Basal Plane Anisotropy Research Articles

Exchange interactions and basal-plane magnetocrystalline anisotropy in R 2Co 17 intermetallics

The transition fields that recently have been observed in the basal-plane magnetisation curves of Ho 2Co 17 can successfully be described in a two-sublattice model and provide a direct method to evaluate the molecular field acting on the holmium moment. Its value of 63.5 T corresponds, in a molecular-field approximation, to a value of 0.924x10 -22 J for the coupling between the holmium and cobalt spins. The basal-plane magnetocrystalline anisotropy of the holmium moment is found to be 2.2x10 -22 J. On the basis of these numbers the molecular field acting on the rare-earth moment and the basal-plane anisotropy are calculated for the whole series of R 2Co 17 compounds.

Field-induced transitions in hexagonal ferrimagnets

It is shown that the basal plane anisotropy in hexagonal easy-plane ferrimagnets of 3d−4f systems yields discontinuities in the magnetisation curve for external fields applied in the easy plane. At the discontinuities first-order momentreorientation (FOMR) transitions occur. They are governed by the basal plane anisotropy and take place in the easy plane as a result of a competition of the exchange and the magnetostatic energies of the two sublattice magnetisations. The value of the transition field gives a direct method to evaluate the intersublattice molecular field coefficient.

Field-induced first-order moment reorientation transitions in R2T17ferrimagnets

The basal-plane anisotropy in a hexagonal easy-plane ferrimagnetic system yields discontinuities in the magnetisation curve for external fields applied in the easy plane. At the discontinuities first-order moment reorientation (FOMR) transitions occur. The lowest transition field depends strongly on the difference between the values of the sublattice magnetisations and is very sensitive to the intersublattice coupling. The transition field provides a direct method for evaluating the exchange coupling between the 3d and 4f spins. The lowest transition field in the series of the easy-plane R2T17 compounds (where R=rare-earth metal and T=Fe, Co) occurs for Ho2Co17 and amounts to 21 T.

Field induced moment-reorientation transitions in hexagonal ferrimagnets

It is shown that the basal plane anisotropy in a hexagonal easy-plane ferrimagnetic 3d-4f system yields discontinuities in the magnetisation curve for external fields applied in the easy plane. These discontinuities are believed to be the origin of the anomalously large high-field susceptibility in the Dy 2Fe 17− y Al y compounds. At the discontinuities First-Order Moment-Reorientati on (FOMR) transitions occur. They are governed by the basal plane anisotropy and take place in the easy plane as a result of a competition between the exchange and the magnetostatic energies of the two sublattice magnetisations. The moment reorientation process should be taken into consideration even at low fields in the case of a small difference between the two magnetisation values. The transition fields give a direct method to evaluate the exchange coupling between the 3d and 4f spins.

The magnetocrystalline anisotropy of cobalt

Recent high precision measurements of the uniaxial anisotropy constants K 1 and K 2 are reported taken from three samples grown by different techniques. The results vindicate the early work of Succksmith and Thompson and agree well with the recent measurements of Ono. While some variation was observed between results from the three samples we conclude that these are insufficient to account for the spread of results in the literature and suggest inaccurate shearing corrections as the most probable cause of discrepancy. A very good fit to the K 1 data was obtained using a single ion model and the c/a ratio as an adjustable parameter. These c/a values gave a satisfactory fit to K 2 and also lay within the scatter of the experimentally measured c/a values. However, a definitive test of the single ion theory was not possible due to these experimental uncertainties in c/a. Data for the temperature variation of the basal plane anisotropy constant K 4 are reported for the first time. The single ion model predictions are not in very good agreement with the K 4 data.

Torque measurements in the basal plane of a DyNi5 crystal

The basal plane anisotropy of DyNi5 below and above Tc exhibits a rather complex behavior. It can be fairly well explained by a single ion model with crystal field parameters in quantitative agreement with those deduced from magnetization and susceptibility data.

