Magnetic susceptibility curves of a nanoparticle assembly II. Simulation and analysis of ZFC/FC curves in the case of a magnetic anisotropy energy distribution

Starting from the theoretical results established in Tournus and Bonet (2010 [1]) to describe ZFC/FC (zero-field cooled/field cooled) susceptibility curves, we examine the limitations of the widely used two states model (or abrupt transition model) where the magnetic particles are supposed to be either fully blocked or fully superparamagnetic. This crude model appears to be an excellent approximation in most practical cases, i.e. for particle assembly with broad enough size distributions. We improve the usual model by taking into account the temperature sweep existing in experimental measurements. We also discuss a common error made in the use of the two states model. We then investigate the relation between the ZFC peak temperature and the particle anisotropy constant, and underline the strong impact of the size dispersion. Other useful properties of ZFC/FC curves are discussed, such as invariance properties, the reversibility of the FC curve and the link between the susceptibility curves and the magnetic anisotropy distribution. All these considerations lay solid bases for an accurate analysis of experimental magnetic measurements.     

The effect of randomly oriented anisotropy on the zero-field-cooled magnetization of a non-interacting magnetic nanoparticle assembly

A model based on localized partition function and master equation was set up to calculate the zero-field-cooled (ZFC) and field-cooled (FC) curves of a non-interacting magnetic nanoparticle assembly with randomly oriented anisotropy. The peak temperature of the ZFC curve corresponds to the highest energy barrier that acts against the unblocking process, and could be described well by an equation covering the heating rate effect. The predicted H^2/3 field dependence of the peak temperature is in good agreement with published results.     

Non-equilibrium effects in the magnetic behavior of Co3O4 nanoparticles

We report detailed studies of the non-equilibrium magnetic behavior of antiferromagnetic Co₃O₄ nanoparticles. The temperature and field dependence of magnetization, wait time dependence of magnetic relaxation (aging), memory effects, and temperature dependence of specific heat have been investigated to understand the magnetic behavior of these particles. We find that the system shows some features that are characteristic of nanoparticle magnetism such as bifurcation of field-cooled (FC) and zero-field-cooled (ZFC) susceptibilities and a slow relaxation of magnetization. However, strangely, the temperature at which the ZFC magnetization peaks coincides with the bifurcation temperature and does not shift on application of magnetic fields up to 1 kOe, unlike most other nanoparticle systems. Aging effects in these particles are negligible in both FC and ZFC protocols, and memory effects are present only in the FC protocol. We show that Co₃O₄ nanoparticles constitute a unique antiferromagnetic system which enters into a blocked state above the average Néel temperature.     

Equilibrium magnetic properties of dipolar interacting ferromagnetic nanoparticles

We use Monte Carlo simulations to study the influence of dipolar interaction on the equilibrium magnetic properties of monodisperse single-domain ferromagnetic nanoparticles. Low field magnetizations simulated in zero field cooling (ZFC)/field cooling (FC) procedures and field-dependent magnetization curves above the blocking temperatures show strong dependence on the concentration and the spatial arrangement (cubic or random) of the magnetic particles. The field-dependent magnetizations can not be simply described by the T^* model at relative low temperatures due to the interplay between anisotropy and dipolar interactions, as well as the spatial arrangement effect.     

Temperature behavior of magnetization of DyCo2 compound

Zero field cooled (ZFC) and field cooled (FC) magnetization measurements were performed on the binary DyCo₂ cubic compound. Maxima for this compound were observed under ZFC magnetization. Below the broad maximum, irreversibility is observed. The magnetization curves for ZFC and FC regimes are split and magnetic moments for FC are higher than for ZFC. The dependence of the maxima upon the magnetic field and the time dependence of remanence is similar to the case of spin-glass-like systems.     

Polyol synthesis and magnetic study of Mn3O4 nanocrystals of tunable size

Nanosized manganese oxide particles were prepared by the so-called polyol process. The average diameter of the particles was controlled by the growth time. X-ray diffraction (XRD), transmission electron microscopy (TEM) and X-ray photon spectroscopy (XPS) show that the particles are well crystallized, pure, stoichiometric Mn₃O₄ single crystals of uniform size ranging from about 5 to 12 nm. The variation of their dc-magnetization, M, as a function of the magnetic field, H, and temperature, T, clearly corresponds to ferromagnetic ordering at low temperature, with a Curie temperature slightly higher than 40 K. The evidence for superparamagnetism in these particles, due to their very small size, has been discussed in the light of their M(H) and M(T) for zero-field-cooled (ZFC) and field-cooled (FC) plots.     

