Electronic Energy Level Structure

Liu, Guokui

doi:10.1007/3-540-28209-2_1

Cited by 77 publications

(90 citation statements)

References 110 publications

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“…The local anisotropy axis of the crystal field levels yields a strong Ising anisotropy along the 111 axis. The intermultiplet splitting of ≈ 300 meV is a typical value for the transition between the ground and first excited multiplet in Ce 3+ compounds [40]. This crystal field scheme of Ce 2 Sn 2 O 7 is generally consistent with the calculations using the multiX computer program [41] if the semi-empirical values for the spin-orbit coupling and crystal field scalers are adjusted accordingly.…”

supporting

confidence: 69%

Candidate Quantum Spin Liquid in theCe3+Pyrochlore StannateCe2
Sibille
¹
,
Lhotel
²
,
Pomjakushin
³

et al. 2015
Phys. Rev. Lett.
105
6
78
0
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We report the low temperature magnetic properties of Ce2Sn2O7, a rare-earth pyrochlore. Our susceptibility and magnetization measurements show that due to the thermal isolation of a Kramers doublet ground state, Ce2Sn2O7 has Ising-like magnetic moments of ∼ 1.18 µB. The magnetic moments are confined to the local trigonal axes, as in a spin ice, but the exchange interactions are antiferromagnetic. Below 1 K the system enters a regime with antiferromagnetic correlations. In contrast to predictions for classical 111 -Ising spins on the pyrochlore lattice, there is no sign of longrange ordering down to 0.02 K. Our results suggest that Ce2Sn2O7 features an antiferromagnetic liquid ground state with strong quantum fluctuations. [5,6], which have no conventional order parameter associated with a broken symmetry, but whose defining character is a longrange entangled groundstate wavefunction [7,8]. Spin liquids are of great interest thanks to the remarkable collective phenomena that they can present, such as emergent gauge fields and fractional quasiparticle excitations [9,10]. Such states may also offer the possible application of coherent or topologically protected ground states in quantum information processing devices [11].Quantum coherence of a spin system lacking symmetry-breaking order is well established in onedimensional spin chains forming a spin fluid with a quantum coherence length almost an order of magnitude larger than the classical antiferromagnetic correlation length [12]. In higher dimensions two paradigms are employed, often simultaneously, to try to obtain a quantum spin liquid (QSL). Firstly, for Heisenberg spins with S=1/2, where quantum mechanical corrections are most significant compared to classical states, quantum melting of the Néel ground state may be possible when spins pair into valence bond singlets [13]. The result may be a valence bond crystal (translationally ordered valence bonds) [14], a resonating valence bond state (singlet configurations resonate around a plaquette) [15], or a true spin liquid when valence bonds can be formed at all lengthscales so that the ground state wavefunction has a genuine long-range entanglement [5,16]. Secondly, geometrically frustrated magnets are a natural landscape for liquid-like states of magnetic moments. In two dimensions, the triangular and kagome lattices are important examples [17][18][19][20], and neutron scattering experiments on the S=1/2 kagome lattice antiferromagnet ZnCu 3 (OH) 6 Cl 2 (herbertsmithite) have provided evidence of fractionalized excitations in a 2D QSL [21,22] [27] have illustrated how quantum effects can become important in materials where they may not be expected, i.e. in rare earth materials where crystal field effects lead to highly anisotropic magnetic moments.The spin system of a pyrochlore with a thermally isolated doublet ground state can be described by a generalized Hamiltonian for effective S = 1/2 spins [24,28]. This Hamiltonian includes all symmetry-allowed near neighbour magnetic exchange interactions, with a lea...

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supporting

confidence: 69%

Candidate Quantum Spin Liquid in theCe3+Pyrochlore StannateCe2
Sibille
¹
,
Lhotel
²
,
Pomjakushin
³

et al. 2015
Phys. Rev. Lett.
105
6
78
0
View full text Add to dashboard Cite

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“…7,9 The parameters of the Hamiltonian are configuration specific. Namely, for the f n and f n−1 d configurations, parameterization is achieved separately based on freeion wave functions of individual configurations and the crystal-field-induced configuration coupling is not considered.…”

Section: Crystal-field Theory Including Configuration Interactionmentioning

confidence: 99%

“…1-3͒ has been applied successfully to modeling the electronic energy-level structures of the 4f n configurations of lanthanide ions in crystalline solids. [4][5][6][7] In the conventional framework of CFT, an effective Hamiltonian including both free-ion interactions and ion-lattice interactions is usually parameterized by fitting the calculated energy levels to those observed in spectroscopic experiments. [6][7][8][9] This method is also effective for isolated multiplets of the 5f n configurations of actinide ions in crystals where configuration coupling is weak.…”

Section: Introductionmentioning

confidence: 99%

“…[4][5][6][7] In the conventional framework of CFT, an effective Hamiltonian including both free-ion interactions and ion-lattice interactions is usually parameterized by fitting the calculated energy levels to those observed in spectroscopic experiments. [6][7][8][9] This method is also effective for isolated multiplets of the 5f n configurations of actinide ions in crystals where configuration coupling is weak. [10][11][12][13] Based on the symmetry properties of crystal field, the intraconfiguration crystal-field interactions are induced by the crystal-field operators of even ranks ͑B q k , k =2,4,6͒, whereas the odd ranks of crystal-field operators ͑k =1,3,5͒ only couple the free-ion states of two configurations with different parities.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

