The contribution of 5d electrons to the saturation magnetic moments and magnetic hyperfine fields in the heavy rare earth metals

The main results of a model for 5d electrons in the heavy rare earth metals are presented. The model involves the use of wave functions based on published analyses for 4fⁿ5d6s² atomic configurations, and the spreading of each of these energy levels uniformly over a band of width W in the metals. Excess saturation magnetic moments above those of the tripositive ions can be explained by the model with W in the range 0.84±0.16eV in the five metals Gd, Tb, Dy, Er and Tm. The magnetic hyperfine fields in the metals include negative contributions from the 5d electrons which have been shown to amount to about ?250koe in Gd, Er and Tm.     

Models for the heavy rare earth metals and (rare earth) Fe2 compounds involving 5d and 6s electrons

A model involving 5d electrons is introduced to explain the differences between the observed saturation moments in the heavy rare earth metals and those of the corresponding tripositive ions. Atomic 5d states, whose energies are determined by 4f–5d and spin-orbit interactions, are assumed to be broadened into partly overlapping bands with individual widths of the order of 1 eV. The 5d electrons produce negative contributions to the hyperfine fields but positive or near zero contributions to the magnetic moments. It is postulated that the 5d electrons are transferred from the rare earth ions to those of the iron in the (Rare Earth) Fe₂ compounds. This leads to increases in the magnetic hyperfine fields because the negative 5d contributions are lost, but in detailed application of the model increases in the 6s contributions also play a large part. Published energy level and wave function analyses for atomic Gd, Tb, Dy, Er and Tm are used in order to apply the theory to these materials.     

Investigation of the impurity hyperfine field polarization in polycrystalline Rare Earth ferromagnets

Time differential perturbed angular correlation spectra of¹¹¹Cd in ferromagnetic polycrystalline Dy have been measured at 4.2 K in external magnetic fields up to 60 kG. The experimental data were well reproduced by a calculation which assumed that the angular distribution of the magnetic hyperfine fields is identical to that of the magnetic moments of the 4f-shells. The distribution of the 4f-moments was derived from magnetic anisotropy data. The results of this work seem to justify the application of the integral perturbed angular correlation technique for the determination of magnetic hyperfine fields in incompletely polarized ferromagnetic samples. The magnetic hyperfine fields of¹⁷⁷Hf:Gd and¹⁷⁷Hf:Dy have been measured by this method as:H _hf(Hf:Gd)=–375(60)kG andH _hf(Hf:Dy)=–225(45)kG.     

Hyperfine interactions in intermetallic compounds between Gd and 3d transition metals

Measurements of hyperfine interactions at ¹⁵⁵Gd nuclei in metallic compounds between Gd and 3d transition metals and at ⁶¹Ni in GdNi compounds by Mössbauer spectroscopy are reported. The results are discussed in terms of various models proposed for the electronic structure of these compounds. The Gd isomer shifts with respect to metallic Gd are at variance with the model of a strong d electron transfer from rare earths to transition metal ions. From the observation of a linear relation between magnetic hyperfine fields at Gd and at Dy nuclei in corresponding compounds it is inferred that crystal-field induced variations of Dy moments are neglible and that the conduction electron polarization induced by 4f moments is directly related to that caused by 3d moments.     

The magnetic hyperfine field at Cd nuclei in the rare earth ferromagnets Gd,Tb, Dy,Ho, Er and Tm

The time differential perturbed angular correlation technique has been used to study the combined magnetic and electric hyperfine interactions at the site of a¹¹¹Cd impurity in the rare earth ferromagnets Gd, Tb, Dy, Ho, Er, and Tm at 4.2 °K. The following magnetic hyperfine fields at the site of¹¹¹Cd have been found: ¦H _hf ¦=340(7) kG in Gd, 275 (5) kG in Tb, 221 (4) kG in Dy, 116 (3) kG in Er and 60 (6) kG in Tm. In Ho two magnetically different sites were observed with magnetic fields of 159 (3) and 139 (3) kG. Both sites are equally populated. The coupling constantJ _5f of the conduction electron-4f interaction has been calculated for the different rare earth metals from the measured hyperfine fields by means of the RKKY theory.     

