G. Wigger - Academia.edu (original) (raw)
Papers by G. Wigger
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2000
Abstract This paper applies a recent semi-analytical treatment of the slowing-down and penetratio... more Abstract This paper applies a recent semi-analytical treatment of the slowing-down and penetration of positrons in condensed matter to the slowing down of slow positrons in aluminium. The computations are based on the age equation (formally identical with the equation of heat conduction), of which a simplified derivation is given. The dominant energy loss mechanisms, scattering off conduction electrons and long wavelength acoustic phonons, have been treated using the Lindhard dielectric function and the deformation potential approximation, respectively.
Physical Review B, 2005
We report the results of measurements of the electrical resistivity, the magnetization, and the s... more We report the results of measurements of the electrical resistivity, the magnetization, and the specific heat of PrB 4 below room temperature. The crystal electric field ͑CEF͒ splits the 4f 2 multiplet of the Pr ions into nine singlets. In its ground state, PrB 4 is an induced-moment ferromagnet with a saturation magnetization as high as 2.1 B / ͑Pr ion͒. Contrary to previous experiments, we observe a first-order ferromagnetic to antiferromagnetic transition at T C Ϸ 15.9± 0.1 K with a latent heat ⌬Q = 8.6 J / mol. The antiferromagnetic long-range order is quenched above T N = 19.5 K. Susceptibility and specific heat data, as well as the enormous magnetic anisotropy, can quantitatively be reproduced by a mean-field calculation which takes into account the CEF, obtained from a point-charge model using effective charges obtained from a self-consistent electronic band-structure calculation and a Zeeman term, as well as an anisotropic dipolar magnetic exchange and an effective quadrupole-quadrupole interaction term.
Physical Review B, 2001
We report on measurements of the specific heat of the recently discovered superconductor MgB2 in ... more We report on measurements of the specific heat of the recently discovered superconductor MgB2 in the temperature range between 3 and 220 K. Based on a modified Debye-Einstein model, we have achieved a rather accurate account of the lattice contribution to the specific heat, which allows us to separate the electronic contribution from the total measured specific heat. From our result for the electronic specific heat, we estimate the electron-phonon coupling constant λ to be of the order of 2, significantly enhanced compared to common weak-coupling values ≤ 0.4. Our data also indicate that the electronic specific heat in the superconducting state of MgB2 can be accounted for by a conventional, s-wave type 74.25.Kc The recent discovery of superconductivity in MgB 2 below T c ≈ 39 K [1] has caused a remarkable excitement in the solid-state physics community. Critical temperatures of this magnitude inevitably raise the question whether mechanisms other than the common electron-phonon interaction are responsible for the transition. In their very recent work, Bud'ko et al.
Physical Review B, 2002
ABSTRACT We have measured the electrical resistivity, the magnetoresistance, the magnetization M,... more ABSTRACT We have measured the electrical resistivity, the magnetoresistance, the magnetization M, and the Hall effect of single-crystalline Eu0.6Ca0.4B6 at temperatures between 0.34 and 300 K and in magnetic fields between 0 and 70 kOe. The compound orders ferromagnetically at 4.5 K. The Hall coefficient RH is well described by a single function of M at all covered temperatures and external magnetic fields. In the magnetically ordered phase, the electrical resistivity at constant temperature decreases exponentially with increasing bulk magnetization M, suggesting the presence of some intrinsic spin-filter-type tunnel barriers in this material.
ABSTRACT We present structural, magnetic susceptibility \chi(T) and electrical resistivity rho(T)... more ABSTRACT We present structural, magnetic susceptibility \chi(T) and electrical resistivity rho(T) data for single crystals in the Eu_xCa_1-xB6 series. The lattice constant in this series decreases linearly from 4.1854 Åfor EuB6 to 4.1534 Åfor CaB6 following Vegard's law. The paramagnetic Curie temperature, theta, as determined from fitting the high temperature data assuming Curie Weiss behavior \chi = C(T-theta)-1 decreases rapidly with decreasing Eu concentration from 15.1 K for pure EuB6 to 4.5 K for Eu_0.8Ca_0.2B_6. For Eu concentrations below x=0.2, theta decreases linearly to zero, indicating ferromagnetic interactions for all Eu concentrations. A sharp peak in rho(T) is observed at the ordering temperature Tc for Eu concentrations down to 0.2. Lowering the Eu concentration further leads to a rho(T) which increases monotonically with decreasing T down to 4 K and a decrease of partial rho/partial T with decreasing x. The highest rho values at 4 K are observed for Eu_0.35Ca_0.65B6 with a temperature dependence of rho(T) similar to what is observed in CaB6 prepared using excess Ca. However, samples with Eu concentrations below x=0.35 again show a weaker T-dependence and lower values of rho at 4 K.
