Magnetostriction of TbxHo0.75−xPr0.25(Fe0.9B0.1)2 (x=0–0.3) compounds

The Tb_xHo_0.75−xPr_0.25(Fe_0.9B_0.1)₂ (x=0, 0.1, 0.15, 0.2, 0.25, and 0.3) compounds are found to stabilize in a cubic Laves phase structure. The lattice parameter, magnetostriction (at 10 kOe), and Curie temperature are found to increase with increasing Tb content. The compound with x=0.15 exhibits a possible anisotropy compensation between the Tb and (Ho/Pr) sublattices. The easy magnetization direction rotates towards the 〈1 1 1〉 from the 〈1 0 0〉 direction, with increasing Tb content. The splitting of the (4 4 0) peak accompanied by the spontaneous magnetostriction-induced rhombohedral distortion is observed for compounds with x?0.15 and the spontaneous magnetostriction (λ_1 1 1) is found to increase with Tb content.     

Influence of Si and Co substitutions on magnetoelastic properties of R2Fe17 (R=Y, Er and Tm) intermetallic compounds

The magnetostriction of the off-stoichiometric R₂Fe₁₇-type intermetallic compounds based on R₂Fe_14−xCo_xSi₂ (R=Y, Er, Tm and x=0, 4) was measured, using the strain gauge method in the temperature range 77-460 K under applied magnetic fields up to 1.5 T. All compounds show sign change and reduction in magnetostriction values compared to the R₂Fe₁₇ compounds by Si substitution. For Y₂Fe₁₄Si₂ and Er₂Fe₁₄Si₂, saturation behaviour is observed near magnetic ordering temperature (T_C), whereas for Tm₂Fe₁₄Si₂, saturation starts from T>143 K. Also, Co substitution has different effects on the magnetostriction of R₂Fe₁₄Si₂ compounds. In Er₂Fe₁₀Co₄Si₂ and Tm₂Fe₁₀Co₄Si₂, saturation occurs below the spin reorientation temperature (T_SR). In addition, in Er₂Fe₁₄Si₂, a sign change occurs in the anisotropic magnetostriction (Δλ) as well as the volume magnetostriction (ΔV/V) at their T_SR values. The volume magnetostrictions of the Tm-containing compounds show an anomaly around their T_SR. In R₂Fe₁₄Si₂ compounds, parastrictive behaviour is also observed in ΔV/V near their T_C values. In addition, the magnetostriction of the sublattices is investigated. Results show that in R₂Fe₁₄Si₂ compounds, the rare-earth sublattice contribution to magnetostriction is negative and comparable to the iron sublattice, whereas, in R₂Fe₁₀Co₄Si₂ compounds, the rare-earth sublattice contribution is positive and larger than Fe sublattice. These results are discussed based on the effect of Si and Co substitutions on the anisotropy field of these compounds. Influence of the spin reorientation transition on the magnetostriction of these compounds is discussed in terms of the anisotropic sublattice interactions.     

Quantitative Model of Large Magnetostrain Effect in Ferromagnetic Shape Memory Alloys

A quantitative model describing large magnetostrain effect observed in several ferromagnetic shape memory alloys such as Ni₂MnGa is briefly reported. The paper contains an exact thermodynamic consideration of the mechanical and magnetic properties of similar type materials. As a result, the basic mechanical state equation including magnetic field effect is directly derived from a general Maxwell relation. It is shown that the magnetic field induced deformation effect is directly connected with the strain dependence of magnetisation. A simple model of magnetisation and its dependence on the strain is considered and applied to explain the results of experimental study of large magnetostrain effects in Ni₂MnGa.     

Influence of H and N insertion on the magnetostriction and thermal expansion of YFe10V2Zx (Z=N,H) compositions

Experimental results on the thermal expansion and magnetostriction of YFe₁₀V₂ composites are reported and the influence of H and N interstitial atoms is studied. The anisotropic magnetostriction is about 30% larger in the composite than in the starting alloy. Also, the anisotropic magnetostriction remains positive after insertion of H (N) ion while the sign of volume magnetostriction changes by hydrogenation. The anisotropic magnetoelastic interactions are enhanced by insertion of H and especially N interstitial atoms. The results are discussed considering the effect of H and N, and of temperature on magnetic anisotropy and microstructure.     

