Magnetic properties of Y-type trigonal ferrites first-order magnetization processes in trigonal systems

Magnetic properties of the single crystal ferrite Ba₂(Zn_1-xCo_x)₂Fe₁₂O₂₂ with O ? x ? 1, which has a trigonal symmetry around the c-axis, were investigated. The presence of Co ion strongly affects the properties of the Y-type ferrite: easy cone of magnetization, spin reorientation phase transition and first-order magnetization processes (FOMP) have been observed in this system. The observed effects as well as the origin of the magnetocrystalline anisotropy are discussed on the basis of a phenomenological analysis. The anisotropy constants K₁, K₂ and K_t trigonal of the ferrite are given versus temperature and composition. The magnetic phase diagram of a trigonal system is also presented. The condition for the existence of FOMP are obtained in term of the anisotropy constants ratios.     

Magnetic anisotropy,first-order phase transition,and Brown’s paradox in rare-earth metals

The anomalous behavior of magnetization curves (first-order magnetization process, FOMP) of highly anisotropic rare-earth metal compounds was studied. It is pointed out that FOMP assignment to a large contribution from higher magnetic anisotropy constants K_i comes into conflict with the point-ion approximation of crystal field theory. An alternative interpretation based on the multisublattice model is proposed; this model makes use only of first-order sublattice constants k_j derived from independent experimental NMR data. Direct calculations provide a satisfactory explanation of the FOMP in Tb₂Fe₁₇. A possible connection of the FOMP with Brown’s paradox in the theory of domain structure and coercive force is proposed.     

Micromagnetic studies for bit patterned media above 2 Tbit/in.

Bit patterned media (BPM) recording is a candidate for extremely high density magnetic recording. A micromagnetic model is built up to analyze the phase diagram of the correct-write-in condition in BPM above 2 Tb/in.² fabricated by lithography or ion irradiation methods. The target of the study is to acquire the relationship between the recording performance and the magnetic properties of the media. The medium includes the polycrystalline grains and grain boundary. In BPM fabricated by lithography with FCT structure, two phase diagrams of the correct-write-in condition are found for the anisotropy angular distribution Δθ, the ratio of tetragonal anisotropy K₂₂ to uniaxial anisotropy K₁ and the uniaxial anisotropy distribution ΔK₁. In BPM fabricated by ion irradiation methods, two phase diagrams of the correct-write-in condition are analyzed for the ratio of saturation magnetization M′_s/M_s, anisotropy field H′_k/H_k and the exchange field H′_ex/H_ex in the ion irradiated region and the bit islands.     

Theoretical prediction of a surface-induced spin-reorientation phase transition in BaFe<Subscript>12</Subscript>O<Subscript>19</Subscript> nanocrystals

The equation of the magnetization of a hexagonal crystal is derived for the first time for an arbitrary orientation of the external magnetic field relative to the crystallographic c axis. In order to clarify the magnetization mechanism for a real ensemble of small particles in the framework of the given problem, surface anisotropy (which is significant for nanosize objects) was taken into account along with crystalline magnetic anisotropy and anisotropy in the particle shape. Model computer experiments prove that the magnetization curves for nanocrystals oriented in a polar angle range of 65–90° exhibit an anomaly in the form of a jump, indicating a first-order spin-reorientation phase transition. This explains a larger steepness of the experimental curve reconstructed taking into account the interaction between particles as compared to the theoretical dependence obtained by Stoner and Wohlfarth [IEEE Trans. Magn. MAG 27 (4), 3469 (1991)]. An analysis of variation of the characteristic anisotropy surface and its cross section with increasing ratio |K₂|/K₁ of the crystalline magnetic anisotropy constants upon a transition from a macroscopic to a nanoscopic crystal shows that surface anisotropy leads to a change in the magnetic structure. As a result, an additional easy magnetization direction emerges in the basal plane apart from the easiest magnetization direction (along the c axis). The direction of hard magnetization emerges from the basal plane, the angle of its orientation relative to the c axis being a function of the ratio | K₂|/K₁.     

Influence of anisotropy constants of higher order on the magnetic reversal of uniaxial magnets

Within the framework of a simple model in which only homogeneous states of magnetization are considered, the influence of the constants of magnetic crystallographic anisotropy of higher order on the critical field of domain formation and the hysteresis loops of uniaxial magnets is investigated. It is shown that the critical field depends strongly on both the sign of K₁ and on the ratio of the magnitudes and signs of K₂/K₁ and K₃/K₁. On the basis of stability analysis for the free energy, hysteresis loops of uniaxial magnets as a function of K_i are calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 39–43, April, 1990.     

