# Spin Caloritronics in 3D Interconnected Nanowire Networks

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. Homogeneous Nanowire Networks

#### 3.2. Multilayered Nanowire Networks

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Schematics of the 3D nanoporous polymer template, (

**b**) crossed nanowire and (

**c**) crossed nanowire network with alternating magnetic and non-magnetic layers. (

**d**,

**e**) SEM images of self-supported interconnected nanowire network with different magnifications. (

**d**) Low-magnification image showing the 50${}^{\circ}$ tilted view of a macroscopic nanowire network film with 105 nm diameter and ∼20% packing density. The inset displays an optical image showing the size and mechanical robustness of the macroscopic self-supporting network. (

**e**) Low magnification image showing the top view of the NW network with 80 nm diameter and ∼3% packing density. The inset shows the nanowire branched structure at higher magnification.

**Figure 2.**3D interconnected nanowire networks and experimental set-ups for measurement of transport properties. (

**a**) Schematic of 3D interconnected nanowire network film grown by electrodeposition from a Au cathode into a 20 $\mathsf{\mu}$m thick polycarbonate template with crossed-nanopores. (

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

**c**,

**d**) Device configuration for successive measurements of the resistance and the Seebeck coefficient. (

**c**) The voltage differential $\Delta V$ induced by the injected current I between the two metallic electrodes is measured while the two electrodes are maintained at an identical and constant temperature. (

**d**) Heat flow is generated by a resistive element at one electrode while the other electrode is maintained at desired temperature. The temperature difference $\Delta T$ between the two metallic electrodes is measured by a thermocouple while thermoelectric voltage $\Delta V$ settles. (

**e**) Photograph of a flexible device made of 3D interconnected nanowires embedded in a polycarbonate matrix and with the two gold electrodes design. The inset SEM image shows the nanowire branched structure with diameter of 80 nm and ∼3% packing density.

**Figure 3.**(

**a**–

**h**) Room-temperature variation of the electrical resistance and Seebeck coefficient of Co (

**a**,

**b**), Co${}_{50}$Ni${}_{50}$ (

**c**,

**d**), Ni${}_{80}$Fe${}_{20}$ (

**e**,

**f**) and Ni (

**g**,

**h**) nanowire networks obtained with the magnetic field applied along the in-plane (IP—green) and out-of-plane (OOP—purple) directions of the nanowire network film. (

**i**) Variation of the Seebeck coefficient vs Ni content in NiFe nanowire networks at room temperature. Values previously reported for bulk alloys [41] are also shown. (

**j**) Magnetoresistance (MR—blue) and magneto-thermopower (MTP—red) ratios as a function of Ni content in NiFe nanowire networks at room temperature.

**Figure 4.**(

**a**,

**b**) Magnetoresistance (MR) ratio as a function of the Cr content for interconnected NiCr (

**a**) and CoCr (

**b**) nanowire networks at room temperature (RT—blue) and $T=$ 100 K (red). The gray areas in (

**a**,

**b**) indicates negative anisotropic magnetoresistance. The inset in (

**a**) compares the MR curves measured along the out-of-plane (red) and in-plane (blue) directions for the Ni${}_{96}$Cr${}_{4}$ crossed nanowire network at RT and $T=$ 11 K. The inset in (

**b**) compares the RT MR curves measured along the out-of-plane (red) and in-plane (blue) directions for the interconnected Co and Co${}_{95}$Cr${}_{5}$ nanowire networks. (

**c**,

**d**) Seebeck coefficient S at zero magnetic field as a function of the Cr content of for interconnected NiCr (

**c**) and CoCr (

**d**) nanowire networks at RT (blue), $T=$ 200 K (yellow) and $T=$ 100 K (red). The recommended values for chromel (Ni${}_{90}$Cr${}_{10}$) are indicated by star symbols. The green and gray areas in (

**c**,

**d**) indicate positive and negative S values, respectively. The symbol size encompasses the experimental error bars, which are set to two times the standard deviation of the experimental measurements of the electrical and temperature measurements, gathering 95% of the data variation.

