Uniaxial Term Research Articles

Magnetic anisotropies and dispersion relation of epitaxial Fe/InAs(001) films

Magneto-transport effects investigated for the application in some hybrid structures need also a careful magnetic characterization. In our studies the angular dependence of the uniform mode excited in ferromagnetic resonance was measured at various frequencies for epitaxially grown Fe films on a semiconducting InAs(001) substrate. The results enable a precise determination of the magnetic anisotropies in this system. A large out-of-plane twofold anisotropy (K 2⊥=2.8×10 6 erg/ cm 3) and an in-plane fourfold anisotropy (K 4∥=0.51×10 6 erg/ cm 3) were found. The latter appeared to be modulated by a small uniaxial term with the easy axis rotated by 45° with respect to the [100] direction, the easy axis of the fourfold anisotropy. Based on multi-frequency measurements the dispersion relation has been verified, i.e. the resonance field versus the microwave frequency has been plotted and compared with calculations.

Interplay between Anisotropic Strain Relaxation and Uniaxial Interface Magnetic Anisotropy in Epitaxial Fe Films on (001) GaAs

Grazing incidence x-ray diffraction study of Fe epitaxial ultrathin films (1.5-13 nm) on GaAs (001) reveals an anisotropy of both domain shape and strain, with [110] and [1-10] as the principal directions. It is shown that the observed thickness-dependent strain anisotropy, together with a uniaxial interface term, can provide an unambiguous explanation to the usual in-plane magnetic anisotropy and its thickness dependence observed in this magnetic thin-film system.

Scaling Hysteresis of Dynamical Transition in Dilute Heisenberg Spin Systems

The Monte Carlo method was employed to perform a numerical simulation for a classical discrete diluted Heisenberg spin system driven by an oscillating external magnetic field. To form the diluted spin system based on the isotropic Heisenberg model, we introduced in the Hamiltonian of the typical Heisenberg model both a random uniaxial anisotropy energy term characterizing an amorphous state with a proportion X and a deterministic uniaxial or triaxial anisotropy energy term representing a crystalline state with a proportion 1—X as balance. The dynamical transitional behavior of the diluted spin system mentioned above, i.e. the hysteresis loop scaled against parameter X and random uniaxial as well as deterministic uniaxial/triaxial anisotropy constants D and A, respectively, was studied in detail. For the first time, a scaling formula correlating the hysteresis loop area Aarea with the parameters X, A, and D has been put forward by us as Aarea ∼ AδDηXσ. The main conclusions are summarized in the following: (i) At a specific value X (defined as Xmin), the investigated spin system gains the minimal hysteresis, which has been supported experimentally in another part of our investigation. (ii) The scaling exponents δ, η, and σ of the diluted spin system are constants independent of the lattice size, the frequency, the amplitude of the driving field, and the temperature of system. The sum of exponents δ + η (≈0.9) of the diluted spin system equals the exponents δ, η of a single either deterministic uniaxial/triaxial or random uniaxial anisotropy spin system. (iii) The specific value Xmin versus the logarithm of the ratio A/D shows a peculiar sigmoidal trend.

Large in-plane anisotropies in Co/Re superlattices: What’s happening at the interface?

We have performed magnetization and 36 GHz ferromagnetic resonance measurements as a function of in-plane angle and Co layer thickness in order to determine the interface anisotropies in epitaxial hcp (101̄0) Co(x)/Re(1.2 nm) superlattices (1.0 nm<x<3.5 nm), whose Co c axis lies in the film plane. The linear dependence of magnetization upon inverse Co layer thickness indicates the bulk of the Co layer has a magnetization of 1390 emu/cm3, and nonmagnetic Co within 0.5 nm of each Re interface. The angular variation in the resonance position yields out-of-plane, and first and second order uniaxial in-plane anisotropies. These coefficients are plotted as a function of the inverse magnetic Co layer thickness (1/tCo), yeilding their interface and volume contributions. The volume out-of-plane term is 10.7×106 erg/cm3, which compares favorably with the 12.3×106 erg/cm3 expected from shape anisotropy. Despite the c axis being in plane, a significant out-of-plane interface energy of −0.074 erg/cm2 was detected, which favors out-of-plane magnetization. The first order uniaxial in-plane term is independent of tCo. Its average value of 1.2×106 erg/cm3 is a factor of 4 smaller than that observed in macroscopic Co. The second order in-plane uniaxial term does vary linearly with 1/tCo, yielding volume and interface contributions of 1.3×105 erg/cm3 (a factor of 10 smaller than that observed in macroscopic Co and −7×10−4 erg/cm2, respectively).

