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Ab initio calculations of erbium crystal field splittings in oxide hosts

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read One fitted parameter predicts erbium splittings in oxides

desk verdict A useful semi-empirical scheme for Er crystal field splittings in oxides, but the ab initio claim is undercut by per-host fitting and an internal inconsistency in the radial wavefunction screening. read the letter →

arxiv 2501.03348 v1 pith:TOQ463A2 submitted 2025-01-06 cond-mat.mtrl-sci quant-ph

Yogendra Limbu , Yueguang Shi , Joseph Sink , Tharnier O. Puel , Durga Paudyal , Michael E. Flatté This is my paper · ORCID
classification cond-mat.mtrl-sciquant-ph
keywords erbiumcrystalfieldsplittingdensityfunctionaltheory4fcoreapproximationrareearthoxidehostsquantummemorydielectricscreening
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that the crystal field coefficients of Er3+ ions in five wide-band-gap oxide hosts can be computed from density functional theory (DFT) within the 4f-core approximation, where the 4f electrons are frozen in the core. The only adjustable input is a per-host dielectric constant that sets the radial extent of a hydrogenic 4f wavefunction; fitted values cluster near 2, which shrinks the orbital by about a factor of two relative to the extent inferred from Wannier functions or the Er3+ ionization energy. With these coefficients, an effective Hamiltonian reproduces the ground and excited manifold splittings measured at low temperature to within tens of wavenumbers across four different local site symmetries. If the method holds, it offers a cheap, single-parameter route to predicting erbium crystal-field splittings in candidate quantum-memory hosts.

What carries the argument

The working object is the hydrogenic 4f radial wavefunction $R_{4f}(r) = A r^3 \exp(-r Z_{\mathrm{eff}}/(n a_0 \epsilon))$, with $Z_{\mathrm{eff}}$ obtained from atomic screening constants and $\epsilon$ a per-host dielectric constant fitted to experiment. This wavefunction is used to evaluate the radial integrals that convert the DFT crystal-field potential into the coefficients $B^k_q$; the coefficients are then diagonalized together with the free-ion Hamiltonian (electrostatic, spin-orbit, two- and three-body interactions) to produce the crystal-field splittings.

What would settle it

Compute the crystal field coefficients for a new oxide host using the same workflow with an epsilon near 2, then compare the predicted Z- and Y-manifold splittings to low-temperature spectra; disagreement beyond about 30 cm-1 in the relative splittings would falsify the single-parameter claim.

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Extended reading notes

Core claim

The central discovery is that the crystal field coefficients $B^k_q$ of Er3+ in oxide hosts can be obtained from the self-consistent DFT charge density and local potential after freezing the 4f electrons in the core, provided the radial part of the 4f orbital is taken to be hydrogenic with an exponent controlled by a fitted dielectric constant near 2. With these coefficients, the effective Hamiltonian reproduces the measured splittings of the ground ($^4I_{15/2}$) and first excited ($^4I_{13/2}$) manifolds for all five hosts, spanning local site symmetries $O_h$, $C_{3v}$, $D_{2h}$, and $S_4$. The authors argue that the single fitted factor of about two accounts for the known inadequacy of DFT in describing the strongly correlated, partially filled 4f shell.

Load-bearing premise

The entire calculation rests on representing the 4f orbital as hydrogenic with a single fitted dielectric constant per host; if that functional form or the fitted epsilon value is wrong, all computed splittings change.

Editorial extensions

If this is right

  • The method gives a practical workflow: one DFT calculation with 4f in the core, one fitted epsilon, then an effective-Hamiltonian diagonalization, yielding CFCs and splittings for a new oxide host without iterative fitting to spectroscopy.
  • Agreement across four local site symmetries suggests the single-parameter correction captures the dominant screening error, so the approach may transfer to other trivalent rare-earth ions.
  • Predicted CFCs can be used to design erbium-based quantum memories and spin-photon interfaces, since the Y1-Z1 transition energy and manifold structure are reproduced.
  • The Wannier and ionization-energy estimates of epsilon (around 4) bracketing the fitted value (around 2) indicate the parameter is an effective screening correction rather than the true bulk dielectric constant.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the fitted epsilon differs from both the Wannier-derived value (~3-4) and the bulk static dielectric constants of these oxides, the parameter likely absorbs several distinct errors—DFT self-interaction, the hydrogenic approximation to the 4f orbital, and neglect of lattice relaxation around the dopant. A direct test would be to compare CFCs computed with a self-consistently relaxed 4f orbi
  • The near-constancy of the fitted epsilon (1.90-2.24) across hosts with very different dielectric properties suggests the correction is ionic rather than host-specific; if so, a universal epsilon near 2 may work for other wide-band-gap oxides and even for other rare-earth ions, a claim the paper does not make.
  • The paper aligns calculated Y-manifold centers to experiment, so the method predicts splittings within a manifold, not the absolute 4f-4f transition energy. A stronger test would be to predict both and check whether the residual ~30-60 cm-1 discrepancies in Y1-Z1 gaps are systematic.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes an effective method for computing crystal-field coefficients (CFCs) B_k^q of Er3+ in five wide-band-gap oxide hosts (MgO, ZnO, TiO2, CaWO4, PbWO4) by combining DFT calculations with the 4f electrons placed in the core and a hydrogenic 4f radial wavefunction whose extent is controlled by a per-host dielectric constant epsilon. These CFCs are then fed into the qlanth Hamiltonian to compute crystal-field splittings of the ground 4I15/2 and first excited 4I13/2 manifolds. The authors report good agreement with low-temperature measurements, provided the 4f radial wavefunction is contracted by about a factor of two. The central claim is that this constitutes an ab initio method with a single physically justifiable adjustable parameter.

