The exchange bias and coercivity of FM/AFM films: Monte Carlo simulation

The exchange bias (H_E) and coercivity (H_C) of the ferromagnet/antiferromagnet (FM/AFM) films have been simulated with Monte Carlo method. The simulated results indicate that, the value of H_E decreases with increasing temperature, and the values of H_E and the blocking temperature T_b at which H_E=0 reduce evidently with decreasing absolute value of interlayer exchange coupling JI. It also is found that for the large absolute values of JI, the maximum in H_C occurs very close to T_b. At the same time, it is observed that the diluted ratio of FM at FM/AFM interface influences clearly the value of H_E. The simulated results are consistent with the experimental facts. The maximum behaviour in the H_C−T curves has been explained by the interplay of the softening of some fraction of the spins in the AFM layer near T_N′ and the disorder of the spins in FM layer near Curie temperature T_C.     

Thickness dependence of positive exchange bias in ferromagnetic/antiferromagnetic bilayers

For the ferromagnetic (FM)/antiferromagnetic (AFM) bilayers, both negative and positive exchange bias H_E have been observed for low and high cooling field H_CF, respectively. The thickness dependence of H_E and coercivity H_C have been investigated for the cases of negative and positive H_E. It is found that the negative H_E and the positive one have similar FM thickness dependence that is attributed to the interfacial nature of exchange bias. However, the AFM thickness dependence of positive H_E is completely contrary to that of the negative one, which clearly demonstrates that the AFM spins play different roles for the cases of positive and negative H_E. In particular, the AFM thickness of positive H_E was first highlighted by an AFM spin canting model. These results should be attributed to the interfacial spin configuration after field cooling procedure.     

Peculiarities of the magnetic,galvanomagnetic, elastic,and magnetoelastic properties of Sm<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript>x</Subscript>MnO<Subscript>3</Subscript> manganites

Manganites of the Sm1?xSr_xMnO₃ system (x=0.33, 0.4, and 0.45) possess giant negative values of the magnetoresistance Δρ/ρ and the volume magnetostriction ω near the Curie temperature T_C. In the compound with x=0.33, the isotherms of Δρ/ρ, ω, and magnetization σ exhibit smooth variation and do not reach saturation up to maximum magnetic field strengths (120 kOe) studied (according to the neutron diffraction data, this substance comprises a ferromagnetic (FM) matrix with distributed clusters of a layered antiferromagnetic (AFM) structure of the A type). In the compounds with x=0.4 and 0.45 containing, besides the FM matrix and A-type AFM phase, a charge-ordered AFM phase of the CE type (thermally stable to higher temperatures as compared to the A-type AFM and the FM phases), the same isotherms measured at T ≥ T_C show a jumplike increase in the interval of field strengths between H_c1 and H_c2 and then reach saturation. In the interval H_c1 > H > H_c2, the σ, ω, and Δρ/ρ values exhibit a metastable behavior. At temperatures above T_C, the anisotropic magnetostriction changes sign, which is indicative of rearrangements in the crystal structure. The giant values of ω and Δρ/ρ observed at T ≥ T_C for all compounds, together with excess (relative to the linear) thermal expansion and a maximum on the ρ(T) curve, are explained by the phenomenon of electron phase separation caused by a strong s-d exchange. The giant values of magnetoresistance and volume magnetostriction (with ω reaching ～10^?3) are attributed to an increase in the volume of the FM phase induced by the applied magnetic field. In the compound with x=0.33, this increase proceeds smoothly as the FM phase grows through the FM layers in the A-type AFM phase. In the compounds with x=0.4 and 0.45, the FM phase volume increases at the expense of the charge-ordered CE-type AFM structure (in which spins of the neighboring manganese ions possess an AFM order). The jumps observed on the σ(H) curves, whereby the magnetization σ reaches ～70% of the value at T=1.5 K, are indicative of a threshold character of the charge-ordered phase transition to the FM state. Thus, the giant values of ω and Δρ/ρ are inherent in the FM state, appearing as a result of the magnetic-field-induced transition of the charge-ordered phase to the FM state, rather than being caused by melting of this phase.     

