Unified nonequilibrium dynamical theory for exchange bias and training effects

We have investigated the exchange bias and training effect in the ferromagnetic/antiferromagnetic (FM/AF) heterostructures using a unified Monte Carlo dynamical approach. The magnetization of the uncompensated AF layer is still open after the first field cycling is finished. Our simulated results show obvious shift of hysteresis loops (exchange bias) and cycling dependence of exchange bias (training effect) when the temperature is below 45~K. The exchange bias field decreases with decreasing cooling rate or increasing temperature and the number of the field cycling. Essentially, these two effects can be explained on the basis of the microscopical coexistence of both reversible and irreversible moment reversals of the AF domains. Our simulations are useful to understand the real magnetization dynamics of such magnetic heterostructures.     

Influence of magnetic field sweep rate on the hysteresis loops of Ni0.8Fe0.2/Fe0.5Mn0.5 exchange bias bilayer

The influence of the magnetic field sweep rate on the hysteresis loops of exchange bias Ni0.8Fe0.2/Fe0.5Mn0.5 bilayers has been investigated with a vibrating sample magnetometer. It was found that the sweep rate of 13.6 kA/4πms is high enough to bring about obvious changes in the hysteresis loops of the exchange bias bilayer. High sweep rate in the magnetization reversal stage enlarges the coercivity of the sample, while high sweep rate in the saturation state reduces the coercivity. The above phenomena were attributed to magnetic viscosity in the ferromagnetic layer enhanced by the interface exchange interaction and domain magnetization reversals assisted by thermal fluctuation in the antiferromagnetic layer respectively.     

Types of the jump phenomenon in the angular dependence of the noncollinear exchange bias

Based on the principle of minimal energy and the coherent rotation model, two types of the jump phenomena, complete and incomplete jump phenomenon, are proved to exist in the angular dependence of the exchange bias with noncollinear unidirectional and uniaxial anisotropies. It is found that the transition between complete and incomplete jump phenomena occurs on condition that the exchange-coupling constant exceeds a critical value. Additionally, two different modes of the magnetization rotation, the whole-plane rotation, and the half-plane rotation are present in the magnetization reversal process, and they are dependent on the direction of the external field. Furthermore, the equations of the critical angle, at which orientation the exchange bias field reaches a maximum value and the coercivity disappears, are also derived in this paper. The numerical calculations in this paper are consistent with the relevant experimental observations, indicating that our method to study the angular dependence of the exchange bias as well as the magnetization reversal behaviors is valid. Our discussion about the jump phenomenon, the critical angle, and the modes of the magnetization reversal can explain the observed differences in results between different experiments.     

The magnetization reversal behaviour for SmCo6.8Zr0.2 and SmCo6.8Zr0.2a-（Fe,Co） nanocrystalline magnets at low temperature

This paper reports that the SmCo6.8Zr0.2 nanocrystalline permanent magnets and SmCo6.8Zr0.2/a-（Fe,Co） nanocomposite permanent magnets are successfully produced by mechanical alloying and subsequently annealing at 700℃ for 10 minutes. The x-ray diffraction results show that the phase structure of SmCo6.8Zr0.2 nanocrystalline permanent magnets is composed of SmCo7 phase and SmCo6.8Zr0.2/a-（Fe,Co） nanocomposite permanent magnets is composed of SmCo7 and a-（Fe,Co） phases. The mechanism of magnetization reversal is mainly controlled by inhomogeneous domain wall pinning in SmCo6.8Zr0.2 and SmCo6.8Zr0.2/a-（Fe,Co） magnets. The inter-grain exchange interaction at low temperature is investigated, which shows that the inter-grain exchange interaction of SmCo6.8Zr0.2/a-（Fe,Co） magnets increases greatly by the decrease of the measured temperature. According to Amirr-H/Hcj, Amrev-H/Hcj and Xirr-H/Hcj curves at room temperature and 100 K, the changes of irreversible and reversible magnetization behaviours of SmCo6.8Zr0.2 and SmCo6.8Zr0.2/a-（Fe,Co） magnets with the decreasing temperature are analysed in detail. The magnetic viscosity and the activation volume of SmCo6.8Zr0.2 and SmCo6.8Zr0.2/a-（Fe,Co） magnets at different temperatures are also studied.     

The synthesis and exchange bias effect of monodisperse NiO nanocrystals

Monodisperse NiO nanocrystals with an average particle size of 3 ± 0.4 nm are successfully synthesized by the thermal decomposition of Ni-oleylamine complex in an organic solvent under a continuous O2 flux. The crystalline structure and the morphology of the product are investigated by X-ray diffraction, X-ray photoelectron spectroscopy, and transmission electron microscopy. Magnetization and alternating-current (ac) susceptibility measurements indicate that the structure of the particles can be considered as consisting of an antiferromagnetically ordered core and a spin-glass-like surface shell. In addition, both the exchange bias field and the vertical magnetization shift can be observed in this system at 10 K after field cooling. This observed exchange bias effect is explained in terms of the exchange interaction between the antiferromagnetic core and the spin-glass-like shell.     

