Thickness dependence of the magnetic anisotropy of Fe layers separated by Al

Magnetic multilayers of ⁵⁷Fe with nominal thickness, T _nom, between 0.4 and 1.0 nm separated by 3.0 nm Al spacer layers were prepared by alternate deposition of the constituents in high vacuum. The samples were investigated at 4.2 K in external magnetic field. A fraction of Fe atoms corresponding to about 0.3 nm equivalent Fe-thickness was found to mix into the Al spacer. The extremely strong magnetic anisotropy observed for T _nom < 0.8 nm is attributed to Fe layers of approximately two atomic planes thick. The anisotropy decreases considerably after the building up of the third Fe atomic layer starts at T _nom = 0.8 nm, but full saturation was not achieved even for T _nom = 1 nm and 3 T magnetic field applied perpendicularly to the sample plane.     

Anisotropy of the upper critical field and specific heat in V3Si — a superconductor with cubic symmetry

The specific heat of a V₃Si single crystal (T _c=17 K, H _c2=20 T) in magnetic fields up to 8 T isinvestigated experimentally for three orientations of the field relative to the crystallographic directions — H∥〈001〉, H∥〈110〉, and H∥〈111〉. Both the upper critical magnetic field and the specific heat of the mixed state are observed to depend on the orientation of the magnetic field relative to the crystallographic directions (anisotropy): The critical field reaches its maximum value and the specific heat its minimum value in a field along the 〈001〉 direction. The anisotropy scale in both phenomena increases as the magnetic field and reaches 3% in a 6 T field. The interrelationship of the upper critical field anisotropy and the specific-heat anisotropy in type-II superconductors is studied. It is shown that the anisotropy of the specific heat in the mixed state in weak fields can serve as a criterion for nontrivial pairing. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 26–29 (10 January 1999)     

Theory of stripe domains in magnetic shape memory alloys

The evolution of multivariant patterns in thin plates of magnetic shape memory materials with an applied magnetic field was studied theoretically. A geometrical domain-model is considered composed of straight stripe-like martensite variants with constant internal magnetization (high anisotropy limit) and magnetic domain wall orientation fixed by the twin boundaries. Through integral transforms of the demagnetization energy, the micromagnetic energy is cast into a form convenient for direct numerical evaluation and analytical calculations. The equilibrium geometrical parameters of multivariant patterns with straight and oblique twin boundaries have been derived as functions of the applied field and the material parameters of a plate. It is shown that the oblique multivariant states exist only in plates with thicknesses L larger than a certain critical value L₀. In samples with L<L₀ a magnetic-field-driven transformation occurs directly between single variant states.     

Giant strain associated with microstructure control by magnetic field in Fe-31.2Pd, CoO and Nd0.5Sr0.5MnO3

We have made in situ optical microscope observation for the microstructure control driven by magnetic field in Fe-31.2Pd (at%), CoO and Nd_0.5Sr_0.5MnO₃. These materials exhibit structural transitions, and their low-temperature phases are composed of several crystallographic domains (variants), which are separated by twinning planes. In the case of ferromagnetic Fe-31.2Pd and antiferromagnetic CoO, the magnetic field promotes the twinning plane movement. This movement gives a large strain of several percent and is essentially explained by the fact that the magnetic shear stress, which corresponds to the magnetic anisotropy energy divided by the twinning shear, is larger than the twinning stress. In the case of Nd_0.5Sr_0.5MnO₃, the twinned microstructure of the charge-ordered phase disappears under a magnetic field in association with the melting of the charge-ordered phase.     

Structural and magnetic phases of Bi<Subscript>1−x</Subscript>A<Subscript>x</Subscript>FeO<Subscript>3−</Subscript><Subscript>δ</Subscript> (A = Sr,Pb) perovskites

The Bi_1−xA_xFeO_{3− δ} (A = Sr, Pb) systems have been studied using the X-ray, neutron powder diffraction and magnetization measurements in a magnetic field up to 14 T. It was found that around x ∼ 0.06 the crystal symmetry changes from a rhombohedral (space group R3c) to pseudo-tetragonal. In the composition range 0.07 ≤ x ≤ 0.14 the phases with different symmetry of the unit cell coexist independent of synthesis conditions. The neutron powder diffraction shows that the iron ions have average oxidation state close to 3+. The magnetic structure for Bi_0.5Sr_0.5FeO_{3− δ} is found to be G-type antiferromagnetic with magnetic moment of about 3.8 μ_B/Fe³⁺. The weak ferromagnetic state due to magnetoelectric interactions was revealed in the lightly doped rhombohedrally distorted compositions. No evidence for a spontaneous magnetization was observed for the pseudo-tetragonal phases. These compositions show irreversible nonlinear magnetization vs. field behavior apparently due to small local deviations from the collinearity of the magnetic moments.     