Correlation of thickness and magnetization in LCMO film

High quality thin films of La_0.67Ca_0.33MnO₃ (LCMO) of different thickness were grown on LAO substrates by pulsed laser deposition (KrF, λ = 278 nm). The AFM images suggest a twodimensional step-growth. DC magnetization measurements of the films in a field of 500 Oe show that the magnetic ordering temperature is the same for all the films in both FC and ZFC conditions and is the same as that for the bulk. However, a difference is seen between the FC and ZFC magnetization of the films. There seems to be a systematic in this difference with respect to the thickness of the film, with the difference decreasing with thickness. We suggest that the difference in the magnetization under FC and ZFC conditions may be due to strain-induced anisotropy arising from the lattice mismatch between the substrate and the film or due to the shape anisotropy due to epitaxial growth Article presented at the International Symposium on Advances in Superconductivity and Magnetism: Materials, Mechanisms and Devices, ASMM2D-2001, 25–28 September 2001, Mangalore, India.     

Thermomagnetic hysteresis and electrical transport in amorphous films

We report resistivity and magnetization measurements on an amorphous Ni₇₄Mn₂₄Pt₂ thin film in the temperature range of 3–300 K. Two significant features are apparent in both the magnetic susceptibility and electrical resistivity. A low-temperature (low-T) anomaly is observed at about 40 K, where a cusp appears in the resistivity, while a concomitant step-like increase in zero-field-cooled (ZFC) magnetization (M) appears with increasing temperature. The low-T anomaly is attributed to a crossover from a pure re-entrant spin-glass within individual domains to a mixed ferro-spin-glass regime at lower temperatures. By contrast, the high-temperature (high-T) anomaly, signaled by the appearance of hysteresis below 250 K, corresponds to the freezing of transverse spins in individual domains acting independently. Between the low-T and high-T anomalies a small but discernable magnetic hysteresis is observed for warming vs. cooling in the field-cooled (FC) case. This behavior clearly indicates the presence of domain structure in the sample, while the disappearance of this hysteresis at lower temperatures indicates the complete freezing of the spin orientation of these domains. According to these results, we have divided the magnetic state of this sample into three regions: at temperatures above 250 K, the sample behaves like a soft ferromagnet, exhibiting M vs. H loops with very small hysteresis (less than 5 Oe). As the temperature is lowered into the intermediate region (the range 40–250 K), spins become frozen randomly and progressively within the individual domains. These domains behave independently, rather than as a cooperative behavior of the sample. Weak irreversibility sets in, indicating the onset of transverse spin freezing within the domains. At temperatures below 40 K, the M vs. H loops exhibit larger hysteresis, for both the ZFC and FC cases, as in a pure spin-glass. We have also demonstrated giant noise in the resistivity at temperatures just below 250 K. Such noise can originate from fluctuations of the domains near the film surface because of competing effective bulk and surface anisotropy fields. The large observed amplitude may be explained by means of a large ferromagnetic anisotropy in the resistivity due to the large spin–orbit effect seen in NiMn systems. Finally, the low-T peak in the resistivity has been analyzed using Fisher and Langer's expression based on the Friedel Model proposed for critical transitions in transition metals (s–d systems). The fitted results are in satisfactory agreement with the predictions of this model.     

Tailoring the magnetic properties of manganese ferrite with substitution of a small fraction dysprosium for iron

Manganese ferrite nanoparticles with dysprosium (Dy) ions substituted for iron ions have been prepared by using a sol-gel method. Substitution of a small fraction Dy for Fe results in the larger magnetocrystallite anisotropy of MnFe_2−xDy_xO₄ (x=0.2, 0.4) nanoparticles than that of MnFe₂O₄ nanoparticles. The magnetosrystallite anisotropy was enhanced with the increase in the substituted dysprosium content. Combining the result of Mössbauer spectra with ZFC and FC curves, we know clearly that the Dy substitution can modify the anisotropy of MnFe₂O₄ nanoparticles for its strong spin-orbital coupling. Through this simple substitution, we can control the magnetosrystallite anisotropy of the magnetic nanoparticles and make good use of the products according as we need.     

Anisotropy and relaxation processes of uniaxially oriented CoFe2O4 nanoparticles dispersed in PDMS

When a uniaxial magnetic field is applied to a non-magnetic dispersive medium filled with magnetic nanoparticles, they auto-assemble into thin needles parallel to the field direction, due to the strong dipolar interaction among them. We have prepared in this way magnetically oriented nanocomposites of nanometer-size CoFe₂O₄ particles in a polydimethylsiloxane polymer matrix, with 10% w/w of magnetic particles. We present the characteristic magnetic relaxation curves measured after the application of a magnetic field forming an angle α with respect to the needle direction. We show that the magnetic viscosity (calculated from the logarithmic relaxation curves) as a function of α presents a minimum at α=0, indicating slower relaxation processes associated with this configuration of fields. The results seems to point out that the local magnetic anisotropy of the nanoparticles is oriented along the needles, resulting in the macroscopic magnetic anisotropy observed in our measurements.     