Electron spin resonance aboveTCin layered manganites

We have performed electron spin resonance (ESR) and dc magnetization measurements on single crystals of La{sub 2(1-x)}Sr{sub 1+2x}Mn{sub 2}O{sub 7} up to 800 K with special emphasis on the x=0.4 composition. The ESR linewidth shows behavior similar to that observed in the three-dimensional perovskites and above -500 K can be described by a universal expression {Delta}H{sub pp}(T)=[C/T{sub x}(T)]{Delta}H{sub pp}({sup {infinity}}). The linewidth and the resonance field become anisotropic below -500 K. The anisotropy in the resonance field is proportional to the magnetization M, and we concluded that it is intrinsic to the system. We show that demagnetization effects can explain only part of the anisotropy. The remainder arises from short-range uniaxial terms in the Hamiltonian that are associated with the crystal field and Dzialozhinsky-Moriya interactions. The anisotropy in the linewidth is attributed to the easy-plane ferromagnetic ordering, which also arises from the short-range anisotropy.

SCALING HYSTERESIS OF DYNAMICAL TRANSITION OF DILUTED HEISENBERG SPIN SYSTEM 

The Monte Carlo method was employed to perform the numerical simulation for classical discrete diluted Heisenberg spin system driven by an oscillating external magnetic field. To form the diluted spin system based on isotropic Heisenberg model, we introduced in the Hamiltonian of a typical Heisenberg model both random anisotropy energy term characterizing amorphous state with a proportion X and uniaxial anisotropy energy term representing crystalline state with a proportion 1-X. The dynamical transition behavior of the Spin system mentioned above, hysteresis loop scaled with parameter X and random as well as uniaxial anisotropy constant D and A, respectively, was studied in detail. It has been put forward a scaling relationship between hysteresis loop area and parameter X, A and D as below: Aarea-AδDηXσ . The main conclusions can be summarized below:(1)At a specific value X(defined as Xmin), the investigated system gains minimal hysteresis which has been proved experimentally in our another investigation. (2) The exponents δ,η and σ of the diluted spin system are universal constants, and the sum of δ+η(～0.9) equals the exponent δ,η of single either uniaxial or random anisotropy spin system. (3)The specific value Xmin versus logarithm of the ratio of A/D shows a peculiar sigmoidal trend.

Angular dependence of characteristic fields in spin-valves

Spin-valves are commonly characterised by a series of representative field values such as the coercivity of the magnetic layers, the exchange bias field and the interlayer coupling field. As the angle of an applied field is varied, these values have been observed to vary as periodic functions containing many high order harmonic terms. We analyse the magnetic behaviour of a spin-valve in terms of an extended Stoner–Wohlfarth model, and show that only the fundamental terms are necessary in the free energy of the system for these complex angular dependences to arise. We present illustrative data for spin-valve multilayer films. The complex angular dependences are seen to arise when the unidirectional and uniaxial energy terms are of comparable size, as in the free layer of a weakly coupled spin-valve.

