Ground State Multiplet Research Articles

Optical control of 4f orbital state in rare-earth metals.

A change of orbital state alters the coupling between ions and their surroundings drastically. Orbital excitations are hence key to understand and control interaction of ions. Rare-earth elements with strong magneto-crystalline anisotropy (MCA) are important ingredients for magnetic devices. Thus, control of their localized 4f magnetic moments and anisotropy is one major challenge in ultrafast spin physics. With time-resolved x-ray absorption and resonant inelastic scattering experiments, we show for Tb metal that 4f-electronic excitations out of the ground-state multiplet occur after optical pumping. These excitations are driven by inelastic 5d-4f-electron scattering, altering the 4f-orbital state and consequently the MCA with important implications for magnetization dynamics in 4f-metals and more general for the excitation of localized electronic states in correlated materials.

Slow magnetic relaxation in a europium(II) complex.

Single-ion anisotropy is vital for the observation of Single-Molecule Magnet (SMM) properties (i.e., a slow dynamics of the magnetization) in lanthanide-based systems. In the case of europium, the occurrence of this phenomenon has been inhibited by the spin and orbital quantum numbers that give way to J = 0 in the trivalent state and the half-filled population of the 4f orbitals in the divalent state. Herein, by optimizing the local crystal field of a quasi-linear bis(silylamido) EuII complex, the [EuII(N{SiMePh2}2)2] SMM is described, providing an example of a europium complex exhibiting slow relaxation of its magnetization. This behavior is dominated by a thermally activated (Orbach-like) mechanism, with an effective energy barrier of approximately 8 K, determined by bulk magnetometry and electron paramagnetic resonance. Ab initio calculations confirm second-order spin-orbit coupling effects lead to non-negligible axial magnetic anisotropy, splitting the ground state multiplet into four Kramers doublets, thereby allowing for the observation of an Orbach-like relaxation at low temperatures.

Vanishing RKKY interactions in Ce-based cage compounds

We report the results of thermodynamic measurements in external magnetic field of the cubic Ce-based cage compounds CeT 2Cd20 (T = Ni,Pd). Our analysis of the heat-capacity data shows that the Γ7 doublet is the ground state multiplet of the Ce3+ ions. Consequently, for the Γ7 doublet it can be theoretically shown that the Ruderman–Kittel–Kasuya–Yosida interaction between the localized Ce moments mediated by the conduction electrons, must vanish at temperatures much lower than the energy separating the ground state doublet from the first excited Γ8 quartet. Our findings provide an insight as to why no long range order has been observed in these compounds down to temperatures in the milliKelvin range.

Structure and Magnetic Properties of Homoleptic Trivalent Tris(alkyl)lanthanides.

Six new solvent-free, homoleptic paramagnetic tris(alkyl)lanthanides Ln{C(SiHMe2)3}3 (1Ln) and Ln{C(SiHMe2)2Ph}3 (2Ln) (Ln = Gd, Dy, and Er) were synthesized to investigate the magnetic properties of 4f organometallic compounds stabilized by secondary Ln↼H-Si and benzylic interactions. The unit cell of 1Gd contains one independent molecule (Z = 2), while 1Dy and 1Er crystallize with four independent isostructural molecules per unit cell (Z = 16). In all molecules, as in other 1Ln compounds, the three tris(dimethylsilyl)methyl ligands form a trigonal planar LnC3 core, and six secondary interactions involving Ln↼H-Si bonding in Ln{C(SiHMe2)3}3 form above and below the equatorial plane. Two and five crystallographically independent molecules of each 2Ln (2Gd, Z = 8; 2Dy, Z = 20) form with three π-coordinated phenyl groups in addition to either one or two secondary Ln↼H-Si interactions per molecule. The packing of these midseries organolanthanide compounds contrasts the single crystallographically unique molecules in previously reported La{C(SiHMe2)3}3 (1La, Z = 2, Z' = 1) and La{C(SiHMe2)2Ph}3 (2La, Z = 2, Z' = 1/3). 2La doped with 2Dy can adopt the crystallographic structure of 2La, which promotes magnetic properties, namely a higher χmT value at low temperatures as well as stronger magnetic anisotropy. The ac susceptibility data for 10% 2Dy doped into 2La suggests slow relaxation at low temperatures with a relaxation barrier of ∼45 K. The computed saturated magnetization of 1Er (M ≈ 4.5 μB) and 1Dy (M ≈ 6 μB) matches the experimental values, while the computed value for 2Dy better matches the value measured for 2Dy diluted in 2La (M ≈ 5 μB). Gas-phase calculations predict that the ground-state and first excited-state multiplet separations are larger for 1Er than 2Er, while the ordering for dysprosium is 1Dy > 2Dy.

