First-order Anisotropy Constant Research Articles

Low-temperature phase MnBi compound: A potential candidate for rare-earth free permanent magnets

The low-temperature phase (LTP) MnBi is one of the few rare-earth free compounds that exhibit a large magnetocrystalline anisotropy energy in the order of 106J/m3. A large coercive field (μ0Hcj) above 1T can be obtained readily by reducing the crystallite size (D) through mechanical grinding (MG). The room-temperature Hcj values follow a phenomenological expression μ0Hcj=μ0Ha(δ/D)n where the anisotropy field (μ0Ha) is ∼4T, the Bloch wall width (δ) is 7nm and the exponent (n) is about 0.7 in our study. The grain refinement upon MG is accompanied by suppression of the spin reorientation transition temperature (TSR) from 110K to below 50K. The coercive field starts to exhibit positive temperature dependence approximately 50K above TSR and the room-temperature magnetic hardening induced by MG could partially be brought about by the lowered onset of this positive temperature dependence. The suppression of TSR by MG is likely to be induced by the surface anisotropy with which the 2nd order crystal field term is enhanced. One of the shortcomings of LTP-MnBi is its poor phase stability under the ambient atmosphere. The spontaneous magnetization decreases considerably after room-temperature aging for 1week. This is due to oxidation of Mn which leads to decomposition of the MnBi phase. Hence, the surface passivity needs to be established before this material is considered for a permanent magnet in practical uses. Another shortcoming is the limited spontaneous magnetization. The theoretical upper limit of the maximum energy product in LTP-MnBi remains only a quarter of that in Nd2Fe14B. Nevertheless, owing to the unique positive temperature dependence of the first-order anisotropy constant (K1), the hardness parameter (κ) of LTP-MnBi is enhanced above room temperature; κ reaches as large as 2.8 at 580K. This makes LTP-MnBi a possible candidate for the hard phase in rare-earth free nanocomposite magnets.

Temperature dependence of the uniaxial magnetic anisotropy of rhombohedral antiferromagnetic crystals with ions in the S state

The contributions of the anisotropic exchange to the firstand second-order uniaxial anisotropy constants have been calculated for hematite at T = 0 K and arbitrary temperatures. The results of the calculations and the most significant mechanisms are taken into account in interpreting the temperature dependence of the anisotropy in rhombohedral antiferromagnetic crystals. The first-order anisotropy constant for hematite is described by the dipole interaction, contributions of the “single-ion” nature, and relatively small contributions of the anisotropic exchange. The second-order constant for hematite includes the “single-ion” contribution and the contribution of the anisotropic exchange. For FeBO3 and MnCO3 crystals, the main contributions to the first-order anisotropy constant come from the dipole and single-ion mechanisms.

Magnetic resonance in FexMn1−xS single crystals

The results of the experimental study and computer simulation of the resonance spectra of a single crystal of the iron-manganese sulfide FexMn1−xS (0≤x≤0.29) are presented. The resonance properties of the concentrated solid solutions are explained by the formation of a homogeneous FexMn1−xS matrix with randomly distributed superparamagnetic iron nanoparticles. The mean diameter (⟨D⟩=6.19 nm at T=250 K) and the axial first-order anisotropy constant (К1=4.08 erg/cm3 at T=250 K) of the ferromagnetic particles are determined. The volume fraction of the iron phase is estimated.

Magnetic anisotropy of LuFe 10Si 2

Field and temperature dependences of magnetization have been measured for the first time along the principal axes of a LuFe 10Si 2 single crystal. The compound is a ferromagnet with a spontaneous magnetic moment of 18.0 μ B per formula unit (at 4.2 K), a Curie temperature of 540 K and a uniaxial magnetic anisotropy described by a first-order anisotropy constant of 1.77 MJ/m 3 at 4.2 K.

Structural, thermal, and magnetic properties of Ni2MnGa

The two main effects underlying the magnetic shape memory effect in Ni2MnGa are martensitic transformations and magnetic anisotropy energies. Both issues are addressed here with first-principles calculations. First, we examine how the tetragonality in the martensitic phase varies with the composition. Then, the actual transformation is investigated by comparing the free energies of different phases. The transition from the cubic structure to the tetragonal structure with c/a=1.27 is driven by the vibrational free energy and occurs at a temperature of 200 K which is in the experimental range. Finally, we focus on the magnetic anisotropy energy for the tetragonal structure with c/a=0.94. It is shown to be a magnetically nearly ideal uniaxial system determined by the first-order anisotropy constant. However, it is estimated that the twinned microstructure can cause higher-order anisotropies to show up in the measured anisotropy.

