Spontaneous magnetostriction in R2Fe14B (R=Y,Nd, Gd,Tb, Er)

Thermal expansion anomalies of R₂Fe₁₄B (R=Y, Nd, Gd, Tb, Er) stoichiometric compounds were studied by X-ray diffraction with high-energy synchrotron radiation using a Debye–Scherrer geometry in temperature range of ∼10–1000 K. A large invar effect with a corresponding large temperature dependence of lattice parameters ∼10–15 K above their Curie temperatures (T_c) are observed. The a-axes show a larger invar effect than the c-axes in all compounds. The spontaneous magnetostrain of the lattices and bonds are calculated. The iron sublattice is shown to dominate the volumetric spontaneous magnetostriction of the compounds and the contribution from the rare-earth sublattice is roughly proportional to the spin magnetic moment of the rare earths. The bond-length changes are consistent with the theoretical spin-density calculation. The average bonds magnetostrain around Fe sites is approximately proportional to their magnetic moments.     

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.     

Hydrogen absorption and its effect on the magnetic properties of rare-earth iron intermetallics

X-ray diffraction studies of the hydrogen absorption in several YFe and CeFe intermetallic compounds showed that no structural changes occur upon hydrogen absorption in Y₆Fe₂₃, YFe₃, YFe₂. The lattice constants of the hydrides were found to be appreciably larger than those of the pure intermetallic compounds. The magnetic properties of the hydrides were determined and compared with the original compounds. In all cases the magnetic moment per Fe atom proved to be much larger in the hydride phases. Hydrogen absorption can lead to a decrease as well as to an increase of the magnetic ordering temperature (T_c). These changes in T_c could adequately be explained in terms of the observed increases in lattice constant and the data available for the pressure derivative of T_c of these compounds.     

Effect of hydrogenation on the magnetic and magnetoelastic properties of R 2Fe14B compounds (R = Nd, Gd, Er, Lu)

The temperature dependences of the magnetization σ(T), magnetostriction λ(T), and linear thermal expansion coefficient α(T) of R ₂Fe₁₄B intermetallic compounds (R = Nd, Gd, Er, Lu) and of their hydrides R ₂Fe₁₄BH_2.5 are studied. The magnetization was measured with a pendulum magnetometer within the temperature interval 77–700 K in a magnetic field H = 500 Oe. Magnetostriction and thermal expansion were measured using the tensometric technique in the temperature interval 77–420 K. It was established that Gd₂Fe₁₄BH_2.5 undergoes a spin-reorientational (SR) transition at T _SR = 235 K. In compounds with Nd and Er, anomalies associated with the SR transition were found in the σ(T), λ(T), and α(T) curves. The SR transition temperatures were refined and magnetic phase diagrams were constructed for the compounds studied. The α(T) curves of the R ₂Fe₁₄BH_2.5 hydrides (R = Nd, Er) revealed anomalies of a nonmagnetic origin associated with hydrogen ordering in the crystal lattice of these compounds.     

A Mössbauer spectroscopic study of 3d magnetism of R2Fe14B

Guided by the occupancies and iron magnetic moments μ³, ⁵⁷Fe Mössbauer parameters of Y₂Fe₁₄B at 250K, and in turn for other temperatures, of the sublattices of iron were deduced. Plots of μ(T) in reduced coordinates, through the established correlation between hyperfine field Hn and μ, show that the corresponding state of different iron sites is different and all experimental points fall below Brillouin function. The relation between exchange integral deviation parameter Δ and standard deviation of Fe-Fe interatomic distances S is linear, indicating electrostatic nature of exchange interactions between spins in neighboring atoms. It is inclined to the view that fluctuations of exchange integral is responsible for low T_c of R₂Fe₁₄B.     

