Kneller's Law Research Articles

Weak ferromagnetic interactions of [formula omitted] induced by coupling of the crystal and related lattice vibrations

There is an increase in demand of the next-generation spintronic devices with stable structural and magnetic properties in varying temperatures. An orthoferrites structure of the Pnma space group has been successfully prepared using high temperature solid-state reaction. In the Sm2Fe2O5+δ (SFO) material, Fe3+ ions occupy edge-cantered and face-cantered positions forming the tilted FeO6 octahedrons with Glazer's notation tilt a−a−c+. The ordering of the rare-earth ions at compensation temperature (Tcomp=2.3K), spin-flip transition in the range of 9.4−45.6K, and a second-type spin-reorientation transition around the anisotropy barrier with lower and higher transitional temperatures, TL=465 and TH=480K respectively. The canting of spins along with disordered spins at the surface results in a non-zero Tcomp and unsaturated magnetization. It is inferred that thermal activation of particle's moment over the anisotropy barriers (known as Kneller's law) only occurs above room temperature.

Room and low-temperature magnetic characterization of Cr doped CoFe2O4 nanostructures

The macroscopic magnetism in nanoparticulated systems is the consequence of numerous contributions, ranging from the spatial arrangement of nanoparticles to their intrinsic nanostructure. Understanding and unraveling these temptations is essential to scientifically and technologically introduce nanomaterials. In the present work, we investigate how the magnetic properties of Co ferrite can be significantly ameliorated by Cr substitution. At first, applied the co-precipitation strategy to synthesize stoichiometric Co ferrite nanoparticles followed by the Cr substitution to achieve CoCrxFe2-xO4 (0 ≤ x ≤ 1) nanoparticles. The phase and structural analysis by X-ray diffraction identified the formation of spinel structure with the Fd-3m space group. An increasing behaviour in X-ray density with Cr substitution in Co ferrite has been observed due to lattice contraction. Field-emission scanning electron microscopic images confirmed that the particle size ranged from 14 to 17 nm. Room temperature magnetic investigations showed that the magnetic coercivity of the synthesized nanoparticles increased up to 40% Cr substitution, followed by a monotonic decrease in the magnetic properties. Low-temperature magnetic properties were carried out for 40% Cr substituted Co ferrite. The increase in saturation magnetization with a reduction in temperature followed Bloch's law, and the trend of temperature-dependent coercivity was confirmed with Kneller's law.

Structural and temperature-dependent magnetic characteristics of Ho doped CoFe2O4 nanostructures

The magnetism in low-dimensional materials is the consequence of several factors, including the type of crystal structure and spatial distribution of nanoparticles. Understanding and exploring these challenges are vital to introduce nanomaterials for industrial applications. The present study reveals the substitutional effect of Holmium on the magnetic properties of cobalt ferrite. The nanostructures are prepared by co-precipitation procedure for the stoichiometric growth of CoHoxFe2-xO4 (0 ≤ x ≤ 0.1); Δx = 0.025 ferrite compositions. The crystal structure and phase determination of all the samples identify a typical cubic structure (Fd-3m); however, a secondary phase, appearing at x = 0.1, originates due to the formation of HoFeO3. An increasing trend in lattice constant, X-ray density and hopping lengths with Ho doping in Co ferrite is observed in the synthesized nanoparticles. The structural analysis by high-resolution transmission electron microscopy confirms the crystal structure of spinel ferrite. The magnetic characteristics measured at room temperature depict that the coercivity, saturation magnetization, and magneton number increase due to the impact of Ho3+ substitution. The saturation magnetization of CoHo0.05Fe1.95O4 nanoparticles as a function of temperature satisfies Bloch's law, and the coercivity of the sample remained in good agreement with Kneller's law.

Temperature-dependent magnetic behavior of Mn-Mg spinel ferrites with substituted Co, Ni & Zn, synthesized by hydrothermal method

Mn0.1Mg0.2(Co, Ni, Zn)0.7Fe2O4 compounds with particles sizes ranging between 11 nm and 17 nm were successfully synthesised by hydrothermal process. These particles sizes are in agreement with TEM results. Bulk samples with particle sizes ranging between 69 nm and 72 nm were subsequently produced by annealing at 1100 °C under argon gas. SEM and EDX were used to study the morphology and confirm the elemental compositions. Temperature-dependent magnetization showed a strong dependence of coercive fields on measuring temperature and substituent. The coercive field variation followed Kneller's law with values varying between 0.5 kOe and 12 kOe from about 300 K to 2 K. An average moment of about ≈104 was deduced from the magnetic measurements of the as-prepared samples. Temperature-dependent magnetic measurements in as-prepared samples showed superparamagnetic behavior with. The Langevin function fittings on M-H data at 300 K give particle size distributions with average diameters corresponding well with that estimated from XRD analysis. Field cooling (FC) and zero-field cooling (ZFC) measurements showed the dependence of bifurcation temperature on the applied magnetic field.