Effect of the second-order anistropy constant on the transverse susceptibility of uniaxial ferromagnets

A generalized theoretical approach of the transverse susceptibility, χT, in the case of uniaxial ferromagnets is presented. This advances the classical model of transverse susceptibility where only the first-order anisotropy constant, K1, is taken into account and makes possible the study of the influence of the second-order anisotropy constant, K2 on the χT curves. It is shown that additional Barkhausen jumps driven by higher-order anisotropy constants emerge more evidently in the field dependence of χT making their detection much easier than from the hysteresis loop. Based on the obtained results, we propose a simple method to determine both, K1 and K2 independently from χT experiments.

Micromagnetic study of reversible transverse susceptibility

A generalized theoretical approach of the transverse susceptibility in the case of uniaxial ferromagnets is presented. This advances the classical model of transverse susceptibility where only the first-order anisotropy constant is taken into account, and makes possible the study of the influence of the second-order anisotropy constant on the transverse susceptibility curves. The complicated switching behavior occurring in certain cases was analyzed and discussed from the dynamical point of view, comparing the results with those obtained with a Landau–Lifshitz–Gilbert approach.

Magnetic and magnetostrictive properties of the Dy0.9−xPrxTb0.1Fe2 compounds

Measurements of Curie temperature, temperature dependence of magnetization, magnetostriction, and magnetization curve are carried out on Dy0.9-xPrxTb0.1Fe2 (x = 0, 0.1, 0.2, 0.4) polycrystalline compounds. A decrease of Curie temperature and saturation magnetization caused by the Pr substitution is observed. The calculated first-order anisotropy constant of the compounds also decreases with increasing Pr content, which causes the increase of the magnetostriction of the compounds near x = 0.1.

First-principles calculation of the magnetocrystalline anisotropy energy of the pnictide MnSb

The magnetocrystalline anisotropy energy (MAE) of the pnictide MnSb is investigated by means of the augmented spherical wave method. The spin-orbit coupling enters the variational step of the procedure and the force theorem is applied to determine the dependence of the MAE on the directions of magnetization. The authors numerical results agree well with the first-order development of anisotropy energy in uniaxial crystal structures. The easy axis of magnetization is then found to be in the basal plane of the hexagonal structure in agreement with experiment, and the first-order anisotropy constant is given.

R.f.-sputtered CoCr layers for perpendicular magnetic recording: II: Magnetic anisotropy

The magnetic anisotropy of CoCr layers was investigated with a torque magnetometer, using Fourier analysis. The results could be fitted to the hexagonal anisotropy, described by a first-order and a second-order uniaxial anisotropy constant. The second-order uniaxial anisotropy constant K 2 was 2%–4% of the first- order anisotropy constant K 1. Higher order anisotropy constants were not significant. The magnetic anisotropy and the saturation magnetization appeared to be almost independent of the layer thickness. Magnetostriction was found to give a negative contribution to the first-order anisotropy constant.

Anomalous Behavior of the Anisotropy and Linewidth due to Pr in Iron Garnets

The contribution of ${\mathrm{Pr}}^{3+}$ in iron garnets to the first-order anisotropy constant and to the microwave loss is highly nonlinear with respect to the ${\mathrm{Pr}}^{3+}$ concentration and is shown to be strongly dependent on the lattice constant. The value of the anisotropy constant per Pr ion goes from -18\ifmmode\times\else\texttimes\fi{}${10}^{4}$ to about +3\ifmmode\times\else\texttimes\fi{}${10}^{4}$ erg/${\mathrm{cm}}^{3}$ as the lattice constant increases from 12.4 to 12.7 \AA{}. The microwave linewidth of ${\mathrm{Pr}}_{3}$Sc${\mathrm{Fe}}_{4}$${\mathrm{O}}_{12}$ is 21 times narrower than expected from the extrapolation of the low-concentration data of ${\mathrm{Pr}}^{3+}$ in yttrium iron garnet.

