Finite size and surface effects on the magnetic properties of cobalt ferrite nanoparticles

Cobalt ferrite, CoFe₂O₄, nanoparticles in the size range 2–15 nm have been prepared using a non-aqueous solvothermal method. The magnetic studies indicate a superparamagnetic behavior, showing an increase in the blocking temperatures (ranging from 215 to more than 340 K) with the particle size, D _TEM. Fitting M versus H isotherms to the saturation approach law, the anisotropy constant, K, and the saturation magnetization, M _S, are obtained. For all the samples, it is observed that decreasing the temperature gives rise to an increase in both magnetic properties. These increases are enhanced at low temperatures (below ~160 K) and they are related to surface effects (disordered magnetic moments at the surface). The fit of the saturation magnetization to the T ² law gives larger values of the Bloch constant than expected for the bulk, increasing with decreasing the particle size (larger specific surface area). The saturation magnetization shows a linear dependence with the reciprocal particle size, 1/D _TEM, and a thickness of 3.7 to 5.1 Å was obtained for the non-magnetic or disordered layer at the surface using the dead layer theory. The hysteresis loops show a complex behavior at low temperatures (T ≤ 160 K), observing a large hysteresis at magnetic fields H > ~1000 Oe compared to smaller ones (H ≤ ~1000 Oe). From the temperature dependence of the ac magnetic susceptibility, it can be concluded that the nanoparticles are in magnetic interaction with large values of the interaction parameter T ₀, as deduced by assuming a Vogel–Fulcher dependence of the superparamagnetic relaxation time. Another evidence of the presence of magnetic interactions is the almost nearly constant value below certain temperatures, lower than the blocking temperature T _b, observed in the FC magnetization curves.     

Magnetic properties of Fe<Subscript>3</Subscript>C ferromagnetic nanoparticles encapsulated in carbon nanotubes

The low-temperature dependences of magnetic characteristics (namely, the coercive force H _c , the remanent magnetization M _r , local magnetic anisotropy fields H _a, and the saturation magnetization M _s ) determined from the irreversible and reversible parts of the magnetization curves for Fe₃C ferromagnetic nanoparticles encapsulated in carbon nanotubes are investigated experimentally. The behavior of the temperature dependences of the coercive force H _c (T) and the remanent magnetization M _r (T) indicates a single-domain structure of the particles under study and makes it possible to estimate their blocking temperature T _B = 420–450 K. It is found that the saturation magnetization M _s and the local magnetic anisotropy field H _a vary with temperature as ～T ^5/2.     

Ferrimagnetic nanoparticles for self-controlled magnetic hyperthermia

Based on the Heisenberg model including single-site uniaxial anisotropy and using aGreen’s function technique we studied the influence of size and composition effects on theCurie temperature T _C , saturationmagnetization M _S and coercivityH _C of spherical nanoparticles with astructural formulaM e _1?x Zn _x Fe₂O₄,Me = Ni, Cu, Co, Mn. It is shown that for x = 0.4–0.5and d = 10–20 nm these nanoparticles have aT _C  = 315 K and are suitable for aself-controlled magnetic hyperthermia.     

Structure and magnetic properties of iron–platinum particles with <Emphasis Type="Italic">γ</Emphasis>-ferric-oxide shell

Nanoparticles of solid solution Fe _x Pt_1?x , where 0.25≥x≥0 (?fcc lattice) with γ-Fe₂O₃ shell (lattice of the spinel type) were synthesised and characterised by high-resolution transmission electron microscopy, energy dispersive X-ray analysis, electron energy loss spectroscopy, Mössbauer spectroscopy and magnetometry. From the point of view of magnetic properties, such two-phase particles are interesting because their core is antiferromagnetic or paramagnetic (at very small values of x) whereas the shell is ferrimagnetic. The size of the particles was in the range of several nanometers. The Mössbauer measurements revealed a blocking temperature of about 100 K above which the particles are superparamagnetic. Towards lower temperatures, the magnetic characteristics of an ensemble of such particles show an increase of magnetic rigidity.     