Magnetic phase transitions of antiperovskite Mn3−xFexSnC (0.5≤x≤1.3)

The magnetization and electrical resistivity of Mn_3−xFe_xSnC (0.5≤x≤1.3) were measured to investigate the behavior of the complicated magnetic phase transitions and electronic transport properties from 5 to 300 K. The results obtained demonstrate that Fe doping at the Mn sites of Mn₃SnC induces a more complicated magnetic phase transition than that in its parent phase Mn₃SnC from a paramagnetic (PM) state to a ferrimagnetic (FI) state consisting of antiferromagnetic (AFM) and ferromagnetic (FM) components, while, with the change of Fe-doped content and magnetic field, there is a competition between the AFM component and FM component in the FI state. Both the Curie temperature (T_C) and the saturated magnetization M_s increase with increasing x. The FM component region becomes broader with further increasing Fe-doped content x. The external magnetic field easily creates a saturated FM state (and increased T_C) when . Fe doping quenches the negative thermal expansion (NTE) behavior from 200 to 250 K reported in Mn₃SnC.     

Observation of mixed-phase behavior in the Mn-doped cobaltite La0.7Sr0.3Co1−xMnxO3 (x=0-0.5)

Studies on La_0.7Sr_0.3Co_1−xMn_xO₃ (x=0-0.5) compounds evidence that the interaction between Mn and Co ions in this system is antiferromagnetic super-exchange and not ferromagnetic (FM) double-exchange (DE). As a result, antiferromagnetism and magnetic glassiness develop steadily with increasing Mn content and the system becomes a spin glass at x∼0.1. Analyses of high-field magnetization data indicate that the system consists of two major phases: a metallic FM phase which magnetically saturates in rather low field, and an insulating non-FM phase which has a linear dependence of magnetization on magnetic field. In the low doping regime, the fraction of the non-FM component expands with temperature at the expense of the FM phase and becomes maximal at T_C. Ferromagnetism reappears in highly doped (x≥0.2) compounds due to the presence of DE interaction between the Mn ions. The small volume fraction of the FM phase derived from the M(H) data in high-field region supports the coexistence of insulating and FM behaviors in the highly doped samples.     

Exchange bias in bulk Ni-Mn-In-based Heusler alloys

The crystal structure and exchange bias of the bulk Heusler alloys Ni₅₀Mn_50−xIn_x with 14.5?x?15.2 have been investigated using X-ray diffraction and magnetization measurements, respectively. Magnetic measurements were performed with SQUID magnetometry after samples were zero-field cooled and field cooled (FC) in positive magnetic fields up to H=50 kOe, from a temperature T=380 K. Three temperatures of the phase transitions, T₁<T_M<T_C, and a shift of the FC (50 kOe) magnetic hysteresis loops up to 120 Oe at 5 K have been detected for all samples. The exchange bias field (H_E) was almost constant for intermediate In concentrations 14.8<x<15.2, and sharply decreased to about 20 Oe on the borders of this concentration interval (x?14.5; 15.2?x). The changes of H_E have been related to changes in the ratio of T₁ to T_M: the overlapping of transitions at T₁ and T_M (for x=14.8, and 15.2) results in a decrease in H_E.     

Fine structure of the field-induced magnetic transition in Nd0.1La0.9Fe11.5Al1.5

For the Nd_0.1La_0.9Fe_11.5Al_1.5 compound, the fine structure of the magnetic transition from the ferromagnetic (FM) to the antiferromagnetic (AFM) states has been studied carefully by means of magnetization (M) and heat capacity (C_p) measurements. Although a single phase with the cubic NaZn₁₃-type structure (Fm3c) has been proved by the room temperature X-ray diffraction pattern, the phase transition has been clearly found to be a stepwise process in M(T) and C_p(T) curves under proper fields. Due to the strong competition between the FM order and AFM order, the characteristic is especially evident under low fields, weakens gradually with the increasing applied field and finally vanishes when the field is higher than 2 T. This multi-step magnetic transition results from the inhomogeneity of the sample, probably due to the inhomogeneous distribution of Nd atoms.     