We have measured the resistivity and magnetisation of several samples of the Eu1-xCaxB6 series un... more We have measured the resistivity and magnetisation of several samples of the Eu1-xCaxB6 series under pressure in order to probe the evolution of itinerant electron ferromagnetism in CaB6 from a localised moment ordered state in EuB6. Starting with pure EuB6, the Curie temperature TC is reduced upon increasing x. In particular, we have investigated the magnetic field and pressure dependence
We have measured the resistivity and magnetisation of several samples of the Eu1-xCaxB6 series un... more We have measured the resistivity and magnetisation of several samples of the Eu1-xCaxB6 series under pressure in order to probe the evolution of itinerant electron ferromagnetism in CaB6 from a localised moment ordered state in EuB6. Starting with pure EuB6, the Curie temperature TC is reduced upon increasing x. In particular, we have investigated the magnetic field and pressure dependence
Physical Review Letters, 2004
Upon substituting Ca for Eu in the local-moment ferromagnet EuB6, the Curie temperature TC decrea... more Upon substituting Ca for Eu in the local-moment ferromagnet EuB6, the Curie temperature TC decreases substantially with increasing dilution of the magnetic sublattice and is completely suppressed for x ≤ 0.3. The Ca substitution leads to significant changes of the electronic properties across the EuxCa1−xB6 series. Electron microscopy data for x ≈ 0.27 indicate a phase separation into Eu-and Ca-rich clusters of 5 to 10 nm diameter, leading to percolation-type phenomena in the electrical transport properties. The related critical concentration xp is approximately 0.3. For x ≈ 0.27, we observe colossal negative magnetoresistance effects at low temperatures, similar in magnitude as those reported for manganese oxides.
Physical Review B, 2004
EuB 6 is a magnetic semiconductor in which defects introduce charge carriers into the conduction ... more EuB 6 is a magnetic semiconductor in which defects introduce charge carriers into the conduction band with the Fermi energy varying with temperature and magnetic field. We present experimental and theoretical work on the electronic magnetotransport in single-crystalline EuB 6 . Magnetization, magnetoresistance and Hall effect data were recorded at temperatures between 2 and 300 K and in magnetic fields up to 5.5 T. The negative magnetoresistance is well reproduced by a model in which the spin disorder scattering is reduced by the applied magnetic field. The Hall effect can be separated into an ordinary and an anomalous part. At 20 K the latter accounts for half of the observed Hall voltage, and its importance decreases rapidly with increasing temperature. As for Gd and its compounds, where the rare-earth ion adopts the same Hund's rule ground state as Eu 2+ in EuB 6 , the standard antisymmetric scattering mechanisms underestimate the size of this contribution by several orders of magnitude, while reproducing its shape almost perfectly. Well below the bulk ferromagnetic ordering at T C = 12.5 K, a two-band model successfully describes the magnetotransport. Our description is consistent with published de Haas van Alphen, optical reflectivity, angular-resolved photoemission, and soft X-ray emission as well as absorption data, but requires a new interpretation for the gap feature deduced from the latter two experiments.
Physical Review B, 2007
The electronic band structure of YbRh2Si2 is calculated in a relativistic framework including cor... more The electronic band structure of YbRh2Si2 is calculated in a relativistic framework including correlation corrections and magnetization of the Yb ion and compared to detailed angle-resolved photoemission spectra. The photoemission spectra for LuRh2Si2 are used as reference to identify electronic bands with no f symmetry. The calculated band structure manifests a 4f13 spin-polarized configuration leaving the unoccupied state at 1.4eV above the Fermi energy. At the band theory level, the 4f bands are located far below the Fermi level and the anisotropic Coulomb interaction within the 4f shell spreads the multilevel into broader 4f complexes below -2.5eV . The photoemission spectra obtained on YbRh2Si2 show a clear f -multilevel splitting into j=7/2 and 5/2 excitations. The interaction of the 4f7/2 levels close to the Fermi energy with two conduction bands shows visible hybridization gaps of 45 and 80meV , respectively. We discuss the origin of these excitations and provide an analysis according to Anderson's single-impurity model with parameters suggested by the band-structure calculation and the photoemission spectra. Both experiment and theory indicate nearly identical Fermi surfaces for LuRh2Si2 and YbRh2Si2 . The valency of Yb in YbRh2Si2 is estimated to be close to +3 .