Magnetism of gadolinium nanoparticles near <Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript>

Influence of temperature and magnetic field H on magnetism of spherical Gd nanoparticles of different sizes (89, 63, 47, 28, and 18 nm) was studied in the temperature range 250 K < T < 325 K. The particles were obtained by metal vapor condensation in the flow of helium. The particles with d = 18 nm did not show a magnetic transition; their structure is a combination of two cubic phases (FCC1 and FCC2). Large particles remained in the HCP phase and had an admixture of the FCC1 phase, the amount of which decreased as the particle sizes increased; magnetic transition took place at T _c = 293 K. The admixture of O₂ did not alter the structure but decreased the magnetization σ and magnetic permeability μ. An orientation transition in polycrystalline gadolinium initiated by the magnetic field H was proved in an experiment. The orientation transition in Gd particles smaller than 63 nm, the magnetic structure of which is close to the single-domain structure, occurred near T _c without the influence of H.     

Controlling the demagnetizing field of an in-plane free layer by exchange coupling with a perpendicular multilayer

The demagnetizing field of a Co₅₀Fe₅₀ free layer in an in-planemicron-sized magnetic tunnel junction (MTJ) can be partially compensated by exchangecoupling with a [Co₉₀Fe₁₀/Pt] _N multilayer with perpendicular magnetic anisotropy via a Ru interlayer. The perpendicularanisotropy for N = 5 is optimized for nominal CoFe and Pt thicknessof 0.4 nm and 1.0 nm, respectively. An increase of tunnel magnetoresistance (TMR) from 2%to 75% is observed in MTJs as the free layer thickness, t variesfrom 1.0 nm to 3.0 nm. A phenomenological model is developed to interpret the TMRdependence in terms of the free layer magnetization rotation from in-plane to out-of-planewith decreasing t, a consequence of interlayer exchange coupling with theperpendicular multilayer. We suggest that this strategy could significantly reduce theswitching current density in such MTJs.     

Mössbauer Spectroscopy Study of the Superparamagnetism of Ultrasmall ϵ-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript> Nanoparticles

The superparamagnetism of an ensemble of ?-Fe₂O₃ nanoparticles with a mean size of 3.9 nm dispersed in a xerogel SiO₂ matrix is studied by the Mössbauer spectroscopy method. It is shown that most nanoparticles at room temperature are in the superparamagnetic (unblocked) state. As the temperature decreases, the progressive blocking of the magnetic moments of the particles occurs, which is manifested in the Mössbauer spectra as the transformation of the quadrupole doublet into a Zeeman sextet. The analysis of the relative intensity of the superparamagnetic (quadrupole doublet) and magnetically split (sextets) spectral components in the range of 4–300 K provides the particle size distribution, which is in agreement with the transmission electron microscopy data. The values of the effective magnetic anisotropy constants (K_eff) are determined, and the contribution of surface anisotropy (K_S) is estimated for particles of various sizes. It is shown that the quantity K_eff is inversely proportional to the particle size, which indicates the significant contribution of the surface to the magnetic state of the ?-Fe₂O₃ nanoparticles with the size of several nanometers.     

Magnetic properties of arrays of cobalt nanoparticles on the CaF<Subscript>2</Subscript>(110)/Si(001) surface

The Co/CaF₂/Si(001) heterostructures with the corrugated (110) surface of the CaF₂ buffer layer have been grown by molecular beam epitaxy. The structures are nanoparticle arrays of single-crystal Co, mostly of the cubic fcc modification. The behavior of the magnetic hysteresis loops as a function of the density of coverage of the substrate by cobalt islands, the island size, and the temperature is studied using the magnetooptical technique. At low coverage densities, where the effective cobalt film thickness d _eff is less than the critical value d _eff ^c , the magnetic structure of the films at T = 294 K can be visualized as an ensemble of superparamagnetic, weakly interacting nanoparticles and is characterized by small values of the coercive field H _c and the remanent magnetization M _rem. A decrease in the temperature leads to a strong increase in H _c and M _rem, which is associated with the transition of the islands to the blocked state. The blocking temperature of the structures is T _b ～ 280 K. The magnetic anisotropy parameter K and the saturation magnetization M _s of the islands depend on the growth temperature of cobalt T _Co. An increase in the coverage density above the critical thickness d _iff ^c at T = 294 K brings about a strong increase in H _c and M _rem and the appearance of a hysteresis loop anisotropy originating from the corrugated structure of the CaF₂ buffer layer. The experimental results are compared with the model of an ensemble of noninteracting superparamagnetic particles.     