Anisotropic magnetic exchange in orthorhombic RCu2 compounds (R = rare earth)

The magnetic excitations in the field induced ferromagnetic phase F3 of a NdCu₂ single crystal were investigated by means of inelastic neutron scattering experiments. A mean field model using the random phase approximation in connection with anisotropic magnetic bilinear R-R (R denotes a rare earth) exchange interactions is proposed to account for the observed dispersion. The relevance of this model to the analysis of the magnetic ordering process in other RCu₂ compounds is discussed. Received 21 April 1999     

Magnetostructural transition in NdCu2

The magnetic (H , T)-phase diagram of the orthorhombic compound NdCu₂ was investigated for external magnetic fields up to 15 T parallel to the crystallographic c-direction. Magnetization and magnetostriction measurements reveal an anomalous change of the magnetic properties as well as giant magnetostriction (GMS) and large hysteretic effects. This behaviour is similar to that observed in some other RCu₂ compounds where it has been interpreted as a conversion of the magnetic Ising axis. In contrast to these other RCu₂ compounds, however, the easy axis of magnetization in NdCu₂ is the b-axis. The macroscopic measurements are compared with neutron diffraction experiments which reveal GMS along the b-axis and a new magnetic phase with propagation vector in the converted crystal. Received 27 March 2000 and Received in final form 11 September 2000     

Shape of the ferromagnetic resonance absorption band of textured powder samples of maghemite

The shape of the ferromagnetic resonance absorption band of powder microcrystalline ferrite γ-Fe₂O₃ has been studied. Samples in the form of a ferromagnetic fluid have been subjected to preliminary particle orientation and frozen in a magnetic field. The shape of the absorption bands has been computer processed with allowance for the anisotropy of the shape of particles and their spatial cubic anisotropy, as well as for the contribution from nondispersed fraction of the bulk of the powder. Satisfactory agreement with the experiment has been obtained for several orientations of the measuring magnetic field with respect to the preliminary orientation.     

Frustration driven magnetic states of A-site spinels probed by <Emphasis Type="Italic">μ</Emphasis>SR

The normal A-site spinels MnAl₂O₄, FeAl₂O₄, CoAl₂O₄, as well as related mixed (Mn_0.5Fe_0.5Al₂O₄) and partially inverted (Fe_1.4Al_1.6O₄) spinels have been studied by μSR. The magnetic ions are subject to magnetic frustration by competing interactions. In all materials and at all temperatures the μSR spectra consist of two signals suggesting a bimodal distribution of the fluctuation rates of magnetic moments. A characteristic temperature T _M is found in each compound, representing either a magnetic phase transition into a long-range ordered state (MnAl₂O₄, Fe_1.4Al_1.6O₄) or the formation of a spin liquid phase (FeAl₂O₄, CoAl₂O₄, Mn_0.5Fe_0.5Al₂O₄). The magnetic ground state of MnAl₂O₄ shows coexistence of antiferromagnetic and spin liquid phases. In FeAl₂O₄ and CoAl₂O₄ long-range order is suppressed altogether, the ground state can be characterized as a fast relaxing spin liquid coexisting with a small fraction of paramagnetic spins. The partial replacement of Mn by Fe in Mn_0.5Fe_0.5Al₂O₄ prevents long-range order and leads to a spin liquid state in the low temperature limit. The partial occupancy of B-sites by magnetic ions in Fe_1.4Al_1.6O₄ strengthens the exchange coupling, allowing the formation of long-range magnetic order at a rather high temperature (~100 K). Magnetic phase diagrams are presented demonstrating that for the studied compounds the magnetic properties are determined by the degree of frustration.     

Examining Magnetic Models and Anisotropies in <Emphasis Type="Italic">β</Emphasis>-Cu<Subscript>2</Subscript>V<Subscript>2</Subscript>O<Subscript>7</Subscript> by High-Frequency ESR

High-frequency electron spin resonance (ESR) measurements were carried out on a single crystal β-Cu₂V₂O₇, where Cu–O edge-sharing chains are connected by non-magnetic VO₄ tetrahedrons. Due to sizable anisotropies, analyses of bulk magnetic properties alone have not yielded any definite conclusion and the modeling of the magnetic lattice is controversial. By means of high-frequency ESR with operating frequencies of 135–405 GHz and at a temperature range of 4.2–50 K, the large g value anisotropy is determined, which removes the ambiguity of susceptibility fitting. Moreover, non-negligible exchange anisotropy is evaluated by analyzing high-field magnetization and antiferromagnetic resonance in antiferromagnetic state appearing below T _N = 26 K. Based on these microscopic information, we found that alternating-chain model is the most reasonable candidate for explaining properties of the crystal. The present study shows the importance of combining macroscopic and microscopic probes in analyzing magnetic network of complex magnetic materials.     