Experimental and theoretical thermodynamic studies in Ba2MgReO6—the ground state in the context of Jahn-Teller effect

We address the degeneracy of the ground state multiplet on the 5d 1 Re6+ ion in double perovskite Ba2MgReO6 using a combination of specific heat measurements and density functional calculations. For Ba2MgReO6, two different ground state multiplets have previously been proposed—a quartet (with degeneracy N = 4) (Hirai and Hiroi 2019 J. Phys. Soc. Japan 88 064712) and a doublet (N = 2) (Marjerrison et al 2016 Inorg. Chem. 55 10701). Here we employ two independent methods for the estimation of phonon contribution in heat capacity data to obtain the magnetic entropy , which reflects the degeneracy of the ground state multiplet N through lnN. In both cases, we obtain that in the temperature range covering 2 to 120 K the released entropy is better described by ln2. The detailed nature of the ground state multiplet in Ba2MgReO6 remains an open question.

Charge density wave and crystalline electric field effects inTmNiC2

Single crystals of ${\mathrm{TmNiC}}_{2}$ were grown by the optical floating-zone technique and were investigated by x-ray diffraction (XRD), thermal expansion, electrical resistivity, specific heat, and magnetic susceptibility measurements. Single-crystal XRD reveals the formation of a commensurate charge density wave (CDW) characterized by a CDW modulation vector ${\mathbf{q}}_{\mathbf{2}\mathbf{c}}=(0.5,0.5,0.5)$, which is accompanied by a symmetry change from the orthorhombic space group $Amm2$ to the monoclinic space group $Cm$, i.e., to a CDW superstructure which is isostructural with that of ${\mathrm{LuNiC}}_{2}$. For all transport and thermodynamic properties, anomalies related to a second order-type thermodynamic CDW phase transition are observed at around ${T}_{\mathrm{CDW}}\ensuremath{\simeq}375\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The large specific heat anomaly at ${T}_{\mathrm{CDW}}, \mathrm{\ensuremath{\Delta}}C\ensuremath{\simeq}6.2\phantom{\rule{4pt}{0ex}}\mathrm{J}\phantom{\rule{0.16em}{0ex}}{\mathrm{mol}}^{\ensuremath{-}1}{\mathrm{K}}^{\ensuremath{-}1}$, together with noticeable changes in entropy and enthalpy related to the CDW transition, suggests that this point group symmetry breaking CDW phase transition affects more significant parts of the Fermi surface as compared to the incommensurate CDW transition of, e.g., ${\mathrm{SmNiC}}_{2}$ with no change in point group symmetry. The results on the antiferromagnetic and paramagnetic state of ${\mathrm{TmNiC}}_{2}$ obtained by the above macroscopic techniques were complemented by microscopic studies via inelastic neutron scattering. A crystalline electric field modeling of macroscopic susceptibility and magnetic specific heat and entropy contributions as well as microscopic neutron scattering data, reveal crystal field eigenstates and eigenvalues with a ground-state doublet of the Tm-$4f$ electrons, which is well separated by about 25 meV from exited states of the $J=6$ ground-state multiplet.