A characteristic class of quantities in nonequilibrium thermodynamics and a statistical justification of the local equilibrium approximation

A theory of bandwidth anisotropy in metallic ferromagnets developed previously is specialised to the case of 5d electrons in a hexagonal close-packed lattice. This theory is combined with a model for 5d electrons in the heavy rare earth metals to give a new theory for the low temperature values of the magnetic anisotropy coefficientsκ ₂ ⁰ andκ ₄ ⁰ in Tb, Dy, Ho, Er and Tm. In this theory the magnetic anisotropy is due to a combination of (i) crystal fields acting on 5d and 4f electrons and (ii) bandwidth anisotropy associated with a dependence of 5d bandwidths on magnetization direction. After use is made of empirical upper limits on the eighth order magnetic anisotropy in Gd, there remain four partially adjustable parameters of importance in the theory. These can be chosen to give a good fit to the six observed values forκ ₂ ⁰ andκ ₄ ⁰ in Tb, Dy and Ho. Crystal fields corresponding to negative point charges are seen by 5d electrons, but because of 4f – 5d interactions effective fields of larger magnitude and opposite sign act on 4f shells. Bandwidth anisotropy gives a significant contribution toκ ₄ ⁰ of opposite sign to that due to crystal fields, and dominates the latter in Tb and Er.     

Investigation of the magnetic hyperfine field at197Au impurities in the heavy Rare Earth metals

The Mössbauer effect has been used to measure the magnetic hyperfine field at the site of¹⁹⁷Au impurities in the heavy Rare Earth metals Gd, Tb, Dy, Ho and Er at 4.2 K. The magnetic hyperfine field decreases in a non linear way with decreasing spin of the Rare Earth host. For¹⁹⁷Au this decrease is stronger than for any other impurity investigated up to now. Possible reasons for this behaviour are discussed.     

Magnetic properties of some RPd2Si2 compounds (R=Gd,Tb, Dy,Ho and Er)

The magnetic susceptibility of the ternary compounds, RPd₂Si₂ (where R=Gd, Tb, Dy, Ho and Er) has been measured. GdPd₂Si₂ order antiferromagnetically at 13 and 20 K respectively; the rest of the compounds do not show clear ordering down to 4.2 K. Palladium carries no moment in these compounds. The De Gennes formula is not obeyed indicating that the exchange interaction between the 4f moments via conduction electrons is not isotropic     

Hyperfine field of156Gd in TbFe2, TbFe3, TbCo2 and TbCo3 compounds

Time integral γ-γ angular correlation measurements have been made on¹⁵⁶Gd in Tb-3d metal compounds, TbFe₂, TbFe₃, TbCo₂ and TbCo₃, using two Ge(Li) detetctors. From the observation of a linear relation between magnetic hyperfine fields at Gd and Tb nuclei in corresponding compounds, it is inferred that crystalfield induced variations of the Tb moment are negligible. The experimental results are discussed in terms of the conduction electron polarization caused by the magnetic moment of 3d metals.     

Investigations of crystal and magnetic properties of Dy-Fe intermetallic compounds

The crystal and magnetic properties of Dy₂Fe₁₇, Dy₆Fe₂₃, DyFe₃ and DyFe₂ intermetallic compounds are investigated with X-ray, magnetometric, ⁵⁷Fe and ¹⁶¹Dy Mössbauer effect methods. The X-ray analysis shows that investigated compounds are single phases with Th₂Ni₁₇, Th₆Mn₂₃, PuNi₃ and NgCu₂ type crystal structures, respectively. The magnetometric measurements prove their ferrimagnetic behaviour, localization of Fe magnetic moments and long range Fe-Fe exchange magnetic interactions. The crystal field effects induce magnetic anisotropy which results in local magnetic symmetry or iron atoms lower than the crystal one. This is observed by the Mössbauer effect method. The values of ¹⁶¹Dy hyperfine magnetic fields measured for investigated compounds exceed that found in metallic dysprosium due to polarization of conduction electrons by 3d-electrons of iron atoms. The weighted average value of ⁵⁷Fe hyperfine magnetic field decreases with the increase of Dy content in the compounds.     