A Precise Formulation of the Third Law of Thermodynamics

The third law of thermodynamics is formulated precisely: all points of the state space of zero temperature  Γ₀  are physically adiabatically inaccessible from the state space of a simple system. In addition to implying the unattainability of absolute zero in finite time (or “by a finite number of operations”), it admits as corollary, under a continuity assumption, that all points of  Γ₀  are adiabatically equivalent. We argue that the third law is universally valid for all macroscopic systems which obey the laws of quantum mechanics and/or quantum field theory. We also briefly discuss why a precise formulation of the third law for black holes remains an open problem.     

Influence of magnetism on the structural stability of cubic L2<Subscript>1</Subscript>Ni<Subscript>2</Subscript>MnGa

We present calculations of magnetic field-dependent properties of magnetic shape memory (MSM) Heusler alloys by means of density functional theory calculations. The effects of an external magnetic field on structural properties are simulated by fixing the magnetic moments within the framework of the fixed spin moment (FSM) method. We calculate the binding surface as a function of the magnetic moment and the tetragonal distortion. For magnetizations of 10% below the equilibrium value, the energy of the martensitic L1₀ phase steeply increases leading to a relative stabilization of the L2₁ phase in a confined magnetization range. Calculations of the phonon dispersion in the direction [ξξ0]2π/a suggest that the instability at ξ≈1/3 disappears with decreasing magnetization, allowing a nearly stable spectrum in a small magnetization interval.     

Ferromagnetic resonance study of sputtered Co|Ni multilayers

We report on room temperature ferromagnetic resonance (FMR) studies of [ t Co|2t Ni]  × N sputtered films, where 0.1 ≤ t ≤ 0.6 nm. Two series of films were investigated: films with the same number of Co|Ni bilayer repeats (N = 12), and samples in which the overall magnetic layer thickness is kept constant at 3.6 nm (N = 1.2/t). The FMR measurements were conducted with a high frequency broadband coplanar waveguide up to 50 GHz using a flip-chip method. The resonance field and the full width at half maximum were measured as a function of frequency for the field in-plane and field normal to the plane, and as a function of angle to the plane for several frequencies. For both sets of films, we find evidence for the presence of first and second order anisotropy constants, K₁ and K₂. The anisotropy constants are strongly dependent on the thickness t, and to a lesser extent on the total thickness of the magnetic multilayer. The Landé g-factor increases with decreasing t and is practically independent of the multilayer thickness. The magnetic damping parameter α, estimated from the linear dependence of the linewidth ΔH, on frequency, in the field in-plane geometry, increases with decreasing t. This behaviour is attributed to an enhancement of spin-orbit interactions with decreasing Co layer thickness and in thinner films, to a spin-pumping contribution to the damping.     

Magnetic and structural properties of non-stoichiometric Ni-Mn-Ga ferromagnetic shape memory alloys

Structural and magnetic transition temperatures of ferromagnetic shape memory alloys present a strong dependence on slight departures from the stoichiometry, as does the mobility of twin boundaries responsible for the large magnetic field induced strains. In this work we study four non stoichiometric Ni-Mn-Ga polycrystalline alloys with compositions of 43–52 at.% nickel, excess manganese and deficient in gallium, and a single crystal of composition Ni₅₂Mn₂₆Ga₂₂. Those compounds are of technical interest due to the observed large room temperature magnetic field induced strains. Calorimetric and magnetic measurements determined the martensitic transition and Curie temperatures of the alloys (A_S = 331 K and T_Curie = 366 K for 52 at.% nickel alloy). Nickel defective alloys present a martensitic transition region broader than excess nickel ones. Neutron powder diffraction analysis confirmed orthorhombic martensitic structures for nickel defective alloys, and tetragonal for excess nickel ones. In the 52 atomic % nickel alloys case the crystallographic structure of the martensitic phase was also obtained on a single crystal with the same composition, trained to get a single variant in agreement with determined in the powder sample.     

Effect of the electric field on “incommensurate-commensurate” magnetic phase transitions in BiFeO3-type multiferroics

The specific features of the “incommensurate-commensurate” phase transitions induced by a magnetic field in multiferroics (materials with coexisting magnetic and electric ordering) are considered. These materials are ferroelectromagnets, for example, bismuth ferrite BiFeO₃ and BiFeO₃-based compounds, which have spatially modulated spin structures. It is shown that the interaction between the electric and magnetic subsystems of the multiferroic material can lead to an electric-field-induced shift of the critical magnetic field corresponding to the transition from a spatially modulated state to a homogeneous antiferromagnetic state. According to the theoretical estimates obtained for material parameters characteristic of the bismuth ferrite, this shift is of the order of 0.5 T in an electric field of 50 kV/cm. The phase diagrams are constructed in the “electric field-magnetic field” coordinates. The results of calculations performed in the harmonic incommensurate structure approximation are compared with the exact soliton solution.     