Surface demagnetizing field as a source of uniaxial surface anisotropy in GdCoMo thin amorphous films

Surface magnetic anisotropy energy was studied for (Gd_0.26Co_0.74)_0.96Mo_0.04 and (Gd_0.29Co_0.71)_0.96Mo_0.04 thin amorphous films by means of microwave spectroscopy at the X-band within the temperature range 4–295 K. Excitations of surface spin waves were observed in the spin wave resonance spectra. The experiment was performed in a rotating external magnetic field. The angular dependence of the resonance field for the uniform mode (spin wave vector k=0) and the surface mode made it possible to determine the surface uniaxial anisotropy constant K_s and its temperature dependence. An inhomogeneity of the saturation magnetization M_s within a close-to-surface layer of thickness d can generate the surface anisotropy energy with anisotropy constant K_s given by the formula: K_s=4πM^b_s (M^b_s−M^surf_s)d, where the indexes b and surf correspond to the bulk and surface values, respectively. The temperature dependence of K_s calculated by means of the formula agrees qualitatively with temperature dependence of K_s found in the experiment.     

Anisotropy and dynamic properties of Co2MnGe Heusler thin films

Co₂MnGe films of 30 and 50 nm in thickness were grown by RF-sputtering. Their magnetic anisotropies, dynamic properties and the different excited spin wave modes have been studied using conventional ferromagnetic resonance (FMR) and Microstrip line FMR (MS-FMR). From the in-plane and the out-of-plane resonance field values, the effective magnetization (4πM_eff) and the g-factor are deduced. These values are then used to fit the in-plane angular-dependence of the uniform precession mode and the field-dependence of the resonance frequency of the uniform mode and the first perpendicular standing spin wave to determine the in-plane uniaxial, the four-fold anisotropy fields, the exchange stiffness constant and the magnetization at saturation. The samples exhibit a clear predominant four-fold magnetic anisotropy besides a smaller uniaxial anisotropy. This uniaxial anisotropy is most probably induced by the growth conditions.     

Effect of hydrogenation on spin-reorientation phase transitions and magnetic anisotropy constants of RFe11Ti single crystals (R=Lu, Ho, and Er)

The magnetic anisotropy and spin-reorientation phase transitions in single crystals of the RFe₁₁Ti (R=Lu, Ho, and Er) compounds and their hydrides are investigated. Measurements are carried out on capacitance and torque magnetometers. The magnetic anisotropy constants K ₁ and K ₂ are determined by the mathematical processing of experimental magnetization curves in terms of the phenomenological theory of the anisotropic ferromagnet magnetization. It is demonstrated that the hydrogenation strongly affects the magnitude and the sign of magnetic anisotropy constants, as well as the spin-reorientation phase transitions. The hydrogenation of the HoFe₁₁Ti compound leads to the change in sign of the magnetic anisotropy constant K ₁. The inference is made that a change in the atomic volume and the axial ratio c/a cannot result in the observed effects. A change in the magnetic anisotropy constants upon hydrogenation is primarily due to the change in the interaction of the quadrupole moment of a 4f electron subshell of rare-earth ions with surrounding ions of the crystal lattice and also with valence and conduction electrons.     

Anisotropy and FOMP in Tb3 (Fe28−xCox) V1.0 (x=0, 3 and 6) compounds

In this work, the structural and magnetic properties of Tb₃ (Fe_28−xCo_x) V_1.0 (x=0, 3, 6) compounds have been investigated. The structural characterization of compounds by X-ray powder diffraction is an evidence for a monoclinic Nd₃(Fe, Ti)₂₉-type structure (A2/m space group). The refined lattice parameters a and b (but not c) and the unit cell volume V, obtained from the XRD data by the Rietveld method, are found to decrease with increasing Co concentration. The unit cell parameters behavior has been attributed to the smaller Co atoms and a preferential substitution of Fe by Co. The anisotropy field (H_a) as well as critical field (H_cr) was measured using the singular point detection (SPD) technique from 5 to 300 K in a pulsed magnetic field of up to 30 T. At T=5 K, a FOMP of type 2 was observed for all samples and persists at all temperatures up to 300 K. For sample x=0, H_cr=10.6 and 2.0 T at 5 and 300 K, respectively, is equal to that reported earlier. The occurrence of canting angles between the magnetic sublattices during the magnetization process instead of high-order anisotropy contributions (at room temperature are usually negligible) has been considered to explain the survival of the FOMP at room temperature. The anisotropy and critical fields behave differently for samples with x=0, 3 compared with x=6. The observed behavior has been related to the fact that the Co substitution for Fe takes place with a preferential entrance in the inequivalent crystallographic sites of the 3:29 structure. The contribution of the Tb-sublattice in the Tb₃(Fe, V)₂₉ compound with uniaxial anisotropy has been scaled from the anisotropy field measured on a Y₃(Fe, V)₂₉ single crystal with easy plane anisotropy.     

Properties of amorphous CoZr(RE) (RE=Gd,Sm, Dy) films with various uniaxial anisotropies,prepared by a new process

If a DC magnetic field is applied parallel to the plane of amorphous CoZr(RE) thin films during sputter depositing, a uniaxial anisotropy is formed the direction of which depends upon the choice of RE substituted and its concentration. When RE=Gd a perpendicular anisotropy K_p forms over a large concentration range, a spin reorientation process being at the origin of the process. A well-defined K_p is developed also in CoFeZrGd and CoZrGdSm films. CoZrGdDy films exhibit simultaneously a perpendicular and an in-plane uniaxial anisotropy. The related magnetization process and domain structures are quite peculiar.     