Europhysics Letters (EPL), 2004
Replacing U for Ca in semiconducting CaB 6 at the few at.% level induces metallic behaviour and K... more Replacing U for Ca in semiconducting CaB 6 at the few at.% level induces metallic behaviour and Kondo-type phenomena at low temperatures, a rather unusual feature for U impurities in metallic hosts. For Ca 0.992 U 0.008 B 6 , the resistance minimum occurs at T = 17 K. The subsequent characteristic logarithmic increase of the resistivity with decreasing temperature merges into the expected T 2 dependence below 0.8 K. Data of the low-temperature specific heat and the magnetization are analyzed by employing a simple resonance-level model. Analogous measurements on LaB 6 with a small amount of U revealed no traces of Kondo behavior, above 0.4 K.
The European Physical Journal B, 2005
We investigated the stability of magnetic moments in Al69.8Pd12.1Mn18.1. This alloy exists in bot... more We investigated the stability of magnetic moments in Al69.8Pd12.1Mn18.1. This alloy exists in both, the icosahedral (i) and the decagonal (d) quasicrystalline form. The transition from the i-to the d-phase is achieved by a simple heat treatment. We present the results of measurements of the 27 Al NMR-response, the dc magnetic susceptibility, and the low-temperature specific heat of both phases. In the icosahedral compound, the majority of the Mn ions carries a magnetic moment. Their number is reduced by approximately a factor of two by transforming the alloy to its decagonal variety. For both compounds, we have indications for two different local environments of the Al nuclei. The first reflects a low density of states of conduction electrons and a weak coupling of the Al nuclei to the Mn-moments. The second type of environment implies a large d-electron density of states at the Fermi level and a strong coupling to the magnetic Mn moments. Spin-glass freezing transitions are observed at T deca f = 12 K for the decagonal, and T ico f = 19 K for the icosahedral phase. PACS. 61.44.Br Quasicrystals -76.60.-k Nuclear magnetic resonance and relaxation -75.50.Lk Spin glasses and other random magnets
The European Physical Journal B, 2005
ABSTRACT We report the results of measurements of the low-temperature specific heat C p (T) and t... more ABSTRACT We report the results of measurements of the low-temperature specific heat C p (T) and the ac susceptibility χ ac (T) in low applied magnetic fields for a series of samples of Eu 1-x Ca x B 6</Subsc ript>. The anomalies in C p (T), together with the results for χ ac (T) and M(H), confirm the onset of phase transitions to long range magnetic order for x > 0.7 and provide evidence that for x ≥ 0.7, the Eu moments, which are captured in large magnetic clusters with magnetic moments of the order of 260 μ B , adopt a spin-glass type ground state. The data set allows to establish the low-temperature [ T,x] phase diagram of this alloy series. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005
Physical Review B, 2005
We report the results of measurements of the electrical resistivity, the magnetization, and the s... more We report the results of measurements of the electrical resistivity, the magnetization, and the specific heat of PrB4 below room temperature. The crystal electric field (CEF) splits the 4f2 multiplet of the Pr ions into nine singlets. In its ground state, PrB4 is an induced-moment ferromagnet with a saturation magnetization as high as 2.1muB/(Prion) . Contrary to previous experiments, we observe a first-order ferromagnetic to antiferromagnetic transition at TC≈15.9±0.1K with a latent heat DeltaQ=8.6J/mol . The antiferromagnetic long-range order is quenched above TN=19.5K . Susceptibility and specific heat data, as well as the enormous magnetic anisotropy, can quantitatively be reproduced by a mean-field calculation which takes into account the CEF, obtained from a point-charge model using effective charges obtained from a self-consistent electronic band-structure calculation and a Zeeman term, as well as an anisotropic dipolar magnetic exchange and an effective quadrupole-quadrupole interaction term.