Mott Quantum Critical Points at Finite Doping.

We demonstrate that a finite-doping quantum critical point (QCP) naturally descends from the existence of a first-order Mott transition in the phase diagram of a strongly correlated material. In a prototypical case of a first-order Mott transition the surface associated with the equation of state for the homogeneous system is "folded" so that in a range of parameters stable metallic and insulating phases exist and are connected by an unstable metallic branch. Here we show that tuning the chemical potential, the zero-temperature equation of state gradually unfolds. Under general conditions, we find that the Mott transition evolves into a first-order transition between two metals, associated with a phase separation region ending in the finite-doping QCP. This scenario is here demonstrated solving a minimal multiorbital Hubbard model relevant for the iron-based superconductors, but its origin-the splitting of the atomic ground state multiplet by a small energy scale, here Hund's coupling-is much more general. A strong analogy with cuprate superconductors is traced.

α-AsW9O33]9- bridged hexagonal clusters of Ln(III) showing field induced SMM behavior: experimental and theoretical insight.

Polyoxometalates (POM), as inorganic polydentate oxygen donors, provide binding opportunities for oxophilic lanthanide metal centers to construct novel Ln-substituted POM materials with exciting structures and attractive properties. Herein, we have reported four arsenotungstate [α-AsW9O33]9- based lanthanide-containing polyoxometalates [CsxK36-x{Ln6(H2O)12(α-AsW9O33)6}]·yH2O (Ln = Er (1), Gd (2), Ho (3), and Tb (4)), which are synthesized in an alkaline medium. Complexes 1-3 are the dimeric structures of [Ln3(H2O)6(α-AsW9O33)3]18- polyanions, whereas complex 4 is a hexamer of the polyanion [Tb (H2O)2(α-AsW9O33)]6- as a building unit. In all the complexes, [α-AsW9O33]9- units are staggered up and down and give rise to the chair conformation, where one [α-AsW9O33]9- unit bridges two Ln(III) centers through four μ2-oxygen and two terminal oxygen atoms, resulting in the hexagonal arrangement of lanthanides. The dynamic magnetic measurement indicates that only complex 1 exhibits slow relaxation of magnetization with an applied dc field (1500 Oe). To gain insight into the slow relaxation of magnetization in complex 1, the ligand-field parameters and the splitting of the ground-state multiplet of the Er(III) ions have been estimated. The ab initio calculation results confirm that the ground state wave function of these molecules (1, 3, and 4) is mainly composed of a mixture of mJ states, and the non-axial crystal field (CF) terms are more predominant than the axial CF term. The solid-state fluorescence spectra of 1-4 reveal that the photoexcitation O → M ligand-to-metal charge-transfer (LMCT) of arsenotungstate fragments is effectively quenched due to the spatial coordination environment around the Ln(III) ion.

Adiabatic continuity of the spinful quantum Hall states

By using the extended Hubbard model of anyons, we numerically demonstrate the adiabatic deformation of the spinful quantum Hall (QH) states by transmutation of statistical fluxes. While the ground state is always spin-polarized in a series of $\nu=1$ integer QH system, the adiabatic continuity between the singlet QH states at $\nu=2$ and $\nu=2/5$ is confirmed. These results are consistent with the composite fermion theory with spin. The many-body Chern number of the ground state multiplet works as an adiabatic invariant and also explains the wild change of the topological degeneracy during the evolution. The generalized Streda formula of spinful systems is justified.

Seniority and configurations in neutron-rich Nickel isotopes * *Supported by the Interdisciplinary Scientific and Educational School of Moscow University "Fundamental and Applied Space Research"

Excited states in low-energy spectra of Ni are considered. Accordingly, pairing forces in the form of surface delta interaction are employed to account for the formation of the ground state multiplet with seniority states. The multiplet splitting is described with mass relationships of masses of neighboring nuclei. Subsequently, the seniority model is adopted to reproduce or predict the states in odd-even isotopes and in even-even isotopes. The correct account of the state should allow for the description of the reversed order of states with and observed in experiments. The results obtained are compared with the structure of similar multiplets in isotones.