Comparison of surface effects in bare and titanium oxide coated CoFe2O4 nanoparticles

Comparison of surface effects in bare and titanium oxide coated CoFe2O4 nanoparticles has been done with the help of magnetic measurements. The average crystallite size was 31 for bare CoFe2O4 nanoparticles. For titanium oxide coated nanoparticles, the CoFe2O4 and titanium oxide phases have crystallite size of 46 and 38 nm, respectively. TEM images confirmed the coating behavior of titanium oxide on CoFe2O4 nanoparticles. Both kinds of nanoparticles were in magnetically blocked state at room temperature as evident by ZFC/FC measurements. The effective anisotropy constant was calculated from simulated ZFC curve and found higher for bare CoFe2O4 nanoparticles due to large surface spin disorder and strong interparticle interactions. In modified Bloch's law fit for Ms vs. T data, the higher value of Bloch's constant for titanium oxide coated CoFe2O4 nanoparticles demonstrates the weak exchange coupling constant J. The Kneller's law fit for Hc vs. T data showed a lower value of constant α for titanium oxide coated CoFe2O4 nanoparticles which is due to the reduced surface magnetic and weak interparticle interactions. In summary, crystalline titanium oxide coating on CoFe2O4 nanoparticles showed reduction in surface spin disorder and weaken interparticle interactions.

Fabrication and temperature dependent magnetic properties of Co-Ni nanotube arrays

Parallel arrays of Co-Ni nanotubes with external diameter of 150 nm, wall thickness of 20 nm, and length of about 0.8 μm were successfully fabricated in ion-track etched polycarbonate (PC) templates by electrochemical deposition. The morphology and composition of the nanotubes were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDS). Temperature dependent magnetic analyses were performed with superconducting quantum interference device (SQUID) magnetometer which indicate that saturation magnetization of the nanotubes follows modified Bloch's law in the range 80–300 K. An abrupt deviation of the experimental curve (increase in magnetization) was observed from the modified Bloch's law below 80 K, which can be attributed to the disordered surface spins in the nanotubes due to the finite size effects. Finally, it was found that coercivity measured at different temperatures follows Kneller's law within the premises of Stoner–Wohlfarth model for ferromagnetic nanostructures.

Role of surface spins on magnetization of Cr2O3 coated γ-Fe2O3 nanoparticles

Effect of surface spins in chromium oxide (Cr2O3) coated maghemite (γ-Fe2O3) nanoparticles (13 nm) as prepared by microwave plasma technique have been studied in detail. The temperature dependent zero field cooled/field cooled (ZFC/FC) measurements revealed the blocking temperature at TB = 75 K. Simulated ZFC/FC curves exhibited large value of effective anisotropy of Cr2O3 coated γ-Fe2O3 nanoparticles as compared to bulk γ-Fe2O3 but less than bare γ-Fe2O3 nanoparticles. Bloch's law was fitted on MS-T data and revealed the values of Bloch's constant B = 3.523 × 10−4 K−b and Bloch's exponent b = 1.10. The higher value of B than in bulk is due to weaker exchange coupling J (B ̴ 1/J) on the surface of nanoparticle due to disorder surface spins, while lower value of b is due to no spin wave excitation in presence of large energy band gap at nanoscale. Kneller's law fit on HC-T data deviated in all temperature range which is due to strong surface anisotropy, core-shell interactions and superparamagnetism. Interparticle interactions and spin glass behavior were investigated by using different physical laws for f-dependent ac susceptibility and they confirmed the presence of spin glass behavior which is due to disordered frozen surface spins and random interparticle interactions.

Structural and magnetic behavior of nanocrystalline Cr doped Co-Mg ferrite

Nanoparticles of Cr substituted Co-Mg ferrites with chemical composition Co0.5Mg0.5CrxFe2−xO4 (0 ≤ x ≤ 1) have been synthesized by sol-gel auto combustion route. Rietveld refined powder X-ray diffraction patterns confirmed nanocrystalline single phase formation of all the ferrite samples in the face centred cubic spinel structure in the space group of Fd3m (No. 192). Cr doping for Fe in the Co-Mg ferrite leads to monotonic decrease in the saturation magnetization at 300K as well as at 5K, which can be described due to the weakening of super exchange interaction because of the replacement of Fe3+ ions by weak magnetic Cr3+ ions at the octahedral site. Decrement observed in coercivity from 0.085T to 0.044T at room temperature with increase in Cr concentration is indicative of the decrement in the isotropic field. Coercivity follows the Kneller's law for Co0.5Mg0.5Fe2O4 ferrite within the temperature range 5–300K. Interestingly the saturation magnetization was observed to increase whereas the coercivity decreases with increase in the annealing temperature in Co0.5Mg0.5Cr0.6Fe1.4O4 ferrite.