Significance. If the predictive claim were established, the method would provide a practical DFT-based route to crystal-field splittings of Er3+ in oxides, which is valuable for quantum communication and memory applications. The paper has clear strengths: it treats four distinct site symmetries, respects the symmetry-dictated form of the CFCs (e.g., the MgO relations B4±4 = sqrt(5/14) B4_0 and B6±4 = -sqrt(7/2) B6_0 are satisfied), and uses an open-source Hamiltonian code with documented improvements. However, the central claim is not yet demonstrated because the per-host dielectric constant is fitted to the same experimental levels used for validation and because the fitted values contradict the paper's own independent Wannier- and ionization-energy-based estimates. The significance is therefore conditional on resolving these load-bearing issues.

major comments (4)
  1. [Methods, R4f paragraph] The central result depends on the per-host dielectric constant epsilon, which the text says is 'carefully optimized by fitting the calculated and the experimental energy levels.' The same experimental splittings are then displayed as validation in Fig. 2. Since B_k^q is computed from integrals involving R_4f^2 and the radial moments scale approximately as (a0 epsilon/Z_eff)^k, fitting epsilon per host can absorb a large part of the systematic error. The paper should report the fit protocol explicitly: which Z and Y levels entered the fit, how the residual was minimized, and the per-host residuals after fitting. It should also provide an out-of-sample test, such as a single epsilon fixed across all hosts or a leave-one-host-out prediction, before claiming predictive ab initio accuracy.
  2. [Methods, R4f paragraph and Wannier/ionization comparison] The fitted epsilon values (1.96 for MgO, 1.90 for ZnO, 2.00 for TiO2, 2.24 for CaWO4 and PbWO4) directly contradict the paper's own independent estimates. The text states that the Wannier-extracted 4f function agrees with the hydrogenic form when epsilon is between 3 and 4, and that the ionization-energy estimate gives epsilon = 3.96. With the hydrogenic form R4f(r) = A r^3 exp(-r Zeff/(4 a0 epsilon)), a smaller epsilon produces a more contracted orbital, and the CFC integrals scale as powers of (a0 epsilon/Zeff). This discrepancy is therefore not cosmetic: it undermines the claim that epsilon is the physically justified dielectric constant. Either the fitted values must be reconciled with the independent estimates, or the paper should explicitly describe epsilon as an empirical scaling parameter and remove the claim of physical justification.
  3. [Fig. 2 and Y-manifold alignment] The comparison in Fig. 2 is restricted to splittings within each manifold because, for every host, the calculated Y manifold is shifted so that Y1 aligns with the experimental Y1 value (e.g., -31 cm^-1 for Er:MgO). The stated Y1-Z1 transition energies differ from experiment by tens of wavenumbers in several cases (e.g., +63.32 cm^-1 for ZnO and +64.30 cm^-1 for CaWO4). The paper should state clearly that absolute multiplet energies are not predicted and should tabulate these Y1-Z1 residuals for all hosts. As it stands, the excellent agreement for the excited manifold is partly a consequence of this alignment convention.
  4. [PbWO4, section 3 and Table I] PbWO4 is included in Table I and in the abstract, but no level-by-level comparison of the Z and Y manifolds is presented for PbWO4. The text reports only the Y1-Z1 transition (6570.05 cm^-1) and states that it shows good agreement. A figure or table analogous to Fig. 2 for PbWO4 is needed to support the claimed agreement for this host.
minor comments (5)
  1. [Abstract and Introduction] The phrase 'reducing the radial extent of the 4f wavefunctions by approximately a factor of 2' is directionally confusing when read against the formula R4f(r) = A r^3 exp(-r Zeff/(4 a0 epsilon)), because increasing epsilon in this formula spreads the orbital. Please specify the baseline (e.g., epsilon ~ 4 from Wannier/ionization versus the fitted epsilon ~ 2) and state the contraction factor explicitly.
  2. [Methods, atomic parameters] The free-ion parameters (F^k, zeta_4f, alpha, beta, gamma, T^i, M^h, P^f) are taken from Ref. [17], which is a LaF3 analysis. The paper does not assess whether these parameters are transferable to the five oxide hosts; a sensitivity test with respect to these parameters would strengthen the conclusions.
  3. [Table I] Table I uses entries with real and imaginary parts indicated by signs such as '∓' and '±' without fully defining the convention for B_k,±q. Please state the convention explicitly (e.g., column lists both B_k, q and B_k, -q with the stated sign relations) and ensure the table is self-explanatory.
  4. [Methods, DFT setup] The choice to keep 4f electrons in the core and to treat 6s2, 5p6, and 5d1 as valence electrons is central to the method, but the paper does not justify this choice or test its sensitivity. A brief discussion or a supplementary test would help establish the robustness of the CFCs.
  5. [Reproducibility and companion paper] Several details of the calculation are deferred to the simultaneously submitted companion works (Refs. [36] and [64]). The core method should be reproducible from the present manuscript alone, so please include the essential procedural details and either provide explicit data or clearly indicate where they will be permanently available.