Magnetoelastic contribution to the elastic constants of terbium, dysprosium and erbium

We have measured the dependence of the longitudinal and shear elastic waves velocity of Tb, Dy and Er single-crystals on magnetization and temperature. Data were taken in magnetic fields up to 75 kOe, in the temperature range of 4.2-300 K, which included all the ordered phases of these materials. We found qualitatively that to explain the observed behavior, the magnetoelastic interaction have to be treated up to 2nd order in the strains and that the 3rd order elastic energy can not be neglected. 1 . Introduction. The strong magnetoelastic coupling found in the heavy rare-earths elements is responsible for measurable effects on the dimensions and on the second order elastic constants (SOE) of these materials. In this work we correlate the SOE with the state of magnetization of the samples. Using a model similar to that of Freyne [I], which details are going to be published elsewhere, we found that although the magnetostriction values found in the literature for Tb [2], Dy [3] and Er [4] can be satisfactorily described by a magnetoelastic interaction linear in the strains, the SOE do not. This is undoubtedly clear when analysing the behavior of the shear SOE of Tb (rotational strains included). We found that it was important to consider the magnetoelastic interactions up to 2nd order in the strains and also the 3rd order elastic energy, to explain the measured non-degeneracy in the equivalent ways of measuring the shear SOE's and the strong dependence they show on the direction of the basal plane magnetization, although these higherorder terms contributions to the magnetostriction are small. Detailed calculation of the magnetoelastic contribution to the SOE envolves many magnetoelastic coupling constants and is beyond the purpose of this paper. (*) Work partially supported by FAPESP and CNPq. 2. The experiment. The SOE were determined with ultrasonic techniques, using the echo-overlap method. The magnetization curves were obtained with a vibrating sample magnetometer. The experiment was performed in a flowing-gas cryostat inserted in the bore of a 75 kOe superconductive magnet, and the SOE and magnetization. curves were determined in the same samples. 3. Experimental results. 3.1 TERBIUM. The magnitude of the dependence of Tb SOE on the 0 01 0.2 0 3 0 0.1 0 2 0 3 REDUCED MAGNETIZATION ( M / M O ) (a I b ) Fig. 1. General behavior of Tb and Dy elastic constants on magnetization, in the paramagnetic phase of these materials. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979511 MAGNETOELASTIC CONTRIBUTION TO THE ELASTIC CONSTANTS OF Tb, Dy AND Er C5-31 magnetization is more or less equal to that of Dy, in the paramagnetic region (figure 1). The nondegeneracy in 2 ways of measuring C,, is seen in the behavior of C,, , , and C3,,, (figure la), for magnetic field in the basal plane. The same effect occurs for Hd'c-axis (figure 2). Figure 3 shows that C,,,, is dependent on the direction of the applied field in the basal plane. The basal plane anisotropy is small in the paramagnetic region, so that this effect can only be attributed to the higherorder elastic and magnetoelastic terms. The contribution of the calculated 3rd order elastic energy to the magnetization dependence of Tb SOE is seen in figure 3 to be comparable, in magnitude, to the measured dependence. The 3rd order elastic energy was determined using calculated 3rd order elastic constants (TOE) [5] and static strains calculated in a numerical model in which the magnetoelastic constants were chosen to force the calculated strains to be equal to those measured experimentally [2]. Fig. 2. Non-degeneracy of C,3,3(u) and C,,,,(u). TO is the 3rd order elastic energy contribution to both these constants.

Basal plane magnetocrystalline anisotropy and ferromagnetic ordering in TbSc alloys

The basal plane anisotropy coefficient K66 has been measured for alloys of composition TbxSc1-x where x=0.89 and 0.825, at temperatures above 77K. The results have been compared with those of Bly (1967) for pure terbium and used in estimating the driving energies Fd to ferromagnetism at the Curie temperatures of the alloys. These are about -0.7K/atom, at least four times as great as for pure terbium, and indicate the extent to which a small scandium content makes the helical phase energetically favourable. The magnitude of Fd at 0K falls below 0.75K/atom when the scandium content reaches 20 at.%, in agreement with the absence of spontaneous ferromagnetic ordering in alloys with greater scandium content.

