Hund's Rule Ground State Research Articles

Resonant inelastic x-ray scattering investigation of the crystal-field splitting ofSm3+inSmB6

The crystal-field (CF) splitting of the $^6H_{5/2}$ Hund's rule ground state of Sm$^{3+}$ in the strongly correlated topological insulator SmB$_6$ has been determined with high resolution resonant inelastic x-ray scattering (RIXS) at the Sm M$_5$ edge. The valence selectivity of RIXS allows isolating the crystal-field-split excited multiplets of the Sm$^{3+}$ (4$f^5$) configuration from those of Sm$^{2+}$ (4$f^6$) in intermediate valent SmB$_6$. The very large energy range of RIXS allows the crystal-field analysis of a high lying multiplet at about 2.4\,eV that has the same total angular momentum $J$ as the ground state so that ambiguities due to the elastic tail can be avoided. We find that the $\Gamma_7$ doublet and $\Gamma_8$ quartet of the $^6H_{5/2}$ Hund's rule ground state are split by $\Delta^{CF}_{^6H_{5/2}}$\,=\,20$\pm$10\,meV which sets an upper limit for the 4$f$ band width. This indicates an extremely large mass renormalization from the band structure value, pointing out the need to consider the coefficients of fractional parentage for the hopping of the 4$f$ electrons.

Crystal electric field in CeRh2Si2 studied with high-resolution resonant inelastic soft x-ray scattering

The magnetic properties of rare earth compounds are usually well captured by assuming a fully localized f shell and only considering the Hund's rule ground state multiplet split by a crystal electrical field (CEF). Currently, the standard technique for probing CEF excitations in lanthanides is inelastic neutron scattering. Here we show that with the recent leap in energy resolution, resonant inelastic soft X-ray scattering has become a serious alternative for looking at CEF excitations with some distinct advantages compared to INS. As an example we study the CEF scheme in CeRh2Si2, a system that has been intensely studied for more than two decades now but for which no consensus has been reached yet as to its CEF scheme. We used two new features that have only become available very recently in RIXS, high energy resolution of about 30 meV as well as polarization analysis in the scattered beam, to find a unique CEF description for CeRh2Si2. The result agrees well with previous INS and magnetic susceptibility measurements. Due to its strong resonant character, RIXS is applicable to very small samples, presents very high cross sections for all lanthanides, and further benefits from the very weak coupling to phonon excitation. The rapid progress in energy resolution of RIXS spectrometers is making this technique increasingly attractive for the investigation of the CEF scheme in lanthanides.

Magnetic ordering in Ho‐doped Bi2Te3 topological insulator

We investigate the magnetic properties of Ho‐doped Bi2Te3 thin films grown by molecular beam epitaxy. Analysis of the polarized X‐ray absorption spectra at the Ho M5 absorption edge gives an effective 4f magnetic moment which is ∼45% of the Hund's rule ground state value. X‐ray magnetic circular dichroism (XMCD) shows no significant anisotropy, which suggests that the reduced spin moment is not due to the crystal field effects, but rather the presence of non‐magnetic or antiferromagnetic Ho sites. Extrapolating the temperature dependence of the XMCD measured in total electron yield and fluorescence yield mode in a field of 7 T gives a Curie–Weiss temperature of ϑCW ≈ –30 K, which suggests antiferromagnetic ordering, in contrast to the paramagnetic behavior observed with SQUID magnetometry. From the anomaly of the XMCD signal at low temperatures, a Néel temperature TN between 10 K and 25 K is estimated. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)

Schottky effect in thei-Zn-Ag-Sc-Tm icosahedral quasicrystal and its 1/1 Zn-Sc-Tm approximant

