connectivity for Device Integration. Nano Lett.
**2011**, 11, 2304–2310. [Google Scholar] [CrossRef] [PubMed] - Hrkac, G.; Dean, J.; Allwood, D.A. Nanowire spintronics for storage class memories and logic. Philos. Trans. R. Soc. Math. Phys. Eng. Sci.
**2011**, 369, 3214–3228. [Google Scholar] [CrossRef] - Wang, W.; Tian, M.; Abdulagatov, A.; George, S.M.; Lee, Y.C.; Yang, R. Three-Dimensional Ni/TiO
_{2}Nanowire Network for High Areal Capacity Lithium Ion Microbattery Applications. Nano Lett.**2012**, 12, 655–660. [Google Scholar] [CrossRef] [PubMed] - Kwon, O.S.; Park, S.J.; Yoon, H.; Jang, J. Highly sensitive and selective chemiresistive sensors based on multidimensional polypyrrole nanotubes. Chem. Commun.
**2012**, 48, 10526–10528. [Google Scholar] [CrossRef] - Wei, C.; Pang, H.; Zhang, B.; Lu, Q.; Liang, S.; Gao, F. Two-Dimensional β-MnO
_{2}Nanowire Network with Enhanced Electrochemical Capacitance. Sci. Rep.**2013**, 3, 2193. [Google Scholar] - Vlad, A.; Antohe, V.A.; Martinez-Huerta, J.M.; Ferain, E.; Gohy, J.F.; Piraux, L. Three-dimensional interconnected Ni
_{core}NiO_{shell}nanowire networks for lithium microbattery architectures. J. Mater. Chem. A**2016**, 4, 1603–1607. [Google Scholar] - Piraux, L.; Antohe, V.A.; Ferain, E.; Lahem, D. Self-supported three-dimensionally interconnected polypyrrole nanotubes and nanowires for highly sensitive chemiresistive gas sensing. RSC Adv.
**2016**, 6, 21808–21813. [Google Scholar] [CrossRef] - Piraux, L.; da Câmara Santa Clara Gomes, T.; Abreu Araujo, F.; De La Torre Medina, J. 3D magnetic nanowire networks. In Magnetic Nano- and Microwires, 2nd ed.; Vázquez, M., Ed.; Elsevier: Amsterdam, The Netherlands, 2020; Chapter 27. [Google Scholar]
- Omale, J.O.; Rupp, R.; Van Velthem, P.; Van Kerckhoven, V.; Antohe, V.A.; Vlad, A.; Piraux, L. Three-dimensional microsupercapacitors based on interdigitated patterns of interconnected nanowire networks. Energy Storage Mater.
**2019**, 21, 77–84. [Google Scholar] [CrossRef] - Scherer, M.R.J.; Steiner, U. Efficient Electrochromic Devices Made from 3D Nanotubular Gyroid Networks. Nano Lett.
**2013**, 13, 3005–3010. [Google Scholar] [CrossRef] - Crossland, E.J.W.; Kamperman, M.; Nedelcu, M.; Ducati, C.; Wiesner, U.; Smilgies, D.M.; Toombes, G.E.S.; Hillmyer, M.A.; Ludwigs, S.; Steiner, U.; et al. A Bicontinuous Double Gyroid Hybrid Solar Cell. Nano Lett.
**2009**, 9, 2807–2812. [Google Scholar] [CrossRef] [PubMed] - Wang, S.; Xu, L.P.; Liang, H.W.; Yu, S.H.; Wen, Y.; Wang, S.; Zhang, X. Self-interconnecting Pt nanowire network electrode for electrochemical amperometric biosensor. Nanoscale
**2015**, 7, 11460–11467. [Google Scholar] [CrossRef] [PubMed] - Rahong, S.; Yasui, T.; Yanagida, T.; Nagashima, K.; Kanai, M.; Klamchuen, A.; Meng, G.; He, Y.; Zhuge, F.; Kaji, N.; et al. Ultrafast and Wide Range Analysis of DNA Molecules Using Rigid Network Structure of Solid Nanowires. Sci. Rep.
**2014**, 4, 5252. [Google Scholar] [CrossRef] [PubMed] - da Câmara Santa Clara Gomes, T.; Abreu Araujo, F.; Piraux, L. Making flexible spin caloritronic devices with interconnected nanowire networks. Sci. Adv.