Negative and anomalous T-dependent magnetization trend in CoCr2O4 nanoparticles

We studied the temperature dependent magnetic properties of cobalt chromite (CoCr2O4) nanoparticles. X-ray diffraction revealed the cubic spinel structure of the nanoparticles and average crystallite size was about 42 nm. Raman and Fourier transform infrared spectroscopy confirmed the formation of single phase spinel structure. ZFC/FC curves revealed a paramagnetic (PM) to ferromagnetic (FiM) transition at TC = 100 K with conical spiral state at TS = 27 K and lock-in state at TL = 13 K. Negative magnetization is observed in the ZFC curve under 50 Oe applied field, which gets suppressed upon the application of higher field. The TC was shifted towards higher temperature with the application of higher field, while TS and TL remain unaffected. M-H loops showed FiM behavior below 100 K and nearly PM at TC = 100 K. Below 75 K, an abnormal decrease in MS is observed down to 5 K, which may be due to presence of stiffed/strong conical spin spiral and lock in states at low temperatures. Modified Kneller's law showed a good fit for temperature dependent Hc at higher temperature and deviated at low temperature (<25 K) which was attributed to frozen disordered surface spins. Nanoparticles showed slow spin relaxation in both ZFC and FC protocols at 5 K, which signifies the presence of spin-glass like behavior at low temperatures. Both curves were fitted with stretched exponential law and the value of β lies in the spin-glass regime. In summary, CoCr2O4 nanoparticles showed anomalous decrease of MS with decreasing temperature, negative magnetization at low field and rather stiffed/strong conical spin spiral and lock-in states in combination with spin-glass behavior at the low temperatures.

Surface effects in uncoated and amorphous SiO2 coated cobalt ferrite nanoparticles

Surface effects in uncoated and amorphous silica (SiO2) coated cobalt ferrite nanoparticles have been studied by using dc magnetization. Both uncoated and SiO2 coated nanoparticle samples were synthesized by using sol–gel method. SiO2 coated nanoparticles exhibit smaller average crystallite size as compared to uncoated nanoparticles. Saturation magnetization (Ms) revealed decreasing trend at low temperatures for uncoated nanoparticles as compared to coated nanoparticles which may be due to magnetically dead nanoparticle's surface layer for uncoated nanoparticles. A step-like behavior near remanent field was observed for both the samples but more pronounced for SiO2 coated nanoparticles. This fast magnetic relaxation near remanent field in coated nanoparticles is due to lesser dipolar (interparticle) interactions among nanoparticles. Bloch's law shows a good fit for coated nanoparticles. SiO2 coated nanoparticles showed larger values of coercivity at low temperatures due to their enhanced surface anisotropy as compared to uncoated nanoparticles. Kneller's law for temperature dependent coercivity shows a good fit for SiO2 coated nanoparticles and is attributed to lesser dipolar interactions among coated nanoparticles as compared to uncoated nanoparticles. The exchange bias phenomenon was also observed for both the samples, which signify the presence of core–shell interactions. However, SiO2 coated nanoparticles exhibit larger values of exchange bias at low temperatures due to their strong surface anisotropy as compared to uncoated nanoparticles. The presence of exchange bias in uncoated nanoparticles indicates that their surface layer is not totally magnetically dead. In summary, (i) the SiO2 coated nanoparticles have lesser dipolar interactions due to SiO2 coating and (ii) surface layer in uncoated nanoparticles is not magnetically dead but may have different preferred ordering at low temperatures as compared to SiO2 coated nanoparticles.

Surface and interparticle interactions effects on nano-cobalt ferrites

Cobalt ferrites nanoparticles CoxFe3-xO4 (1≤x<1.8) were synthesized by a solvothermal route. X-ray diffraction, Transmission Electron Microscopy and magnetic measurements show a strong correlation between the structural and the magnetic properties. The highest cobalt amount substituted samples (x=1.6 and 1.8) show a jump at low temperature in the hysteresis loops in the range of low applied fields (<10 kOe). This behavior has been explained by surface effects and interparticle interactions. A difference has been found using two different estimation of the magnetic anisotropy: from the law of approach to saturation and using the Neel-Brown approach. The last approach leads to an increase of the anisotropy for x=1.6 and 1.8 coming from finite size effects. Surface effects have been pointed out using the Bloch law fitting. Zero Filed Cooling (ZFC) measurements exhibit a blocking temperature (TB) range from 294 to 240 K. Kneller's law fitting of the coercive field dependence on the temperature exhibits a non-neglected interparticle interaction and a wide size distribution according to the difference found between TB and the Kneller transition temperature TBK.