The analysis of low-temperature specific heat of rare-earth (RE)-containing quasicrystals and periodic approximants and consequent interpretation of their electronic properties in the $T\ensuremath{\rightarrow}0$ limit is frequently hampered by the Schottky effect, where crystalline electric fields lift the degeneracy of the RE-ion Hund's rule ground state and introduce additional contribution to the specific heat. In this paper we study the low-temperature specific heat of a thulium-containing $i$-Zn-Ag-Sc-Tm icosahedral quasicrystal and its 1/1 Zn-Sc-Tm approximant, both being classified as ``Schottky'' systems. We have derived the crystal-field Hamiltonian for pentagonal symmetry of the crystalline electric field, pertinent to the class of Tsai-type icosahedral quasicrystals and their approximants, where the RE ions are located on fivefold axes of the icosahedral atomic cluster. Using the leading term of this Hamiltonian, we have calculated analytically the Schottky specific heat in the presence of an external magnetic field and made comparison to the experimental specific heat of the investigated quasicrystal and approximant. When the low-temperature specific heat $C$ is analyzed in a $C/T$ versus ${T}^{2}$ scale (as it is customarily done for metallic specimens), the Schottky specific heat yields an upturn in the $T\ensuremath{\rightarrow}0$ limit that cannot be easily distinguished from a similar upturn produced by the electron-electron interactions in exchange-enhanced systems and strongly correlated systems. Our results show that extraction of the electronic properties of RE-containing quasicrystals from their low-temperature specific heat may be uncertain in the presence of the Schottky effect.

Magnetic properties of single-crystalline CeCuGa3

The magnetic behavior of single-crystalline CeCuGa3 has been investigated. The compound forms in a tetragonal BaAl4-type structure consisting of rare-earth planes separated by Cu-Ga layers. If the Cu-Ga site disorder is reduced, CeCuGa3 adopts the related, likewise tetragonal BaNiSn3-type structure, in which the Ce ion are surrounded by different Cu and Ga layers and the inversion symmetry is lost. In the literature conflicting reports about the magnetic order of CeCuGa3 have been published. Single crystals with the centrosymmetric structure variant exhibit ferromagnetic order below approx. 4 K with a strong planar anisotropy. The magnetic behavior above the transition temperature can be well understood by the crystal-field splitting of the 4f Hund's rule ground-state multiplet of the Ce ions.

Geometrical Control of Spin Transitions in Quantum Rings

We compute the energy difference between spin states in a quantum ring by employing the path integral Monte Carlo method. The focus is put on the effect of changes of the ring radius and the elliptical deformation on the spin of the ground state. The numerical results for three electrons reveal that the ground state can be tuned between a spin-unpolarized state and a spin-polarized state as the ring radius is modified. A circular ring with four electrons exhibits a Hund's rule ground state. With elliptical deformation the energy levels in the quantum ring hybridize which causes a spin depolarization of the ground state.

Spin transitions in semiconductor quantum rings

We adopt the path integral Monte Carlo method to accurately resolve the total spin of the ground state of electrons confined in a quantum ring with different geometries. Using this method, an evaluation of the ground state of three electrons in a ring shows a spin transition to the fully polarized state by increasing the radius and thereby enhancing the Coulomb interaction. The total spin of the ground state is determined by the mutual interplay of confinement and electron-electron interaction. An analysis of the four-electron ring demonstrates that in this case no spin transitions take place. Furthermore, the effect of geometric distortion of the ring on its ground state has been investigated. Elliptically deforming the ring breaks the symmetry of the system and leads to the removal of orbital degeneracy. For strong distortion the splitting between hybridized states is sufficient to overcome the exchange-energy saving associated with a higher spin state. We have found that this effect removes the polarization of three electrons. Even in a four-electron ring the ground state is forced by the distortion to be unpolarized and thus suppressing the Hund's rule ground state.

Ordering and Crossover in a Pseudo-Sextet Localized Electron Model –Possible Scenario for SmRu4P12Skutterudite–

A crystalline electric field (CEF) model of localized 4 f 5 electrons is proposed for understanding intriguing ordering phenomena in SmRu 4 P 12 . We take the CEF quartet and doublet (pseudo-sextet) of the Hund's rule ground state with J =5/2, and include intersite interactions between multipoles by the mean-field theory. The model leads to a multipole order with representation Γ 5 u , and shows the following features: (i) increasing transition temperature T MI with increasing magnetic field; (ii) an anomaly in specific heat and other thermodynamic quantities at lower temperature \(T^{\star}\), (iii) sharpening of the anomaly at \(T^{\star}\) as the magnetic field increases. These behaviors reproduce salient features observed experimentally in SmRu 4 P 12 . Possible mechanisms for spontaneous magnetic moment are discussed.

