Effects of component ratio and easy axes distribution on the exchange bias in ferromagnetic-antiferromagnetic random alloys

For a ferromagnetic (FM)-antiferromagnetic (AFM) system with composition x(FM)+(AFM)_1−x, a modified Monte Carlo Metropolis method is performed to study the effects of x and easy axes distribution at the FM/AFM nearest neighbors on exchange bias field H_E, coercivity H_C, and vertical magnetization shift M_E after cooling under different magnetic fields h_CF. When the orientations of easy axes are uniform, the x dependence of H_E and M_E undergo a non-monotonous to monotonous process with the increase of h_CF, whereas H_C shows a more complex behavior. On the other hand, for the case of the random orientation, H_C has a peak around x=0.5, while M_E decreases with the increase of x. H_E exhibits negative extrema at small x and disappears for larger x. However, abnormal positive H_E observed depends on the frustration and the distinct trends of two coercive fields with x in such a special model.     

Glassy behaviour of random field Ising spins on Bethe lattice in external magnetic field

The thermodynamics and the phase diagram of random field Ising model (RFIM) on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field (B). A Gaussian distribution of random field (hi) with zero mean and variance hi2 = HR2F is considered. The free-energy (F ), the magnetization (M) and the order parameter (q) are investigated for several values of coordination number (z). The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature TC = J/k and when HRF = 0 for finite z. The free-energy (F) values increase as T increases for different intensities of random field (HRF) and finite z. The internal energy (U) has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field HRF increases. The ferromagnetic (FM)-paramagnetic (PM) phase boundary is clearly observed only when z →∞. While FM-PM-spin glass (SG) phase boundaries are present for finite z. The magnetic susceptibility (χ) shows a sharp cusp at TC in a small random field for finite z and rounded different peaks on increasing HRF.     

The random field Ising model with an asymmetric trimodal probability distribution

The Ising model in the presence of a random field is investigated within the mean field approximation based on Landau expansion. The random field is drawn from the trimodal probability distribution P(h_i)=pδ(h_i−h₀)+qδ(h_i+h₀)+rδ(h_i), where the probabilities p,q,r take on values within the interval [0,1] consistent with the constraint p+q+r=1 (asymmetric distribution), h_i is the random field variable and h₀ the respective strength. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays second order phase transitions, which, for some values of p,q and h₀, are followed by first order phase transitions, thus confirming the existence of a tricritical point and in some cases two tricritical points. Also, reentrance can be seen for appropriate ranges of the aforementioned variables. Using the variational principle, we determine the equilibrium equation for magnetization, solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h₀.     

Magnetization processes of CuMn below the freezing temperature Tf

A simple classical model [5] that is based on a blocking of magnetic clusters in a uniaxial anisotropy field explains characteristic properties of magnetization processes of Cu(5–15 at.%) Mn as transition states between the “zero point magnetization” M₀ = M(T → OK) and the thermal equilibrium magnetization M_∞ = M(t → ∞, T). Further it shows two facts the experimental confirmations of which we report in this paper: (a) a magnetization decrease with increasing temperature in high fields and (b) a superposition rule for the magnetization processes in small fields and at low temperatures.     

Behaviour of the optical gap of trigonal Se under pressure

The behaviour of the optical gap of trigonal Se under pressure is studied up to 140 kbar using the self-consistent symmetrized OPW method. We conclude that (i) the minimum optical gap at zero pressure is indirect M₂ → H₁, (ii) the change of the minimum optical gap from M₂ → H₁ to H₃ → H₁ causes the anomaly found in the experimental absorption edge at 35–50 kbar, and (iii) the gap is not expected to close at 140 kbar.     

Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field

Phase diagram and thermodynamic parameters of the random field Ising model (RFIM) on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field (B). The random field (hi) is assumed to be Gaussian distributed with zero mean and a variance     

Lamellar structure and nanomechanical properties of quasicrystalline Al-Cu-Fe alloys

The kinetics of structural phase transformations in quasicrystal-forming Al-Cu-Fe alloys with compositions in the region of stability of the icosahedral (i) phase has been investigated. It has been shown that, depending on the development of metastable transformations i → pentagonal phases P1 and P2, a homogeneous lamellar structure (i + P1 + P2) or a polygrain i-phase is formed in the alloys. The P-h diagrams obtained upon nanoindentation, atomic force microscopy, and scanning electron microscopy of indentations have demonstrated signs of elasto-plastic deformation of the alloys with lamellar and polygrain icosahedral structures. It has been found that, in contrast to the polygrain icosahedral alloys with a normal size effect of nanoindentation, the alloys with a lamellar structure are characterized by a nonmonotonic dependence of the hardness (H) on the maximum load (P _max) and exhibit the effect of strain hardening in the range of loads 50 mN ≤ P _max < 500 mN. The strain hardening is considered as the result of resistance exerted by boundaries of the lamellar structure to the development of plastic deformation.     

Coercivity of anisotropic γ-Fe2O3 particles at high temperatures

The coercivity of five different samples of anisotropic γ-Fe₂O₃ particles is studied in the temperature range 0°–600°C. It is found that their relative coercive force h _c = H _c (T)/H _c (0) is almost a linear function of the relative magnetization of the particles m _s = M _s (T)/M _s (0), where H _c (0) and M _s (0) are the values of H _c and M _s of the particles at 0°C. It is experimentally found that h _c = βm _s + α, where β = 1.103 ± 0.015 and α = ?0.114 ± 0.009. This character of the dependence of h _c on m _s suggests that, at high temperatures, H _c of anisotropic γ-Fe₂O₃ particles can depend on both their shape anisotropy and other factors. It is assumed that, as the temperature increases, anisotropic γ-Fe₂O₃ particles in a zero magnetic field are divided into small structurally and magnetically unstable nanoclusters with magnetization spontaneously changing its direction. As a result, H _c disappears near the Curie temperature, although the saturation magnetization of the particles in a field of 1 T is still retained at this temperature.     

In-plane magnetization with high coercivity in terbium iron garnet thin films deposited on Pt/Si substrate by PLD

We report on the growth of terbium iron garnet (TbIG, Tb₃Fe₅O₁₂) thin films having anomalously large coercivity and in-plane easy axis of magnetization. The TbIG thin films were prepared at room temperature (RT) on Pt/Si(1 0 0) substrates by pulsed laser deposition technique. The films deposited at RT were X-ray amorphous and do not show any magnetic order. Annealing of the RT deposited film at 900 °C resulted into fully textured (532) TbIG film. Atomic force microscopy and cross-sectional scanning electron microscopy studies of the TbIG films showed good surface quality with an average surface roughness of 5.0 nm and thickness of about 300 nm, respectively. The M-H loops measured at 20 K for TbIG films, exhibit about an order of magnitude enhancement in the coercivity value (H_c) than the single crystal. In-plane and out-of-plane M-H loops revealed that the easy axis of the magnetization lies within the film’s plane. In-plane magnetization combining with large H_c value of the TbIG thin film may be of scientific interest for the possible applications.     

SU(3)×SU(2)×U(1) next-to-leading corrections for proton decay in the SU(5) model

We compute in the standard model of SU(3)^c×(SU(2)×U(1)) with massless quarks and leptons the two-loop anomalous dimensions of the four-fermion operators relevant to proton decay in process involving (u, d, e, ν_e). The calculation is carried out by the use of dimensional reduction, a variant of dimensional regularization. Our aim is to give a complete calculation within the SU(5) GUT model of the next-to-leading enhancement-suppression factor for nucleon decay due to renormalization effects arising from hard gluons, W's and B's in process which involve (u, d, e, ν_e). It turns out that the result is sensitive to the ratios x_(i) = M_{H (i)}/M_X where M_H(i) are the masses of the twelve superheavy Higgs scalars in the $\text{24}$ multiplet which breaks SU(5) → SU(3)×SU(2)×U(1).     