Positive muon spectroscopy of R2Fe14B

Muon spin rotation (μSR) experiments were performed on polycrystalline samples of R₂Fe₁₄B in zero applied field. In all samples a single spin precession frequency was observed. In Nd₂Fe₁₄B and Ho₂Fe₁₄B pronounced anomalies showed up in the temperature dependence of the μSR frequencies at the spin reorientation temperatures of 150 K and 60 K, respectively. Our data can be explained with the assumption that only thec-axis component of the magnetization is sampled by the muon. We find a strong dependence of the local field on the magnetic moment of the rare earth ion. This is in accordance with calculations of the dipolar fields at the assumed muon stopping site.     

Mössbauer study of the intermetallic compound Nd2Fe14B. II. Temperature dependence and spin reorientation

The ⁵⁷Fe Mössbauer effects of Nd₂Fe₁₄B were measured in a temperature range of 4.2−300 K. Below the spin reorientation transition temperature T_sc = 148 K, the spectra were satisfactorily analyzed with twelve Zeeman sextuplets due to splitting of six crystallographic Fe-sites into twelve non-equivalent sites. It was shown that the magnetic moments of the Fe and the Nd atoms are non-collinearly coupled in the magnetic structure with canted moments below T_sc. The directions of the moments at 4.2 K are inclined at 27° for Fe and at 58° for Nd from the c-axis to the [110] direction. The average moments are 2.27μ_B for Fe and 3.3μ_B for Nd at 4.2 K. The increase of the average hyperfine field with decreasing temperature is suppressed below T_sc, and its value at 4.2 K is reduced by 1% from the value of 337 kOe which is observed in Y₂Fe₁₄B and also estimated for Nd₂Fe₁₄B by extrapolating the values above T_sc. On the other hand, the Nd moment increases abruptly around T_sc as the temperature decreases. The directions of the principal axes of electric field gradients on the six distinct Fe-sites were also obtained. The anomalous temperature dependence of quadrupole splittings and isomer shifts was observed around T_sc. They were discussed in a framework of the changes in the band structure and the lattice parameters incidental to the spin reorientation transition.     

Magnetic order and hyperfine interactions in RFe6Al6 (R = rare earth)

The systems RFe₆Al₆(R = Y, Eu, Gd, Tb, Dy, Ho, Er, Tm and Yb) crystallize in the tetragonal body centered I4/mmm structure. In striking contrast to the magnetic behaviour of RFe₄Al₈ (weakly coupled R and Fe sublattices, complicated magnetic structure, low T_c ~ 130 K), in the RFe₆Al₆ systems all magnetic sublattices order simultaneously at a relatively high temperature. The magnetization curves start with low values at low temperatures and rise to very high values at T_max ~ 230 K and then drop to 0 at T_c ~ 330 K. All samples show strong hysteresis effects at temperatures just below T_max. Mossbauer studies of ⁵⁷Fe in the (f) and (j) sites and ¹⁵¹Eu, ¹⁵⁵Gd, ¹⁶¹Dy, ¹⁶⁶Er and ¹⁷⁰Yb in the (a) site yield all hyperfine interaction parameters and temperature dependence of the local magnetic moments. All Mossbauer and magnetization experimental results can be explained in a self consistent way with a simple molecular field model. The Fe in the (j) site plays the dominant role in its strong intrasublattice ferromagnetic exchange and its strong antiferromagnetic exchange with the rare earth site. The Fe in the (f) site have an antiferromagnetic intrasublattice exchange, they have a canted strcuture with the ferromagnetic component parallel to the (j) sublattice magnetization.     

Effective magnetic fields on Fe in R1+εFe4B4 alloys

⁵⁷Fe Mössbauer spectra of magnetically ordered R_1+εFe₄B₄ alloys have been measured at low temperatures. Small (⋍ 0.8 T) hyperfine fields have been found for R = Sm and Dy. Analysis of the spectra in terms of simultaneous magnetic and quadrupolar interactions has revealed the magnetization to be parallel to the c axis for R = Sm and perpendicular to the c axis for R = Dy. These results are consistent with a 2^nd-order CEF mechanism for anisotropy. The ordering temperature of Sm_1+εFe₄B₄ was determined from Mössbauer and magnetization measurements to be T_c = 37 ± 2 K, the highest in the R_1+εFe₄B₄ series.     