Study of the magnetostrictive strains in Pr6Fe11Ga3 alloy

Magnetoelastic properties of the Pr₆Fe₁₁Ga₃ alloy are studied by magnetostriction and thermal expansion measurements. The effects of short- and long-range magnetic ordering processes about Curie temperature clearly appear in the temperature dependence of the spontaneous magnetostriction as two increasing steps with decreasing temperatures. Thermal variations of the total magnetocrystalline anisotropy introduce pronounce changes in the isofield curves of the forced magnetostriction as a negative minimum below 200 K, a compensation phenomena about 250 K, and a positive maximum between 250 K and T_c=320 K. The observed behavior of magnetostriction is discussed in terms of the competitive anisotropies of Pr and Fe sublattices and coupling magnetostrictive constants.     

Magnetostriction and magnetic anisotropy of (Sm,Ce)Fe2 compounds

The structural, magnetic and magnetostrictive properties of Sm_1−xCe_xFe₂ (0≤x≤1) Laves compounds have been investigated. The magnetostriction coefficient λ₁₁₁ and the anisotropy of the Sm_1−xCe_xFe₂ compounds decrease with increasing Ce content. The decreasing of anisotropy results in an enhancement of the anisotropic magnetostriction at low magnetic fields for the compounds with a small amount of Ce substituted for Sm.     

Three-dimensional constitutive equations for Ni–Mn–Ga single crystals

This paper presents a formulation of isothermal three-dimensional (3D) quasi-static magneto-mechanical constitutive equations and 3D magnetisation constitutive equations for tetragonal martensite Ni–Mn–Ga FSMA single crystals (c/a<1)$(c/a<1)$ with both ends restrained from twin-boundary motion. The formulated 3D constitutive equations model the 3D quasi-static magnetic fields as well as the coupling between uniaxial strains and stresses, and shear strains and stresses. The constitutive equations are compared with experimental results available in the literature and are found to correlate well with the experimental results, including magnetic field reversals. Both sets of 3D constitutive equations require only macroscopic parameters that are readily obtainable from magnetisation and mechanical stress–strain curves.     

Anomalies in low-temperature lattice parameters of ErFeO3 and ErAlO3 single crystals: correlation with magnetic properties

The paper presents the results of an experimental study of thermal expansion of isostructural orthorhombic ErFeO₃ and ErAlO₃ single crystals. Changes of lattice parameters have been investigated by X-ray measurements in the 10-300 K temperature range. Above ∼150 K, experimental results correspond well to the phonon mechanism. At low temperatures distinct anisotropic anomalies were observed in both compounds; and a correlation with the magnetic properties of the relevant ions is noted.     

Magnetocaloric effect: Overcoming the magnetic limit

We have studied anomalous peaks observed in magnetocaloric −ΔS(T) curves for systems that undergo first-order magnetostructural transitions. The origin of those peaks, which can exceed the conventional magnetic limit, R ln(2J+1), is discussed on thermodynamic bases by introducing an additional-exchange contribution (due to exchange constant variation arising from magnetostructural transition). We also applied a semiphenomenological model to include this additional-exchange contribution in Gd₅Si₂Ge₂- and MnAs-based systems, obtaining excellent results for the observed magnetocaloric effect.     

Quantitative model of large magnetostrain effect in ferromagnetic shapell memory alloys

A quantitative model describing the large magnetostrain effect observed in several ferromagnetic shape memory alloys such as Ni₂MnGa is briefly reported.The paper contains an exact thermodynamic consideration of the mechanical and magnetic properties of similar types of materials. As a result, the basic mechanical state equation including magnetic field effect is directly derived from a general Maxwell relation. It is shown that the magnetic field induced deformation effect is directly connected with the strain dependence of magnetization. A simple model of magnetization and its dependence on the strain is considered and applied to explain the results of experimental study of large magnetostrain effects in Ni₂MnGa. Received 29 September 1999     

Magnetoelectric interaction and magnetic field control of electric polarization in multiferroics

Various aspects of magnetic field control of magnetoelectric (ME) and electric properties of multiferroics are considered: linear ME effect appearance at magnetic field-induced incommensurate–commensurate phase transition, polarization switching and reversal by magnetic field and magnetic field-induced polarization flop transition. The correlation between magnetic, electric, and magnetoelastic properties is shown.     