Temperature and stress sensitivities of microwave ferrites

The effect of changes in remanent magnetization on the performance of microwave ferrites employed in latching phase shifter applications has been a serious problem for many years. Reductions in the remanence ratio R are caused both by increases in temperature and by stresses which arise from thermal or mechanical origins. Recently, the molecular field theory developed by Neel has been modified to account for the effects of possible sublattice canting on the magnetization-temperature curves of substituted microwave garnets. The results of this work have made it possible to compute magnetization-temperature characteristics for a wide range of substituted iron garnets. The problem of the stress sensitivity of R has also been examined theoretically, and it has been concluded that the ratio of the magnetostriction constant to the first-order anisotropy constant is the important variable. The magnetostriction constant involved depends on the relationship of the stress direction to the applied magnetic field. In comparison with experimental results for Y 3 Mn x Fe 5-x O 12 in both single crystal and polycrystalline forms, the theory was shown to give at least qualitative agreement. This paper will serve as an up-to-date review of this work.

Linewidth Reduction through Indium Substitution in Calcium-Vanadium Garnets

On the garnets Y3−2xCa2xFe5−x−yVxInyO12, with x ≤ 1.5 and y ≤ 0.5, we have measured the polycrystalline linewidth ΔHpoly at X-band and room temperature and have determined from single crystals the first-order anisotropy constant, K1. Since the single-crystal linewidth of these materials is but a few oersteds and the polycrystalline samples had less than 1% porosity and second phase, the observed ΔHpoly is attributed to anisotropy broadening, according to Schlömann. The introduction of indium reduces both | K1 | and ΔHpoly, for example: x = 0.63y = 0TC = 280°C4πMs = 650 GΔHpoly = 98 Oex = 0.80y = 0.50TC = 155°C4πMs = 750 GΔHpoly = 8 Oe. That last value is the lowest yet reported in the range of T ≈ 23 TC.

Permeability, crystalline anisotropy and magnetostriction of polycrystalline managese-zinc-ferrous ferrite

In the mangnese-zinc-ferrous ferrite system (Mnx−yZnyFe3−xO4), which is of considerable technical importance, the magnetocrystalline anisotropy cannot be measured directly because ferrite single crystals containing zinc cannot be produced. It is shown in the paper that the sign and, to some extent, the magnitude of the first-order anisotropy constant, K1 can be determined by measuring the magnetostriction of polycrystalline samples as a function of the applied field. This is possible if the magnetostriction constants λ100 and λ111 have different signs, which is the case in the above system. The result is that in some of the compositions the anisotropy constant K1 passes through zero at around room temperature. This explains the occurrence of a secondary peak in the permeability/temperature curve of these ferrites. As the saturation magnetostriction in the same composition is very small, this represents the oxidic analogue of Permalloy.

Magnetic Anisotropy in Ferrimagnetie Crystals

Absolute values of K1, the first-order anisotropy constant, have been determined at different temperatures from torque measurements on single crystals of the following compositions: MnxFe3−xO4, where 0.7 ≤ x ≤ 1.0; Cox Mn1−xFe2O4, where 0 ≤ x ≤ 0.25; Co0.04Mnx−0.04Fe3−xO4, where 0.70 ≤ x ≤ 0.91; GaxFe3−xO4, where 0 ≤ x ≤ 0.8; Sm3Fe5O12Gd3Fe5O12. The magnetocrystalline anisotropy of manganese ferrous ferrite was found to vary considerably with the concentration of ferrous ions (Fe2+), some compositions even possessing a positive value of K1 at room temperature, as previously found by Penoyer (1959). In these cases, K1 becomes negative at low temperatures in contrast with the behavior of cobalt-substituted crystals which are found to have rapidly increasing positive values of K1 as the temperature is reduced. The anisotropy contribution of cobalt ions(Co2+) substituted in manganese ferrous ferrite varies with crystals of different compositions. The experimental values of K1 are compared wherever possible with present theories of magnetic anisotropy. In particular, the recent theory proposed by Slonczewski (1958) to explain the anisotropy of cobalt ions substituted in magnetite (Fe3O4) is found to be unsuccessful in the case of Co2+ ions in manganese ferrite (MnFe2O4). Measurements at low temperatures on the gallium-substituted magnetite crystals reveal an additional interesting effect. For certain crystals, the torque curves at 80°K exhibit considerable rotational hysteresis in fields above 10000 oe, when the material should certainly be saturated. This hysteresis is shown to be related to the ordering of the ferrous (Fe2+) and ferric (Fe3+) ionswhich takes place on the octahedral sites at low temperatures.