Temperature Dependence of Saturation Magnetization and Coercivity in Mn0.5Zn0.5Gd0.02Fe1.98O4 Ferrite Nanoparticles

The influence of temperature on coercivity, Hc and saturation magnetization, Ms were investigated experimentally in Mn0.5Zn0.5Gd0.02Fe1.98O4 ferrite nanoparticles (average size 35 nm). Isothermal magnetization curves M (H) were obtained in the field range from -5 kOe to +5 kOe at different temperatures after the zero field cooling (ZFC) process. The temperature dependence of the coercivity, Hc(T) deviated slightly from the classical Kneller's law. The temperature dependence of saturation magnetization, Ms(T) was found to have an excellent agreement with the Bloch's law. These results are discussed in terms of several factors such as the size and size distribution of the particles, inter-particle interactions and the surface spin.

Synthesis, structural and magnetic properties of ZnxMg1−xFe2O4 nanoferrites

Abstract Zn x Mg 1 − x Fe 2 O 4 nanoparticles ( 0 ≤ x ≤ 1 in steps of 0.1) have been produced by centrifugation using the low temperature glycol-thermal method at 200 °C. Single-phase formation was confirmed by X-ray powder diffraction which revealed a well-defined cubic spinel structure with space group Fd3m. HRTEM and TEM were also used for the morphology studies. The crystallite size of the compounds ranged from 10.6 to 22.2 nm. A strong correlation was found between X-ray density and Zn-concentration, x . The magnetic properties as a function x were investigated by using 57 Fe Mossbauer spectroscopy, magnetization measurements using a Lakeshore vibrating sample magnetometer (VSM) at room temperature. We also report VSM measurement on a cryogen free measurement system at isothermal temperatures between 4 K and 300 K in external applied magnetic fields of up to 5 T. For x 0.8 , the room-temperature Mossbauer results show that the samples were transformed from paramagnetic state to magnetic ordered state. The temperature-dependences of saturation magnetization and coercive field follow the modified Bloch's law and Kneller's law, respectively. Strong correlation between saturation magnetization M S ( 0 ) and crystallite size D is observed. Two distinct composition ranges with Zn content are identified for which M S ( 0 ) variation with x is explained by the Neel and Yafet–Kittel models.

Sol–gel auto combustion synthesis of CoFe2O4/1-methyl-2-pyrrolidone nanocomposite with ethylene glycol: Its magnetic characterization

Magnetic nanoparticles were generated by sol–gel auto combustion synthesis of metal salts in the presence of 1-methyl-2-pyrrolidone, a functional solvent and ethylene glycol as usual solvent. The average crystallite size was obtained by using line profile fitting as 11±5nm. The saturation magnetization value decreases with usage of the ethylene glycol in synthesis. The observed exchange bias effect further confirms the existence of the magnetically ordered core surrounded by spin-disordered surface layer and the ethylene glycol. Square-root temperature dependence of coercivity can be fitted to Kneller's law in the temperature range of 10–400K. The reduced remanent magnetization values lower than the theoretical value of 0.5 for non-interacting single domain particles indicate the CoFe2O4-1-methyl-2-pyrrolidone nanocomposite to have uniaxial anisotropy instead of the expected cubic anisotropy according to the Stoner–Wohlfarth model.

Temperature dependent magnetic properties of CoFe 2 O 4 /CTAB nanocomposite synthesized by sol–gel auto-combustion technique

A CoFe 2 O 4 /cetyl trimethylammonium bromide (CTAB) nanocomposite has been fabricated by a sol–gel auto-combustion method. Characterization of the material revealed the composition of the crystalline phase as CoFe 2 O 4 while FT-IR confirmed the presence of CTAB on the nanoparticles. From X-ray line profile fitting, average crystallite size was estimated to be 22±6 nm. SEM analysis showed a porous sheet-like morphology with internal nanosize grains of about 30 nm. The room temperature coercive field ( H c ) of the CoFe 2 O 4 /CTAB nanocomposite was found to be 1045 Oe which is close to the previously reported room temperature values for bulk CoFe 2 O 4 . The H c was observed to decrease almost linearly with the square root of the temperature (√T) according to Kneller's law . From the linear fit of H c versus √T, the zero-temperature coercivity ( H c 0 ) and superparamagnetic blocking temperature ( T B ) of the CoFe 2 O 4 /CTAB nanocomposite were found to be ∼9.1 kOe and ∼425 K, respectively. The remanence magnetization ( M r ), the reduced remanent magnetization ( M r / M s ), and the effective magnetic anisotropy ( K eff ) decrease with increasing temperature. The M r / M s value of 0.6 at 10 K higher than the theoretical value of 0.5 for non-interacting single domain particles with the easy axis randomly oriented suggests the CoFe 2 O 4 /CTAB nanocomposite to have cubic magnetocrystalline anisotropy according to the Stoner–Wohlfarth model.

