# Observation of Spin-Glass-like Behavior over a Wide Temperature Range in Single-Domain Nickel-Substituted Cobalt Ferrite Nanoparticles

## Abstract

**:**

## 1. Introduction

^{2+}ions with soft magnetic Ni

^{2+}ions in a controlled manner [5,8]. Nickel ferrite (${\mathrm{NiFe}}_{2}{\mathrm{O}}_{4}$) is a soft magnetic material that crystallizes into an inverse spinel structure. It has a low coercivity, high saturation magnetization, and high resistivity [5,6]. Magnetic ferrites have been made using a variety of techniques, including sol–gel, coprecipitation, hydrothermal, and mechanical alloying [9,10,11,12,13].

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. XRD Analysis

^{2+}ions of a smaller radius (0.69 Å) replace Co

^{2+}ions of a bigger radius (0.76 Å) on the octahedral sites, the ${\mathrm{R}}_{\mathrm{B}}$ was predicted to decrease and the ${\mathrm{R}}_{\mathrm{A}}$ to remain unchanged. However, this trend was not followed in the prepared ferrites, suggesting that cation disorder may occur in the spinel structure of the prepared ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ ferrites, which in turn affects structural properties such as the bond length between cations. The behavior of the parameters ${\mathrm{R}}_{\mathrm{A}}$ and ${\mathrm{R}}_{\mathrm{B}}$ should be related to the behavior of the parameter $\mathrm{u}$. As $\mathrm{u}$ changes, the anion sublattice expands or contracts, until the volumes of the A and B sites match the radii of the constituent cations [5].

#### 3.2. TEM Characterization

#### 3.3. FT-IR Analysis

#### 3.4. Magnetic Properties

#### 3.4.1. M vs. H Curves

#### 3.4.2. LA Approach

^{2+}ions with lower-magnetic-moment ($2{\mu}_{B}$) Ni

^{2+}at the octahedral sites. The obtained ${\mathrm{M}}_{\mathrm{s}}$ values for ${\mathrm{CoFe}}_{2}{\mathrm{O}}_{4}$ ferrite (68.1 emu/g) and ${\mathrm{NiFe}}_{2}{\mathrm{O}}_{4}$ ferrite (36.9 emu/g) were found to be lower than the reported values of 93 emu/g and 55 emu/g for their bulk counterparts [23]. The presence of a magnetically dead layer on the surface of the nanoparticles, the presence of canted spins, or the presence of a spin-glass-like behavior of surface spins can all be attributed to the decrease in magnetization of these nanoparticles [28]. The decrease in ${\mathrm{K}}_{1}$ was attributed to the replacement of higher-anisotropy Co

^{2+}ions having three unpaired electrons ($\left[\mathrm{Ar}\right]3{\mathrm{d}}^{7}4{s}^{2}$) with lower-anisotropy Ni

^{2+}ions having two unpaired electrons ($\left[\mathrm{Ar}\right]3{\mathrm{d}}^{8}4{s}^{2}$). The measured values of ${\mathrm{K}}_{1}$ for ${\mathrm{CoFe}}_{2}{\mathrm{O}}_{4}$ ferrite ($3.28\times {10}^{6}$$\mathrm{erg}/{\mathrm{cm}}^{3}$) and ${\mathrm{NiFe}}_{2}{\mathrm{O}}_{4}$ ferrite ($0.75\times {10}^{6}$$\mathrm{erg}/{\mathrm{cm}}^{3}$) were consistent with the reported values of ($3.8\times {10}^{6}$$\mathrm{erg}/{\mathrm{cm}}^{3}$) [29] and ($0.9\times {10}^{6}$$\mathrm{erg}/{\mathrm{cm}}^{3}$) [12] for ${\mathrm{CoFe}}_{2}{\mathrm{O}}_{4}$ and ${\mathrm{NiFe}}_{2}{\mathrm{O}}_{4}$, respectively. The squareness ratio, ${\mathrm{M}}_{\mathrm{r}}/{\mathrm{M}}_{\mathrm{s}}$, values are displayed in Table 3. These values were consistent with the reported values of 0.36, 0.48, 0.47, 0.61, and 0.18 for corresponding concentrations of x = 0, 0.25, 0.5, 0.75, and 1 for single-domain ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ ferrite nanoparticles prepared by the hydrothermal method [25]. When the squareness ratio fell below 0.6, the prepared nanoparticles were said to be in the single-domain regime [30]. The LA model was only implemented for magnetization data at 300 K. When applied to low temperature data, particularly at 10 K, this model did not produce good results because the coercive field had a higher value than at 300 K, resulting in the validity condition ($\mathrm{H}\gg {\mathrm{H}}_{\mathrm{c}}$) not being met [5].