**2019**, 5, eaav2782. [Google Scholar] [CrossRef] [PubMed][Green Version] - da Câmara Santa Clara Gomes, T.; Marchal, N.; Abreu Araujo, F.; Piraux, L. Spin Caloritronics in 3D Interconnected Nanowire Networks. Nanomaterials
**2020**, 10, 2092. [Google Scholar] [CrossRef] [PubMed] - da Câmara Santa Clara Gomes, T.; de la Torre Medina, J.; Velázquez-Galván, Y.G.; Martínez-Huerta, J.M.; Encinas, A.; Piraux, L. Interplay between the magnetic and magneto-transport properties of 3D interconnected nanowire networks. J. Appl. Phys.
**2016**, 120, 043904. [Google Scholar] [CrossRef] - da Câmara Santa Clara Gomes, T.; De La Torre Medina, J.; Lemaitre, M.; Piraux, L. Magnetic and Magnetoresistive Properties of 3D Interconnected NiCo Nanowire Networks. Nanoscale Res. Lett.
**2016**, 11, 466. [Google Scholar] [CrossRef][Green Version] - de la Torre Medina, J.; da Câmara Santa Clara Gomes, T.; Velázquez Galván, Y.G.; Piraux, L. Large-scale 3-D interconnected Ni nanotube networks with controlled structural and magnetic properties. Sci. Rep.
**2018**, 8, 14555. [Google Scholar] [CrossRef] - da Câmara Santa Clara Gomes, T.; Marchal, N.; Abreu Araujo, F.; Piraux, L. Tunable magnetoresistance and thermopower in interconnected NiCr and CoCr nanowire networks. Appl. Phys. Lett.
**2019**, 115, 242402. [Google Scholar] [CrossRef] - Araujo, E.; Encinas, A.; Velázquez-Galván, Y.; Martinez-Huerta, J.M.; Hamoir, G.; Ferain, E.; Piraux, L. Artificially modified magnetic anisotropy in interconnected nanowire networks. Nanoscale
**2015**, 7, 1485–1490. [Google Scholar] [CrossRef] - Abreu Araujo, F.; da Câmara Santa Clara Gomes, T.; Piraux, L. Magnetic Control of Flexible Thermoelectric Devices Based on Macroscopic 3D Interconnected Nanowire Networks. Adv. Electron. Mater.
**2019**, 5, 1800819. [Google Scholar] [CrossRef][Green Version] - Marchal, N.; da Câmara Santa Clara Gomes, T.; Abreu Araujo, F.; Piraux, L. Large Spin-Dependent Thermoelectric Effects in NiFe-based Interconnected Nanowire Networks. Nanoscale Res. Lett.
**2020**, 15, 137. [Google Scholar] [CrossRef] [PubMed] - Piraux, L.; George, J.M.; Despres, J.F.; Leroy, C.; Ferain, E.; Legras, R.; Ounadjela, K.; Fert, A. Giant magnetoresistance in magnetic multilayered nanowires. Appl. Phys. Lett.
**1994**, 65, 2484–2486. [Google Scholar] [CrossRef] - Fert, A.; Piraux, L. Magnetic nanowires. J. Magn. Magn. Mater.
**1999**, 200, 338–358. [Google Scholar] [CrossRef] - Nasirpouri, F.; Southern, P.; Ghorbani, M.; zad, A.I.; Schwarzacher, W. GMR in multilayered nanowires electrodeposited in track-etched polyester and polycarbonate membranes. J. Magn. Magn. Mater.
**2007**, 308, 35–39. [Google Scholar] [CrossRef] - Melzer, M.; Kaltenbrunner, M.; Makarov, D.; Karnaushenko, D.; Sekitani, T.; Someya, T.; Schmidt, O.G. Imperceptible magnetoelectronics. Nat. Commun.
**2015**, 6, 6080. [Google Scholar] [CrossRef][Green Version] - Makarov, D.; Melzer, M.; Karnaushenko, D.; Schmidt, O.G. Shapeable magnetoelectronics. Appl. Phys. Rev.
**2016**, 3, 011101. [Google Scholar] [CrossRef][Green Version] - Wang, Z.; Wang, X.; Li, M.; Gao, Y.; Hu, Z.; Nan, T.; Liang, X.; Chen, H.; Yang, J.; Cash, S.; et al. Highly Sensitive Flexible Magnetic Sensor Based on Anisotropic Magnetoresistance Effect. Adv. Mater.