Electron mass enhancement and magnetic phase separation near the Mott transition in double-layer ruthenates

We present a detailed investigation of the specific heat of Ca₃(Ru_1-xM_x)₂O₇ (M = Ti, Fe, Mn) single crystals. Depending on the dopant and doping level, three distinct regions are present: a quasitwo-dimensional metallic state with antiferromagnetic (AFM) order formed by ferromagnetic bilayers (AFM-b), a Mott insulating state with G-type AFM order (G-AFM), and a localized state with a mixed AFM-b and G-AFM phase. Our specific heat data provide deep insights into the Mott transitions induced by Ti and Mn doping. We observed not only an anomalous large mass enhancement, but also an additional term in the specific heat, i.e., C ∝ T², in the localized region. The C ∝ T² term is most likely due to long-wavelength excitations with both FM and AFM components. A decrease in the Debye temperature is observed in the G-type AFM region, indicating lattice softening associated with the Mott transition.     

Theoretical investigation of exchange bias

The exchange bias of bilayer magnetic films consisting of ferromagnetic (FM) and antiferromagnetic (AFM) layers in an uncompensated case is studied by use of the many-body Green's function method of quantum statistical theory. The effects of the layer thickness and temperature and the interfacial coupling strength on the exchange bias H_E are investigated. The dependence of the exchange bias H_E on the FM layer thickness and temperature is qualitatively in agreement with experimental results. When temperature varies, both the coercivity H_C and H_E decrease with the temperature increasing. For each FM thickness, there exists a least AFM thickness in which the exchange bias occurs, which is called pinning thickness.     

Ferromagnetic/antiferromagnetic exchange coupling in SrFe<Subscript>12</Subscript>O<Subscript>19</Subscript>/CoO composites

The surface of SrFe₁₂O₁₉ coated with a CoO layer reveals a strong exchange bias characterized by magnetic hysteresis loops. The low-temperature coercivity, H_C, and the squareness, M_R/M_S, of a permanent magnet of SrFe₁₂O₁₉/CoO powder prepared by the sol–gel method are enhanced after field cooling through the Néel temperature (T_N=290 K) when compared to those after zero-field cooling. The existence of loop shifts and the enhancement of H_C indicate that exchange-bias effects, which are induced by the ferromagnetic/antiferromagnetic (FM/AFM) exchange-coupling interactions, are responsible for these behaviors. According to our experimental results, some of the factors controlling the exchange bias, such as FM/AFM interfaces and the CoO amount of the antiferromagnetic layer, are discussed. PACS 75.30.Et; 75.50.Ee; 75.60.Ej; 75.60.Gm; 75.70.Cn     

Charge order melting and magnetic transition in Nd0.5(1+x)Ca0.5(1−x)Mn(1−x)CrxO3 system

The magnetic property of double doped manganite Nd_0.5(1+x)Ca_0.5(1−x)Mn_(1−x)Cr_xO₃ with a fixed ratio of Mn³⁺:Mn⁴⁺=1:1 has been investigated. For the undoped sample, it undergoes one transition from charge disordering to charge ordering (CO) associated with paramagnetic (PM)-antiferromagnetic (AFM) phase transition at T<250 K. The long range AFM ordering seems to form at 35 K, rather than previously reported 150 K. At low temperature, an asymmetrical M-H hysteresis loop occurs due to weak AFM coupling. For the doped samples, the substitution of Cr³⁺ for Mn³⁺ ions causes the increase of magnetization and the rise of T_c. As the Cr³⁺ concentration increases, the CO domain gradually becomes smaller and the CO melting process emerges. At low temperature, the FM superexchange interaction between Mn³⁺ and Cr³⁺ ions causes a magnetic upturn, namely, the second FM phase transition.     