Anisotropy modulated stepwise magnetization in triangular Heisenberg antiferromagnet

During the course of tuning anisotropy from Ising type to zero, the variation of magnetization (M) steps against magnetic field (h) is investigated in a triangular antiferromagnetic Heisenberg model using Monte Carlo techniques. It is revealed that the anisotropy is an essential key to induce the temperature-dependent stepwise M(h) curve observed in frustrated magnetic system, and it can be employed to modulate this steplike magnetic behavior effectively. When the anisotropy is strengthened, a ground state transition occurs from the homogeneous 120° triangular structure to the collinear partially disordered antiferromagnetic state. No M step is detected in the system without anisotropy. But if the anisotropy is nonzero, the M₀/3 step (where M₀ is the saturated M) will emerge on M(h) curve, which is due to an h-induced quasi-collinear ferrimagnetic state. This M₀/3 step can be extended by increasing the anisotropy. When the M₀/3 plateau dominates the h-range broad enough, the equidistant metastable substeps, which originates from the disorders frozen in the frustrated collinear spin structure, appear to be superposed on the M₀/3 plateau. Thus the system with a strong anisotropy presents the whole temperature evolution of stepwise M(h) curve in quantitative agreement with the experiments of Ca₃Co₂O₆.     

Superparamagnetism and spin-glass like state for the MnFe2O4 nano-particles synthesized by the thermal decomposition method

MnFe₂O₄ nano-particles with an average size of about 7 nm were synthesized by the thermal decomposition method. Based on the magnetic hysteresis loops measured at different temperatures the temperature-dependent saturation magnetization (M_S) and coercivity (H_C) are determined. It is shown that above 20 K the temperature-dependence of the M_S and H_C indicates the magnetic behaviors in the single-domain nano-particles, while below 20 K, the change of the M_S and H_C indicates the freezing of the spin-glass like state on the surfaces. By measuring the magnetization–temperature (M–T) curves under the zero-field-cooling (ZFC) and field-cooling procedures at different applied fields, superparamagnetism behavior is also studied. Even though in the ZFC M–T curves peaks can be observed below 160 K, superparamagnetism does not appear until the temperature goes above 300 K, which is related with the strong inter-particle interaction.     

Microstructure and magnetic properties of Sn-substituted MnZn ferrites

Sn-substituted MnZn ferrites were prepared by conventional oxide ceramic process. The influences of Sn substitution on microstructure and magnetic properties of MnZn ferrites were investigated. The results indicated that with increase of Sn substitute concentration, the diffraction peaks shifted slightly towards the lower angles and the lattice parameter (a) increased. And at room temperature, the bulk density (d_m), initial permeability (μ_i), saturation magnetic induction (B_s) and electrical resistivity (ρ) of Sn-substituted MnZn ferrites all increased initially and then decreased with the further increase of Sn substitute concentration, while the power losses decreased first and then increased subsequently. Meanwhile, the temperature of secondary maximum peak of μ_i-T curve and the minimum losses moved to lower temperature while the Sn substitute concentration increased. When the content of Sn substitution was 0.3 mol%, at room temperature, the initial permeability, saturation magnetic induction, density and electrical resistivity reached their maxima, while the hysteresis loss (P_h), eddy current loss (P_e) and total losses (P_cv) achieved their minima. The P_h∼T and μ_i-T curves varied contrarily, and due to the contribution of extra eddy current loss (P_e,exc) that was proportional to P_h, the P_e-T curve did not agree with its classical expression. Finally, MnZn ferrite substituted with 0.3 mol% SnO₂ shows the highest initial permeability (3894) and lowest losses (303 kW/m³) at room temperature.     