Crystal-field ground state of the noncentrosymmetric superconductorCePt3Si: A combined polarized soft x-ray absorption and polarized neutron study

We determined the crystal-field split Hund's rule ground state of the non-centrosymmetric heavy fermion superconductor CePt3Si with polarization dependent soft X-ray absorption spectroscopy (XAS) and polarized neutron scattering. We are also able to give the sequence of the crystal-field states from the temperature evolution of the linear dichroic signal in the XAS. The quantitative analysis of the XAS temperature dependence together with the neutron transition energies complete the identification of the crystal-field level scheme.

Magnetic properties ofRFe2Zn20andRCo2Zn20(R=Y,Nd,Sm,Gd–Lu)

Magnetization, resistivity, and specific heat measurements were performed on solution-grown single crystals of $R{\text{Fe}}_{2}{\text{Zn}}_{20}$ and $R{\text{Co}}_{2}{\text{Zn}}_{20}$ $(R=\text{Y},\text{Nd},\text{Sm},\text{Gd-Lu})$. Whereas ${\text{LuCo}}_{2}{\text{Zn}}_{20}$ and ${\text{YCo}}_{2}{\text{Zn}}_{20}$ manifest unremarkable metallic behavior, ${\text{LuFe}}_{2}{\text{Zn}}_{20}$ and ${\text{YFe}}_{2}{\text{Zn}}_{20}$ display behaviors such as characteristic of nearly ferromagnetic Fermi liquids. When the well-defined $4f$ local moments $({\text{Gd}}^{3+}{\text{-Tm}}^{3+})$ are embedded into this strongly polarizable host, they manifest enhanced ferromagnetic ordering and the values of ${T}_{\text{C}}$ for $R{\text{Fe}}_{2}{\text{Zn}}_{20}$ $(R=\text{Gd-Tm})$ scale with the de Gennes factor. In addition, data on the $R{\text{Fe}}_{2}{\text{Zn}}_{20}$ compounds indicate a small crystal electric field (CEF) effect compared with the interaction energy scale. On the other hand, the local moment bearing members of $R{\text{Co}}_{2}{\text{Zn}}_{20}$ $(R=\text{Nd},\text{Sm},\text{Gd-Tm})$ manifest weak magnetic interactions and the magnetic properties for $R=\text{Dy-Tm}$ members are strongly influenced by the CEF effect on the $R$ ions. The magnetic anisotropy and specific heat data for the Co series were used to determine the CEF coefficient of $R$ ion with its cubic point symmetry. These CEF coefficients, determined for the Co series, are consistent with the magnetic anisotropy and specific heat data for the Fe series, which indicates similar CEF effects for the Fe and Co series. Such analysis, combined with specific heat and resistivity data, indicates that for $R=\text{Tb-Ho}$, the CEF splitting scale is smaller than their ${T}_{\text{C}}$ values, whereas for ${\text{ErFe}}_{2}{\text{Zn}}_{20}$ and ${\text{TmFe}}_{2}{\text{Zn}}_{20}$ the $4f$ electrons lose part of their full Hund's rule ground state degeneracy above ${T}_{\text{C}}$. ${\text{YbFe}}_{2}{\text{Zn}}_{20}$ and ${\text{YbCo}}_{2}{\text{Zn}}_{20}$ manifest typical but distinct heavy fermion behaviors associated with different Kondo temperatures.

Electronic transport inEuB6

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.

Systematic study of anisotropic transport and magnetic properties of RAgSb 2 (R=Y, La–Nd, Sm, Gd–Tm)

Anisotropic measurements of the magnetic and transport properties have been performed on high-quality single crystals of the RAgSb 2 series of compounds with R=Y, La–Nd, Sm, Gd–Tm. For most of these compounds, strong magnetic anisotropies, created by crystalline electric field (CEF) splitting of the Hund's rule ground state, confine the moments to the basal plane. Additional anisotropy within the basal plane is also observed in DyAgSb 2, leading to a series of metamagnetic transitions. All of the compounds order antiferromagnetically at low temperatures except for the nonmagnetic compounds LaAgSb 2 and YAgSb 2 and the ferromagnetic compound CeAgSb 2. For R=Y, La–Nd, and Sm clear de Haas–van Alphen oscillations in fields as low as 30 kOe and at temperatures as high as 25 K can be measured. Throughout the series, the low-temperature transverse magnetoresistance is large [Δ ρ( H)/ ρ(0)≈60 in SmAgSb 2 at 55 kOe] and deviates strongly from quadratic behavior with field the dependence of Δ ρ( H)/ ρ(0) ranging between H 0.8 and H 1.5.