On the low-field susceptibility and the helical-ferromagnetic field-induced phase transition in holmium

The low-field susceptibility of holmium metal is calculated from the formula of Nagamiya et al. (1962) using the values of the exchange derived from inelastic neutron scattering. The temperature variation of the calculated susceptibility is in good agreement with the experimental data. The measured values are larger than the calculated values and this is tentatively ascribed to the presence of 'ferromagnetic' domain walls separating spirals of opposite sense. The field-induced transitions from the helical or conical to the ferromagnetic phase seem to be driven solely by the combined effects of the basal plane anisotropy and the b and c magnetostrictive energies. In contrast to the case of Dy it seems that in Ho there is no change of the exchange parameters at the field-induced transitions. The estimated effect of the anisotropic exchange K22(q), using the known values for Er, seems to be relatively unimportant within the temperature range covered by the helical phase.

Mossbauer effect study of Fe3Sn2

The intermetallic compound Fe3Sn2 has been studied by Mossbauer spectroscopy and magnetisation measurements. This compound is ferromagnetic from approximately 220K to Tc=657K. In this temperature range, the spin directions are close to or parallel to the c axis while at low temperature they are perpendicular to it. The mean magnetic moment is 2.1 mu B per iron atom at 4K. The spread in the 57Fe hyperfine fields is due to anisotropic contributions while the spread in the spin directions at low temperature is related to a weak basal plane anisotropy energy. The transferred fields at the 119Sn nucleus agree with the model deduced from 57Fe Mossbauer spectroscopy.

Magnetization and magnetocrystalline anisotropy of ND<inf>x</inf>Y<inf>1-x</inf>Co<inf>5</inf>alloys

The saturation magnetizations and anisotropy constants of alloys in the system Nd <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Y <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> Co <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</inf> have been determined as a function of temperature from 4.2K to the Curie temperature. Measurements were performed on specimens cut from single crystals grown from the melt. The saturation magnetizations of the alloys do not show the expected monotonic dependence on temperature, but peak at a temperature at which <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K_{1}\approx0</tex> . This behavior suggests the presence of large basal plane anisotropy. The anisotropy constants of the Nd <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> ion have been determined as a function of composition. The anisotropy of the Nd <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> ion is apparently not exclusively single ion.

Magnetocrystalline anisotropy in Y2Co17, Dy2Co17, and Y2xDy2(1−x)Co17 (x=1/3, 2/3)

The anisotropy constant K1 in the intermetallic compounds Y2Co17, Dy2Co17, and two pseudobinaries Y2xDy2(1−x)Co17 (x=1/3,2/3) is determined over the temperature range 77.4–383 °K. This constant is obtained by fitting the measured magnetization curves to the equation for magnetization along the hard axis derived by minimizing the sum of the magnetocrystalline anisotropy energy and the magnetic potential energy. All of the four compounds have an easy basal plane over the entire temperature range. The two pseudobinaries Y2/3Dy4/3Co17 and Y4/3Dy2/3Co17 develop basal-plane anisotropy at low temperatures. The contribution of the Dy sublattice to the anisotropy constant and the saturation magnetization is treated for single-ion behavior.

Magnetic anisotropy in dysprosium

The magnetic anisotropy of dysprosium has been measured with a vibrating sample magnetometer. In the ferromagnetic phase the basal plane anisotropy constant K6 was found to follow K6=15*105 sigma n J m-3, n=20.5+or-1, where sigma is the relative magnetization. K6 becomes positive in the fan phase. In the helix phase and in the paramagnetic phase, the susceptibilities in the basal plane ( chi ab) and along the c axis ( chi c) were found. A mean-field model which includes temperature-dependent exchange parameters is proposed, and chi ab and chi c have been calculated in this model with the strong crystal field taken fully into account.

The basal plane anisotropy in lithium rare earth fluorides

The paramagnetic phase magnetic properties of LiRF 4 (R = Tb, Dy, Ho, Er,Yb) are studied. Linear axial anisotropy has been used to fix R-site crystal field parameters excepting a common phase factor for B 4 4 and B 6 6. Nonlinear basal plane anisotropy is determined, fixing this phase and delivering sensitive checks on some crystal field parameters.

Measurements of the basal plane anisotropy energy of terbium at low temperatures

Measurements have been made of the basal plane anisotropy energy of terbium between 17.4 and 201.4 K in magnetic fields up to 4 T using a rotating sample magnetometer. The values found for K 6 6 are larger than existing data at low temperatures and are in good agreement with the temperature variation predicted for anisotropy of single-ion origin.