Anisotropy dispersion in (CoCrPt)1−x(SiO2)x perpendicular recording media

The distribution of easy axis orientation in perpendicular media is of technological importance because it affects the value of S^* (see Fig. 1), which quantifies the switching field distribution (SFD) and hence partially determines the data density achievable on a given medium. The distribution is controlled by the crystallographic orientation of grains and factors such as intergranular exchange and dipolar coupling. Due to strong demagnetising fields in the perpendicular orientation, traditional measurements of remanence as a function of angle are difficult to interpret and have required the use of large-scale computational models. In this work we have utilised the variation of coercivity H_C with angle, which has the advantage that at H_C the global demagnetising field is zero. Additionally, since such materials follow essentially the Stoner–Wohlfarth mode of reversal, the variation of H_C with angle, H_C(θ), is much greater than that for the remanence. We find that for (CoCrPt)_1−x(SiO₂)_x, where the level of exchange coupling is controlled, the distribution of magnetic easy axes is narrower when the exchange coupling is reduced, but dipolar coupling between the grains is strong and affects the magnetisation reversal significantly.     

Geometry of multidimensional universes

LetG be a compact group of transformation (global symmetry group) of a manifoldE (multidimensional universe) with all orbits of the same type (one stratum). We studyG invariant metrics onE and show that there is one-to-one correspondence between those metrics and triples (g _μv,A _μ ^ä ,h _αβ), whereg _μv is a (pseudo-) Riemannian metric on the space of orbits (space-time),A _μ ^ä is a Yang-Mills field for the gauge groupN|H, whereN is the normalizer of the isotropy groupH inG, andh _αβ are certain scalar fields characterizing geometry of the orbits (internal spaces). The scalar curvature ofE is expressed in terms of the component fields onM. Examples and model building recipes are also given. The results generalize those of non-abelian Kaluza-Klein theories to the case where internal spaces are not necessarily group manifolds.     

Possible nonanalytic behavior of Ising models in random fields

The magnetization, M, of dilute Ising ferromagnets with quenched random fields is shown to have accumulation points of poles in each of these fields h_i(at h_i → 0) and in the external uniform field H (at H → -h_i). This occurs for all temperatures for which the nonrandom (zero-field) system has H ≠ 0. If both h_i and -h_i are possible then M is probably nonanalyti c for many values of h_i. This casts doubts on expansions in the random fields.     

The magnetism for NN AFM ground state in Fe-based superconductor: Sr1−xKxFe2As2

The crystal structure, magnetism properties, and density of states for FeAs layered compound SrFe₂As₂ have been investigated by using the density functional theory (DFT) method. The magnetism under a checkerboard nearest neighbor anti-ferromagnetic (NN AFM) and ferromagnetic (FM) order ground-state have been analyzed with substitution for Sr with K ion in Sr_1−xK_xFe₂As₂. The results indicate that the distortion of FeAs tetrahedrons is sensitive to the electron doping concentration. The system magnetism was suppressed by K doping in NN-AFM ground state instead of FM. The density of states at Fermi level N(E_F) under NN AFM ground state would be regarded as a driving force for the increased T_c of Sr_1−xK_xFe₂As₂ system as observed experimentally. Our calculation reflects that NN AFM type spin fluctuation may still exist in the Sr_1−xK_xFe₂As₂ system and it may be an origin of strong spin fluctuation in this system besides the spin density wave (SDW) states.     

Farbzentren rhombischer und monokliner Symmetrien in NaF

A number of zero-phonon absorption lines ofF aggregate color centers is studied inx-irradiated NaF crystals under uniaxial stress. The color centers associated with the lines are found to exhibit rhombic (D_2h, D₂, C_2v; rotation axes along 〈110〉 and 〈100〉) and monoclinic (C_2h, C₂, C_s; rotation axis along 〈110〉) symmetries. The transitions of the rhombic color centers correspond to 〈100〉 and 〈110〉 dipoles, those of the monoclinic centers to 〈112〉 and 〈110〉 dipoles. The most prominent line at 5803 Å is due to a 〈112〉 dipole transition within a monoclinic color center. Several models of centers are discussed.     