On density distribution of Ti atom and ion ground states near the target in HiPIMS discharge using cavity ring-down spectroscopy and laser induced fluorescence

Cavity ring-down spectroscopy combined with laser induced fluorescence was applied during a high-power impulse magnetron sputtering of Ti target to determine the time evolutions and spatial distributions of Ti atom and ion densities of levels belonging to the ground state multiplets (GSM) near the sputtered target. From these densities, an estimate of the time evolution and spatial distribution of the ionization degree near the target was calculated. It was found that the densities (number of particles per unit volume) of levels in GSM of Ti atom and ion increases with their level energies and the highest levels in GSMs show an inversion in their populations (the density of level divided by its statistical weight) during a voltage pulse. The population inversion (a higher population of levels with a higher energy than those with lower ones) is distinct for the highest level in GSM of Ti+ ion and it persists even at 40 μs after the voltage pulse end. The sum of ground state level densities reaches values up to 8.3 × 1011 cm−3 for Ti+ ions above the target racetrack and up to 4.8 × 1011 cm−3 for Ti atoms above the target center for the regime with the peak power density of 498 W cm−2. A frequent ionization of Ti atoms above the target racetrack is manifested by distinct drops in the Ti atom spatial distribution. This leads to a very high ionization degree up to 94% at the racetrack position and the ionization degree stays also high 40 μs after the voltage pulse termination.

A mononuclear iron(III) complex with unusual changes of color and magneto-structural properties with temperature: synthesis, structure, magnetization, multi-frequency ESR and DFT study.

From the reaction of 2-hydroxy-6-methylpyridine (L) with iron(II) tetrafluoroborate, a new mononuclear iron(III) octahedral complex [FeL6](BF4)3 has been isolated. The color of the complex reversibly changed from red at room temperature to yellow-orange at the liquid nitrogen temperature. Magnetization measurements indicate that iron(III) in [FeL6](BF4)3 is in a high-spin state S = 5/2, from room temperature to 1.8 K. The high-spin ground state of iron(III) is also confirmed by DFT calculations. Although the spin-crossover of the complex is not observed, X-band and multifrequency high-field/high-frequency electron spin resonance (ESR) spectroscopy shows rather uncommon iron(III) spectra at room temperature and an unusual change with cooling. Spectral simulations reveal that the S = 5/2 ground state multiplet of the complex can be characterized by the temperature independent axial zero-field splitting parameter of |D| = +2 GHz (0.067 cm-1) while the value of the rhombic parameter E of the order of some tenths MHz increases on lowering the temperature. Single crystal X-ray diffraction (SCXRD) shows that the iron(III) coordination geometry does not change with temperature while supramolecular interactions are temperature dependent, influencing the iron(III) rhombicity. Additionally, the DFT calculations show temperature variation of the HOMO-LUMO gap, in agreement with the changes of color and ESR-spectra of the iron(III) complex with temperature.

Learning crystal field parameters using convolutional neural networks

We present a deep machine learning algorithm to extract crystal field (CF) Stevens parameters from thermodynamic data of rare-earth magnetic materials. The algorithm employs a two-dimensional convolutional neural network (CNN) that is trained on magnetization, magnetic susceptibility and specific heat data that is calculated theoretically within the single-ion approximation and further processed using a standard wavelet transformation. We apply the method to crystal fields of cubic, hexagonal and tetragonal symmetry and for both integer and half-integer total angular momentum values JJ of the ground state multiplet. We evaluate its performance on both theoretically generated synthetic and previously published experimental data on CeAgSb_22, PrAgSb_22 and PrMg_22Cu_99, and find that it can reliably and accurately extract the CF parameters for all site symmetries and values of JJ considered. This demonstrates that CNNs provide an unbiased approach to extracting CF parameters that avoids tedious multi-parameter fitting procedures.