Circularity Check

1 steps flagged · score 6.0 of 10

The per-host dielectric constant epsilon is fit to the same experimental crystal-field splittings used for validation, making the reported 'excellent agreement' substantially in-sample.

  1. fitted input called prediction [Methods/CFC extraction, paragraph defining the crystal field potential B_q^k and the radial function R_4f, before Table I]
    "Here the dielectric constant, ϵω,q, which depends upon the frequency and crystal structure, and controls the spreading of the 4f radial wave function, is carefully optimized by fitting the calculated and the experimental energy levels. The optimized ϵω,q for MgO, ZnO, TiO2, PbWO4, and CaWO4 are 1.96, 1.90, 2.00, 2.24, and 2.24, respectively. The corresponding ϵω,q are then used to extract CFCs from the self-consistent DFT charge densities and local potentials."

    The CFCs are computed as B_q^k = (2k+1)/4π ∫ V_CF(r) R_4f(r,ϵ)^2 C^{k*}_q r^2 dr, with R_4f(r,ϵ) = A r^3 exp(-r Z_eff/(n a0 ϵ)). Every host-dependent radial moment that sets the relative strength of B2, B4, and B6 therefore depends on ϵ, and the resulting crystal-field splittings depend on those CFCs. Fitting ϵ per host to the experimental energy levels—the same low-temperature measurements later used as the validation target in Fig. 2—makes the calculated splittings in-sample rather than out-of-sample predictions. The paper does not state which experimental levels entered the fit or the fit residuals, so the displayed agreement cannot be separated from the flexibility of this one fitted parameter.

full rationale

The derivation chain is: DFT charge density -> V_CF(r) -> B_q^k = (2k+1)/4π ∫ V_CF R_4f^2 C^{k*}_q r^2 dr -> qlanth effective Hamiltonian -> crystal-field splittings. The only host-specific adjustable parameter in this chain is the dielectric constant ϵ entering the hydrogenic 4f radial function R_4f(r,ϵ). The paper states explicitly that this parameter is 'carefully optimized by fitting the calculated and the experimental energy levels,' and the optimized per-host values (1.90–2.24) are then used to extract the CFCs and generate the splittings shown against the same low-temperature measurements. Thus the central 'excellent agreement' claim is substantially in-sample: the radial moments controlling the relative weights of the second-, fourth-, and sixth-order crystal-field terms are tuned host-by-host to the target spectra. The abstract's statement that the 4f radial extent is reduced 'by approximately a factor of 2' is a post-fit description of the fitted ϵ values rather than an independent input, especially since the paper's own Wannier-function and ionization-energy analyses suggest ϵ ≈ 3–4. Additionally, the Y1 manifold energy is explicitly aligned to experiment in Fig. 2, an acknowledged calibration that further reduces the predicted content of the excited-state comparison. There is genuine non-circular residue: symmetry-imposed zero CFCs, ratios among CFCs of the same rank, and the ordering/spacing of the 15 Kramers levels under a single scalar are not fully forced by the fit, and qlanth's atomic parameters and screening constants come from external sources. However, as reported, the paper does not demonstrate an out-of-sample predictive-from-DFT method; the per-host fit to the validation data is the load-bearing step, giving a partial circularity score of 6.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on one fitted scalar per host (epsilon) plus a set of inherited atomic parameters from a prior LaF3 fit. No new physical entities are introduced. The method is therefore semi-empirical rather than fully ab initio.