**2016**, 28, 9370–9377. [Google Scholar] [CrossRef] - Liu, Y.W.; Zhan, Q.F.; Li, R.W. Fabrication, properties, and applications of flexible magnetic films. Chin. Phys. B
**2013**, 22, 127502. [Google Scholar] [CrossRef] - Du, Y.; Xu, J.; Paul, B.; Eklund, P. Flexible thermoelectric materials and devices. Appl. Mater. Today
**2018**, 12, 366–388. [Google Scholar] [CrossRef] - Wong, D.W.; Purnama, I.; Lim, G.J.; Gan, W.L.; Murapaka, C.; Lew, W.S. Current-induced three-dimensional domain wall propagation in cylindrical NiFe nanowires. J. Appl. Phys.
**2016**, 119, 153902. [Google Scholar] [CrossRef] - Ruffer, D.; Huber, R.; Berberich, P.; Albert, S.; Russo-Averchi, E.; Heiss, M.; Arbiol, J.; Fontcuberta i Morral, A.; Grundler, D. Magnetic states of an individual Ni nanotube probed by anisotropic magnetoresistance. Nanoscale
**2012**, 4, 4989–4995. [Google Scholar] [CrossRef] [PubMed][Green Version] - Wegrowe, J.E.; Kelly, D.; Franck, A.; Gilbert, S.E.; Ansermet, J.P. Magnetoresistance of Ferromagnetic Nanowires. Phys. Rev. Lett.
**1999**, 82, 3681–3684. [Google Scholar] [CrossRef] - Pignard, S.; Goglio, G.; Radulescu, A.; Piraux, L.; Dubois, S.; Declémy, A.; Duvail, J.L. Study of the magnetization reversal in individual nickel nanowires. J. Appl. Phys.
**2000**, 87, 824–829. [Google Scholar] [CrossRef] - Ohgai, T.; Gravier, L.; Hoffer, X.; Lindeberg, M.; Hjort, K.; Spohr, R.; Ansermet, J.P. Template synthesis and magnetoresistance property of Ni and Co single nanowires electrodeposited into nanopores with a wide range of aspect ratios. J. Phys. Appl. Phys. D
**2003**, 36, 3109. [Google Scholar] [CrossRef] - da Câmara Santa Clara Gomes, T.; De La Torre Medina, J.; Velázquez-Galván, Y.G.; Martínez-Huerta, J.M.; Encinas, A.; Piraux, L. 3-D Interconnected Magnetic Nanofiber Networks With Multifunctional Properties. IEEE Trans. Magn.
**2017**, 53, 1–6. [Google Scholar] [CrossRef] - Piraux, L.; Dubois, S.; Duvail, J.L.; Ounadjela, K.; Fert, A. Arrays of nanowires of magnetic metals and multilayers: Perpendicular GMR and magnetic properties. J. Magn. Magn. Mater.
**1997**, 175, 127–136. [Google Scholar] [CrossRef] - Velázquez Galván, Y.G.; da Câmara Santa Clara Gomes, T.; Piraux, L.; De La Torre Medina, J. Scale ratio modulated magnetic anisotropy of 3D Co
_{x}Ni_{1-x}crossed nanowire networks. J. Magn. Magn. Mater.**2020**, 166615. [Google Scholar] [CrossRef] - Wang, Q.; Wang, G.; Han, X.; Wang, X.; Hou, J.G. Controllable Template Synthesis of Ni/Cu Nanocable and Ni Nanotube Arrays: A One-Step Coelectrodeposition and Electrochemical Etching Method. J. Phys. Chem. B
**2005**, 109, 23326–23329. [Google Scholar] [CrossRef] - Liu, Z.; Xia, G.; Zhu, F.; Kim, S.; Markovic, N.; Chien, C.L.; Searson, P.C. Exploiting finite size effects in a novel core/shell microstructure. J. Appl. Phys.
**2008**, 103, 064313. [Google Scholar] [CrossRef][Green Version] - Velázquez-Galván, Y.; Martínez-Huerta, J.M.; de la Torre Medina, J.; Danlée, Y.; Piraux, L.; Encinas, A. Dipolar interaction in arrays of magnetic nanotubes. J. Phys. Condens. Matter
**2014**, 26, 026001. [Google Scholar] [CrossRef] - Tabasum, M.R.; Zighem, F.; Medina, J.D.L.T.; Encinas, A.; Piraux, L.; Nysten, B. Magnetic force microscopy investigation of arrays of nickel nanowires and nanotubes. Nanotechnology
**2014**, 25, 245707. [Google Scholar] [CrossRef] [PubMed][Green Version] - Antohe, V.A.; Nysten, E.; Martínez-Huerta, J.M.; Pereira de Sá, P.M.; Piraux, L. Annealing effects on the magnetic properties of highly-packed vertically-aligned nickel nanotubes. RSC Adv.