Magnetic anisotropy of the VBO<Subscript>3</Subscript> and CrBO<Subscript>3</Subscript> transition-metal borates

Temperature and field dependences of the magnetization of VBO₃ and CrBO₃ single crystals with the magnetic field applied parallel and perpendicular to the (111) basal plane were measured. VBO₃ was found to have a considerable uniaxial anisotropy with a field H_a≈6.25 T. CrBO₃ was shown to exhibit not only uniaxial but also hexagonal anisotropy. The experimental anisotropy constants were estimated, and their temperature dependences are presented.     

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.     

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.     

2-D magnetism

Influence of the spatial dimensionality on magnetic ordering phenomena has been discussed. Recent work on ideal 2 dimensional magnets like Rb₂FeF₄, Rb₂MnF₄, K₂NiF₄, Rb₂Mn_xMg_1-x and K₂CuF₄, K₂Cu_xZn_{1 -x}F₄, MnSt₂ possessing planar antiferro- and ferromagnetism, respectively, has been reviewed with a view to doing planar anisotropy calculations based on the reportedly common orthorhombic structures. Existence of easy axes, easy cones in the plane and first order magnetisation processes (FOMP) in the plane and out of plane in the presence of applied magnetic field can be predicted. The results have been presented in the graphical forms as well.     

Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.     

Investigation of the magnetic properties and magnetic structure parameters of nanocrystalline Fe<Subscript>79</Subscript>Zr<Subscript>10</Subscript>N<Subscript>11</Subscript> films

The magnetic properties (magnetization curve, ferromagnetic resonance spectrum) of nanocrystalline Fe₇₉Zr₁₀N₁₁ films obtained by RF magnetron sputtering with subsequent annealing were studied experimentally, along with the fundamental magnetic constants of these films (saturation magnetization M _S, local magnetic anisotropy energy K, and the exchange coupling constant A). The magnetic properties are discussed within the random magnetic model, which determines the correlation of the magnetic properties with the fundamental magnetic constants and nanostructure parameters (grain size, magnetic anisotropy, and correlation radius R _C). The exchange correlation length 2R _L for the film magnetic microstructure was determined by correlation magnetometry.     

Magnetic properties of CdSb doped with Ni

Magnetic properties of the group II–V semiconductor CdSb single crystals doped with Ni (2 at%) are investigated. Deviation of the zero-field-cooled susceptibility, χ_ZFC, from the field-cooled susceptibility is observed below 300 K, along with a broad maximum of χ_ZFC (T) at T_b in fields below the anisotropy field B_K∼4 kG. T_b(B) obeys the law [T_b(B)/T_b(0)]^1/2=1–B/B_K with T_b(0)∼100 K. The magnetization exhibits saturation above ∼20–30 kG, a weak temperature dependence and anisotropy of the saturation value M_s. The coercive field is much smaller then B_K and displays anisotropy inverted with respect to that of M_s. Such magnetic behavior is expected for spheroidal Ni-rich Ni_1−xSb_x nanoparticles with high aspect ratio, broad distribution of the sizes and with orientations of the major axis distributed around a preferred direction.     

Complete magnetizing field relating with magnetization reversal dynamics

We report the experimental finding that a complete magnetizing field H_M exists in magnetization reversal dynamics of ferromagnetic thin films, which is much larger than the apparent magnetic saturation field measured from the major hysteresis loop. Magnetization reversal dynamics contrastingly changes from nucleation dominated to wall-motion dominated according to an initial magnetization state magnetized by a field below H_M, whereas it is basically unchanged when the field is larger than H_M. The complete magnetizing field is found to be 1.5–2.0 times larger than the apparent magnetic saturation field and 6–10 times smaller than the anisotropy field in Co/Pd multilayer thin films.     

Determination of the in-plane anisotropy field in hexagonal systems via rotational magnetization: Theoretical model and Monte Carlo simulations

The magnetic anisotropy field in thin films with in-plane uniaxial anisotropy can be deduced from the VSM magnetization curves measured in magnetic fields of constant magnitudes. This offers a new possibility of applying rotational magnetization curves to determine the first- and second-order anisotropy constant in these films. In this paper we report a theoretical derivation of rotational magnetization curve in hexagonal crystal system with easy-plane anisotropy based on the principle of the minimum total energy. This model is applied to calculate and analyze the rotational magnetization process for magnetic spherical particles with hexagonal easy-plane anisotropy when rotating the external magnetic field in the basal plane. The theoretical calculations are consistent with Monte Carlo simulation results. It is found that to well reproduce experimental curves, the effect of coercive force on the magnetization reversal process should be fully considered when the intensity of the external field is much weaker than that of the anisotropy field. Our research proves that the rotational magnetization curve from VSM measurement provides an effective access to analyze the in-plane anisotropy constant K ₃ in hexagonal compounds, and the suitable experimental condition to measure K ₃ is met when the ratio of the magnitude of the external field to that of the anisotropy field is around 0.2. Supported by the National Natural Science Foundation of China (Grant Nos. 90505007 and 10774061) Recommended by LI FaShen