Sol–gel auto combustion synthesis of CoFe 2 O 4 /1-methyl-2-pyrrolidone nanocomposite: Its magnetic characterization

Abstract A magnetic nanocomposite was generated by the sol–gel auto-combustion method in the presence of 1-methyl-2-pyrrolidone, a functional solvent. The temperature-dependent magnetic properties of the CoFe 2 O 4 nanoparticles have been extensively studied in the temperature range of 10–400 K and magnetic fields up to 80 kOe. Zero field cooled (ZFC) and field cooled (FC) curves indicate that the blocking temperature ( T B ) of the CoFe 2 O 4 nanoparticles is above 400 K. It was found from M–H curves that the low temperature saturation magnetization values are higher than bulk value of CoFe 2 O 4 . The saturation magnetization ( M s ), remanence magnetization ( M r ), reduced remanent magnetization ( M r / M s ) and coercive field ( H c ) values decrease with increasing temperature. The M r / M s value of 0.75 at 10 K indicates that the CoFe 2 O 4 nanoparticles used in this work have, as expected, cubic magnetocrystalline anisotropy according to the Stoner–Wohlfarth model. T 1/2 dependence of the coercive field was observed in the temperature range of 10–400 K according to Kneller's law. The extrapolated T B and the zero-temperature coercive field values calculated according to Kneller's law are almost 427 K and 13.2 kOe, respectively. The room temperature H c value is higher than that of the previously reported room temperature bulk values. The effective magnetic anisotropy constant ( K eff ) was calculated as about 0.23×10 6 erg/cm 3 which is lower than that of the bulk value obtained due to disordered surface spins.

Effect of temperature on the magnetic characteristics of Ni0.5Co0.5Fe2O4 nanoparticles

Magnetic nanoparticles of Ni0.5Co0.5Fe2O4 (size: 18±3nm) have been synthesized by chemical co-precipitation route. Coercivity (HC) of the particles shows an increasing behavior with decreasing temperature and observes deviation from the Kneller's law for ferromagnetic nanostructures. Exchange bias effect (Hex) shows an exponential increase with decreasing temperatures followed by a sharp fall below ∼5K. The saturation magnetization (Ms) follows modified Bloch's law in the high temperature range (100–300K), while below 100K it shows a decreasing trend with decreasing temperature followed by slow increase in Ms at very low temperatures. Blocking behavior shows a decreasing trend in blocking temperature (Tb) of the system as the applied field in M(T) measurements is increased. The results have been discussed in terms of the variation of anisotropy with temperature, modified spin-wave theory predictions, interparticle interactions, and the presence of spin glass (SG) like phase at the surface of Ni0.5Co0.5Fe2O4 nanoparticles.

Influences of cobalt substitution and size effects on magnetic properties of coprecipitated Co–Fe ferrite nanoparticles

Co-substituted ferrite nanoparticles with narrow size distribution have been prepared by coprecipitation method. X-ray diffraction (XRD) showed that the samples have cubic spinel structure of which the lattice constant slightly decreases upon cobalt substitution. The mean crystallite size of the samples was in the range 9.5–11 nm as deduced from the XRD line broadening. Energy dispersive X-ray spectroscopy (EDX) verified the presence of cobalt in the substituted samples. The morphology and size distribution of the nanoparticles were studied using transmission electron microscopy (TEM). Magnetic properties were determined using a vibrating sample magnetometer (VSM). The samples are characterized by a superparamagnetic transition at blocking temperatures T B below room temperature. The coercivity H c at low temperatures follows a simple model of thermal activation of particle's moment over the anisotropy barrier in the temperature range below T B which is in accordance with Kneller's law for ferromagnetic materials. From the blocking temperature and from the thermal decay of the coercivity, the effective anisotropy constant values were determined to be in order of 10 6 erg/cm 3. The Curie temperature T C and saturation magnetization M s at nanoscale are lower than those of the bulk and decrease with the increase of cobalt content.