**2017**, 7, 18609–18616. [Google Scholar] [CrossRef][Green Version] - McGuire, T.; Potter, R. Anisotropic magnetoresistance in ferromagnetic 3d alloys. IEEE Trans. Magn.
**1975**, 11, 1018–1038. [Google Scholar] [CrossRef] - Smit, J. Magnetoresistance of ferromagnetic metals and alloys at low temperatures. Physica
**1951**, 17, 612–627. [Google Scholar] [CrossRef] - Gondo, Y.; Funatoyawa, Z. On the temperature dependency of magneto-resistance of iron single crystal. J. Phys. Soc. Japan
**1952**, 7, 41–43. [Google Scholar] [CrossRef] - Darques, M.; Encinas, A.; Vila, L.; Piraux, L. Controlled changes in the microstructure and magnetic anisotropy in arrays of electrodeposited Co nanowires induced by the solution pH. J. Phys. D Appl. Phys.
**2004**, 37, 1411. [Google Scholar] [CrossRef] - Kim, D.; Park, D.Y.; Yoo, B.; Sumodjo, P.; Myung, N. Magnetic properties of nanocrystalline iron group thin film alloys electrodeposited from sulfate and chloride baths. Electrochim. Acta
**2003**, 48, 819–830. [Google Scholar] [CrossRef] - Tóth, B.G.; Péter, L.; Révész, Á.; Pádár, J.; Bakonyi, I. Temperature dependence of the electrical resistivity and the anisotropic magnetoresistance (AMR) of electrodeposited Ni-Co alloys. Eur. Phys. J. B
**2010**, 75, 167–177. [Google Scholar] [CrossRef][Green Version] - Myung, N.V.; Nobe, K. Electrodeposited Iron Group Thin-Film Alloys: Structure-Property Relationships. J. Electrochem. Soc.
**2001**, 148, C136–C144. [Google Scholar] [CrossRef] - Ferré, R.; Ounadjela, K.; George, J.M.; Piraux, L.; Dubois, S. Magnetization processes in nickel and cobalt electrodeposited nanowires. Phys. Rev. B
**1997**, 56, 14066–14075. [Google Scholar] [CrossRef] - Wernsdorfer, W.; Doudin, B.; Mailly, D.; Hasselbach, K.; Benoit, A.; Meier, J.; Ansermet, J.P.; Barbara, B. Nucleation of Magnetization Reversal in Individual Nanosized Nickel Wires. Phys. Rev. Lett.
**1996**, 77, 1873–1876. [Google Scholar] [CrossRef] [PubMed][Green Version] - Martínez-Huerta, J.M.; de la Torre Medina, J.; Piraux, L.; Encinas, A. Self consistent measurement and removal of the dipolar interaction field in magnetic particle assemblies and the determination of their intrinsic switching field distribution. J. Appl. Phys.
**2012**, 111, 083914. [Google Scholar] [CrossRef][Green Version] - Proenca, M.P.; Sousa, C.T.; Escrig, J.; Ventura, J.; Vazquez, M.; Araujo, J.P. Magnetic interactions and reversal mechanisms in Co nanowire and nanotube arrays. J. Appl. Phys.
**2013**, 113, 093907. [Google Scholar] [CrossRef][Green Version] - Albrecht, O.; Zierold, R.; Allende, S.; Escrig, J.; Patzig, C.; Rauschenbach, B.; Nielsch, K.; Görlitz, D. Experimental evidence for an angular dependent transition of magnetization reversal modes in magnetic nanotubes. J. Appl. Phys.