Magnetic anisotropy and anisotropic ballistic conductance of thin magnetic wires

The magnetocrystalline anisotropy of thin magnetic wires of iron and cobalt is quite different from the bulk phases. The spin moment of monatomic Fe wire may be as high as 3.4 μ_B, while the orbital moment as high as 0.5 μ_B. The magnetocrystalline anisotropy energy (MAE) was calculated for wires up to 0.6 nm in diameter starting from monatomic wire and adding consecutive shells for thicker wires. I observe that Fe wires exhibit the change sign with the stress applied along the wire. It means that easy axis may change from the direction along the wire to perpendicular to the wire. We find that ballistic conductance of the wire depends on the direction of the applied magnetic field, i.e. shows anisotropic ballistic magnetoresistance. This effect occurs due to the symmetry dependence of the splitting of degenerate bands in the applied field which changes the number of bands crossing the Fermi level. We find that the ballistic conductance changes with applied stress. Even for thicker wires the ballistic conductance changes by factor 2 on moderate tensile stain in our 5×4 model wire. Thus, the ballistic conductance of magnetic wires changes in the applied field due to the magnetostriction. This effect can be observed as large anisotropic BMR in the experiment.     

Spin-wave resonance and magnetic anisotropy in FePt thin films

Ferromagnetic Resonance (FMR) measurements at room temperature and X-band microwave frequency were performed on polycrystalline FePt thin films with face-centered cubic structure. With the external field perpendicular to the film plane, the absorption fields H_n of the odd and even spin-wave resonance modes n detected for the Fe_0.44Pt_0.56(45 nm)/Si(1 0 0) and Fe_0.51Pt_0.49(105 nm)/Pt(55 nm)/MgO(1 0 0) films, were found to obey the well-known H_n×n² ratio, giving for these films the exchange stiffness constant values of 3.9×10⁻⁸ and 4.4×10^–7 erg/cm, respectively. The study of the out-of-plane angular dependence of the absorption field of the uniform FMR mode allowed the measurement of the effective magnetic anisotropy constants of 5.3×10⁶ , 6.4×10⁶ , and 6.7×10⁶ erg/cm³, related, respectively, to the [1 1 1], [1 0 0], and [1 1 0] textures present in the films.     

Comprehensive theory for reduction of products of spin operators

We present a comprehensive theory that reduces the total power of products of spin operators. This theory improves the previous one [P.J. Jensen, F. Aguilera-Granja, Phys. Lett. A 269 (2000) 158] in two aspects. One is that for the set of spin operators S⁺, S⁻, Sz, a new method is suggested where the expansion coefficients in the reduction formula can be solved from linear equations. This new method is of direct physical meaning and is easier to handle. The other is that we show a method to reduce the products of another set of spin operators Sx, Sy, Sz. For this set of operators, the use of permutation regulation of x→y, y→z and z→x can save much time in obtaining some reduction formula. The present comprehensive theory enables one to deal more easily with the decoupling problems in Green' function theory where the set of either S⁺, S⁻, Sz or Sx, Sy, Sz operators is used.     

Breakdown of an intermediate plateau in the magnetization process of anisotropic spin-1 Heisenberg dimer: Theory vs. experiment

The magnetization process of the spin-1 Heisenberg dimer model with the uniaxial or biaxial single-ion anisotropy is particularly investigated in connection with recent experimental high-field measurements performed on the single-crystal sample of the homodinuclear nickel(II) compound [Ni₂(Medpt)₂(μ-ox)(H₂O)₂](ClO₄)₂·2H₂O (Medpt=methyl-bis(3-aminopropyl)amine). The results obtained from the exact numerical diagonalization indicate a striking magnetization process with a marked spatial dependence on the applied magnetic field for arbitrary but finite single-ion anisotropy. It is demonstrated that the field range, which corresponds to an intermediate magnetization plateau emerging at a half of the saturation magnetization, basically depends on a single-ion anisotropy strength as well as a spatial orientation of the applied field. The breakdown of the intermediate magnetization plateau is discussed at length in relation to the single-ion anisotropy strength.     

The effect of boron on the structure and magnetic properties of Pr0.15Tb0.3Dy0.55Fe1.85 alloy

The structure, Curie temperature and magnetostriction of Pr_0.15Tb_0.3Dy_0.55Fe_1.85−xB_x   (x=0–0.3$x=0–0.3$) alloys have been investigated using X-ray diffraction, AC susceptibility and standard strain gauge techniques. It was found that all the samples possess entirely MgCu₂-type cubic Laves structure. With increasing B concentration, the lattice parameter decreases, while the Curie temperature remains unchanged. The magnetostriction of Pr_0.15Tb_0.3Dy_0.55Fe_1.85−xB_x alloys at room temperature increases with increasing B concentration firstly, and then decreases slightly.     

