# Magnetic Nanowires for Nanobarcoding and Beyond

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Why Magnetic Nanowires for Nanobarcodes?

#### 2.1. Encoding and Sensing of Magnetic Nanowire (MNW)-Based Nanobarcodes

#### 2.1.1. DC Measurements

**Figure 3.**Demonstrating different approaches for tailoring the magnetization saturation and the coercivity of MNWs for encoding. (

**a**,

**b**) Single component MNWs; (

**c**) multi-component or alloyed MNWs; (

**d**) MNWs with modulated composition; (

**e**) SEM image of modulated composition MNWs, adapted from [74]; and (

**f**) represents a Slater–Pauling curve illustrating the dependency of the magnetic moment on the composition, adapted from [58].

**Figure 4.**Illustrating the different techniques for tailoring the coercivity of the MNWs, where (

**a**,

**b**) changing the diameter (or aspect ratio) of single diameter MNWs; (

**c**) modulated diameter MNWs; (

**d**) multi-segmented MNWs; (

**e**–

**h**) SEM images of varying and modulating the MNWs diameter, adapted from [95]; and (

**i**) a SEM image of multi-segmented MNWs, adapted from [96].

#### 2.1.2. AC Measurements

#### 2.2. Decoding of Magnetic Nanobarcodes

^{1}, where superscript one indicates N = 1. Next, N is increased to 2 and the new optimum RMS error, RMS

^{2}, is calculated. Then, RMS

^{2}is compared with RMS

^{1}to determine how much the RMS error decreased, by increasing N from 1 to 2. If the reduction meets the cutoff, then there are at least two nanobarcodes at the readout (N ≥ 2), as shown in Figure 7b. Then, it is necessary to increase N to 3 and repeat the same procedure, to determine whether or not there are more nanobarcodes present. Note, at this step, RMS

^{3}and RMS

^{2}must be considered, and their ratio must be compared with the cutoff value, as in Figure 6c. If the reduction in RMS

^{3}compared to RMS

^{2}was not sufficient, the decoding process can be terminated, because it would appear that only two nanobarcodes were present at the readout (N = 2). This process must be continued until the ratio of RMS

^{N}-to-RMS

^{N-1}is no longer smaller than the cutoff value. The main drawback of this technique for reliable decoding is finding the correct value for the cutoff. For example, as the number of nanobarcodes at the readout increases, the magnetic signatures start overlapping, which makes the decoding difficult. It should be emphasized that this drawback is not limited only to magnetic nanobarcodes, as the reliable decoding of any nanobarcodes suffers from this problem. To resolve this problem, we proposed two alternatives. The first alternative is to use a floating cutoff value, which is a function of the predicted number of nanobarcodes. The second alternative, which could be a more effective approach, is to eliminate the need for a cutoff, which could be accomplished by using the artificial intelligent (AI) or the machine learning (ML) approaches. To accelerate the transition of MNW-based nanobarcodes to real-life applications, the reliable decoding of multiple nanobarcodes demands a huge amount of attention, with many research opportunities in computer science and signal processing domains, which are expected to flourish soon.

## 3. Summary and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Schematically depicting the hysteresis loop method (

**a**) and the FORC method (

**b**,

**c**), where (

**b**) is the FORC data collection and (

**c**) is a FORC heat-map. In subfigures (

**a**,

**b**), the green arrows show the data acquisition direction. In subfigure (

**c**), the red distribution is the projection of the FORC heat-map on the applied field (H), the blue distribution is the projection of the FORC heat-map on the interaction field axis (interaction field distribution), the black distribution is the projection of the FORC heat-map on the reversal field (Hr), and the green distribution is the projection of the FORC heat-map on the coercivity axis (coercivity distribution). Figure adapted from [34,35].

**Figure 5.**Schematically demonstrating the data collection protocols for (

**a**) the projection method, (

**b**) backward remanence method, (

**c**) isothermal remanence method, and (

**d**) DC demagnetization method. The projection method (

**a**) provides the irreversible switching (equivalent to the residual magnetization) at the reversal field, Hr. While, the remanence methods (

**b**–

**d**) provide the residual magnetization at the zero applied field, H, such as points 3 and 3’. The key feature that separates the backward remanence (

**b**) from the isothermal remanence (

**c**) and the DC demagnetization remanence (

**d**) is the saturating the whole system before applying the Hr and removing it.

**Figure 6.**Schematically demonstrating (

**a**–

**d**) magnetic particle spectroscopy data, adapted from [127], and (

**e**,

**f**) ferromagnetic resonance spectroscopy data, adapted from [123]. In magnetic particle spectroscopy, superparamagnetic nanoparticles are exposed to an alternating magnetic field (

**b**), which forces them to oscillate (

**c**). By linearizing their response in frequency domain, multiple peaks appear at odd higher frequencies (

**d**) that are being used for sensing them. In magnetic resonance spectroscopy, the MNWs are exposed to an RF signal while a biased magnetic field is applied. By sweeping the RF signal frequency or the biased magnetic field magnitude, the RF absorption of the MNWs varies due to their spins’ precession, where the absorption signal is being used for sensing the MNWs.

**Figure 7.**Depicting a decoding method based on using the fitting quality (RMS) as an indicator for determining the number of nanobarcodes at the readout, (

**a**) a flowchart for decoding and (

**b**,

**c**) data analysis for finding the number of the nanobarcodes were produced. The algorithm assumes that one (N = 1) nanobarcode exists, thus, it fits the data with one Gaussian function and calculates the RMS1. Then, it increases N to two, and it calculates RMS2. If the RMS2/RMS1 (

**b**) is larger than the cutoff value, there was only one nanobarcode at the readout. Otherwise, there are at least two nanobarcodes and the procedure must be repeated for N=3, which means RMS3/RMS2 must be evaluated (

**c**).

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**MDPI and ACS Style**

Zamani Kouhpanji, M.R.; Stadler, B.J.H.
Magnetic Nanowires for Nanobarcoding and Beyond. *Sensors* **2021**, *21*, 4573.
https://doi.org/10.3390/s21134573

**AMA Style**

Zamani Kouhpanji MR, Stadler BJH.
Magnetic Nanowires for Nanobarcoding and Beyond. *Sensors*. 2021; 21(13):4573.
https://doi.org/10.3390/s21134573

**Chicago/Turabian Style**

Zamani Kouhpanji, Mohammad Reza, and Bethanie J. H. Stadler.
2021. "Magnetic Nanowires for Nanobarcoding and Beyond" *Sensors* 21, no. 13: 4573.
https://doi.org/10.3390/s21134573