Fabrication and magnetic properties of Fe3O4 nanowire arrays in different diameters

Fe₃O₄ nanowire arrays with different diameters of D=50, 100, 150 and 200 nm were prepared in anodic aluminum oxide (AAO) templates by an electrodeposition method followed by heat-treating processes. A vibrating sample magnetometer (VSM) and a Quantum Design SQUID MPMS magnetometer were used to investigate the magnetic properties. At room temperature the nanowire arrays change from superparamagnetism to ferromagnetism as the diameter increases from 50 to 200 nm. The zero-field-cooled (ZFC) and field-cooled (FC) magnetization measurements show that the blocking temperature T_B increases with the diameter of nanowire. The ZFC curves of D=50 nm nanowire arrays under different applied fields (H) were measured and a power relationship between T_B and H were found. The temperature dependence of coercivity below T_B was also investigated. Mössbauer spectra and micromagnetic simulation were used to study the micro-magnetic structure of nanowire arrays and the static distribution of magnetic moments of D=200 nm nanowire arrays was investigated. The unique magnetic behaviors were interpreted by the competition of the demagnetization energy of quasi-one-dimensional nanostructures and the magnetocrystalline anisotropy energy of particles in nanowires.     

Influence of a transport current on the local magnetic field distribution in sintered YBa2Cu3Ox

The influence of a transport current on the magnetic flux-line distribution in sintered YBCO was studied by means of μSR. Pronounced differences between zero-field-cooled (ZFC) and field-cooled (FC) signals and irreversible behavior were observed. In the ZFC case even a small transport current (10 A/cm²) tends to orderirreversibly the inhomogeneous flux-line distribution considerably, suggesting a broad distribution of pinning barriers. However, for a FC sample no noticeable change in the flux distribution in the presence of a transport current (up to 40 A/cm²) was detected, indicating that the FC state represents a stable flux-line configuration.     

Hydrogen absorption and field-dependent diamagnetism of SmNiAl

Hydrogen absorption properties of SmNiAl were systematically investigated between room temperature and 673 K over the pressure range from 0 to 10 MPa. It absorbs hydrogen without clear plateaus, forms hydride SmNiAlH_x (x=0.75–2.04) without structural change below 623 K and decomposes into SmH₂ and NiAl at higher temperatures. Then, the magnetic curves, the field-cooled (FC) and the zero-field-cooled (ZFC) susceptibilities of SmNiAl and its hydride were investigated. SmNiAl behaves as paramagnetic above 65 K, but has three antiferromagnetic transitions at lower temperatures. Hydrogenation enhances its magnetism, but weakens the interaction between magnetic moments. In the FC process, hydrogenation especially induces an anomalous diamagnetism. Mechanisms for the hydrogen absorption, structural change and magnetism were discussed.     

Magnetization curves of randomly oriented ferromagnetic single-domain nanoparticles with combined symmetry of magnetic anisotropy

The magnetization curves of randomly oriented nanoparticles with combined symmetry of magnetic anisotropy were studied. The composite mode of the Stoner–Wolfarth model has been used. In terms of this model each nanoparticle is characterized by random cubic crystalline magnetic anisotropy and by random uniaxial magnetic anisotropy. The series of simulated magnetization curves have been obtained. Each curve corresponds to different contributions of cubic and uniaxial magnetic anisotropy energy to the full energy of an individual nanoparticle k_u. Within this series we discuss the values of remnant magnetization, coercive force, both initial and maximal susceptibilities as the function of k_u. It is found that the magnetic properties are not monotonous functions of k_u. We discuss the possibility of comparing the calculated magnetization curves with the experimental curves in order to obtain new information on the magnetic constant.     

Theoretical study of enhanced ferromagnetism and tunable magnetic anisotropy of monolayer CrI3 by surface adsorption

Magnetic anisotropy energy (MAE) plays a key role for 2D magnetic materials, which have attracted significant attention for their promising applications in spintronic devices. Based on first-principles calculations, we have investigated the influence of surface adsorption on the ferromagnetism and MAE of monolayer CrI₃. We find that Li adsorption can dramatically enhance its ferromagnetism, and tune its easy magnetization axis to the in-plane direction from original out-of-plane at certain coverage of Li. The monotonic enhancement of in-plane magnetism in CrI₃ as the coverage of Li increases are attributed to electrostatic doping induced by charge transfer between Li atoms and I atoms, as supported by the charge doping simulation. The tunable robust magnetic anisotropy may open new promising applications of CrI₃–based materials in spintronic devices.     