Interacting holes in Si and Ge double quantum dots: From a multiband approach to an effective-spin picture

The states of two electrons in tunnel-coupled semiconductor quantum dots can be effectively described in terms of a two-spin Hamiltonian with an isotropic Heisenberg interaction. A similar description needs to be generalized in the case of holes due to their multiband character and spin-orbit coupling, which mixes orbital and spin degrees of freedom and splits $j=3/2$ and $j=1/2$ multiplets. Here we investigate two-hole states in prototypical coupled Si and Ge quantum dots via different theoretical approaches. Multiband $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ and configuration-interaction calculations are combined with entanglement measures in order to thoroughly characterize the two-hole states in terms of band mixing and justify the introduction of an effective spin representation, which we analytically derive a from generalized Hubbard model. We find that, in the weak interdot regime, the ground state and first excited multiplet of the two-hole system display---unlike their electronic counterparts---a high degree of $J$ mixing, even in the limit of purely heavy-hole states. The light-hole component additionally induces $M$ mixing and a weak coupling between spinors characterized by different permutational symmetries.

Magnetic structure and crystal field excitations of NdOs2Al10: a neutron scattering study

We have investigated the magnetic properties of a polycrystalline sample of NdOs2Al10 using neutron diffraction and inelastic neutron scattering, magnetic susceptibility and heat capacity measurements. The magnetic susceptibility data reveal an antiferromagnetic transition at T N1 = 2.2 K while the heat capacity data which extend to lower temperatures show a further transition at T N2 = 1.1 K. The INS measurements detect four well-resolved crystal field excitations at 7.4, 12.4, 17.6 meV and 19.2 meV at 5 K. The positions and intensities of the observed CEF excitations and the temperature dependence of previously published single crystal susceptibility data are analysed based on the orthorhombic CEF model of the J = 9/2 ground state multiplet of Nd3+ ion. The neutron diffraction study reveals the magnetic structure at T = 1.6 K to be of sine wave type (κ = [0, 0.723, 0]) with an ordered state moment of μ Nd 3+ = 1.59(1) μ B aligned along the a-axis in agreement with the single ion crystal field anisotropy. This indicates that the magnetism of NdOs2Al10 is governed by the RKKY interactions in agreement with other RT 2Al10 (R = Nd, Sm, Tb, T = Fe, Ru and Os), but different to that of R = Ce based compounds where anisotropic two ions interaction as well as Kondo interaction govern the anomalous direction of the ordered state moment.

Direct determination of the zero-field splitting for the Fe3+ ion in a synthetic polymorph of NaMgFe(C2O4)3·9H2O : A natural metal-organic framework

We employed inelastic neutron scattering (INS), specific heat, and magnetization analysis to study the magnetism in a synthetic polymorph of the quasi-two-dimensional natural metal-organic framework material, stepanovite NaMgFe(C$_2$O$_4$)$_3\cdot$9H$_2$O. No long-range magnetic order can be observed down to 0.5 K. The INS spectra show two dispersionless excitations at energy transfer 0.028(1) and 0.050(1) meV at base temperature, which are derived from the magnetic transitions between zero-field splitting (ZFS) of $S$ = 5/2 ground state multiplets of Fe$^{3+}$ ion. Further analysis of the INS results shows that the Fe$^{3+}$ ion has an easy-axis anisotropy with axial ZFS parameter $D$ = $-$0.0128(5) meV and rhombic parameter $E$ = 0.0014(5) meV. The upward behavior at zero field and Schottky-like peak under magnetic field of the low-temperature magnetic specific heat further support the INS results. Our results clearly reveal the magnetic ground and excited state of this stepanovite polymorph.