Pressure-Induced Decrease in the Curie Temperature of Gd<Subscript>2</Subscript>Fe<Subscript>17</Subscript>: LSDA+U Calculations

To explain the magnetic properties of advanced ferromagnetic intermetallic compounds of the R₂Fe₁₇ (R is a rare-earth element) class, experimentalists often use the hypothesis of competition between ferromagnetic exchange and antiferromagnetic exchange between four types of the nearest iron atoms in nonequivalent lattice sites. For the rhombohedral Gd₂Fe₁₇ ferromagnet, we calculate the magnetic moments of iron and gadolinium ions, the parameters of exchange between Fe atoms, and Curie temperature T_C at a zero pressure and during hydrostatic lattice compression. The magnetic moment of the unit cell of Gd₂Fe₁₇ is shown to decrease under pressure, and this decrease is almost completely associated with a decrease in the magnetic moments of Fe rather than Gd ions, the pressure dependence of the magnetic moments of which is weaker by an order of magnitude. In contrast to the hypothesis regarding the competition of exchange interactions between different kinds of Fe atoms, the parameters of exchange between the nearest iron atoms in different crystallographic sites are found to be positive ferromagnetic (at a zero pressure and during compression), and a ferromagnetic character of interaction is shown to remain unchanged under pressure even for Fe atoms in the so-called dumbbell sites with the nearest interatomic distances. The Curie temperature T_C of Gd₂Fe₁₇ is shown to decrease with increasing pressure. The changes in the exchange parameters and the magnetic moments of Gd₂Fe₁₇ during compression are found to be mainly related to a change in the position of energy spectrum branches with respect to each other and the Fermi level ?_F rather than to a change in the overlapping of wavefunctions, which play a minor role.     

Angular dependence of the coercive force of textured rare earth permanent magnets

On the basis of model calculations experimental results on the angular dependence of the coercivity H_c and the remanence coercivity H_R of hard magnetic materials of the type SmCo₅, Sm₂(Co, Fe, Cu, Zr)₁₅ and Nd₂Fe₁₄B are discussed. In the model coherent rotation as well as incoherent magnetization jumps (e.g. 180°-Bloch walls) are included. The texture is described by an axial symmetric distribution of the easy axes with only oneparameter. For Sm₂(Co, Fe, Cu, Zr)₁₅ the model explains irreversible (H_R (θ)-curves) as well as reversible (H_R(θ)−H_c(θ)) magnetization processesin good agreement with the experiments, whereas stronger deviations exist for SmCo₅ and Nd₂Fe₁₄B, especially in the H_c(θ)-curves. These deviations should be caused by other reversible magnetization processes     

Changes in vibrational modes near the magnetic phase transition in magnetostrictive materials

Mössbauer studies of ⁵⁷Fe in RFe₂ (R = Y, Tb, Dy, Ho) at temperatures 300 to 800 K and in R(Co_0.98Fe_0.02)₂ (R = Tb, Dy) at temperatures 85 to 300 K have been performed. The spectra yield the temperature dependence of the easy axis of magnetization, the magnetic hyperfine fields, electric field gradients and isomer shift. From the total Mössbauer absorption area the recoil free fraction was determined. The relative intensities of the various Mössbauer absorption lines yield the anisotropy in the recoil free fraction. In all compounds, except in YFe₂, all measured quantities show large variations near the magnetic phase transition temperature (T_c). The variation in the recoil free fraction and in its anisotropy and the variation in the electric field gradient are all consistent, quantitatively, with anisotropic softening in the vibration modes of the Fe nucleus near T_c In RFe₂ the modes in which the iron vibrates along the local C_3h symmetry axes are softened less than the perpendicular modes. In RCo₂ it is the other way around. It seems, that these critical softening phenomena are due to the strong magnon-phonon coupling present in these materials and absent in YFe₂. This conclusion is confirmed by a theoretical analysis given in an adjacent paper. In it we use the Green function method to calculate the average of the square of vibrational amplitudes in a Debye solid with a strong magnon-phonon coupling at temperatures close to the magnetic phase transition. We show that these amplitudes may increase or decrease near T_c depending on the details of the coupled system.     