In-plane magnetic anisotropies in Fe films on vicinal Ag(001) and Au(001) surfaces

In-plane fourfold and uniaxial magnetic anisotropies were studied in Fe films epitaxially grown on vicinal Ag(001) and Au(001) surfaces, which were prepared by molecular beam epitaxy on miscut GaAs(001) substrates. The effective fourfold and uniaxial anisotropy constants, K1eff and Kueff, which are determined from magnetisation curves measured with the magneto-optic Kerr effect, are linear functions of the inverse Fe layer thickness. The fourfold anisotropy shows a rotation of the easy and hard axes by 45° below a critical thickness of 6–7 ML. The uniaxial term is mainly an interface contribution. We find that the orientation of the uniaxial easy axis depends on the Fe thickness. In thinner films (tFe⩽20 ML) it is oriented perpendicular to the step edges, i.e., parallel to Fe[100]. This excludes shape anisotropy as the main mechanism. Above a critical thickness the uniaxial easy axis is aligned parallel to the step edges, i.e., along Fe[010]. This step-induced uniaxial anisotropy may be due to modified electronic states and to strain from the large vertical misfit at the steps.

Magnetic films epitaxially grown on semiconductors

Future ‘magneto-electronics’ exploiting the spin of the electron in addition to its charge will require the injection of spin-polarized electrons from a ferromagnetic metal into a semiconductor. To this purpose an attempt has been made in the present study to avoid the formation of a non-magnetic interface phase or ‘magnetically dead layers’ which have been found in the past in Fe films epitaxially grown on GaAs(0 0 1). Fe(0 0 1) films were grown by molecular beam epitaxy and magnetron sputtering on As depleted GaAs(0 0 1) surfaces held at room temperature. Very good epitaxial growth is achieved by both deposition methods. MBE grown ultrathin films show an enhanced ground state net magnetization and the full bulk magnetic moments at the Fe/GaAs interface in contrast to previous reports. This might be an important step towards semiconductor devices using spin polarized electron transport. The in-plane magnetic anisotropy of the films generally consists of a fourfold and a uniaxial term. At 7 monolayer thickness only a strong uniaxial contribution is observed which is supposed to result from the intrinsic anisotropy of the dangling bonds at the GaAs(0 0 1) surface. This could also be a useful property for future memory or switching applications.

An ESR study on amorphous NiFe films

Amorphous Ni 90Fel 10 alloy films with thickness 500 Å and 2000 Å deposited on quartz substrates by flash evaporation method have been studied by electron spin resonance (ESR) technique at x-band. The ESR spectra were taken as a function of both temperature and the applied magnetic field whose direction was varied from normal to parallel with respect to the film plane. The field derivative absorption line mainly consists of two major peaks for the thicker film and only a single major peak for the thinner one. The spectra have been analyzed by using the classical spin wave resonance (SWR) theory and the magnetic parameters of the system have been deduced. The surface anisotropy energy with uniaxial and biaxial terms have been used to simulate the experimental spectra. It has been found that noncrystalline nature of the sample considerably effects the magnetic behavior. The exchange stiffness constant was found to be seriously reduced compared to those of the polycrystalline films in the literature. However with room temperature aging, this value has increased visibly. Surface anisotropy has been determined to have an easy-plane character.

Epitaxial structure and magnetic anisotropies of metastable single crystal Co0.70Mn0.30 film

Alloy films of Co0.70Mn0.30 were grown on GaAs (001) substrates by molecular beam epitaxy at room temperature. The metastable tetragonally distorted single crystal structure was confirmed by reflection high energy electron diffraction and x-ray diffraction measurement, which exhibited a 2.87 Å in-plane lattice parameter. Ferromagnetic resonance measurements and theoretical fitting were performed and showed that, with a Mn capping layer, a uni-directional anisotropy existed. In addition, a fourfold tetragonal magnetocrystalline anisotropy as well as a uniaxial term in the film plane was also confirmed. The hysteresis loops recorded by longitudinal magneto-optical Kerr-effect also demonstrated the existence of different kinds of in-plane magnetic anisotropy. The origins of the anisotropy are explained tentatively.