Magnetic Properties of Nickel-Iron Ferrite

The magnetic anisotropy of a single crystal of nickel-iron ferrite with composition Fe1.003+[Ni0.792+Fe0.363+Fe0.903+]O4 is given between 450 and 4.2°K. At high temperatures the anistropy energy has cubic symmetry, and the absolute value of the first-order anisotropy constant is a maximum at ca 200°K. Below 200°K, |K1| decreases until 10°K, at which temperature there is an abrupt transition in the anisotropy characteristics. Below 10°K the anisotropy energy contains a uniaxial term of the form Εi αi2βi2 where αi and βi are the direction cosines of the magnetization at the measuring temperature and at the annealing temperature (10°K), respectively. This low-temperature behavior has been explained on the basis of existent theory of magnetic annealing. The model used to explain the uniaxial anisotropy term given above is shown to be consistent with the noncubic anisotropy energy obtained upon cooling the sample through 10°K in the absence of an external field. The model is also shown to lead directly to a relaxation effect which contributes a term of the form K′(α12α22+α22α32+α32α12) to the anisotropy energy above 10°K and explains the observed maximum in |K1|.

Magnetic Anisotropy Constant of Yttrium Iron Garnet at 0°K

The anisotropy energy of yttrium iron garnet is separated into two parts, the normal part predominant at high temperatures, and the anomalous part important below 50\ifmmode^\circ\else\textdegree\fi{}K. By comparison with ferrite data, the cause of the normal anisotropy is expected to be the coupling of the ${\mathrm{Fe}}^{3+}$ ions to the crystalline field. The following expression for ${K}_{1}$, the first-order anisotropy constant, as a function of the fine structure coupling constants ${a}_{24}$ (tetrahedral sites) and ${a}_{16}$ (octahedral sites) is obtained: $\frac{{K}_{1}}{\mathrm{unit}\mathrm{cell}}=\ensuremath{-}46.6{a}_{24}\ensuremath{-}13.6{a}_{16}$.

Ferromagnetic Resonance Absorption in Magnetite Single Crystals

The microwave resonance absorption technique, at both 1.25 and 3.3 cm wave-lengths, was used to study the ferromagnetic crystalline anisotropy characteristics and $g$-factor of magnetite ${\mathrm{Fe}}_{3}$${\mathrm{O}}_{4}$. The experiments were performed on single crystals, both synthetic and natural, from room temperature to -195\ifmmode^\circ\else\textdegree\fi{}C. Depending upon the temperature, magnetite single crystals were found to have magnetic anisotropy characteristics similar to those of single crystals of the three ferromagnetic elements. From room temperature to -143\ifmmode^\circ\else\textdegree\fi{}C, they behave like nickel; between -143\ifmmode^\circ\else\textdegree\fi{} and the transition which magnetite is known to undergo at $\mathrm{ca}$. -160\ifmmode^\circ\else\textdegree\fi{}C, like iron; and below the transition, somewhat like cobalt. At room temperature, values of $g=2.12$ and ${K}_{1}$ (first-order anisotropy constant) = -1.10\ifmmode\times\else\texttimes\fi{}${10}^{4}$ joule/${\mathrm{m}}^{3}$ (-1.10\ifmmode\times\else\texttimes\fi{}${10}^{5}$ erg/${\mathrm{cm}}^{3}$) were obtained. It was found that below about -90\ifmmode^\circ\else\textdegree\fi{}C the absolute value of ${K}_{1}$ decreases with decreasing temperature, reaching zero at $\mathrm{ca}$. -143\ifmmode^\circ\else\textdegree\fi{}C. Between -143\ifmmode^\circ\else\textdegree\fi{} and the transition ${K}_{1}$ is positive and increases with decreasing temperature. The vanishing of crystalline anisotropy at -143\ifmmode^\circ\else\textdegree\fi{}C accounts for the peak in initial permeability found near this temperature. The $g$-value was found to decrease gradually and monotonically with decreasing temperature. The behavior of magnetite in the resonance experiments below the transition seems to indicate that the magnetic symmetry is uniaxial in this temperature region. This conclusion is consistent with the findings of other investigators. Below the transition the magnetic axis is that [100] direction most nearly parallel to a strong magnetic field applied to the crystal as it is cooled through the transition. At temperatures not far below the transition it is possible to change the magnetic axis from one [100] direction to another by means of a strong magnetic field.