**Figure 5.**Calculated thermopowers for (

**a**) Co/Cu and (

**b**) Ni${}_{80}$Fe${}_{20}$/Cu multilayers in the layer parallel (dash-doted line—CIP) and perpendicular (solid line—CPP) directions as a function of the thickness ratio $\lambda ={t}_{\mathrm{FM}}/{t}_{\mathrm{Cu}}$, using Equations (2) and (3) and the bulk values for ${S}_{\mathrm{FM}}$, ${\rho}_{\mathrm{FM}}$, ${S}_{\mathrm{Cu}}$ and ${\rho}_{\mathrm{Cu}}$, with (

**a**) FM = Co and (

**b**) FM = Ni${}_{80}$Fe${}_{20}$. The grey dashed line shows the values for $\lambda =$ 1. The insets in (

**a**,

**b**) show FM/Cu multilayer stacks with CIP (

**a**) and CPP (

**b**) configurations.

**Figure 6.**(

**a**–

**h**) Room-temperature variation of the electrical resistance and Seebeck coefficient of Co/Cu (

**a**,

**b**), Co${}_{50}$Ni${}_{50}$/Cu (

**c**,

**d**), Ni${}_{80}$Fe${}_{20}$/Cu (

**e**,

**f**) and Ni/Cu (

**g**,

**h**) multilayered nanowire samples obtained with the applied field in-plane (IP—green) and out-of-plane (OOP—purple) of the NW network film.

**Figure 7.**(

**a**–

**c**) MR and −MTP values as a function of temperature with the field applied in the plane of the (

**a**) Co/Cu, (

**b**) Co${}_{50}$Ni${}_{50}$/Cu and (

**c**) Ni${}_{80}$Fe${}_{20}$/Cu nanowire network films. (

**d**) Temperature dependencies of the ratio MTP/MR obtained in IP for the samples in (

**a**–

**c**) compared to the Ni/Cu nanowire network. The error bars in (

**a**–

**d**) reflect the uncertainty of the electrical and temperature measurements and is set to two times the standard deviation, gathering 95% of the data variation.

**Figure 8.**Linear variation of $\Delta S\left(H\right)=S\left(H\right)-{S}_{\mathrm{AP}}$ vs. $\Delta (1/R\left(H\right))=1/R\left(H\right)-1/{R}_{\mathrm{AP}}$ at different measured temperatures, illustrating the Gorter-Nordheim characteristics for the (

**a**) Co/Cu, (

**b**) Co${}_{50}$Ni${}_{50}$/Cu and (

**c**) Ni${}_{80}$Fe${}_{20}$/Cu nanowire networks. The solid lines correspond to the theoretical relation shown in Equation (4).

**Figure 9.**(

**a**) The two-current model for the resistivity and the thermopower considering both parallel (P) and antiparallel (AP) magnetic configurations. (

**b**–

**d**) Measured Seebeck coefficients at zero applied fields ${S}_{\mathrm{AP}}$ (blue circles) and at saturating magnetic fields ${S}_{\mathrm{P}}$ (red circles) of interconnected (

**b**) Co/Cu, (

**c**) Co${}_{50}$Ni${}_{50}$/Cu and (

**d**) Ni${}_{80}$Fe${}_{20}$/Cu nanowire networks, along with the corresponding calculated spin-dependent Seebeck coefficients ${S}_{\uparrow}$ (orange circles) and ${S}_{\downarrow}$ (violet circles) using Equations (9) and (10). The error bars reflect the uncertainty of the electrical and temperature measurements and is set to two times the standard deviation, gathering 95% of the data variation.

**Table 1.**Room-temperature Seebeck coefficient S, resistivity $\rho $, power factor (PF), figure of merit $ZT$, magnetoresistance ratio (MR) and magnetothermopower ratio (MTP) of interconnected homogeneous nanowire networks made of ferromagnetic metals and alloys.

S ($\mathsf{\mu}$V/K) | $\mathit{\rho}$ ($\mathsf{\mu}\mathsf{\Omega}$cm) | PF (mW/K${}^{2}$m) | $\mathit{ZT}$ (-) | MR (%) | MTP (%) | |
---|---|---|---|---|---|---|