EPR study of tetragonal and monoclinic Fe3+ centres in Rb2ZnF4 crystals

EPR measurements have been made on tetragonal and monoclinic Fe3+ centres in Rb2ZnF4 at room temperatures. The fine-structure terms for the monoclinic centre are separated into uniaxial and cubic terms for comparison with the Fe3+-VK centre in KZnF3 and for the uncompensated tetragonal centre. The monoclinic centre is ascribed to a Fe3+ ion associated with the nearest Rb+ vacancy and the principal z-axis is found to be 7 degrees from the (001)-axis in the opposite direction to that of the Rb+ vacancy. Rudowicz's NCC parameters for the monoclinic Fe3+ and Cr3+ centres are examined in relation to the separation of the spin-Hamiltonians. The calculated metal-ligand distances and deviation angles for the front and back fluorines by Newman's superposition model are in good agreement with, respectively, the distances for the uncompensated centre and angles for the Fe3+-VK centre in KZnF3 determined from 19F-ENDOR measurements. The relationships between the bnm and the axial and cubic parameters obtained by the superposition model are similar to those obtained from the spin-Hamiltonian separation.

EPR Study of Tetragonal and Orthorhombic Fe3+Centres in Rb2CdF4Crystals

EPR measurements for the substitutional Fe 3+ ions in layered perovskite-type Rb 2 CdF 4 crystals have been made at room temperatures using a X-band spectrometer. A tetragonal spectrum is ascribed to an uncompensated Fe 3+ centre. An orthorhombic spectrum is analysed by separating the fine structure terms into uniaxial terms and a cubic one. Obtained uniaxial parameters are well compared to those for the other tetragonal Fe 3+ centres. By the analysis, the orthorhombic centre is ascribed to a Fe 3+ ion associated with a nearest-Cd 2+ vacancy. The fine structure parameters are analysed further by the Newman's superposition model to obtain metal-ligand distances. Results are discussed together with those for the Cr 3+ and Gd 3+ centres in A 2 MF 4 crystals.

Effect of uniaxial KU term in magnetocrystalline anisotropy energy on magnetoelectric polarization in low temperature phase of magnetite (Fe 3O 4)

Phenomenological theory of the magnetoelectric effect is applied to the monoclinic magnetic anisotropy energy, which procedure makes clear the effect of the K u term in the energy on magnetoelectric polarization. Based on this elucidation, a possible interpretation is proposed for the anomaly observed below 10 K in the temperature dependence of magnetoelectric polarization of magnetite.

Magnetic Properties of Synthetic Analogues of the Altered Olivines of Igneous Rocks

SUMMARY A laboratory simulation has been made of the high temperature deuteric alteration of olivine such as occurs in slowly cooled basic intrusions. Three compositions in the Forsterite/ Fayalite solid solution series were synthesized by a three-firing method using self buffering and controlled atmosphere to obtain material containing no detectable magnetite (Fe,O,) as a contaminant (<0.005 per cent). The prepared olivines were oxidized between 850 and 1280°C at oxygen fugacities of between lo-”.’ and lop5.’ atmospheres. The composition and concentration of the multiphase oxidation products were studied by magnetic, optical, electron optical and X-ray methods. The magnetic constituent of the intergrowth was magnetite. Below about 1150 “C the microstructure is similar to the ‘dendritic’ intergrowths found, for example, in the altered olivine of the Central Layered Intrusion of the Isle of Rhum. Above about 1150 “C the form may be similar to ‘symplectite’ intergrowths. The magnetization process parameters (coercive force, etc.) vary systematically with temperature of oxidation ( To,) which evidently controls the microstructure of the magnetite. The magnetite produced is magnetically ‘hard’, samples altered at 900 “C and 950 “C having higher coercive force (Hc) than any magnetite reported in the literature. The room temperature properties appear to bridge the published trends found in ‘grown crystal’ magnetites and ‘crushed grains’. Inferred effective grain sizes of the complex intergrowths range from 0.1 to 3 pm as To, increases from 900 to 1200 “C. The temperature dependence of magnetization process parameters (principally H,) measured between room temperature and the Curie point are modelled in terms of (i) monodomain grains subject to thermal fluctuations, (ii) monodomain grains not subject to thermal fluctuations, and (iii) as multidomain grains. Model (i) yields plausible values for effective grain dimensions and length/diameter ratios, higher To, producing larger, more equidimensional particles. Model (ii) suggests that the relative importance of cubic and uniaxial anisotropies may be influenced by a microstructure-dependent uniaxial particle-particle interaction term. Model (iii) implies that, if domain walls are pinned by both surface and volume defects, magnetostriction plays a greater role in volume pinning than in surface pinning. Plausible values of demagnetizing factors appropriate to grains with few domains are produced by model (iii).