^{2+}ions on the octahedral sites were successfully replaced by Ni

^{2+}ions, and hence, the overall magnetization was reduced. The small variations between the calculated and measured values of magnetic moments can be related to the existence of tiny amounts of Ni

^{2+}or Co

^{2+}ions in the tetrahedral sites and/or to the possibility of a tiny amount of Fe

^{3+}ions migrating from the octahedral sites to the tetrahedral sites, suggesting that these nanoparticles adopted a mixed-spinel-type structure rather than an ideal-inverse-spinel-type structure. This is consistent with the appearance of the shoulder peak overlapping with the main tetrahedral peak in the FT-IR spectra (see Figure 5).

#### 3.4.3. M vs. T Curves

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Tahanian, H.; Aliahmadi, M.; Faiz, J. Ferrite Permanent Magnets in Electrical Machines: Opportunities and Challenges of a Non-Rare-Earth Alternative. IEEE Trans. Magn.
**2020**, 56, 1–20. [Google Scholar] [CrossRef] - Šutka, A.; Gross, K.A. Spinel ferrite oxide semiconductor gas sensors. Sens. Actuators B Chem.
**2016**, 222, 95–105. [Google Scholar] [CrossRef] - Bierlich, S.; Gellersen, F.; Jacob, A.; Töpfer, J. Low-temperature sintering and magnetic properties of Sc-and In-substituted M-type hexagonal barium ferrites for microwave applications. Mater. Res. Bull.
**2017**, 86, 19–23. [Google Scholar] [CrossRef] - Srinivasan, S.Y.; Paknikar, K.M.; Bodas, D.; Gajbhiye, V. Applications of cobalt ferrite nanoparticles in biomedical nanotechnology. Nanomedicine
**2018**, 13, 1221–1238. [Google Scholar] [CrossRef] [PubMed] - Alzoubi, G.M.; Alsmadi, A.; Alna’washi, G.; Salameh, B.; Shatnawi, M.; Alnemrat, S.; Albiss, B.; Bsoul, I. Coexistence of superparamagnetism and spin-glass like behavior in zinc-substituted cobalt ferrite nanoparticles. Appl. Phys. A
**2020**, 126, 1–11. [Google Scholar] [CrossRef] - Valenzuela, R. Magnetic Ceramics; Cambridge University Press: Cambridge, UK, 2005; Volume 4. [Google Scholar]
- Alzoubi, G.M.; Albiss, B.; Shatnawi, M.; Bsoul, I.; Alsmadi, A.; Salameh, B.; Alna’washi, G. Influence of High-Temperature Annealing on Structural and Magnetic Properties of Crystalline Cobalt Ferrite Nanoparticles in the Single-Domain Regime. J. Supercond. Nov. Magn.
**2020**, 33, 1–10. [Google Scholar] [CrossRef] - Nandan, B.; Bhatnagar, M.; Kashyap, S.C. Cation distribution in nanocrystalline cobalt substituted nickel ferrites: X-ray diffraction and Raman spectroscopic investigations. J. Phys. Chem. Solids
**2019**, 129, 298–306. [Google Scholar] [CrossRef] - Pubby, K.; Meena, S.; Yusuf, S.; Narang, S.B. Cobalt substituted nickel ferrites via Pechini’s sol–gel citrate route: X-band electromagnetic characterization. J. Magn. Magn. Mater.
**2018**, 466, 430–445. [Google Scholar] [CrossRef] - Dippong, T.; Levei, E.A.; Deac, I.G.; Neag, E.; Cadar, O. Influence of Cu
^{2+}, Ni^{2+}, and Zn^{2+}Ions Doping on the Structure, Morphology, and Magnetic Properties of Co-Ferrite Embedded in SiO_{2}Matrix Obtained by an Innovative Sol-Gel Route. Nanomaterials**2020**, 10, 580. [Google Scholar] [CrossRef] [Green Version] - Bharambe, S.S.; Trimukhe, A.; Bhatia, P. Synthesis Techniques of Nickel Substituted Cobalt Ferrites—An Investigative Study Using Structural Data. Mater. Today Proc.
**2020**, 23, 373–381. [Google Scholar] [CrossRef] - Alzoubi, G.M. Probing the structural and magnetic properties of small crystalline nickel ferrite nanoparticles near the upper size limit of the single-domain regime. Adv. Appl. Ceram.
**2020**, 119, 224–232. [Google Scholar] [CrossRef] - Maity, G.; Maji, P.; Sain, S.; Das, S.; Kar, T.; Pradhan, S. Microstructure, optical and electrical characterizations of nanocrystalline ZnAl
_{2}O_{4}spinel synthesized by mechanical alloying: Effect of sintering on microstructure and properties. Phys. E Low-Dimens. Syst. Nanostruct.**2019**, 108, 411–420. [Google Scholar] [CrossRef] - Mathew, D.S.; Juang, R.S. An overview of the structure and magnetism of spinel ferrite nanoparticles and their synthesis in microemulsions. Chem. Eng. J.