A Variable Temperature X- and W-Band EPR Study of Fe-Doped SiCN Ceramics Annealed at 1000, 1100, and 1285 °C: Dangling Bonds,Ferromagnetism and Superparamagnetism

Polymer-derived SiCN ceramics, annealed (also referred to as pyrolyzed) at 1000, 1100, and 1285 °C, and doped with Fe(III) acetylacetonate, are investigated by electron paramagnetic resonance (EPR) from 4 to 120 K at X-band (9.425 GHz). In addition, the SiCN ceramic, annealed at 1100 °C, was studied by EPR at 300 K at W-band (93.96 GHz). There was observed a significant increase in EPR linewidth due to dangling bonds (g = 2.001) below 20 K at X-band. The low-field X-band FMR line (g ≈ 12) indicated the presence of ferromagnetic Fe₅Si₃ crystallites. There were found two EPR lines due to carbon-related dangling bonds: (1) those present as defects on the surface of the free-carbon phase (as sp² carbon-related dangling bonds with g = 2.0011) and (2) those present within the bulk of carbon phase (as sp³ carbon-related dangling bonds with g = 2.0033). On the other hand, the intense low-field EPR signal observed at X-band was not observed at W-band. As well, there was observed splitting of the single broad EPR signal observed at g = 2.05 at X-band into two signals at W-band at g = 1.99 and g = 2.06, due to two different Fe-containing superparamagnetic nanocrystallites. Two new EPR signals, not observed at X-band, were observed at W-band, namely at g = 2.28 and g = 3.00, which are also due to g_∥ of these superparamagnetic nanocrystallites.     

Physical properties of FeSe<Subscript>0.5</Subscript>Te<Subscript>0.5</Subscript> single crystals grown under different conditions

We report on structural, magnetic, conductivity, and thermodynamic studies of FeSe_0.5Te_0.5 single crystals grown by self-flux and Bridgman methods. The lowest values of the susceptibility in thenormal state, the highest transition temperature T _c of 14.4 K, and the largest heat-capacity anomaly at T _c were obtained for pure (oxygen-free) samples. The criticalcurrent density j _c of 8.6 × 10⁴A/cm² (at 2 K) achieved in pure samples is attributed to intrinsic inhomogeneity due to disorder at the anion sites. The samples containing an impurity phase of Fe₃O₄ show increased j _c up to2.3 × 10⁵A/cm² due to additional pinning centers. The upper critical field\(H_{c2}\)of ~500 kOe is estimated from the resistivity studyin magnetic fields parallel to the c-axis using a criterion of a 50%drop of the normal state resistivity R _n . The anisotropy ofthe upper critical fieldγ _{H c2} =H ^ab _c2/H _c2 ^c reaches a value ~6 at\(T\longrightarrow T_c\). Extremely low values of the residualSommerfeld coefficient \(\gamma_r\) of about 1 mJ/mol K²,compared to the normal state Sommerfeld coefficient γ _n = 25mJ/mol K² for pure samples indicate a high volume fraction of thesuperconducting phase (up to 97%). The electronic contribution to the specific heat in thesuperconducting state is well described within a single-band BCS model with a temperature dependent gapΔ(0 K) = 27(1) K. A broad cusp-like anomaly in the electronic specific heat observed at low temperatures in samples with suppressed bulk superconductivity is ascribed to a splitting of the ground state of the Fe²⁺ ions at the 2c sites. This contribution is fully suppressed in the ordered state in samples with bulk superconductivity.     

Competing contact processes in the Watts-Strogatz network

We investigate two competing contact processes on a set of Watts–Strogatz networks withthe clustering coefficient tuned by rewiring. The base for network construction isone-dimensional chain of N sites, where each site i is directly linked tonodes labelled as i ±1 and i ±2. So initially, each node has the same degree k_i =4. The periodic boundary conditions are assumed as well. For each nodei the linksto sites i +1 and i +2 are rewired to two randomly selected nodes so far not-connected tonode i. Anincrease of the rewiring probability q influences the nodes degree distribution and thenetwork clusterization coefficient ??. For given values of rewiring probabilityq the set ??(q)={??₁,??₂,...,??_M} of M networks is generated. The network’s nodes aredecorated with spin-like variables s_i ∈ { S,D}. During simulation each S node having a D-site in its neighbourhoodconverts this neighbour from D to S state. Conversely, a node in D state having at least oneneighbour also in state D-state converts all nearest-neighbours of this pairinto D-state. The latter is realized with probabilityp. We plotthe dependence of the nodes S final density n_S^T on initial nodes S fraction n_S⁰. Then, we construct the surface of the unstable fixedpoints in (??, p, n_S⁰) space. The system evolves more often toward n_S^T for (??, p, n_S⁰) points situated above this surface while startingsimulation with (??, p, n_S⁰) parameters situated below this surface leads system to n_S^T=0. The points on this surface correspond to such value ofinitial fraction n_S^* of S nodes (for fixed values ?? and p) for which their final density is n_S^T=1/2.     