3sphotoemission spectra of3dtransition-metal adatoms on graphite

We report cluster model calculations on the $3s$ photoemission spectra of $3d$-transition-metal atoms adsorbed on graphite. The spectra are studied for the whole $3d$ series, for three different adsorption sites, and as a function of the adatom-surface distance h. For equilibrium h values, the adatoms are in a high spin (Hund's rule) ground state for all $3d$ elements and adsorption sites. Upon decreasing h, however, we observe in some cases a first-order spin transition to a low spin state. These spin transitions are accompanied by electronic transitions between different d orbitals and can be explained in an effective crystal-field model, where the crystal field is calculated in second-order perturbation in the adatom-surface hybridization. The photoemission spectra show intra-atomic exchange splitting as well as charge-transfer satellites from final-state core-hole screening by graphite $\ensuremath{\pi}$ electrons. The intensity of the charge-transfer satellites increases with d-electron number, i.e., from light to heavy $3d$ elements, which reflects the increasing electron-electron correlation. For the late $3d$ elements, charge transfer and exchange satellites are strongly mixed, and the spectra have essentially a three-peak structure. In this case, the observed splitting cannot directly be used as a measure of the magnetic moment of the adatom. Comparison is made with experimental data for V clusters on graphite.

The 3d–4f exchange interaction, X-ray second-order optical processes and the magnetic circular dichroism (MCD) spin sum rule in rare earths

We discuss the effect of the 3d–4f exchange interaction in rare earths by choosing two subjects on the basis of an atomic model including the full multiplet. One subject is the selection rules in resonant 4f photoemission spectroscopy (PES), 4f→3d X-ray emission spectroscopy (XES) and inverse photoemission spectroscopy (IPES) at the 3d threshold. The other is the applicability of the magnetic circular dichroism (MCD) spin sum rule in 3d→4f X-ray absorption (XAS). The interplay between the diagonal term of the exchange interaction and the 3d core spin–orbital interaction is shown to cause the contribution of the higher-energy final states of PES and XES, which are not accessible at off-resonance, to the process passing through the intermediate state in the higher-energy region at each of the 3d 5/2 and 3d 3/2 thresholds. Furthermore it is shown to cause a suppression of the contribution of the higher-energy final states of IPES seen at off-resonance for the process passing through the intermediate state with the lower-energy region at each of the 3d 5/2 and 3d 3/2 thresholds. We show, on the other hand, that the off-diagonal term of the exchange interaction causes a large amount of 3d 5/2 –3d 3/2 mixing in less-than-half filled 4f shells, but not in the more-than-half filled cases, in the Hund's rule ground state. This means that the use of the so-called M 4 and M 5 edge MCD intensities in the MCD spin sum rule formula, which is the only possible choice in its application, is meaningless in less-than-half filled 4f shells at least, although the M 4 and M 5 edges are apparently separated from each other.

X-ray-absorption sum rules in jj-coupled operators and ground-state moments of actinide ions.