Co | −28.0 | 7.1 | 11.0 | 3.2·10${}^{-2}$ | 1.1 | −1.1 |

Fe | +15.0 | 12.8 | 1.8 | 9.1·10${}^{-3}$ | 0.2 | - |

Ni | −19.6 | 9.1 | 4.2 | 1.6·10${}^{-2}$ | 1.6 | −6.0 |

Co${}_{50}$Ni${}_{50}$ | −18.3 | 15.4 | 2.2 | 1.4·10${}^{-2}$ | 2.9 | −3.8 |

Ni${}_{90}$Fe${}_{10}$ | −34.4 | 18.6 | 6.3 | 4.8·10${}^{-2}$ | 3.3 | −2.1 |

Ni${}_{80}$Fe${}_{20}$ | −36.9 | 25.0 | 5.4 | 5.6·10${}^{-2}$ | 2.4 | −1.5 |

Ni${}_{70}$Fe${}_{30}$ | −40.2 | 32.5 | 5.0 | 6.6·10${}^{-2}$ | 1.5 | −1.3 |

Ni${}_{60}$Fe${}_{40}$ | −46.0 | 42.4 | 5.0 | 8.6·10${}^{-2}$ | 0.7 | −0.8 |

Ni${}_{96}$Cr${}_{4}$ | +15.5 | 27.3 | 0.9 | 9.8·10${}^{-3}$ | 0.1 | - |

**Table 2.**Room-temperature Seebeck coefficient ${S}_{\mathrm{P}}$, resistivity ${\rho}_{\mathrm{P}}$, power factor PF${}_{\mathrm{P}}$ and figure of merit $Z{T}_{\mathrm{P}}$ obtained in the saturated state for interconnected multilayered nanowire networks made of a stack of successive ferromagnetic metal and Cu layers, as well as their magnetoresistance ratio MR and magneto-thermopower ratio MTP.

${\mathit{S}}_{\mathbf{P}}$ ($\mathsf{\mu}$V/K) | ${\mathit{\rho}}_{\mathbf{P}}$ ($\mathsf{\mu}\mathsf{\Omega}$cm) | ${\mathbf{PF}}_{\mathbf{P}}$ (mW/K${}^{2}$m) | ${\left(\mathit{ZT}\right)}_{\mathbf{P}}$ | MR (%) | MTP (%) | |
---|---|---|---|---|---|---|

Co/Cu | −19.9 | 8.7 | 4.6 | 1.6·10${}^{-2}$ | 24.7 | −25.1 |

Co${}_{50}$Ni${}_{50}$/Cu | −21.6 | 10.2 | 4.6 | 1.9·10${}^{-2}$ | 30.2 | −33.7 |

Ni${}_{80}$Fe${}_{20}$/Cu | −24.8 | 15.3 | 4.0 | 2.5·10${}^{-2}$ | 17.1 | −25.8 |

Ni/Cu | −10.2 | 19.8 | 0.5 | 0.4·10${}^{-2}$ | 0.8 | −3.7 |

**Table 3.**Room-temperature spin-dependent Seebeck coefficients, ${S}_{\uparrow}$ and ${S}_{\downarrow}$, of the FM/Cu nanowire networks with FM = Co, Co${}_{50}$Ni${}_{50}$, Ni${}_{80}$Fe${}_{20}$ an Ni, along with $\Delta S={S}_{\uparrow}-{S}_{\downarrow}$ and the spin asymmetry coefficients for resistivity $\beta $ and Seebeck coefficient $\eta $.

${\mathit{S}}_{\uparrow}$ ($\mathsf{\mu}$V/K) | ${\mathit{S}}_{\downarrow}$ ($\mathsf{\mu}$V/K) | $\mathit{\Delta}\mathit{S}$ ($\mathsf{\mu}$V/K) | $\mathit{\beta}$ (-) | $\mathit{\eta}$ (-) | |
---|---|---|---|---|---|

Co/Cu | −23.6 | −15.1 | −8.5 | 0.50 | −0.22 |

Co${}_{50}$Ni${}_{50}$/Cu | −23.9 | −13.9 | −10.0 | 0.55 | −0.26 |

Ni${}_{80}$Fe${}_{20}$/Cu | −28.4 | −16.1 | −12.3 | 0.41 | −0.28 |

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**MDPI and ACS Style**

da Câmara Santa Clara Gomes, T.; Marchal, N.; Abreu Araujo, F.; Piraux, L.
Spin Caloritronics in 3D Interconnected Nanowire Networks. *Nanomaterials* **2020**, *10*, 2092.
https://doi.org/10.3390/nano10112092

**AMA Style**

da Câmara Santa Clara Gomes T, Marchal N, Abreu Araujo F, Piraux L.
Spin Caloritronics in 3D Interconnected Nanowire Networks. *Nanomaterials*. 2020; 10(11):2092.
https://doi.org/10.3390/nano10112092

**Chicago/Turabian Style**

da Câmara Santa Clara Gomes, Tristan, Nicolas Marchal, Flavio Abreu Araujo, and Luc Piraux.
2020. "Spin Caloritronics in 3D Interconnected Nanowire Networks" *Nanomaterials* 10, no. 11: 2092.
https://doi.org/10.3390/nano10112092