Modification of magnetic anisotropy in metallic glasses using high-energy ion beam irradiation

Heavy ion irradiation in the electronic stopping power region induces macroscopic dimensional change in metallic glasses and introduces magnetic anisotropy in some magnetic materials. The present work is on the irradiation study of ferromagnetic metallic glasses, where both dimensional change and modification of magnetic anisotropy are expected. Magnetic anisotropy was measured using Mössbauer spectroscopy of virgin and irradiated Fe₄₀Ni₄₀B₂₀ and Fe₄₀Ni₃₈Mo₄B₁₈ metallic glass ribbons. 90 MeV ¹²⁷I beam was used for the irradiations. Irradiation doses were 5×10¹³ and 7.5×10¹³ ions/cm². The relative intensity ratios D ₂₃ of the second and third lines of the Mössbauer spectra were measured to determine the magnetic anisotropy. The virgin samples of both the materials display in-plane magnetic anisotropy, i.e., the spins are oriented parallel to the ribbon plane. Irradiation is found to cause reduction in magnetic anisotropy. Near-complete randomization of magnetic moments is observed at high irradiation doses. Correlation is found between the residual stresses introduced by ion irradiation and the change in magnetic anisotropy.     

Anisotropy of the local atomic structure in Fe-(5–6 at. %) Si single crystals as the cause of formation and stability of induced magnetic anisotropy

Fe_{1 ? x} Si_x (x = 0.05–0.06) single crystals were prepared and subjected to various heat treatments for structural studies. X-ray diffuse scattering measurements detected an anisotropy of regions with local B2-type atomic ordering in samples with induced magnetic anisotropy. It was shown that the average size of ordered clusters as measured along an applied dc magnetic field during heat treatment is slightly larger than that in a transverse direction and reaches 10 Å. Such anisotropy of B2-type regions is not observed in magnetically isotropic samples obtained by rapid quenching or by annealing and cooling in a rotating field (or in the absence of an external field). A comparative analysis of the atomic structure, domain structure, and hysteresis loop shape in samples subjected to various treatments demonstrated a correlation between the short-range order and magnetic properties.     

Recent topics in microstructure control by magnetic field in Ni<Subscript>2</Subscript>MnGa and CoPt and new transformation behavior in Ti-Ni-Fe alloys

Three topics related to solid-solid phase transformations are presented. The first topic is related to ferromagnetic shape memory alloys. The general condition for rearrangement of martensite variants by magnetic field is discussed quantitatively. The second topic is related to microstructure control of CoPt (tetragonal L1₀-type structure) during ordering heat-treatment under a magnetic field. We show that a single variant state is realized by magnetic field, and magnetic field is especially effective at the early stage of ordering. The third topic is related to the so-called precursor phenomena in Ti-Ni-Fe shape memory alloys. In the topic we will show the existence of a commensurate phase, which inherits the microstructure of the incommensurate phase and is probably different from the R-phase.     

Hard magnetic properties of ErCo7−xCux [0.3⩽x⩽1] system

We report the observation of excellent hard magnetic properties on purely single phase ErCo_7−xCu_x compounds with x=0.3, 0.5, 0.8 and 1. Cu substitution leads to a decrease in the saturation magnetization, but enhances the uniaxial anisotropy in this system. The large anisotropy field (∼100 kOe) is attributed to the Er and the Co sublattices. Domain wall pinning effect seems to play a crucial role in determining the temperature and field dependences of magnetization in these compounds. The hard magnetic properties obtained at room temperature (RT) are comparable to the best results obtained in other RCo₇ based materials.     

Anisotropic contribution of magnetostriction to the elastic compliance constants in hexagonal materials: The Δs-effect

In this paper, we consider the single crystal analogue of the ΔE-effect in hexagonal materials with uniaxial magnetic anisotropy. We define Δs_ijld as the fractional change in the elastic compliance tensor s_ijkl in the demagnetized state relative to its value in the saturated state. The Δs-effect depends in general on the direction of the applied stress and the resulting magnetostrictive strain. We can show, however, that Δs_ijkl is always nonnegative when i=k and j=l. We then consider the measurements of the elastic constants in magnetic materials which have large magnetocrystalline anisotropy. The stresses applied in these measurements are not sufficient to rotate the magnetization away from the magnetically preferred direction, and hence cause no magnetostriction, and no Δs-effect. Therefore, it is not necessary to apply a saturating magnetic field along the easy axis in order to measure the true elastic constants in these materials.