Short and long term behaviour of ferrocement subjected to uniaxial tension

The behaviour of ferrocement elements subjected to uniaxial long term tension is presented. Based on the results of experiments, deformations of ferrocement under short term and long term load are compared. It is shown that in ferrocement during long term loading the number of micro-cracks of crack width 20 to 100 μm is constant.

Electron Paramagnetic Resonance of Gd3+Centres in Rb2CdF4and Cs2CdF4Crystals

EPR measurements on three kinds of Gd 3+ centres in Rb 2 CdF 4 and Cs 2 CdF 4 crystals co-doped with Li + and Na + ions have been made at room temperatures. For the Cd 2+ -vacancy associated centre and the Li + -associated centre, the fine structure terms with orthorhombic symmetry have been separated into uniaxial terms about the crystalline c and b axes and cubic terms. The separated axial parameters have been compared with the axial parameters for the uncompensated centres in the same crystals and the corresponding tetragonal centres in the perovskite crystals. The expressions for the parameters derived by the separation of spin-Hamiltonian terms are coincident with those derived by the superposition model for the local environments of Gd 3+ ions with radial deviation of ligands. The relation of the separation method to the Rudowicz's net charge compensation model has been shown.

EPR Study of Cr3+Centres in Rb2ZnF4, Rb2CdF4and Cs2CdF4Crystals

Results of EPR measurements on Cr 3+ centres in Rb 2 ZnF 4 , Rb 2 CdF 4 and Cs 2 CdF 4 are reported for crystals co-doped with Li + ions. Due to charge compensation some of Cr 3+ ions are associated with a cation vacancy (V M ) or a Li + ion at the nearest divalent-cation site in the c -plane. The fine structure parameters D and E are interpreted by two uniaxial spin-Hamiltonian terms along the c -axis of the host crystal and along the direction of the Cr 3+ –V M or Cr 3+ –Li + pair. The validity of this interpretation is discussed by the superposition model.

Macroscopic anisotropy in transition-metal spin-glass alloys

The nature of the macroscopic anisotropy in a classical Ruderman-Kittel-Kasuya-Yosida (RKKY) spin-glass with weak Dzyaloshinskii-Moriya interactions is studied in a zero-temperature numerical simulation. For rigid rotations of the spin system from a metastable state, we find the expected unidirectional form for the anisotropy energy. Simulations of rotation and inversion of the magnetization by a magnetic field show nearly rigid rotations of the spin system if the anisotropy energy is much smaller than the RKKY energy. For stronger anisotropy, we find substantial deviations from rigidity, especially for large-angle rotations and inversions, resulting in a behavior characteristic of an anisotropy energy with both unidirectional and uniaxial terms. The simulations qualitatively reproduce several features observed in hysteresis and torque experiments.

On the obliqueness of the easy axis in collinear antiferromagnetic FeTiO 3

Magnetic structure of highly anisotropic antiferromagnet FeTiO 3 has been reexamined with a single crystal sample by neutron diffraction. In contrast with the previous report for a powder sample, the magnetic moment direction was found to be slightly oblique away from the hexagonal c -axis on keeping the collinear two sublattice structure which is described by alternating up and down spin layers. The oblique angle was determined to be (2.2 ± 0.2)°. The origin of the obliqueness can be explained by the existence of an anisotropy term which has the easy plane form in addition to the uniaxial term in the Hamiltonian.