**2007**, 129, 51–65. [Google Scholar] [CrossRef] - Chinnasamy, C.; Jeyadevan, B.; Shinoda, K.; Tohji, K.; Djayaprawira, D.; Takahashi, M.; Joseyphus, R.J.; Narayanasamy, A. Unusually high coercivity and critical single-domain size of nearly monodispersed CoFe
_{2}O_{4}nanoparticles. Appl. Phys. Lett.**2003**, 83, 2862–2864. [Google Scholar] [CrossRef] - Issa, B.; Obaidat, I.M.; Albiss, B.A.; Haik, Y. Magnetic nanoparticles: Surface effects and properties related to biomedicine applications. Int. J. Mol. Sci.
**2013**, 14, 21266–21305. [Google Scholar] [CrossRef] [Green Version] - Alijani, H.Q.; Pourseyedi, S.; Torkzadeh-Mahani, M.; Seifalian, A.; Khatami, M. Bimetallic nickel-ferrite nanorod particles: Greener synthesis using rosemary and its biomedical efficiency. Artif. Cells Nanomed. Biotechnol.
**2020**, 48, 242–251. [Google Scholar] [CrossRef] - Djerdj, I. Rietveld Refinement in the Characterization of Crystalline Materials; MDPI: Basel, Switzerland, 2019. [Google Scholar]
- Bujakiewicz-Koro ´nska, R.; Hetma ´nczyk, Ł.; Garbarz-Glos, B.; Budziak, A.; Kalvane, A.; Bormanis, K.; Druzbicki, K. Low temperature measurements by infrared spectroscopy in CoFe
_{2}O_{4}ceramic. Open Phys.**2012**, 10, 1137–1143. [Google Scholar] - Kannan, Y. Structural Rietveld Refinement of Nickel Ferrite Nanoparticles Prepared by Chemical Method. J. Nanosci. Technol.
**2019**, 5, 655–657. [Google Scholar] [CrossRef] - Shannon, R.D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. Sect. A Cryst. Phys. Diffr. Theor. Gen. Crystallogr.
**1976**, 32, 751–767. [Google Scholar] [CrossRef] - Toksha, B.; Shirsath, S.E.; Patange, S.; Jadhav, K. Structural investigations and magnetic properties of cobalt ferrite nanoparticles prepared by sol–gel auto combustion method. Solid State Commun.
**2008**, 147, 479–483. [Google Scholar] [CrossRef] - Torkian, S.; Ghasemi, A.; Razavi, R.S. Cation distribution and magnetic analysis of wideband microwave absorptive Co
_{x}Ni_{1-x}Fe_{2}O_{4}ferrites. Ceram. Int.**2017**, 43, 6987–6995. [Google Scholar] [CrossRef] - Nikam, D.S.; Jadhav, S.V.; Khot, V.M.; Bohara, R.; Hong, C.K.; Mali, S.S.; Pawar, S. Cation distribution, structural, morphological and magnetic properties of Co
_{1-x}Zn_{x}Fe_{2}O_{4}(x = 0–1) nanoparticles. RSC Adv.**2015**, 5, 2338–2345. [Google Scholar] [CrossRef] - Melo, R.; Banerjee, P.; Franco, A. Hydrothermal synthesis of nickel doped cobalt ferrite nanoparticles: Optical and magnetic properties. J. Mater. Sci. Mater. Electron.
**2018**, 29, 14657–14667. [Google Scholar] [CrossRef] - Xu, S.; Ma, Y.; Geng, B.; Sun, X.; Wang, M. The remanence ratio in CoFe
_{2}O_{4}nanoparticles with approximate single-domain sizes. Nanoscale Res. Lett.**2016**, 11, 1–9. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zhang, H.; Zeng, D.; Liu, Z. The law of approach to saturation in ferromagnets originating from the magnetocrystalline anisotropy. J. Magn. Magn. Mater.
**2010**, 322, 2375–2380. [Google Scholar] [CrossRef] - Kodama, R. Magnetic nanoparticles. J. Magn. Magn. Mater.
**1999**, 200, 359–372. [Google Scholar] [CrossRef] - Maaz, K.; Mumtaz, A.; Hasanain, S.; Ceylan, A. Synthesis and magnetic properties of cobalt ferrite (CoFe
_{2}O_{4}) nanoparticles prepared by wet chemical route. J. Magn. Magn. Mater.**2007**, 308, 289–295. [Google Scholar] [CrossRef] [Green Version] - Raut, A.; Barkule, R.; Shengule, D.; Jadhav, K. Synthesis, structural investigation and magnetic properties of Zn
^{2+}substituted cobalt ferrite nanoparticles prepared by the sol–gel auto-combustion technique. J. Magn. Magn. Mater.**2014**, 358, 87–92. [Google Scholar] [CrossRef] - Vincent, E.; Dupuis, V. Spin glasses: Experimental signatures and salient outcomes. In Frustrated Materials and Ferroic Glasses; Springer: Berlin/Heidelberg, Germany, 2018; pp. 31–56. [Google Scholar]