Multiferroic properties and exchange bias in Bi1-xSrxFeO3 （x = 0-0.6） ceramics

Multiferroic properties and exchange bias(EB) in Bi1-xSrxFeO3(x = 0–0.6) ceramics synthesized by a modified Pechini method are investigated. Sr concentration dependence of structure distorting, ferroelectric properties, and dielectric properties were studied at room temperature. Appropriate Sr doping(x = 0.05–0.2) has been found to decrease the conductivity, enhance ferroelectric properties and give rise to high dielectric constant. Compared with antiferromagnetic BiFeO3 compound, BSFO-x(0 ≤ x ≤ 0.4) ceramics show weak ferromagnetism at room temperature, and their exchange bias field and vertical magnetization shift are observed and exhibit a strong dependence on the content of Sr. This observed EB effect which keeps stable in BSFO ceramics at 10 K tend to vanish at room temperature with Sr concentration over 0.4.     

Theoretical Investigation of Exchange Bias in Compensated Cases

The exchange bias （EB） of the ferromagnetic （FM）/antiferromagnetic （AFM） bilayers in a compensated case is studied by use of the many-body Green＇s function method of quantum statistical theory. The so-called compensated case is that there is no net magnetization on the AFM side of the interface. Our conclusion is that the EB in this case is primarily from the asymmetry of the interracial exchange coupling strengths between the FM and the two sublattices of the AFM. The effects of the layer thickness, temperature and the interracial coupling strength oi2 the exchange bias HE are investigated. The dependence of HE on the FM layer thickness and temperature is qualitatively in agreement with experimental results. HE is nearly inversely proportional to FM thickness. When temperature varies, both HE and He decrease with temperature increasing. The anisotropy of the FM layer only slightly influence He, but does not influence HE.     

Charge disproportionation induced exchange bias in La0.5Ca0.5FeO3-δ

We observed an exchange bias effect in La0.5Ca0.5FeO3 perovskite compound.The exchange bias is associated with the charge disproportionation transition from Fe4+ions to Fe3+and Fe5+ions below 175 K.The competition between the ferromagnetic interaction of Fe3+and Fe5+ions and the antiferromagnetic one of Fe3+and Fe3+ions results in a unidirectional anisotropy in the cluster-glass system.An antiferromagnetically interfacial exchange coupling constant Ji1.95 meV at the cluster-glass region was yielded by fitting the cooling field-dependence of the exchange bias field.     

The magnetization reversal behaviour for SmCo6.8Zr0.2 and SmCo6.8Zr0.2/α-（Fe,Co） nanocrystalline magnets at low temperature

This paper reports that the SmCo 6.8 Zr 0.2 nanocrystalline permanent magnets and SmCo 6.8 Zr 0.2 /α-(Fe,Co) nanocomposite permanent magnets are successfully produced by mechanical alloying and subsequently annealing at 700 C for 10 minutes.The x-ray diffraction results show that the phase structure of SmCo 6.8 Zr 0.2 nanocrystalline permanent magnets is composed of SmCo 7 phase and SmCo 6.8 Zr 0.2 /α-(Fe,Co) nanocomposite permanent magnets is composed of SmCo 7 and α-(Fe,Co) phases.The mechanism of magnetization reversal is mainly controlled by inhomogeneous domain wall pinning in SmCo 6.8 Zr 0.2 and SmCo 6.8 Zr 0.2 /α-(Fe,Co) magnets.The inter-grain exchange interaction at low temperature is investigated,which shows that the inter-grain exchange interaction of SmCo 6.8 Zr 0.2 /α-(Fe,Co) magnets increases greatly by the decrease of the measured temperature.According to Δm irr-H/H cj,Δm rev-H/H cj and χ irr-H/H cj curves at room temperature and 100 K,the changes of irreversible and reversible magnetization behaviours of SmCo 6.8 Zr 0.2 and SmCo 6.8 Zr 0.2 /α-(Fe,Co) magnets with the decreasing temperature are analysed in detail.The magnetic viscosity and the activation volume of SmCo 6.8 Zr 0.2 and SmCo 6.8 Zr 0.2 /α-(Fe,Co) magnets at different temperatures are also studied.     

Crystalline and Magnetic Enhancement of Nanocrystalline MnZn Ferrites Fabricated under a High Magnetic Field

Nanocrystalline Mn0.6Zn0.4Fe2O4 particles are synthesized under magnetic fields of O and 6 T, and their structural and magnetic properties are investigated. The magnetic field enhances the grain size and the lattice strain. Magnetic measurements show that the majority of the 6 T nanoparticles are superparamagnetic nearly from 40 to 300 K. It is interesting that the saturation magnetization of the 6 T sample is about 18% and 16% higher than that of the 0 T sample at 120 and 300K, respectively.     