**2011**, 109, 093910. [Google Scholar] [CrossRef] - Escrig, J.; Daub, M.; Landeros, P.; Nielsch, K.; Altbir, D. Angular dependence of coercivity in magnetic nanotubes. Nanotechnology
**2007**, 18, 445706. [Google Scholar] [CrossRef] - Allende, S.; Escrig, J.; Altbir, D.; Salcedo, E.; Bahiana, M. Angular dependence of the transverse and vortex modesin magneticnanotubes. Eur. Phys. J. B
**2008**, 66, 37–40. [Google Scholar] [CrossRef] - Voegeli, B.; Blondel, A.; Doudin, B.; Ansermet, J.P. Electron transport in multilayered Co/Cu nanowires. J. Magn. Magn. Mater.
**1995**, 151, 388–395. [Google Scholar] [CrossRef] - Liu, K.; Nagodawithana, K.; Searson, P.C.; Chien, C.L. Perpendicular giant magnetoresistance of multilayered Co/Cu nanowires. Phys. Rev. B
**1995**, 51, 7381–7384. [Google Scholar] [CrossRef][Green Version] - Ohgai, T.; Hoffer, X.; Fábián, A.; Gravier, L.; Ansermet, J.P. Electrochemical synthesis and magnetoresistance properties of Ni, Co and Co/Cu nanowires in a nanoporous anodic oxide layer on metallic aluminium. J. Mater. Chem.
**2003**, 13, 2530–2534. [Google Scholar] [CrossRef] - Tang, X.T.; Wang, G.C.; Shima, M. Perpendicular giant magnetoresistance of electrodeposited Co/Cu-multilayered nanowires in porous alumina templates. J. Appl. Phys.
**2006**, 99, 033906. [Google Scholar] [CrossRef][Green Version] - Kamimura, H.; Hayashida, M.; Ohgai, T. CPP-GMR Performance of Electrochemically Synthesized Co/Cu Multilayered Nanowire Arrays with Extremely Large Aspect Ratio. Nanomaterials
**2020**, 10, 5. [Google Scholar] [CrossRef] [PubMed][Green Version] - Evans, P.R.; Yi, G.; Schwarzacher, W. Current perpendicular to plane giant magnetoresistance of multilayered nanowires electrodeposited in anodic aluminum oxide membranes. Appl. Phys. Lett.
**2000**, 76, 481–483. [Google Scholar] [CrossRef] - De La Torre Medina, J.; Darques, M.; Blon, T.; Piraux, L.; Encinas, A. Effects of layering on the magnetostatic interactions in microstructures of Co
_{x}Cu_{1-x}/Cu nanowires. Phys. Rev. B**2008**, 77, 014417. [Google Scholar] [CrossRef][Green Version] - Campbell, I.; Fert, A. Transport properties of ferromagnets. Handb. Ferromagn. Mater.
**1982**, 3, 747–804. [Google Scholar] [CrossRef] - Fert, A.; Campbell, I.A. Two-Current Conduction in Nickel. Phys. Rev. Lett.
**1968**, 21, 1190–1192. [Google Scholar] [CrossRef] - Dubois, S.; Marchal, C.; Beuken, J.M.; Piraux, L.; Duvail, J.L.; Fert, A.; George, J.M.; Maurice, J.L. Perpendicular giant magnetoresistance of NiFe/Cu multilayered nanowires. Appl. Phys. Lett.
**1997**, 70, 396–398. [Google Scholar] [CrossRef] - Blondel, A.; Meier, J.P.; Doudin, B.; Ansermet, J.P. Giant magnetoresistance of nanowires of multilayers. Appl. Phys. Lett.
**1994**, 65, 3019–3021. [Google Scholar] [CrossRef] - Dubois, S.; Beuken, J.M.; Piraux, L.; Duvail, J.L.; Fert, A.; George, J.M.; Maurice, J.L. Perpendicular giant magnetoresistance of NiFe/Cu and Co/Cu multilayered nanowires. J. Magn. Magn. Mater.
**1997**, 165, 30–33. [Google Scholar] [CrossRef] - Dubois, S.; Piraux, L.; George, J.M.; Ounadjela, K.; Duvail, J.L.; Fert, A. Evidence for a short spin diffusion length in permalloy from the giant magnetoresistance of multilayered nanowires. Phys. Rev. B
**1999**, 60. [Google Scholar] [CrossRef]