Influence of heat treatment process in In<Subscript>2</Subscript>O<Subscript>3</Subscript>-MWCNTs as photoanode in DSSCs

Indium oxide-multi-walled carbon nanotubes (In₂O₃-MWCNTs) were prepared by sol-gel method for DSSCs. The synthesis of indium oxide (In₂O₃) was carried out by dissolving indium chloride (InCl₃) in a solvent of 2-methoxyethanol. Different annealing temperatures of 400, 450, 500, 550, and 600 °C were proposed in this study. The changes in the structural properties were analyzed by means of X-ray diffraction (XRD) and atomic force microscopy (AFM) analysis. The XRD spectrum estimated the average crystallite sizes of 3 nm for each sample. AFM results indicated very rough surface area of the films where it increased linearly from 1.8 to 11 nm as the annealing temperature increases. The In₂O₃-MWCNTs-based DSSC exhibited good photovoltaic performance with power conversion efficiency (η), photocurrent density (J _sc ), open circuit voltage (V _oc ), and fill factor (FF) of 1.13 %, 5.5 mA/cm², 0.53 V, and 0.42, respectively. Even though the film annealed at 450 °C exhibited low τ _eff, it achieved the greatest D _eff of 29.67 cm² s^?1 which provides an efficient pathway for the photogenerated electrons with minimum electron recombination loss that increased the J _sc and V _oc in the DSSC. The obtained structural and electron transport analysis was proposed as a suitable benchmark for In₂O₃-MWCNTs-based dye-sensitized solar cell (DSSCs) application. Hence, this study suggests that the optimum temperature for In₂O₃-MWCNTs is at annealing temperature of 450 °C prepared via sol-gel method.     

High rotatable magnetic anisotropy in MnBi thin films

The variations of the structural and magnetic properties of Bi/Mn/Bi and Mn/Bi/Mn trilayer film systems of equiatomic composition in the process of vacuum annealing are studied. The annealing of Bi/Mn/Bi films at a temperature of 270°C for an hour results in the synthesis of the well-studied highly oriented low-temperature LT-MnBi(001) phase with the perpendicular magnetic anisotropy K _u ～ 1.1 × 10⁷ erg/cm³ and coercivity H _C ～ 1.5 kOe. In contrast to Bi/Mn/Bi, polycrystalline LT-MnBi nanoclusters are formed in Mn/Bi/Mn films under the same annealing conditions. A high rotatable magnetic anisotropy exceeding the shape anisotropy is detected in the films under consideration: the easy axis of anisotropy with the inclusion of the delay angle in magnetic fields above the coercivity H &gt; H _C = 9.0 kOe can be oriented in any spatial direction. It is shown that the nature of rotatable magnetic anisotropy is due to the structural coexistence of epitaxially coupled LT-MnBi and QHTP-Mn_1.08Bi phases. The reported experimental results indicate the existence of a new class of ferromagnetic film media with the spatially tunable easy axis.     

Magnetic Resonance in Gadolinium Nanoparticles near the Curie Point

The Influence of temperature in the range from 275 to 320 K on ESR spectra and magnetization m of ensembles of spherical gadolinium nanoparticles with the diameter from 89 to 18 nm was studied. The particles with d = 18 nm had a cubic face centered structure and no magnetic transition. At T > T_C all particles were paramagnetic, and their g factors were g = 1.98 ± 0.02 irrespective of their size and structure. At T = T_C the particles having 28 to 89 nm in size experienced a magnetic and orientation transition; at T < T_C their m(H) dependences were described by the Langevin function, and the FMR lines broadened and shifted towards H = 0. FMR lines of the Gd particle ensembles showed a hysteresis behavior during magnetization reversal, which did not correlate with the coercivity of the particles. Dependences of the Gd nanoparticles FMR linewidth ΔH(T) changed proportionally to |T–T_C|.     