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2000
Abstract This paper applies a recent semi-analytical treatment of the slowing-down and penetratio... more Abstract This paper applies a recent semi-analytical treatment of the slowing-down and penetration of positrons in condensed matter to the slowing down of slow positrons in aluminium. The computations are based on the age equation (formally identical with the equation of heat conduction), of which a simplified derivation is given. The dominant energy loss mechanisms, scattering off conduction electrons and long wavelength acoustic phonons, have been treated using the Lindhard dielectric function and the deformation potential approximation, respectively.
Physical Review B, 2005
We report the results of measurements of the electrical resistivity, the magnetization, and the s... more We report the results of measurements of the electrical resistivity, the magnetization, and the specific heat of PrB 4 below room temperature. The crystal electric field ͑CEF͒ splits the 4f 2 multiplet of the Pr ions into nine singlets. In its ground state, PrB 4 is an induced-moment ferromagnet with a saturation magnetization as high as 2.1 B / ͑Pr ion͒. Contrary to previous experiments, we observe a first-order ferromagnetic to antiferromagnetic transition at T C Ϸ 15.9± 0.1 K with a latent heat ⌬Q = 8.6 J / mol. The antiferromagnetic long-range order is quenched above T N = 19.5 K. Susceptibility and specific heat data, as well as the enormous magnetic anisotropy, can quantitatively be reproduced by a mean-field calculation which takes into account the CEF, obtained from a point-charge model using effective charges obtained from a self-consistent electronic band-structure calculation and a Zeeman term, as well as an anisotropic dipolar magnetic exchange and an effective quadrupole-quadrupole interaction term.
Physical Review B, 2001
We report on measurements of the specific heat of the recently discovered superconductor MgB2 in ... more We report on measurements of the specific heat of the recently discovered superconductor MgB2 in the temperature range between 3 and 220 K. Based on a modified Debye-Einstein model, we have achieved a rather accurate account of the lattice contribution to the specific heat, which allows us to separate the electronic contribution from the total measured specific heat. From our result for the electronic specific heat, we estimate the electron-phonon coupling constant λ to be of the order of 2, significantly enhanced compared to common weak-coupling values ≤ 0.4. Our data also indicate that the electronic specific heat in the superconducting state of MgB2 can be accounted for by a conventional, s-wave type 74.25.Kc The recent discovery of superconductivity in MgB 2 below T c ≈ 39 K [1] has caused a remarkable excitement in the solid-state physics community. Critical temperatures of this magnitude inevitably raise the question whether mechanisms other than the common electron-phonon interaction are responsible for the transition. In their very recent work, Bud'ko et al.
Physical Review B, 2002
ABSTRACT We have measured the electrical resistivity, the magnetoresistance, the magnetization M,... more ABSTRACT We have measured the electrical resistivity, the magnetoresistance, the magnetization M, and the Hall effect of single-crystalline Eu0.6Ca0.4B6 at temperatures between 0.34 and 300 K and in magnetic fields between 0 and 70 kOe. The compound orders ferromagnetically at 4.5 K. The Hall coefficient RH is well described by a single function of M at all covered temperatures and external magnetic fields. In the magnetically ordered phase, the electrical resistivity at constant temperature decreases exponentially with increasing bulk magnetization M, suggesting the presence of some intrinsic spin-filter-type tunnel barriers in this material.
ABSTRACT We present structural, magnetic susceptibility \chi(T) and electrical resistivity rho(T)... more ABSTRACT We present structural, magnetic susceptibility \chi(T) and electrical resistivity rho(T) data for single crystals in the Eu_xCa_1-xB6 series. The lattice constant in this series decreases linearly from 4.1854 Åfor EuB6 to 4.1534 Åfor CaB6 following Vegard's law. The paramagnetic Curie temperature, theta, as determined from fitting the high temperature data assuming Curie Weiss behavior \chi = C(T-theta)-1 decreases rapidly with decreasing Eu concentration from 15.1 K for pure EuB6 to 4.5 K for Eu_0.8Ca_0.2B_6. For Eu concentrations below x=0.2, theta decreases linearly to zero, indicating ferromagnetic interactions for all Eu concentrations. A sharp peak in rho(T) is observed at the ordering temperature Tc for Eu concentrations down to 0.2. Lowering the Eu concentration further leads to a rho(T) which increases monotonically with decreasing T down to 4 K and a decrease of partial rho/partial T with decreasing x. The highest rho values at 4 K are observed for Eu_0.35Ca_0.65B6 with a temperature dependence of rho(T) similar to what is observed in CaB6 prepared using excess Ca. However, samples with Eu concentrations below x=0.35 again show a weaker T-dependence and lower values of rho at 4 K.