**Figure 1.**XRD patterns of the ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ spinel ferrites with $0\phantom{\rule{3.33333pt}{0ex}}\le \mathrm{x}\le 1$. The black vertical bars represent the standard Bragg reflections of the space group Fd3m.

**Figure 2.**XRD powder pattern and Rietveld refinement of the ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ ferrites with x = 0.25 as a representative sample. The experimental data are represented by black circles, the calculated data by a red line, and the difference between the two by a blue line. Bragg positions are represented by black vertical bars.

**Figure 3.**Variation of some structural quantities as a function of Ni content: (

**a**) lattice constant, (

**b**) the average bond lengths of ${\mathbf{R}}_{\mathbf{A}}$ and ${\mathbf{R}}_{\mathbf{B}}$, (

**c**) the X-ray density, and (

**d**) the crystallite size.

**Figure 4.**TEM images and particle size distribution histograms for the ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ spinel ferrites with $0\phantom{\rule{3.33333pt}{0ex}}\le \mathrm{x}\le 1$. Starting at the top (x = 0, 0.25, 0.5, 0.75, 1).

**Figure 5.**FT-IR spectra of the ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ spinel ferrites with $0\phantom{\rule{3.33333pt}{0ex}}\le \mathrm{x}\le 1$.

**Figure 6.**Magnetic hysteresis loops for the ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ ferrites with $0\phantom{\rule{3.33333pt}{0ex}}\le \mathrm{x}\le 1$. The figure in the lower right corner shows the variation of ${\mathrm{H}}_{\mathrm{c}}$ (at 10 K) with Ni content.

**Figure 7.**Room temperature magnetization curves of the ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ ferrites with $0\phantom{\rule{3.33333pt}{0ex}}\le \mathrm{x}\le 1$, fit to LA model. The figure in the lower right corner shows the variation of ${\mathrm{M}}_{\mathrm{s}}$ and ${\mathrm{K}}_{1}$ with Ni content.