Tetragonal rare earth (R) Iron borides,R1+εFe4B4 (ε≅0.1), with incommensurate rare earth and iron substructures

Crystallographic and magnetic properties of a new structural series of ternary borides with composition R_1+εFe₄B₄ (R = Ce, Pr, Nd, Sm, Gd, Tb, 0.11(Pr) ≤ε≤ 0.15(Tb) are reported. The compounds are built of incommensurate substructures of rare earth atoms (linear strings ?? c?), iron atoms (chains of edge sharing tetrahedra ?? c?),and boron atom pairs. A single crystal X-ray diffraction study of one representative (Sm_1.13Fe₄B₄) based on a commensurate structure model (composition : Sm₁₇(Fe₄B₄)₁₅, a = 7.07 Å, c ≡ 17c_Sm ≡ 15c_Fe= 58.69 Å, space group P4₂/n) revealed a periodic twist modulation of the Fe tetrahedra chains around c?. Magnetic susceptibility measurements on single crystals of another representative (Nd_1.11Fe₄B₄) revealed ferromagnetic ordering at T_c = 13 K. Above this temperature the magnetic properties are dominated by ferromagnetic inclusions (Fe₂B, Nd₂Fe₁₄B).     

Magnetic properties of rare earth-transition metal compounds

A survey is given of results obtained by means of rare earth and⁵⁷Fe Mössbauer spectroscopy on intermetallic compounds of rare earths (R) and 3d metals (M). It is shown how these results can be used to obtain experimental information on crystal field effects, magnetic anisotropy, magnetic moments and magnetic coupling constants. The types of compounds considered in this review comprise RM₅, R₂M₁₇, R₂Fe₁₄B, R₂Fe₁₄C, R₂Fe₁₇C _x and RFe₁₀V₂. The results obtained by Mössbauer spectroscopy are compared with other techniques and the discussion of relevant theoretical models is included.     

Magnetic and 57Fe Mössbauer studies of collinear spin rotation in Ho2Fe14B

Magnetic properties of Ho₂Fe₁₄B compounds have been studied by the ⁵⁷Fe Mössbauer effect and magnetization measurements. The axes of easy and hard magnetizations lie along the [001] and the [100] directions in the tetragonal structure, respectively, above T_sc = 58 K. From the comparison of the Mössbauer results with the magnetization measurements, it became clear that the Fe and the Ho moments tilt collinearly from the c-axis to the [110] direction throughout the temperature range of 4.2–58 K, and the canting angle reaches to 22° at 4.2 K. The Mössbauer spectra are consistently resolved with six subspectra above T_sc and with twelve below T_sc, together with reasonable site-assignments. We have estimated the mean Ho moment at 10.0μ_B, using the mean Fe moment of 2.3μ_B derived from the average hyperfine field or using the magnetization of Y₂Fe₁₄B as the Fe-sublattice magnetization of Ho₂Fe₁₄B.     

Magnetic hyperfine fields of (Nd2Fe1-xCox)14B AT x = 0.25 between 100 and 780 K

The ⁵⁷Fe Mössbauer spectra are recorded in Nd₂(Fe_1-xCo_x)₁₄B at x = 0.25 in the temperature range 100 to 780 K. T_c the Curie temperature, B̄_hf, the magnetic hyperfine field average over various Fe nuclei of the unit cell and its temperature coefficient α(B̄_hf) in the vicinity of 300 K are found to be 760(5) K, 34.0(3) T and -0.08(1)% K^-1, respectively. The magnetic moment at Fe atoms is estimated to increase up to 12% as a result of the partial substitution by Co atoms. The dependence of the fields upon temperature is observed to be least at the j₂ and k₂ sites as compared to the other sites of Fe. The results for the variation of B_hf at all of the six sites of Fe with respect to temperature are given. A site preference of Fe atoms for the j₂ sites is observed.     