Spin rotations in HoxEr1−xFe2 cubic laves compounds

The temperature dependence of the elastic moduli and the Mössbauer effect in Ho_x,Er_1?x, Fe₂ cubic Laves compounds (x, between 0.3 and 0.9) has been investigated in the temperature region where spin rotation occurs. The composition-dependence minima in the elastic moduli, and the Mössbauer effect measurements, were used to determine the boundaries between the various directions of easy magnetization in these compounds. The experimental spin orientation diagram was found to deviate from the predictions of a one-ion model based on the rare-earth ions alone. From the Mössbauer effect measurement it was deduced that in compounds for which a spin reorientation was observed, the spin rotates continuously with temperature between the major axes of the cubic symmetry. This was attributed to the contribution of higher-order magnetocrystalline anisotropy constants. The ΔE effect, measured in external magnetic fields up to 25 kOe, was found to be constant, and relatively small, in the holmium composition range of x = 0.45–1.00 in the Ho_xEr_1?xFe₂; compounds.     

Dimensionality of a system of exchange-coupled grains and magnetic properties of nanocrystalline and amorphous ferromagnets

Characteristics of random magnetic anisotropy in ferromagnetic films of amorphous Co₉₀P₁₀ and nanocrystalline Ni₇₅C₂₅, Fe₈₀B₄C₁₆, and Co₈₀C²⁰ alloys and also in multilayer films [Co₉₃P₇(x)/Pd(14 Å)]₂₀ and [Co₉₀P₁₀(x)/Pd(14 Å)]₂₀ obtained by various technological procedures were studied experimentally. It was found that the spatial dimensionality (d) of the system of ferromagnetically coupled grains (2R _c ) in the materials under study determined the exponent in the power dependence of the approach of magnetization to saturation in the region of fields H<2A/MR _c ² . The dependence ΔM～H ^?1/2 was observed for nanocrystalline and amorphous films with a three-dimensional grain arrangement. The approach to saturation in multilayer films with a two-dimensional grain arrangement in an individual magnetic layer follows the law ΔM～H ^?1. The main micromagnetic characteristics of random anisotropy, such as the ferromagnetic correlation radius R _f and the average anisotropy 〈K〉 of a ferromagnetic domain with a size of 2R _f , were determined for multilayer Co/Pd films. Correlation was found between the coercive field and these characteristics of random anisotropy.     

On the field dependence of the interface energy in AF/FM bilayers

In the investigations of antiferromagnetic (AF)/ferromagnetic (FM) bilayer samples, often distinct experimental techniques yield different values for the measured exchange anisotropy field (H_E). We propose that the observed discrepancy may be accounted in part by the dependence of the unidirectional anisotropy with the value of the externally applied cooling field (h). Using a simple microscopic model for representing the AF/FM interface, which incorporates the effect of interface roughness, we show that the interface energy between the AF and FM layer indeed varies with h, as recently observed in anisotropic magnetoresistance measurements, lending support to our proposal.     

Structure and magnetization studies of Nd0.5−xPrxSr0.5MnO3 system

The structural and magnetic properties of Nd_0.5−xPr_xSr_0.5MnO₃ (x=0, 0.1, 0.2, 0.3, 0.4 and 0.5) system have been investigated. With the substitution of Pr in Nd_0.5Sr_0.5MnO₃, it shows a gradual structure transformation from the Imma orthorhombic symmetry to the tetragonal I4/mcm phase, and the crystallographic transition remains incomplete, even in Pr_0.5Sr_0.5MnO₃. A large bifurcation between zero-field-cooled (ZFC) and field-cooled (FC) susceptibility has been observed below Curie temperature (T_C), which is characteristic of coexistence of ferromagnetism (FM) and antiferromagnetism (AFM) at low temperature region. The magnetization of Pr_0.5Sr_0.5MnO₃ is larger than that of Nd_0.5Sr_0.5MnO₃, while Nd_0.5Sr_0.5MnO₃ with more CE-type AFM shows larger magnetization than Nd_0.3Pr_0.2Sr_0.5MnO_3, which mixed with CE-type (majority) and A-type (minority) AFM at low temperature, indicating that the magnetization of Nd_0.5−xPr_xSr_0.5MnO₃ system is affected by A-site disorder combined with orbital ordering of A-type AFM and CE-type AFM.