Determination of anisotropy constants of protein encapsulated iron oxide nanoparticles by electron magnetic resonance

Angle-dependent electron magnetic resonance was performed on 4.9, 8.0, and 19 nm iron oxide nanoparticles encapsulated within protein capsids and suspended in water. Measurements were taken at liquid nitrogen temperature after cooling in a 1 T field to partially align the particles. The angle dependence of the shifts in the resonance field for the iron oxide nanoparticles (synthesized within Listeria-Dps, horse spleen ferritin, and cowpea chlorotic mottle virus) all show evidence of a uniaxial anisotropy. Using a Boltzmann distribution for the particles’ easy-axis direction, we are able to use the resonance field shifts to extract a value for the anisotropy energy, showing that the anisotropy energy density increases with decreasing particle size. This suggests that surface anisotropy plays a significant role in magnetic nanoparticles of this size.     

Thermal Expansion Anomaly and Spontaneous Magnetostriction of Y2Fe14Al3 Compound

The structure and magnetic properties of Y2Fe14Al3 compound are investigated by means of x-ray diffraction and magnetization measurements. The Y2Fe14Al3 compound has a hexagonal Th2Ni17-type structure. Negative thermal expansion is found in Y2Fe14Al3 compound in the temperature range from 403 to 491K by x-ray dilatometry. The coefficient of the average thermal expansion is α^- = -2.54Х 10^-5 K^-1. The spontaneous magnetostrictive deformations from 283 to 470 K are caJculated by means of the differences between the experimental values of the lattice parameters and the corresponding values extrapolated from the paramagnetic range. The result shows that the spontaneous volume magnetostrictive deformation ωs decreases from 5.74 × 10^-3 to nearly zero with temperature increasing from 283 to 470K, the spontaneous linear magnetostrictive deformation λc along the c-axis is larger than the spontaneous linear magnetostrictive deformation λa in basal-plane in the same temperature below 350 K.     

Phase composition and magnetic characteristics of Fe-filled multi-walled carbon nanotubes

The work addresses the correlation between the phase composition and the magnetic characteristics of aligned Fe-filled multi-walled carbon nanotubes (Fe-MWCNTs) grown by pyrolysis of ferrocene on oxidized Si substrates. In a combinatorial approach we exploited the extremely high gradients of the technological parameters temperature and ferrocene flow across the surface of a substrate positioned close to the reactor wall to obtain a large variation in the structural and magnetic properties of the Fe-MWCNTs. In this way, we established several clear correlations between the Fe-filling phase composition and the overall magnetic characteristics of the aligned Fe-MWCNTs. The α-Fe rich samples, which possess a more ordered graphitic sheet structure, a higher degree of preferred crystalline orientation of the metal filling and much larger metal crystallites in comparison with the carbide-rich samples, show a much stronger magnetic anisotropy with easy axis perpendicular to the substrate and unusually high values of the coercive field H_c and the saturation field H_s. The changes in the measured saturation magnetisation M_s and the H_c values correlate well with the variation of the α-Fe content and the filling crystallinity. A special annealing treatment of the samples causes a distinct increase of the α-Fe quantity and an increase of the measured average grain size. The respective magnetic characteristics show a significant increase of the overall magnetic moment and decrease of the coercive field. The correlation between the structural and the magnetic characteristics of the annealed samples matches quite well the respective correlations in the case of as-deposited samples.     

Theoretical investigation of magnetic property in paramagnetic neodymium gallium garnet under high magnetic field

The magnetic property in neodymium gallium garnet (NdGaG) is studied by the quantum theory. The ground configuration split states are calculated taking into account the spin–orbit interaction and crystal field effect. Taking account of the Nd–Nd exchange interaction, a good agreement between experimental and theoretical values can be obtained for the variation of the magnetic moment with the external magnetic field under “extreme” conditions (low temperature and high magnetic field). Moreover, the temperature dependence of magnetic moment and the magnetic susceptibility χ is also discussed. Above 30 K, the magnetization (M) shows a linear field (H_e) dependence.