Spin and temperature dependence of the magnetic hyperfine field of Cd in the rare earth-aluminum Lavesphase compounds RAl2

Perturbed angular correlation spectroscopy has been used to investigate the combined magnetic and electric hyperfine interaction of the probe nucleus ¹¹¹Cd in ferromagnetically ordered rare earth (R)-dialuminides RAl₂ as a function of temperature for the rare earth constituents R=Pr, Nd, Sm, Eu, Tb, Dy, Ho and Er. In compounds with two magnetically non-equivalent Al sites (R=Sm, Tb, Ho, Er), the magnetic hyperfine field was found to be strongly anisotropic. This anisotropy is much greater than the anisotropic dipolar fields, suggesting a contribution of the anisotropic 4f-electron density to magnetic hyperfine field at the closed-shell probe nucleus. The spin dependence of the magnetic hyperfine field reflects a decrease of the effective exchange parameter of the indirect coupling with increasing R atomic number. For the compounds with the R constituents R=Pr, Nd, Tb, Dy and Ho the parameters B₄, B₆ of the interaction of the crystal field interaction have been determined from the temperature dependence of the magnetic hyperfine field. The ¹¹¹Cd PAC spectrum of EuAl₂ at 9 K confirms the antiferromagnetic structure of this compound.     

Hyperfine field of156Gd in Tb(Zn1−xCux) with x=0, 0.36, 0.46

Time-integral - perturbed angular correlation measurements have been made on¹⁵⁶Gd nuclei in TbZn_1–xCu_x using two Ge(Li) detectors. The hyperfine fields at¹⁵⁶Gd nuclei in TbZn_1–xCu_x at 77 K are found to be –177±26, –104±24 and –27±38 kOe for TbZn, TbZn_0.64Cu_0.36 and TbZn_0.54Cu_0.46, respectively. These values indicate that the transferred hyperfine fields at Gd nuclei are positive due to the exchange interaction of s-f type.     

The Magnetic Hyperfine Field of 111Cd in the Rare Earth–Nickel Laves Phases RNi2

The magnetic hyperfine field of ¹¹¹Cd in the C15 Laves phases RNi₂ has been investigated by perturbed angular correlation (PAC) spectroscopy as a function of temperature for the rare earth constituents R = Nd, Sm, Gd, Tb, Dy, Ho, Er, and Tm.     

Mössbauer and magnetic studies of orthorhombic FeSiO3

Magnetic properties of orthoferrosilite FeSiO₃ have been examined using susceptibility, magnetization measurements and Mössbauer spectroscopy. From magnetic and Mössbauer measurements, one obtains close values of the magnetic ordering temperature, T_N=39±1 K and T_N=41±1 K, respectively. The magnetic order is characterized by strong ferromagnetic coupling of Fe²⁺ moments within the ribbons and a weak antiferromagnetic coupling of the moments between adjacent ribbons. The 4.2 K Mössbauer spectra can be fitted with two different hyperfine magnetic fields H_hf=68 kOe and H_hf=314 kOe which can be assigned to Fe²⁺ in the octahedrally coordinated M1 and M2 sites, respectively, of the FeSiO₃ structure.     

Hyperfine magnetic fields in Fe−Co alloys and their tempera ture dependences

We obtained⁵⁷Fe hyperfine field parameters from Fe₁−x-Co _x alloys (0≤x≤0.6) from 77 K to 900 K. We first discuss the origin of the low temperature hyperfine fields in terms of the 3d and 4s electrons at⁵⁷Fe atoms. The⁵⁷Fe hyperfine magnetic field (hmf) of Fe-Co alloys depends more weakly on temperature than the hmf of pure Fe. This temperature dependence occurs because the alignment of the magnetic moments at both the Fe atoms and at the Co atoms depend on temperature in the same way as the bulk magnetization of Fe-Co alloys.     

Nuclear magnetic resonance of RCo3(R:Rare earth)

The nuclear magnetic resonance of⁵⁹Co nuclei in magnetic domains of RCo₃(R:Y, Nd, Sm, Gd, Tb, Dy and Ho) has been measured under external fields up to about 50 kOe at 4.2 K. To assign the observed NMR signals to each Co site, the⁵⁹Co nuclear magnetic resonance of R(Co_1−xNi_x)₃ and R(Co_1−xFe_x)₃ has also been measured under the same conditions. The results of NMR studies show that the cobalt atoms at the 6c site in the light R compounds(YCo₃, NdCo₃ and SmCo₃) and these at the 3b site in the heavy R compounds(GdCo₃, TbCo₃ and HoCo₃) have a large orbital contribution.     