Zero—field—cooled and field—cooled magnetizations and magnetic susceptibility of itinerant ferromagnet SrRuO3

Zero-field-cooled(ZFC) magnetization,field-cooled(FC) magnetization,ac magnetic susceptibility and major hysteresis loops of itinerant ferromagnet SrRuO3 have been measured at magnetic ordering temperatures ranging from 5 to 160K.An empirical model is proposed to calculate the measured ZFC magnetization.The result indicates that the calculated ZFC magnetization compares well with the measured one.Based on the generalized Preisach model.both the ZFC and FC curves are reproduced by numerical simulations.The critical temperature and critical exponents are determined by measuring the ac magnetic susceptibility in different bias magnetic fields at temperatures in the vicinity of the point of phase transition.     

Hyperfine and Magnetic Characterization of Fe Particles Hosted in Carbon Nanocapsules

Iron particles encaged in carbon nanocapsules have been produced by the Krätschmer–Huffmann carbon-arc discharge method. Soot, collarette and cathode samples have been characterized by Mössbauer spectroscopy and magnetic measurements in the temperature range 4.2–300 K. Different iron phases and iron-carbon solid solutions have been detected in our samples. The Einstein model has been used to evaluate the coupling constant between the particles and their environment, yielding values of the order 1–10 N/m. Irreversibilities observed at ZFC and FC curves for soot samples would suggest the presence of superparamagnetism only if the particles presented a blocking temperature above 300 K.     

Influence of dipolar interaction on magnetic properties of ultrafine ferromagnetic particles

We use Monte Carlo simulations to study the influence of dipolar interaction and polydispersity on the magnetic properties of single-domain ultrafine ferromagnetic particles. From the zero field cooling (ZFC)/field cooling (FC) simulations we observe that the blocking temperature T(B) clearly increases with increasing strength of interaction, but it is almost not effected by a broadening of the distribution of particle sizes. While the dependence of the ZFC/FC curves on interaction and cooling rate are reminiscent of a spin glass transition at T(B), the relaxational behavior of the magnetic moments below T(B) is not in accordance with the picture of cooperative freezing.     

Exchange bias in bulk layered hydroxylammonium fluorocobaltate (NH?OH)?CoF?

The magnetic properties of layered hydroxylammonium fluorocobaltate (NH(3)OH)(2)CoF(4) were investigated by measuring its dc magnetic susceptibility in zero-field-cooled (ZFC) and field-cooled (FC) regimes, its frequency dependent ac susceptibility, its isothermal magnetization curves after ZFC and FC regimes, and its heat capacity. Effects of pressure and magnetic field on magnetic phase transitions were studied by susceptibility and heat capacity measurements, respectively. The system undergoes a magnetic phase transition from a paramagnetic state to a canted antiferromagnetic state exhibiting a weak ferromagnetic behavior at T(C) = 46.5 K and an antiferromagnetic transition at T(N) = 2.9 K. The most spectacular manifestation of the complex magnetic behavior in this system is a shift of the isothermal magnetization hysteresis loop in a temperature range below 20 K after the FC regime-an exchange bias phenomenon. We investigated the exchange bias as a function of the magnetic field during cooling and as a function of temperature. The observed exchange bias was attributed to the large exchange anisotropy which exists due to the quasi-2D structure of the layered (NH(3)OH)(2)CoF(4) material.     

Locally frozen magnetic field in HTSC ceramics

The value of a locally frozen magnetic field in a region with a diameter of 0.5 mm in a 0.5-mm-thick YBa₂Cu₃O_{7 ? x} plate was investigated as a function of the excitation field (to 2 × 10⁴ Am^?1), plate cooling mode (in the absence or presence of a field; i.e., zero-field cooling (ZFC) or field coupling (FC)), and local demagnetizing field. Analysis of the measurement results in the noted range of excitation fields showed the following: (i) the dependence on the excitation field for the ZFC mode is explained by the local inhomogeneity of critical currents of weak links in the ceramic Josephson medium and is limited by their maximum value at the temperature of the experiment (77 K); (ii) the dependence on the excitation field for the FC mode contains a portion of the magnetic phase transition from the frozen current structure, typical of the initial portion of the dependence, to the current structure characteristic of the ZFC freezing mode, and is limited by this transition; and (iii) the dependence on the demagnetizing field for the ZFC mode can be explained by the stable coexistence (without annihilation) of microscopic current loops with opposite current directions in the ceramics.