Diffraction spectra of order–order transition structural states in titanium monoxide

A new class of M_(n?i)X_(n?i) superstructures (n is an integer constant and i is a rational variable) that are formed after incomplete equilibrium second-order order–order phase transitions in solid solutions and in compounds with atom–vacancy ordering is proposed. New superstructures are superpositions of partially disordered M _n ?X _n superstructures of various symmetries in the matrix of the basic crystal structure. The model parameters affecting the positions and intensities of superstructure reflections on diffraction patterns have been studied by example of the high-temperature ordered phase β-TiO of titanium monoxide. It has been shown that the diffraction spectra of the low-symmetric M_(5-i)X_(5-i) superstructure (space group P1m1) and the high-symmetric M₅X₅ superstructure (space group Pm3?m) at certain parameters are identical in the positions of superstructure reflections.     

Dynamics of the random field Ising model

Dynamics of the kinetic Ising model in the presence of static random fields is investigated using a self-consistent method. It is shown that if the interface fluctuations of the low temperature phase are small the system at low temperatures stays in a state without long range order. For this state the spin correlation function 〈S_q(t)S_?q(O)> averaged over all configurations of random fields decays exponentially in time with a single wavevector dependent relaxation time which is finite at the transition temperature T₀ and remains very long below T₀. In the mean field approximation the correlation time at the magnetic Bragg peak and at T₀ scales with the magnitude of the random field as τ∞h^?z_h with z_h = 1 for d = 2 and $\text{z}{}_{\mathrm{h}}\text{=}\text{4}\text{3}$ for d = 3, respectively.     

Low-energy impact of a heavy Higgs boson sector

The effective theory which characterizes the low-energy sensitivity of the minimal Weinberg-Salam model to a heavy Higgs boson sector is shown to be the gauged SU(2)_L × U(1) non-linear θ model. This theory is the limit of the Weinberg-Salam model as the Higgs boson mass, M_H, is removed (M_H → ∞). Using the symmetry properties of the non-linear theory, along with a power-counting analysis, we are able to classify low-energy observables according to their sensitivity to the regulator (M_H). At one loop, the greatest sensitivity is a logarithmic dependence on the Higgs boson mass. The M_H dependent corrections to some specific, experimentally accessible observables are calculated, and other possible applications of this technique are discussed.     

A DFT study the solvent effects of H2 adsorption on Cu(h k l) surface

Density functional theory (DFT) combined with conductor-like solvent model (COSMO) have been performed to study the solvent effects of H₂ adsorption on Cu(h k l) surface. The result shows H₂ can not be parallel adsorbed on Cu(h k l) surface in gas phase and only vertical adsorbed. At this moment, the binding energies are small and H₂ orientation with respect to Cu(h k l) surfaces is not a determining parameter. In liquid paraffin, when H₂ adsorbs vertically on Cu(h k l) surface, solvent effects not only influences the adsorptive stability, but also improves the ability of H₂ activation; When H₂ vertical adsorption on Cu(h k l) surface at 1/4 and 1/2 coverage, H-H bond is broken by solvent effects. However, no stable structures at 3/4 and 1 ML coverage are found, indicating that it is impossible to get H₂ parallel adsorption on Cu(h k l) surfaces at 3/4 and 1 ML coverages due to the repulsion between adsorbed H₂ molecules.     

Effect of Mn on the magnetic properties of Fe3B/Nd2Fe14B nanocomposites

The magnetic properties of Nd_4.5Fe_77−xMn_xB_18.5 (x=0, 1 and 2) nanocomposites prepared by the crystallization of amorphous precursors were investigated. Addition of Mn is found to decrease the crystallization temperature of the amorphous ribbons. The intrinsic coercivity _iH_c and maximum energy product (BH)_max increase from 2.6 kOe and 9.1 MGOe for x=0 to 3.1 kOe and 10.3 MGOe for x=1, respectively, and the remanence ratio M_r/M_s increases from 0.70 to 0.72. The effect of Mn on Curie temperature T_C and the thermal stability of M_r and _iH_c were also studied. ⁵⁷Fe Mössbauer spectra have been recorded for x=0, 1 and 2 ribbons at room temperature and site preference of the Mn atoms in Fe₃B and Nd₂Fe₁₄B phases is discussed using the Mössbauer spectroscopy.