**Figure 1.**Schematics of (

**a**) a polycarbonate template with 3D crossed nanopore network and (

**b**) an interconnected nanowire network. (

**c**,

**d**) Fabrication of interconnected Ni nanotube networks. (

**c**) Growth of interconnected Cu/Ni core/shell nanocable networks at constant potential of −1 V and (

**d**) dealloying process to selectively etch the Cu core at constant potential +0.2 V. The inset in panel (

**c**) shows a schematic of a crossed Cu/Ni core/shell nanocable network. (

**e**) Schematic of a crossed Ni nanotube network. (

**f**) Fabrication of interconnected multilayered nanowire networks using a pulse electrodeposition technique to successively deposited the ferromagnetic and non-magnetic metal layers. (

**g**) Schematic of a crossed nanowire network with a succession of ferromagnetic and non-magnetic layers.

**Figure 2.**SEM images of (

**a**) a Ni crossed nanowire and (

**b**) a Ni crossed nanotube networks with 230 nm diameter and 20% of packing fraction, both electrodeposited at a potential of −1 V. The images have been obtained after the complete removal of the polymer host template and testify of the nanowire and nanotube interconnections.

**Figure 3.**(

**a**) Schematic of a 3D interconnected nanowire network electrodeposited from a Au cathode into a 22 $\mathsf{\mu}$m thick nanoporous polycarbonate film. (

**b**) Two-probe electrodes design created by local etching of the cathode. (

**c**) Resistance measurement configuration where a current I is injected between the two metallic electrodes while recording the voltage differential $\u2206V$ induced. (

**d**) Anisotropic magnetoresistance curves measured at different temperatures by sweeping an external magnetic field along the out of the plane (OOP; continuous line) and in the plane (IP; dashed line) directions of a permalloy (Ni${}_{82}$Fe${}_{18}$) crossed nanowire network film, deposited in a template with mean pore diameter of 80 nm, ∼3% of porosity. (

**e**) Comparison between the model given by Equation (6) for $\Theta =$ 25${}^{\circ}$ and the experimental data for nanowire networks ($\varphi =$ 80 nm, $P=$ 3%) made of Ni${}_{x}$Fe${}_{1-x}$ alloys with 0.5 $\le x\le $ 1 at room temperature, together with the results at $T=$ 150 K and $T=$ 15 K for $x=$ 0.82. The gray area reflects the calculated relation for $\Theta $ in the range 20${}^{\circ}$ to 30${}^{\circ}$.

**Figure 4.**(

**a**) Anisotropic magnetoresistance (AMR) ratio as a function of the Ni content x at $T=$ 300 K, 150 K, and 15 K for the Ni${}_{x}$Fe${}_{1-x}$, with 0.5 $\le x\le $ 1, and Fe nanowire networks with 80 nm in diameter and 3% in packing fraction. The dashed lines are guides for the eyes provided by polynomial approximation of the data. (

**b**) AMR ratio as a function of the Ni content x at $T=$ 290 K, 150 K, and 20 K for the Ni${}_{x}$Co${}_{1-x}$, with 0 $\le x\le $ 1 networks with 40 nm in diameter and 20% in packing fraction. The dashed lines are guides for the eyes. The hcp-fcc biphasic and fcc microstructures of the NiCo alloy nanowires are indicated by the yellow and light blue areas, respectively.

**Figure 5.**(

**a**,

**b**) Magnetisation curves as a function of the field ratio $H/{H}_{c}$, where ${H}_{c}$ is the corresponding coercive field, recorded while sweeping the external magnetic field in the out-of-plane direction of interconnected nanowire networks with 40 nm in diameter and 20% in packing fraction made of (

**a**) NiFe and Co electrodeposited using different electrolytic pH values of 2.0, 5.0, and 6.4 and (

**b**) various Ni${}_{x}$Co${}_{1-x}$ alloys, with 0 $\le x\le $ 1. (

**c**,

**f**) Room temperature magnetoresistance curves obtained by applying the magnetic field in the out-of-plane (OOP; full lines) and in-plane (IP; dashed lines) directions for (

**c**) the Co nanowire networks in panel (

**a**), as well as the (

**d**) Ni${}_{32}$Co${}_{68}$, (

**e**) Ni${}_{75}$Co${}_{25}$, and (

**f**) Ni crossed nanowire networks in panel (

**b**).

**Figure 6.**(

**a**,

**b**) Room temperature anisotropic magnetoresistance curves measured with the external field applied along the out of the plane (OOP; continuous line) and in the plane (IP; dashed line) directions of interconnected Ni${}_{75}$Co${}_{25}$ nanowire networks with (

