| Summary: | In this study, single-domain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Ni</mi><mi mathvariant="normal">x</mi></msub><msub><mi>Co</mi><mrow><mn>1</mn><mo>−</mo><mi mathvariant="normal">x</mi></mrow></msub><msub><mi>Fe</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>4</mn></msub></mrow></semantics></math></inline-formula> ferrite nanoparticles with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mspace width="3.33333pt"></mspace><mo>≤</mo><mi mathvariant="normal">x</mi><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula> were hydrothermally prepared and characterized using X-ray diffraction, transmission electron microscopy (TEM), Fourier transform infrared spectroscopy (FT-IR), and vibrating sample magnetometry. According to the Rietveld refinement results, all of the prepared nanoparticles were single phase with spinel-type structures. Increasing the Ni content increased the average crystallite size and X-ray density while decreasing the lattice constant. According to the TEM observations, the nanoparticles were spherical in shape. The formation of a single-phase spinel structure with two lattices centered at tetrahedral and octahedral sites was confirmed by the observation of two absorption bands in all FT-IR spectra. Magnetization data showed that the prepared nanoparticles of all compositions were ferrimagnetic across the entire temperature range of 300 K to 10 K. Magnetic properties such as saturation magnetization, remanent magnetization, coercivity, magnetic anisotropy, and magnetic moments per unit cell were found to decrease with increasing Ni content. The big difference in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="normal">H</mi><mi mathvariant="normal">c</mi></msub></semantics></math></inline-formula> of the x = 0, 0.25, 0.5, 0.75 ferrites between 300 K and 10 K suggested that these ferrite nanoparticles are truly single-domain nanoparticles. The small value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="normal">H</mi><mi mathvariant="normal">c</mi></msub></semantics></math></inline-formula> of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>NiFe</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>4</mn></msub><mspace width="4pt"></mspace><mrow><mo>(</mo><mi mathvariant="normal">x</mi><mo>=</mo><mn>1</mn><mo>)</mo></mrow></mrow></semantics></math></inline-formula> ferrite and its very weak temperature dependence suggested that this sample is in a multi-domain regime. The ZFC–FC curves revealed the existence of spin-glass-like behavior in these ferrite nanoparticles over the entire temperature range.
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