Sum rules for magnetic x-ray dichroism, relating the signals of the spin-orbit split core level absorption edges to the ground-state spin and orbital operators, are expressed in jj-coupled operators. These sum rules can be used in the region of intermediate coupling by taking into account the cross term between the j=l+/-1/2 ground-state levels and are, therefore, particularly useful in the study of actinides. The calculated expectation values for the ground-state moments of the actinide ions in intermediate coupling show that the spin-orbit-induced operators, such as the magnetic-dipole term, differ strongly from their Hund's rule ground-state values. We also prove the general rule that, when there is a perturbing interaction which is weak compared to the spin-orbit interaction, the ratio of operators with the same total moment remains constant. This rendition is usually fulfilled for the crystal-field interaction in the lanthanides and actinides. The values of the ground-state moments as a function off count give rise to an interesting trend in the dichroism of the spin-orbit split-core edges. The branching ratio of the 3d and 4d circular dichroism signal gradually increases from nearly zero for 5f(1) to similar to 0.4 for 5f(5) and is close to unity for a more than half-filled shell. The unusual behavior of the branching ratio can be related to the higher (lower) value of the magnetic dipole term, Ti, for a less (more) than half-filled shell of the actinides in the presence of spin-orbit interaction. Uranium compounds will have a much larger value of T-z than the corresponding 4f compounds. Its precise value can be used as a measure for the f count.

Electronic structure of 3d transition metal compounds: systematic chemical trends and multiplet effects

The local electronic structure of 3d transition metal compounds is characterized by a few parameters, namely the ligand p to cation d charge transfer energy Δ, the dd Coulomb repulsion energy U, and the pd transfer integrals T. Values for these parameters deduced from the cluster model analysis of cation core level photoemission spectra are shown to exhibit systematic chemical trends as functions of cation atomic number, ligand, and cation valence. Physical properties of these compounds such as the magnitudes of the band gaps, pd covalency and the character of doped carriers, however, are not necessarily smooth functions of those variables but depend also on the nominal d electron number n due to the multiplet effects leading to the stabilization of the Hund's rule ground state. As an illustrative example, the electronic structure of valence-control Mn and Fe oxides is discussed.

Specific heat, magnetization and resistivity measurements on HoBa 2Cu 4O 8

Measurements on single-phase polycrystalline samples of HoBa 2Cu 4O 8 demonstrate a qualitative similarity to the corresponding 1:2:3 compound with respect to specific heat C p( T), magnetization M( H) and electrical resistivity ρ( T). The C p ( T) data below 25 K suggest a slightly different energy-level scheme of the splitted Hund's-rule ground-state multiplet of the Ho 3+ ion and a spontaneous increase of the splitting between the ground state and the first-excited state below 5 K. A specific-heat anomaly at T c is clearly discernible.

The X-ray absorption branching ratio of transition metal compounds

The origin of non-statistical branching ratios in spin-orbit split X-ray absorption spectra is explained. Atomic calculations for transition metals show a systematic change which is due to initial state spin-orbit splitting and electrostatic interactions between core hole and valence electrons.The results of these atomic calculations can be formulated in general rules, which are also applicable to solids. In the free atom the branching ratio reaches a maximum for the Hund's rule ground state and its value decreases gradually for S, L and J. levels of higher energy. The presence of a crystal field results in a lower branching ratio when it produces a low-spin ground state. The rules can be used to assess the spin state and the spin-orbit splitting from the experimental branching ratio in transition metal- and rare earth compounds.

Branching ratio in x-ray absorption spectroscopy.

The origin of nonstatistical branching ratios in spin-orbit-split x-ray absorption spectra is explained. Atomic calculations for transition metals show a systematic change which is due to initial-state spin-orbit splitting and electrostatic interactions between core hole and valence electrons. We have formulated the results of these atomic calculations in general rules, which are also applicable to solids. In the free atom the branching ratio reaches a maximum for the Hund's-rule ground state and its value decreases gradually for S, L, and J levels of higher energy. The presence of a crystal field results in a lower branching ratio when it produces a low-spin ground state. The rules can be used to assess the spin state and the spin-orbit splitting from the experimental branching ratio in transition-metal and rare-earth compounds. A specific example is given for the influence of second-order spin-orbit interactions in high-spin Ni compounds.

Crystal-field splitting in icosahedral symmetry.

The crystal-field splitting of rare-earth ions in icosahedral symmetry is treated by group-theoretical and numerical methods. From the crystal-field Hamiltonian, which is governed by only one crystal-field parameter, the crystal-field splitting schemes of all rare-earth ions in their Hund's-rule ground state are derived. It is shown that these schemes are expected to survive in quasicrystals as well as in metallic glasses. The derived temperature dependence of the surplus static susceptibility and specific heat, as generated by the icosahedral crystal-field splitting, is discussed and plotted for selected cases.