Effective magnetic moments of the europium-monochalcogenides

We have measured the paramagnetic susceptibility and the saturation magnetic moment of a number of polycrystalline samples of all four europium monochalcogenides. Many of them exhibit a negative susceptibility at 2 K and magnetic fields of 70 kOe, rather than the expected saturation behaviour. These anomalies are believed to be due to lattice defects. Reproducible saturation moments have been obtained after subtraction of this linear high field magnetization. Since all materials were nonstoichiometric to within a few percent, the ratio between the Curie-Weiss constantC and the saturation momentM ₀ has been evaluated in order to eliminate the unreliably known numberN of the Eu^{+ +} ions. The quantityR = g _J (J+1) extracted in this way should have the valueR ₀ = 9.00 forg = 2 andJ ≡S = 7/2. The measured values, 9.72, 9.33, 9.32 and 9.50 for EuO, EuS, EuSe and EuTe, respectively, can be correlated directly with the magnetic hyperfine fields, which are ? 305, ? 330, ? 328 and ? 315 kOe in the ferromagnetic aligned states. Both results together lead to the assumption that the magnetic moment per Eu-ion is enhanced over the⁸ S _7/2-value by spin contributions of outer 5d or 6s electrons.     

Magnetic behaviour of Tb impurities in Gd andY single crystals: a nuclear orientation study

The low temperature nuclear orientation of¹⁶⁰Tb impurities in Gd andY single crystals has been studied in the temperature range 7–40 mK andin the external magnetic field range 0–7.3 T applied alonga-, b- andc-crystal axes. In the case of Tb in Gd we found a considerable noncollinearity of the Tb magnetic moment with respect to the magnetic external field direction even for highB _ext. In the case of Tb in Y the results cannot be described by a simple model, taking into account the simultaneous influence of the crystal andexternal magnetic fields. Some new proposals for interpretation of the experimental dat are given.     

Paramagnetic and spin-glass properties of pyrochlore-like oxides Ln2Mn2/3Mo4/3O7 (Ln=Sm, Gd, Tb, or Y)

The magnetic properties of complex oxides Ln ₂Mn_2/3Mo_4/3O₇ (Ln=Sm, Gd, Tb, or Y) with a pyrochlore-type structure are studied in the temperature range 2–300 K. For all compounds in the paramagnetic state, the temperature dependence of the magnetic susceptibility is described by a generalized Curie-Weiss law with a temperature-independent component of ∼10⁻⁶ cm³/g and with a Weiss constant Θ<0 and |Θ|<16 K. At low temperatures (T<10–12 K), the compounds have spin-glass properties; they exhibit magnetic and temperature hysteresis and the typical dependences of the imaginary and real parts of the dynamic magnetic susceptibility on temperature and the frequency of an ac magnetic field in a wide range of magnetization relaxation times. The data obtained suggest that d electrons are responsible for the formation of frustrated exchange interactions in the compounds and that 4f electrons in the compounds with Sm or Tb provide strong magnetic-anisotropy effects. __________ Translated from Fizika Tverdogo Tela, Vol. 46, No. 2, 2004, pp. 287–295. Original Russian Text Copyright ? 2004 by Korolev, Bazuev.     

The magnetic hyperfine field at140Ce in nickel

The hyperfine interaction of¹⁴⁰Ce in nickel has been investigated by the time-differential perturbed-angular-correlation technique (TDPAC). The probe was produced by isotope separator implantation of the fission product¹⁴⁰Xe, the ^- decay chain of which finally populates excited states of¹⁴⁰Ce.Different spin rotation spectra were observed before and after an 8 h annealing at 415°C. The analysis of the spectra led to the conclusion that the Ce ions were in the diamagnetic 4⁺ state. The dominant contributions to the hyperfine interaction are two different magnetic hyperfine fields: |H _hf ¹|=385±7 kOe and |H _hf ²|=276±12 kOe.H _hf ¹ disappears after annealing. The fraction of nuclei which observeH _hf ² is increased by the annealing procedure from 16% to 75%. It is assumed thatH _hf ¹ is the hyperfine field of CeNi in an unperturbed substitutional site andH _hf ² is attributed to Ce ions which have trapped a single vacancy.