Adiabatic heuristic principle on a torus and generalized Streda formula

Although the adiabatic heuristic argument of the fractional quantum Hall states has been successful, continuous modification of the flux/statistics of anyons is strictly prohibited due to algebraic constrains of the braid group on a torus. We have numerically shown that the adiabatic heuristic principle for anyons is still valid even though the Hamiltonians cannot be modified continuously. The Chern number of the ground state multiplet is the adiabatic invariant, while the number of the topological degeneracy behaves wildly. A generalized Streda formula is proposed that explains the degeneracy pattern. Nambu-Goldston modes associated with the anyon superconductivity are also suggested numerically.

Magnetic structure and crystalline electric field effects in the triangular antiferromagnet CePtAl4Ge2

Kondo metal $\mathrm{CePtA}{\mathrm{l}}_{4}\mathrm{G}{\mathrm{e}}_{2}$ exhibits long-range antiferromagnetic order below 2.3 K. Neutron powder-diffraction experiments reveal that Ce moments order antiferromagnetically with an incommensurate ordering wave vector $\mathbit{k}=(1.39,0,0.09)$. Inelastic neutron powder scattering experiments show a magnetic excitation at 14.5 meV, which corresponds to the first excited state due to the crystalline electric field splitting of the ground-state multiplet of $\mathrm{C}{\mathrm{e}}^{3+}$. The temperature and field dependence of the magnetization of $\mathrm{CePtA}{\mathrm{l}}_{4}\mathrm{G}{\mathrm{e}}_{2}$ is consistent with a doublet ground state with a dominant $|{j}_{\mathrm{z}}=1/2\ensuremath{\rangle}$ character and a first excited doublet $|{j}_{\mathrm{z}}=3/2\ensuremath{\rangle}$ at 14.5 meV.

Kramers doublets, phonons, crystal-field excitations, and their coupling in Nd2ZnIrO6

We report comprehensive Raman-scattering measurements on a single crystal of double-perovskite Nd2ZnIrO6 in temperature range of 4-330 K, and spanning a broad spectral range from 20 cm-1 to 5500 cm-1. The paper focuses on lattice vibrations and electronic transitions involving Kramers doublets of the rare-earth Nd3+ ion with local C1 site symmetry. Temperature evolution of these quasi-particle excitations have allowed us to ascertain the intricate coupling between lattice and electronic degrees of freedom in Nd2ZnIrO6. Strong coupling between phonons and crystal-field excitation is observed via renormalization of the self-energy parameter of the phonons i.e. peak frequency and line-width. The phonon frequency shows abrupt hardening and line-width narrowing below ~ 100 K for the majority of the observed first-order phonons. We observed splitting of the lowest Kramers doublets of ground state (4I9/2) multiplets i.e. lifting of the Kramers degeneracy, prominently at low-temperature (below ~ 100 K), attributed to the Nd-Nd/Ir exchange interactions and the intricate coupling with the lattice degrees of freedom. The observed splitting is of the order of ~ 2-3 meV and is consistent with the estimated value. We also observed a large number of high-energy modes, 46 in total, attributed to the intra-configurational transitions between 4f3 levels of Nd3+ coupled to the phonons reflected in their anomalous temperature evolution.

Non-Hermitian fractional quantum Hall states

We demonstrate the emergence of a topological ordered phase for non-Hermitian systems. Specifically, we elucidate that systems with non-Hermitian two-body interactions show a fractional quantum Hall (FQH) state. The non-Hermitian Hamiltonian is considered to be relevant to cold atoms with dissipation. We conclude the emergence of the non-Hermitian FQH state by the presence of the topological degeneracy and by the many-body Chern number for the ground state multiplet showing Ctot = 1. The robust topological degeneracy against non-Hermiticity arises from the manybody translational symmetry. Furthermore, we discover that the FQH state emerges without any repulsive interactions, which is attributed to a phenomenon reminiscent of the continuous quantum Zeno effect.