**Figure 8.**ZFC–FC magnetization curves of the ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ ferrites with $0\phantom{\rule{3.33333pt}{0ex}}\le \mathrm{x}\le 1$, recorded with a magnetic field of 100 Oe.

**Table 1.**Rietveld refinement input parameters for ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ ferrite nanoparticles with $0\phantom{\rule{3.33333pt}{0ex}}\le \mathrm{x}\le 1$. The description of the parameters is given in the text.

x | $\mathbf{Atom}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\left(8\mathbf{a}\right)$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\left(16\mathbf{d}\right)$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\left(32\mathbf{e}\right)$ | $\mathbf{sof}$ |
---|---|---|---|---|---|

$\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\mathbf{x}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\mathbf{y}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\mathbf{z}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\mathbf{x}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\mathbf{y}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\mathbf{z}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\mathbf{x}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\mathbf{y}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\mathbf{z}$ | |||

0 | Co | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.5\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.5\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.5$ | 0.5 | ||

Fe | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.5\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.5\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.5$ | 0.5 | |||

Fe | $0.125\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.125\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.125$ | 1 | |||

O | $0.25\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.25\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.25$ | 1 | |||

0.25 | Ni | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.5\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.5\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.5$ | 0.125 | ||

Co | 0.375 | ||||

Fe | 0.5 | ||||

Fe | $0.125\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.125\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.125$ | 1 | |||

O | $0.25\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.25\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.25$ | 1 | |||

0.5 | Ni | 0.25 | |||

Co | 0.25 | ||||

Fe | 0.5 | ||||

Fe | $\phantom{\rule{4pt}{0ex}}0.125\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.125\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.125$ | 1 | |||

O | $0.25\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.25\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.25$ | 1 | |||

0.75 | Ni | 0.375 | |||

Co | 0.125 | ||||

Fe | 0.5 | ||||

Fe | $\phantom{\rule{4pt}{0ex}}0.125\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.125\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.125$ | 1 | |||

O | 1 | ||||

1 | Ni | 0.5 | |||

Fe | 0.5 | ||||

Fe | $\phantom{\rule{4pt}{0ex}}0.125\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.125\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}0.125$ | 1 | |||

O | 1 |

**Table 2.**Structural parameters and Rietveld agreement R-factors for the ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ ferrites with $0\phantom{\rule{3.33333pt}{0ex}}\le \mathrm{x}\le 1$. The description of the parameters is given in the text.

x | 0 | $0.25$ | $0.5$ | $0.75$ | 1 |
---|---|---|---|---|---|

D (nm) | 17.4 | 21.1 | 26.1 | 31.7 | 41.7 |

${\mathbf{d}}_{\mathbf{x}}\phantom{\rule{3.33333pt}{0ex}}(\mathbf{g}/{\mathbf{cm}}^{\mathbf{3}})$ | 5.31 | 5.34 | 5.36 | 5.38 | 5.39 |

R-factors (%) | |||||

${\mathbf{R}}_{\mathbf{exp}}$ | 1.261 | 1.378 | 1.402 | 1.454 | 1.414 |

${\mathbf{R}}_{\mathbf{wp}}$ | 1.303 | 1.444 | 1.439 | 1.528 | 1.788 |

$\mathbf{GoF}$ (${\chi}^{2}$) | 1.07 | 1.1 | 1.05 | 1.1 | 1.6 |

Cell parameters (Å) | |||||

${a}_{\mathrm{exp}}$ | 8.3706 | 8.3539 | 8.3458 | 8.3345 | 8.3303 |

u | 0.2564 | 0.2667 | 0.2691 | 0.2698 | 0.2565 |

${\mathbf{R}}_{\mathbf{A}}$ | 1.9051 | 2.0807 | 2.0266 | 1.9214 | 1.8986 |

${\mathbf{R}}_{\mathbf{B}}$ | 2.0405 | 1.9441 | 1.9678 | 2.0184 | 2.0298 |

**Table 3.**${\mathbf{H}}_{\mathbf{c}}$, ${\mathbf{M}}_{\mathbf{r}}$, ${\mathbf{M}}_{\mathbf{s}}$, ${\mathbf{M}}_{\mathbf{r}}/{\mathbf{M}}_{\mathbf{s}}$, and ${\mathbf{K}}_{\mathbf{1}}$ of the ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ ferrites with $0\phantom{\rule{3.33333pt}{0ex}}\le \mathrm{x}\le 1$ measured at 300 K. The description of the parameters is given in the text.

x | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}{\mathbf{H}}_{\mathbf{c}}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}{\mathbf{M}}_{\mathbf{r}}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}{\mathbf{M}}_{\mathbf{s}}$ | ${\mathbf{M}}_{\mathbf{r}}/{\mathbf{M}}_{\mathbf{s}}$ | ${\mathbf{K}}_{1}$ |
---|---|---|---|---|---|

$\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\left(\mathrm{Oe}\right)\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}(\mathrm{emu}/\mathrm{g})\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}(\mathrm{emu}/\mathrm{g})\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}(\mathrm{erg}/{\mathrm{cm}}^{3})\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | ||

0 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}770\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 24.1 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}68.1\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 0.35 | $3.28\times {10}^{6}$ |

0.25 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}802\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 27.7 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}63.6\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 0.44 | $2.52\times {10}^{6}$ |

0.5 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}649\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 27.4 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}57.7\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 0.47 | $1.89\times {10}^{6}$ |

0.75 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}390\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 21.7 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}46.8\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 0.46 | $1.34\times {10}^{6}$ |

1 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}42.1\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 4.6 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}36.9\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 0.12 | $0.75\times {10}^{6}$ |

**Table 4.**Molecular weight ($\mathbf{A}$), RT saturation magnetization (${\mathbf{M}}_{\mathbf{s}}$), calculated net magnetic moment ${\mathbf{n}}_{\mathbf{B}}\left(\mathbf{calculated}\right)$, and measured net magnetic moment ${\mathbf{n}}_{\mathbf{B}}\left(\mathbf{measured}\right)$ of the ${\mathrm{Ni}}_{\mathrm{x}}{\mathrm{Co}}_{1-\mathrm{x}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ ferrites with $0\phantom{\rule{3.33333pt}{0ex}}\le \mathrm{x}\le 1$.

x | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\mathbf{A}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}{\mathbf{M}}_{\mathbf{s}}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}{\mathbf{n}}_{\mathbf{B}}\left(\mathbf{calculated}\right)$ | ${\mathbf{n}}_{\mathbf{B}}\left(\mathbf{measured}\right)$ |
---|---|---|---|---|

$\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}(\mathrm{g}/\mathrm{mol})\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}(\mathrm{emu}/\mathrm{g})\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\left({\mathbf{\mu}}_{\mathbf{B}}\right)\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\left({\mathbf{\mu}}_{\mathbf{B}}\right)\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | |

0 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}234.63\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 68.1 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}3\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 2.86 |

0.25 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}234.57\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 63.6 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}2.75\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 2.67 |

0.5 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}234.51\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 57.7 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}2.5\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 2.42 |

0.75 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}234.45\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 46.8 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}2.25\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 1.96 |

1 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}234.39\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 36.9 | $\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}2\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}$ | 1.55 |

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## Share and Cite

**MDPI and ACS Style**

Alzoubi, G.M.
Observation of Spin-Glass-like Behavior over a Wide Temperature Range in Single-Domain Nickel-Substituted Cobalt Ferrite Nanoparticles. *Nanomaterials* **2022**, *12*, 1113.
https://doi.org/10.3390/nano12071113

**AMA Style**

Alzoubi GM.
Observation of Spin-Glass-like Behavior over a Wide Temperature Range in Single-Domain Nickel-Substituted Cobalt Ferrite Nanoparticles. *Nanomaterials*. 2022; 12(7):1113.
https://doi.org/10.3390/nano12071113

**Chicago/Turabian Style**

Alzoubi, Gassem M.
2022. "Observation of Spin-Glass-like Behavior over a Wide Temperature Range in Single-Domain Nickel-Substituted Cobalt Ferrite Nanoparticles" *Nanomaterials* 12, no. 7: 1113.
https://doi.org/10.3390/nano12071113