We have measured the resistivity and magnetisation of several samples of the Eu1-xCaxB6 series un... more We have measured the resistivity and magnetisation of several samples of the Eu1-xCaxB6 series under pressure in order to probe the evolution of itinerant electron ferromagnetism in CaB6 from a localised moment ordered state in EuB6. Starting with pure EuB6, the Curie temperature TC is reduced upon increasing x. In particular, we have investigated the magnetic field and pressure dependence
We have measured the resistivity and magnetisation of several samples of the Eu1-xCaxB6 series un... more We have measured the resistivity and magnetisation of several samples of the Eu1-xCaxB6 series under pressure in order to probe the evolution of itinerant electron ferromagnetism in CaB6 from a localised moment ordered state in EuB6. Starting with pure EuB6, the Curie temperature TC is reduced upon increasing x. In particular, we have investigated the magnetic field and pressure dependence
Physical Review Letters, 2004
Upon substituting Ca for Eu in the local-moment ferromagnet EuB6, the Curie temperature TC decrea... more Upon substituting Ca for Eu in the local-moment ferromagnet EuB6, the Curie temperature TC decreases substantially with increasing dilution of the magnetic sublattice and is completely suppressed for x ≤ 0.3. The Ca substitution leads to significant changes of the electronic properties across the EuxCa1−xB6 series. Electron microscopy data for x ≈ 0.27 indicate a phase separation into Eu-and Ca-rich clusters of 5 to 10 nm diameter, leading to percolation-type phenomena in the electrical transport properties. The related critical concentration xp is approximately 0.3. For x ≈ 0.27, we observe colossal negative magnetoresistance effects at low temperatures, similar in magnitude as those reported for manganese oxides.
Physical Review B, 2004
EuB 6 is a magnetic semiconductor in which defects introduce charge carriers into the conduction ... more EuB 6 is a magnetic semiconductor in which defects introduce charge carriers into the conduction band with the Fermi energy varying with temperature and magnetic field. We present experimental and theoretical work on the electronic magnetotransport in single-crystalline EuB 6 . Magnetization, magnetoresistance and Hall effect data were recorded at temperatures between 2 and 300 K and in magnetic fields up to 5.5 T. The negative magnetoresistance is well reproduced by a model in which the spin disorder scattering is reduced by the applied magnetic field. The Hall effect can be separated into an ordinary and an anomalous part. At 20 K the latter accounts for half of the observed Hall voltage, and its importance decreases rapidly with increasing temperature. As for Gd and its compounds, where the rare-earth ion adopts the same Hund's rule ground state as Eu 2+ in EuB 6 , the standard antisymmetric scattering mechanisms underestimate the size of this contribution by several orders of magnitude, while reproducing its shape almost perfectly. Well below the bulk ferromagnetic ordering at T C = 12.5 K, a two-band model successfully describes the magnetotransport. Our description is consistent with published de Haas van Alphen, optical reflectivity, angular-resolved photoemission, and soft X-ray emission as well as absorption data, but requires a new interpretation for the gap feature deduced from the latter two experiments.
Physical Review B, 2007
The electronic band structure of YbRh2Si2 is calculated in a relativistic framework including cor... more The electronic band structure of YbRh2Si2 is calculated in a relativistic framework including correlation corrections and magnetization of the Yb ion and compared to detailed angle-resolved photoemission spectra. The photoemission spectra for LuRh2Si2 are used as reference to identify electronic bands with no f symmetry. The calculated band structure manifests a 4f13 spin-polarized configuration leaving the unoccupied state at 1.4eV above the Fermi energy. At the band theory level, the 4f bands are located far below the Fermi level and the anisotropic Coulomb interaction within the 4f shell spreads the multilevel into broader 4f complexes below -2.5eV . The photoemission spectra obtained on YbRh2Si2 show a clear f -multilevel splitting into j=7/2 and 5/2 excitations. The interaction of the 4f7/2 levels close to the Fermi energy with two conduction bands shows visible hybridization gaps of 45 and 80meV , respectively. We discuss the origin of these excitations and provide an analysis according to Anderson's single-impurity model with parameters suggested by the band-structure calculation and the photoemission spectra. Both experiment and theory indicate nearly identical Fermi surfaces for LuRh2Si2 and YbRh2Si2 . The valency of Yb in YbRh2Si2 is estimated to be close to +3 .