**a**) 40 nm in diameter and ∼0.75% (blue curves) or ∼20% (red curves) in packing density, and (

**b**) 105 nm (green curves) and 230 nm (orange curves) in diameter and ∼20% in packing density. (

**c**,

**d**) Close view of the OOP anisotropic magnetoresistance curves in panels (

**a**,

**b**) for low magnetic fields. (

**e**,

**f**) Room temperature hysteresis loops measured with the external field applied along the OOP direction corresponding to panels (

**c**,

**d**).

**Figure 7.**(

**a**) Hysteresis loops measured with the magnetic field applied along the out-of-plane (OOP) direction of Ni crossed nanotube networks with 230 nm in diameter and 20% of packing fraction for different wall thicknesses, compared to the hysteresis loop for a Ni crossed nanowire network with similar diameter and packing density characteristics. (

**b**) Comparison of the anisotropic magnetoresistance curves measured with the external field applied in the OOP (continuous lines) and in-plane (IP, dashed lines) directions of the crossed NT network with wall thickness of ∼37 nm, and crossed NW networks, both with diameter of 230 nm and packing fraction of about 20%. The inset in panel (

**b**) show a zoom at low fields of the OOP AMR curves when sweeping the magnetic field from positive to negative, as indicated by the arrows. The lozenges indicate the resistance states at the corresponding coercive field for each network.

**Figure 8.**(

**a**) Schematic of the giant magnetoresistance measurement in multilayered nanowire-based films, where the electrical transport takes place globally in the plane of the film while the architecture based on crossed nanowires ensures a CPP-type transport. (

**b**,

**c**) Giant magnetoresistance curves obtained at $T=$ 300 K (blue curves) and $T=$ 15 K (red curves) with the magnetic field applied in the plane of interconnected (

**b**) Co/Cu and (

**c**) Co${}_{50}$Ni${}_{50}$/Cu nanowire networks with 80 nm in diameter and ∼3% in packing fraction. (

**d**) Giant magnetoresistance ratio obtained for interconnected Co${}_{x}$Ni${}_{1-x}$/Cu multilayered nanowire networks with 80 nm in diameter and ∼3% as for $0\le x\le 1$ at $T=$ 300 K (in blue) and $T=$ 15 K (in red). The dashed lines are guides for the eyes. (

**e**) Giant magnetoresistance curves obtained at $T=$ 300 K (blue curves) and $T=$ 15 K (red curves) with the magnetic field applied in the plane of interconnected Ni${}_{80}$Fe${}_{20}$/Cu nanowire networks with 80 nm in diameter and ∼3% in packing fraction.

**Table 1.**Highest values reported to date of the room temperature giant magnetoresistance ratio for crossed FM/Cu nanowire networks compared to previous measurements on parallel nanowire arrays.

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**MDPI and ACS Style**

da Câmara Santa Clara Gomes, T.; Marchal, N.; Abreu Araujo, F.; Velázquez Galván, Y.; de la Torre Medina, J.; Piraux, L.
Magneto-Transport in Flexible 3D Networks Made of Interconnected Magnetic Nanowires and Nanotubes. *Nanomaterials* **2021**, *11*, 221.
https://doi.org/10.3390/nano11010221

**AMA Style**

da Câmara Santa Clara Gomes T, Marchal N, Abreu Araujo F, Velázquez Galván Y, de la Torre Medina J, Piraux L.
Magneto-Transport in Flexible 3D Networks Made of Interconnected Magnetic Nanowires and Nanotubes. *Nanomaterials*. 2021; 11(1):221.
https://doi.org/10.3390/nano11010221

**Chicago/Turabian Style**

da Câmara Santa Clara Gomes, Tristan, Nicolas Marchal, Flavio Abreu Araujo, Yenni Velázquez Galván, Joaquín de la Torre Medina, and Luc Piraux.
2021. "Magneto-Transport in Flexible 3D Networks Made of Interconnected Magnetic Nanowires and Nanotubes" *Nanomaterials* 11, no. 1: 221.
https://doi.org/10.3390/nano11010221