Field dependence of the basal plane anisotropy constant of dysprosium

The basal plane anisotropy constant K 6 6 of dysprosium has been measured over the temperature range 4.2–120 K in fields up to 15 T. The field dependence of K 6 6 is found to be −2.5 × 10 −4 Jm −3T −1 and the easy-direction value of K 6 6 is 20% larger than its mean value.

Changes of easy axis during the magnetization of dysprosium

Changes in the easy axis of magnetization of dysprosium, within the basal plane, between 77 and 160 K and in applied fields up to 1.25 T, reported by Bly et al. [1] have been reinvestigated and some inconsistencies have been resolved. Changes were only confirmed above 132 K, where the b axis is easy just above the critical field. On increasing the applied field the basal plane anisotropy dies away reappearing with the a axis easy. The changeover occurs at field and temperature values very close to those where a magnetoresistance anomaly has been observed by Akhavan et al. [2]. It is shown that this change may be explained in principle, without any change in the crystal field, by the narrowing of a fan-like spin structure occurring as an intermediate phase between the helical anti-ferromagnetic and the ferromagnetic phases. Between 77 and 110 K anomalies in torque curves in low fields are attributed to domain processes.

Spin waves in terbium. I. Two-ion magnetic anisotropy

The energies of spin waves propagating in the $c$ direction of Tb have been studied by inelastic neutron scattering, as a function of a magnetic field applied along the easy and hard directions in the basal plane, and as a function of temperature. From a general spin Hamiltonian, consistent with the symmetry, we deduce the dispersion relation for the spin waves in a basal-plane ferromagnet. This phenomenological spin-wave theory accounts for the observed behavior of the magnon energies in Tb. The two $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$-dependent Bogoliubov components of the magnon energies are derived from the experimental results, which are corrected for the effect of the direct coupling between the magnons and the phonons, and for the field dependence of the relative magnetization at finite temperatures. A large $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$-dependent difference between the two energy components is observed, showing that the anisotropy of the two-ion coupling between the magnetic moments in Tb is substantial. The $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$-dependent anisotropy deduced at 4.2 K is of the same order of magnitude as the isotropic part, and depends strongly on the orientation of the moments in the basal plane. The rapid decrease of both the axial- and the basal-plane anisotropy with increasing temperatures implies that the two-ion coupling is effectively isotropic above \ensuremath{\sim} 150 K. We present arguments for concluding that, among the mechanisms which may introduce anisotropic two-ion couplings in the rare-earth metals, the modification of the indirect exchange interaction by the spin-orbit coupling of the conduction electrons is of greatest importance.

Spin waves in terbium. III. Magnetic anisotropy at zero wave vector

The energy gap at zero wave vector in the spin-wave dispersion relation of ferromagnetic. Tb has been studied by inelastic neutron scattering. The energy was measured as a function of temperature and applied magnetic field, and the dynamic anisotropy parameters were deduced from the results. The axial anisotropy is found to depend sensitively on the orientation of the magnetic moments in the basal plane. This behavior is shown to be a convincing indication of considerable two-ion contributions to the magnetic anisotropy at zero wave vector. With the exception of the sixfold basal-plane anisotropy of the unstrained lattice, the dynamic anisotropy parameters deduced from our results agree with macroscopic measurements both with respect to the magnitudes (at zero temperature) and the temperature dependences. The deviations observed cannot be explained by existing theories which include the effects of zero-point deviations from the fully aligned ground state, and we tentatively propose polarization-dependent two-ion couplings as their origin.

Crystal fields and exchange in dilute alloys of Tb, Dy, and Er in Y studied for different concentrations

This is a sequel to an earlier paper reporting magnetization measurements on Y-0.14-at.%-Dy and Y-0.14-at.%-Er. In the present paper we have performed similar measurements on different concentrations of dilute Er, Dy, and Tb alloys and also included specific measurements of the basal-plane anisotropy. Crystal-field and exchange parameters were obtained by fits to the inverse initial susceptibility. The anisotropy measurements provide a confirmation of the crystal-field parameters in Dy and Er and are used to deduce ${B}_{66}$ in Tb. The measurements on different concentrations confirm the adequacy of the theoretical models used. The crystal-field parameters vary substantially with the solute. The molecular-field tensors are highly anisotropic and are approximately independent of concentration at small concentrations.