The interplay between the lattice and magnetism in La(Fe_11.4Al_1.6)C_0.02 studied by powder neutron diffraction

The crystallographic structure and magnetic properties of La(Fe 11.4 Al 1.6 )C 0.02 are studied by magnetic measure- ment and powder neutron diffraction with temperature and applied magnetic field. Rietveld refinement shows that La(Fe 11.4 Al 1.6 )C 0.02 crystallizes into the cubic NaZn 13 -type with two different Fe sites: Fe I (8b) and Fe II (96i), and that Al atoms preferentially occupy the Fe II site. A ferromagnetic state can be induced at a medial temperature of 39 K–139 K by an external magnetic field of 0.7 T, and a large lattice is correspondingly found at 100 K and 0.7 T. In all other conditions, La(Fe 11.4 Al 1.6 )C 0.02 has no net magnetization in the paramagnetic (T > T N = 182 K) or antifer- romagnetic states, and thus keeps its small lattice. Analysis of the Fe–Fe bond length indicates that the ferromagnetic state prefers longer Fe–Fe distances.     

Magnetization relaxation of uniaxial anisotropic ferromagnetic particles with linear reaction dynamics driven by DC/AC magnetic field

The response of uniaxial anisotropic ferromagnetic particles with linear reaction dynamics subjected to alternating current(AC) or direct current(DC) bias magnetic field is evaluated by the reaction–diffusion equation for the probability distribution function of the molecular concentration in the spherical coordinate system. The magnetization function and the probability distribution function of the magnetic particles in the reaction system are derived by using the Legendre polynomials and Laplace transform. We discuss the characteristics of magnetization and probability distribution of the magnetic particles with different anisotropic parameters driven by a DC and AC magnetic fields, respectively. It is shown that both the magnetization and the probability distribution decrease with time increasing due to the reaction process. The uniformity of the probability distribution and the amplitude of the magnetization are both affected by the anisotropic parameters.Meanwhile, the difference between the case with linear reaction dynamics and the non-reaction case is discussed.     

Anisotropic and mutable magnetization in Kondo lattice CeSb_2

We have systematically studied the behaviors of the resistivity and magnetization of CeSb_2 single crystals as a function of temperature and external field. Four anomalies in the resistivity/magnetization-versus-temperature curves are observed at low magnetic field. They are located at 15.5 K, 11.5 K, 9.5 K, and 6.5 K, corresponding to the paramagnetic–magnetically ordered state(MO), MO-antiferromagnetic(AFM), AFM–AFM, and AFM–ferromagnetic(FM) transitions, respectively.The anomaly at 9.5 K is only visible with H‖[010] by magnetic susceptibility measurements, indicating that the AFM–AFM transition only happens along [010] direction in ab-plane. The four magnetic transitions are strongly suppressed by high external field. Finally, the field-temperature phase diagrams of CeSb_2 with different orientations of the applied field in ab-plane are constructed and indicate the highly anisotropic nature of the magnetization of CeSb_2.     

Sm3（F3,Co,Mn）29 compounds：promising materials for permanent magnets

The outstanding hard-magnetic properties are reported of Sm_3Fe_{28.1-x}Co_xMo_{0.9} compounds with x=12, 14, 16. In this alloy system, only a small amount of Mo is needed to stabilize the 3:29 structure so that the magnetic properties are not seriously affected by the presence of this nonmagnetic element. Substitution of Co for Fe leads to a significant increase of the magnetic anisotropy, and for x≥14 the easy magnetization direction changes from easy plane to the easy axis. In this alloy system, the compound Sm_3Fe_{12.1}Co_{16}Mo_{0.9} is a very promising candidate for permanent magnet applications. Its room temperature saturation magnetization (μ_0M_s=1.5 T) and anisotropy field (B_{an}=6.5 T) are comparable to the values for Nd_2Fe_{14}B (μ_0M_s=1.6 T and B_{an}=7 T). However, the Curie temperature of Sm_3Fe_{12.1}Co_{16}Mo_{0.9} is 1020 K, which is appreciably higher than that for Nd_2Fe_{14}B (T_C=588 K).     

Structural and magnetic properties of BiFe_(1-x)Cr_xO_3 synthesized samples

Chromium doping effects on the structure and the magnetic properties of bismuth ferrite BiFe1-xCrxO3 （x = 0-0.3） （BFCxO） polycrystalline samples are examined. The Perovskite-type oxide samples are synthesized by the conventional solid state reaction at a high pressure of 7 GPa and a temperature of 1273 K. The X-ray powder diffraction patterns at room temperature show that all the samples with x = 0.0-0.3 are described by the rhombohedral structure. In the meantime, it is revealed that the doping of Cr can induce noticeable lattice distortions in the doping samples, and the largest distortion is observed in the case x = 0.1. The magnetic hysteresis loops measured at room temperature exhibit week ferromagnetic behaviors of the samples and the magnetization is found to increase with the increase in Cr concentration. The temperature- dependent magnetization curves indicate antiferromagnetic features in samples. Moreover, Cr-doping tends to reduce the ordering temperature.     