New Bounds on the Maximum Ionization of Atoms

We prove that the maximum number N _c of non-relativistic electrons that a nucleus of charge Z can bind is less than 1.22Z + 3Z ^1/3. This improves Lieb’s upper bound N _c  < 2Z + 1 Lieb (Phys Rev A 29:3018–3028, 1984) when Z ≥ 6. Our method also applies to non-relativistic atoms in magnetic field and to pseudo-relativistic atoms. We show that in these cases, under appropriate conditions, \({\limsup_{Z \to \infty}N_c/Z \le 1.22}\).     

Bestimmung der Hyperfeinstrukturaufspaltungen der Scandium-Grundzustände2 D 3/2 und2 D 5/2 und des Quadrupolmomentes des Sc45-Kernes

The hyperfine structure splittings of the electronic ground states² D _3/2 and² D _3/2 of the stable isotope Sc⁴⁵ have been measured by the atomic beam magnetic resonance method. From these splittings the magnetic dipole and electric quadrupole interaction constants are found to bea _3/2=(269,560±0,02) Mc/sb _3/2=?(26,37±0,1) Mc/sa _5/2=(109,034±0,01) Mc/sb _5/2=?(37,31±0,1) Mc/s. The values of the electric quadrupole moment calculated fromb _3/2 andb _5/2 differ by about 5% indicating that the configuration 3d 4s ² of the ground states is perturbed by higher configurations. Averaging these two values we obtain for the quadrupole moment of Sc⁴⁵ Q(Sc⁴⁵)=?(0,22±0,01) · 10^?24 cm².     

Saturation spectra of low lying states of Nitrogen: reconciling experiment with theory

The hyperfine constants of the levels 2p ² \((^{3}\)P)3s ⁴P _J , 2p ² \((^3\)P)3p ⁴P\(^o_J\) and 2p ² \((^3\)P)3p ⁴D\(^o_J\), deduced by Jennerich et al. [Eur. Phys. J. D 40, 81 (2006)] from the observed hyperfine structures of the transitions 2p ² \((^3\)P)3s ⁴P _J \(\rightarrow\) 2p ² \((^3\)P)3p ⁴P\(^o_{J'}\) and 2p ² \((^3\)P)3s ⁴P _J \(\rightarrow\) 2p ² \((^3\)P)3p ⁴D\(^o_{J'}\) recorded by saturation spectroscopy in the near-infrared,strongly disagree with the ab initio values of Jönsson et al. [J. Phys. B: At. Mol.Opt. Phys. 43, 115006 (2010)].We propose a new interpretation of the recorded weak spectral lines. If the latter are indeed reinterpreted as crossover signals, a new set of experimental hyperfine constants is deduced, in very good agreement with the ab initio predictions.     

Frustrated antiferromagnetism in the Sr<Subscript>2</Subscript>YRuO<Subscript>6</Subscript> double perovskite

The spins of Ru⁵⁺ ions in Sr₂YRuO₆ form a face-centered cubic lattice with antiferromagnetic nearest neighbor interaction J≈25 meV. The antiferromagnetic structure of the first type experimentally observed below the Néel temperature T _N =26 K corresponds to four frustrated spins of 12 nearest neighbors. In the Heisenberg model in the spin-wave approximation, the frustrations already cause instability of the antiferromagnetic state at T=0 K. This state is stabilized by weak anisotropy D or exchange interaction I with the next-nearest neighbors. Low D/J～I/J～10^?3 values correspond to the experimental T _N and sublattice magnetic moment values.     

Effects of Final State Interactions in Pure Annihilation Decay of B+ → D+K0*

The decay of the B ⁺ meson to the D ⁺ and K ⁰* mesons is a pure annihilation decay. For this reason, in the framework of the quantum chromodynamics factorization (QCDF) approach, this decay has a small amplitude and a small branching ratio. In this research we find that, before the D ⁺ and K ⁰* mesons are produced in the final states, pair mesons such as D _s ⁺* and D _s ⁺ρ⁰ are produced. The intermediate-state mesons via the exchange of K ⁰(K ⁰*) and D ⁺(D ⁺*) go to the D ⁺ and K ⁰* final state mesons. However we calculate the B ₊ → D ⁺ K ⁰* decay in two different frameworks. The first framework is the QCDF method and the second one is final state interaction (FSI). The experimental branching ratio of B ₊ → D ₊ K ⁰* decay is less than 3 × 10^–6, and our results obtained by the QCDF method and FSI are (0.35 ± 0.04) × 10^–6 and (2.94 ± 0.10) × 10^–6, respectively.