5f−6dorbital hybridization of trivalent uranium in crystals of hexagonal symmetry: Effects on electronic energy levels and transition intensities

et al. 2009

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Orbital hybridization ͑mixing of electron configurations of opposite parities͒ is analyzed in the framework of crystal-field theory with a complete diagonalization of the crystal-field Hamiltonian, including both even and odd terms of crystal-field potential, and with all basis sets of the 5f 3 and 5f 2 6d configurations for the wave functions of open-shell electrons in the U 3+ ion. This method provides a fundamental understanding and quantitative analysis of the crystal-field induced 5f-6d mixing in U 3+ : LaCl 3 and U 3+ : CeCl 3 . The odd terms of the crystal-field interaction ͓B 3 3 ͑fd͒ and B 3 5 ͑fd͒ in C 3h site symmetry͔ selectively couple the states of the 5f 3 and 5f 2 6d configurations, inducing a shift of the energy levels and allow electric dipole transitions between the configuration-mixed states. The mixture of the 5f and 6d configurations is evaluated by introducing an index of configuration mixing. The exchange charge model ͑ECM͒ of crystal-field theory is used to calculate the crystal-field parameters of the U 3+ 5f and 6d electrons in terms of point-charge electrostatic interaction and orbital overlapping and covalent effect. The initial ECM estimations of the crystal-field parameters were optimized along with free-ion parameters of the Hamiltonian in nonlinear least-squares fitting of the calculated U 3+ energy levels to the experimental absorption spectra. The configuration-mixed eigenfunctions of the U 3+ states are directly used to calculate the electric dipole transition intensities and simulate the absorption spectra where the 5f 3 and 5f 2 6d configurations overlap and the Judd-Ofelt theory fails because of significant configuration mixing.

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“…[1][2][3] Systematic experimental studies of the 4f N -4f NÀ1 5d excitation and 4f NÀ1 5d-4f N emission and theoretical modeling of energy-level patterns and transition intensities have been carried out for many systems. [4][5][6] Most measured spectra consist of several broad bands for 4f !…”

Section: Introductionmentioning

confidence: 99%

Study of the d-f Emission, and f-d Ground-State and Excited-State Absorption of Nd³⁺in Crystals Using the Simple Model

Duan

Jiang

2010

Spectroscopy Letters

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The simplified model for 4f-5d transitions is applied to obtain the line strengths for emission, ground-state absorption and excited states absorption involving 4f-5d transitions of Nd 3þ in crystals. The results are host independent for the usual case where 5d crystal-field interaction can be considered as strong, in the sense that the calculated 5d-4f emission relative line strengths will be the same for Nd 3þ in any host. Also the calculated 4f-5d absorption line strengths can be grouped by the 5d crystal-field components. For each 5d crystal-field component, the group of absorption line strengths for different 4f 2 5d transition final states forms a pattern independent of the 5d crystal-field component and the host. For practical cases, due to strong but still limited 5d crystal-field splitting, the transitions to different 5d crystal-field components may overlap each other. The theoretical results are used to interpret available experimental data.

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Electronic Energy Level Structure

Cited by 77 publications

References 110 publications

Candidate Quantum Spin Liquid in theCe3+Pyrochlore StannateCe2
Sibille
¹
,
Lhotel
²
,
Pomjakushin
³

et al. 2015
Phys. Rev. Lett.
105
6
78
0
View full text Add to dashboard Cite

Candidate Quantum Spin Liquid in theCe3+Pyrochlore StannateCe2
Sibille
¹
,
Lhotel
²
,
Pomjakushin
³

et al. 2015
Phys. Rev. Lett.
105
6
78
0
View full text Add to dashboard Cite

5f−6dorbital hybridization of trivalent uranium in crystals of hexagonal symmetry: Effects on electronic energy levels and transition intensities

Study of the d-f Emission, and f-d Ground-State and Excited-State Absorption of Nd³⁺in Crystals Using the Simple Model

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Electronic Energy Level Structure

Cited by 77 publications

References 110 publications

Candidate Quantum Spin Liquid in theCe3+Pyrochlore StannateCe2Sibille1, Lhotel2, Pomjakushin3 et al. 2015Phys. Rev. Lett.1056780View full textAdd to dashboardCite

Candidate Quantum Spin Liquid in theCe3+Pyrochlore StannateCe2Sibille1, Lhotel2, Pomjakushin3 et al. 2015Phys. Rev. Lett.1056780View full textAdd to dashboardCite

5f−6dorbital hybridization of trivalent uranium in crystals of hexagonal symmetry: Effects on electronic energy levels and transition intensities

Study of the d-f Emission, and f-d Ground-State and Excited-State Absorption of Nd3+in Crystals Using the Simple Model

Contact Info

Product

Resources

About

Candidate Quantum Spin Liquid in theCe3+Pyrochlore StannateCe2
Sibille
¹
,
Lhotel
²
,
Pomjakushin
³

et al. 2015
Phys. Rev. Lett.
105
6
78
0
View full text Add to dashboard Cite

Candidate Quantum Spin Liquid in theCe3+Pyrochlore StannateCe2
Sibille
¹
,
Lhotel
²
,
Pomjakushin
³

et al. 2015
Phys. Rev. Lett.
105
6
78
0
View full text Add to dashboard Cite

Study of the d-f Emission, and f-d Ground-State and Excited-State Absorption of Nd³⁺in Crystals Using the Simple Model