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.     

Magnetic phase transition and the corresponding magnetostriction of intermetallic compounds RMnsGe2（R=Sm,Gd）

The temperature dependence of lattice constants a and c of intermetallic compounds RMn₂Ge₂ (R=Sm, Gd) is measured in the temperature range 10－800K by using the x-ray diffraction method. The magnetoelastic anomalies of lattice constants are found at the different kinds of spontaneous magnetic transitions. The transversal and longitudinal magnetostrictions of polycrystalline samples are measured in the pulse magnetic field up to 25T. In the external magnetic field there occurs a first-order field-induced antiferromagnetism－ferromagnetism transition in the Mn sublattice, which gives rise to a large magnetostriction. The magnitude of magnetostrictions is as large as 10^-3. The transversal and longitudinal magnetostrictions have the same sign and are almost equal. This indicates that the magnetostriction is isotropic and mainly caused by the interlayer Mn－Mn exchange interaction. The experimental results are explained in the framework of a two-sublattice ferrimagnet with the negative exchange interaction in one of the sublattices by taking into account the lattice constant dependence of interlayer Mn－Mn exchange interaction.     

Coexistence of positive and negative magnetic entropy changes in CeMn_2(Si_(1-x)Ge_x)_2 compounds

A series of CeMn2(Si1-xGex)2(x = 0.2, 0.4, 0.6, 0.8) compounds are prepared by the arc-melting method. All the samples primarily crystallize in the Th Cr2Si2-type structure. The temperature dependences of zero-field-cooled(ZFC) and FC magnetization measurements show a transition from antiferromagnetic(AFM) state to ferromagnetic(FM) state at room temperature with the increase of the Ge concentration. For x = 0.4, the sample exhibits two kinds of phase transitions with increasing temperature: from AFM to FM and from FM to paramagnetic(PM) at around TN~197 K and T C~300 K,respectively. The corresponding Arrott curves indicate that the AFM–FM transition is of first-order character and the FM–PM transition is of second-order character. Meanwhile, the coexistence of positive and negative magnetic entropy changes can be observed, which are corresponding to the AFM–FM and FM–PM transitions, respectively.     

Transformation behaviors,structural and magnetic characteristics of Ni-Mn-Ga films on MgO （001）

Ferromagnetic Ni-Mn-Ga films were fabricated by depositing on MgO （001） substrates at temperatures from 673 K to 923 K. Microstructure, crystal structure, martensitic transformation behavior, and magnetic properties of the films were studied. With increasing deposition temperature, the surface morphology of the films transforms from granular to continu- ous. The martensitic transformation temperature is not dependent on deposition temperature; while transformation behavior is affected substantially by deposition temperature. X-ray analysis reveals that the film deposited at 873 K has a 7M marten- site phase, and its magnetization curve provides a typical step-increase, indicating the occurrence of magnetically induced reorientation （MIR）. In situ magnetic domain structure observation on the film deposited at 873 K reflects that the marten- sitic transformation could be divided into two periods： nucleation and growth, in the form of stripe domains. The MIR occurs at the temperature at which martensitic transformation starts, and the switching field increases with the decrease of temperature due to damped thermal activation. The magnetically induced martensitic transformation is related to the difference of magnetization between martensite and austenite. A shift of martensite temperature of dT/dH = 0.43 K/T is observed, consistent with the theoretical value, 0.41 K/T.     

The interplay between the lattice and magnetism in La（Fe11.4Al1.6）C0.02 studied by powder neutron diffraction

The crystallographic structure and magnetic properties of La（Fell.4Alz.6）C0.02 are studied by magnetic measurernent and powder neutron diffraction with temperature and applied magnetic field. Rietveld refinement shows that La（Fe11.4Al1.6）C0.02 crystallizes into the cubic NaZn13-type with two different Fe sites： FeI （8b） and FeII （96i）, and that A1 atoms preferentially occupy the FeII site. A ferromagnetic state can he induced at a medial temperature of 39 K-139 K by an external magnetic field of 0.7 T, and a large lattice is correspondingly found at 100 K and 0.7 T. In all other conditions, La（Fe11.4Al1.6）C0.02 has no net magnetization in the paramagnetic （T 〉 TN = 182 K） or antifer- romagnetic states, and thus keeps its small lattice. Analysis of the Fe Fe bond length indicates that the ferromagnetic state prefers longer Fe-Fe distances.