Europhysics Letters (EPL), 2004
Replacing U for Ca in semiconducting CaB 6 at the few at.% level induces metallic behaviour and K... more Replacing U for Ca in semiconducting CaB 6 at the few at.% level induces metallic behaviour and Kondo-type phenomena at low temperatures, a rather unusual feature for U impurities in metallic hosts. For Ca 0.992 U 0.008 B 6 , the resistance minimum occurs at T = 17 K. The subsequent characteristic logarithmic increase of the resistivity with decreasing temperature merges into the expected T 2 dependence below 0.8 K. Data of the low-temperature specific heat and the magnetization are analyzed by employing a simple resonance-level model. Analogous measurements on LaB 6 with a small amount of U revealed no traces of Kondo behavior, above 0.4 K.
The European Physical Journal B, 2005
We investigated the stability of magnetic moments in Al69.8Pd12.1Mn18.1. This alloy exists in bot... more We investigated the stability of magnetic moments in Al69.8Pd12.1Mn18.1. This alloy exists in both, the icosahedral (i) and the decagonal (d) quasicrystalline form. The transition from the i-to the d-phase is achieved by a simple heat treatment. We present the results of measurements of the 27 Al NMR-response, the dc magnetic susceptibility, and the low-temperature specific heat of both phases. In the icosahedral compound, the majority of the Mn ions carries a magnetic moment. Their number is reduced by approximately a factor of two by transforming the alloy to its decagonal variety. For both compounds, we have indications for two different local environments of the Al nuclei. The first reflects a low density of states of conduction electrons and a weak coupling of the Al nuclei to the Mn-moments. The second type of environment implies a large d-electron density of states at the Fermi level and a strong coupling to the magnetic Mn moments. Spin-glass freezing transitions are observed at T deca f = 12 K for the decagonal, and T ico f = 19 K for the icosahedral phase. PACS. 61.44.Br Quasicrystals -76.60.-k Nuclear magnetic resonance and relaxation -75.50.Lk Spin glasses and other random magnets
The European Physical Journal B, 2005
ABSTRACT We report the results of measurements of the low-temperature specific heat C p (T) and t... more ABSTRACT We report the results of measurements of the low-temperature specific heat C p (T) and the ac susceptibility χ ac (T) in low applied magnetic fields for a series of samples of Eu 1-x Ca x B 6</Subsc ript>. The anomalies in C p (T), together with the results for χ ac (T) and M(H), confirm the onset of phase transitions to long range magnetic order for x > 0.7 and provide evidence that for x ≥ 0.7, the Eu moments, which are captured in large magnetic clusters with magnetic moments of the order of 260 μ B , adopt a spin-glass type ground state. The data set allows to establish the low-temperature [ T,x] phase diagram of this alloy series. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005
Physical Review B, 2005
We report the results of measurements of the electrical resistivity, the magnetization, and the s... more We report the results of measurements of the electrical resistivity, the magnetization, and the specific heat of PrB4 below room temperature. The crystal electric field (CEF) splits the 4f2 multiplet of the Pr ions into nine singlets. In its ground state, PrB4 is an induced-moment ferromagnet with a saturation magnetization as high as 2.1muB/(Prion) . Contrary to previous experiments, we observe a first-order ferromagnetic to antiferromagnetic transition at TC≈15.9±0.1K with a latent heat DeltaQ=8.6J/mol . The antiferromagnetic long-range order is quenched above TN=19.5K . Susceptibility and specific heat data, as well as the enormous magnetic anisotropy, can quantitatively be reproduced by a mean-field calculation which takes into account the CEF, obtained from a point-charge model using effective charges obtained from a self-consistent electronic band-structure calculation and a Zeeman term, as well as an anisotropic dipolar magnetic exchange and an effective quadrupole-quadrupole interaction term.