A note on exchange and crystal field interactions in R2Fe14B compounds: Yb2Fe14B

The R₂Fe₁₄B phase has been found to exist for R=Yb. The magnetic properties presented in this paper complete the characterization of the compounds in this series for which the Stevens α_J coefficient of the R³⁺ ion is positive. ⁵⁷Fe Mössbauer spectroscopy establishes the existence of a magnetization reorientation at 115 K of the type observed in Er and Tm compounds associated with a small Fe magnetization anisotropy. From the neutron diffraction measurements obtained at 4.2 K with and without an applied magnetic field, the easy direction of magnetization was found to be along the [100] direction, in the basal plane of the tetragonal structure. These results show that in all compounds where α_J>0 for the R³⁺ ion, the easy direction of magnetization in the plane is determined by the second order crystal field terms and rare earth-Fe exchange interactions and is independent of the sign of the 4th order crystal field terms.     

Mössbauer spectroscopy of R2Fe14B and related compounds

The Mössbauer Spectroscopy (MBS) has been widely used in the last 4 years for the study of the recently discovered ternary compounds R₂Fe₁₄B where R means Y, Th or a rare earth element. The strong interest for this class of intermetallics arose drastically after the discovery of the exceptional properties of Nd₂Fe₁₄ as an ideal material for permanent magnet applications. The newest results about hyperfine fields B_HF, quadrupole splitting E_Q and isomer shifts I.S. at the 6 crystallographically different Fe sites and at the 2 R sites in the R₂Fe₁₄B and their impact on the understanding of the local magnetic moments and magnetocrystalline anisotropy will be reviewed. In the case of RFe_12?xM_x compounds where M=V, Ti, Si, Mo, W, Cr, complex Mössbauer spectra were obtained because of the presence of 3 crystallographically inequivalent Fe sites and the presence of differents amounts of the M component on one or more of these sites.     

Effect of interstitial atoms on the effective exchange fields in ferrimagnetic rare-earth and 3d transition metal compounds R2Fe17 and RFe11Ti

The magnetic properties (magnetic ordering temperature, magnetization) of the ferrimagnetic compounds R ₂Fe₁₇ and RFe₁₁Ti, as well as of their hydrides and nitrides, were studied. The hydrogenation-and nitrogenation-induced variation of the exchange fields acting on the rare-earth (RE) ions from both the Fe sublattice and other RE ions was determined, and the dependence of the Curie temperatures of the starting compounds, their hydrides, and nitrides on the de Gennes factor was revealed. It was found that incorporation of light atoms (H, N) into the crystal lattices of RFe₁₁Ti and R ₂Fe₁₇ increases the Curie temperature T _C substantially, increases the Fe-Fe exchange coupling, and decreases the R-R exchange interactions, as well as increases the R-Fe intersublattice exchange under hydrogenation and decreases it under nitrogenation, an effect that can be understood as resulting from the attendant changes in the electronic structure of these compounds and in the indirect exchange interactions. __________ Translated from Fizika Tverdogo Tela, Vol. 45, No. 10, 2003, pp. 1850–1856. Original Russian Text Copyright ? 2003 by Nikitin, Tereshina.     

Evidence against reentrant magnetic behaviour in AuFe alloys

The temperature and concentration dependence of the transferred hyperfine field in Au_1−xFe_x with 0.15<x<0.28, was measured by perturbed angular correlation spectroscopy. The temperature dependence of the hyperfine field at the ¹¹¹Cd probe shows a slope change at T/T_c=0.25 for all concentrations below 20 at% Fe, but an almost continuous behaviour for higher concentrations. These results manifest a percolation-like magnetic behaviour but no magnetic double transition.