free parameters (2)
  • Per-host dielectric scaling epsilon_wq = MgO 1.96, ZnO 1.90, TiO2 2.00, CaWO4 2.24, PbWO4 2.24
    Fitted to reproduce measured 4f energy levels per host; controls radial extent of hydrogenic 4f wavefunction in the CFC integral.
  • Atomic free-ion parameters (F^k, zeta_4f, alpha, beta, gamma, T^i, M^h, P^f) = Taken from Carnall et al. (Ref [17]) LaF3 fit
    Inherited from a prior fit to LaF3 spectra; assumed transferable to oxide hosts; central to the qlanth effective Hamiltonian.
assumptions (5)
  • domain assumption 4f electrons can be frozen in the core and the DFT local potential approximates the crystal field potential V_CF(r).
    Used to extract B^k_q from self-consistent charge densities; a standard approximation in lanthanide DFT.
  • ad hoc to paper The 4f radial wavefunction is hydrogenic with a single adjustable dielectric constant epsilon.
    R4f formula in the text; the scaling is fitted to data rather than derived.
  • domain assumption Atomic free-ion parameters from LaF3 (Carnall) are transferable to MgO, ZnO, TiO2, CaWO4, PbWO4.
    Used in qlanth without re-fitting for these hosts.
  • domain assumption The experimental energy level assignments from Refs [4, 54, 63] are correct.
    Comparison baseline for the claimed agreement.
  • domain assumption qlanth code correctly implements the effective Hamiltonian.
    The paper cites code validation against Ref [17] within 30 cm^-1.

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Cite this review

Pith. "Pith review of Ab initio calculations of erbium crystal field splittings in oxide hosts." pith.science (2026). https://pith.science/paper/TOQ463A2

@misc{pith2026250103348,
  author       = {Pith},
  title        = {Pith review of: Ab initio calculations of erbium crystal field splittings in oxide hosts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TOQ463A2}},
  note         = {Machine review of arXiv:2501.03348}
}
read the original abstract

We present an effective ab initio method to calculate the crystal field coefficients of an erbium (Er3+) ion experiencing different local site symmetries in several wide-band-gap oxides, and then evaluate crystal field splittings of these Er3+ ions for their ground and excited states. The optical transitions between the ground state (Z) and excited state (Y) manifolds of the environmentally shielded 4f states of these Er3+ ions have wavelengths ~1.5 microns and thus have potential applications to quantum communications and quantum memories. These results are in excellent agreement with recent low-temperature measurements, provided the inadequate calculation of the 4f shell screening is adjusted by reducing the radial extent of the 4f wavefunctions by approximately a factor of 2.

Figures

Figures reproduced from arXiv: 2501.03348 by the authors.

Figure 1
Figure 1. FIG. 1. (a)-(d) Two-dimensional views of the crystal field [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The ground ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

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Reference graph

Works this paper leans on

66 extracted references · 35 canonical work pages · cited by 1 Pith paper

  1. [1]

    Optical and microstructural characterization of Er 3+ doped epitaxial cerium oxide on silicon,

    Gregory D. Grant, Jiefei Zhang, Ignas Masiulionis, Swarnabha Chattaraj, Kathryn E. Sautter, Sean E. Sul- livan, Rishi Chebrolu, Yuzi Liu, Jessica B. Martins, Jens Niklas, Alan M. Dibos, Sumit Kewalramani, John W. Freeland, Jianguo Wen, Oleg G. Poluektov, F. Joseph Heremans, David D. Awschalom, and Supratik Guha, “Optical and microstructural characterizati...

    work page 2024

  2. [2]

    Five non-zero CFCs:B2 0, B4 0, B4 ±4, B6 0, andB6 ±4 are identified in both materials as also suggested in Refs

    In CaWO4 and PbWO4, the Er doped site favorsS4 local site symmetry [53]. Five non-zero CFCs:B2 0, B4 0, B4 ±4, B6 0, andB6 ±4 are identified in both materials as also suggested in Refs. [21, 54]. TheB4 ±4 and B6 ±4 have real and imaginary components, whileB2 0, B4 0, and B6 0 have only the real components. The real components of CFCs follow the relation R...

    work page

  3. [3]

    Optical detection of a single rare-earth ion in a crystal,

    R. Kolesov, K. Xia, R. Reuter, R. Stöhr, A. Zappe, J. Meijer, P. R. Hemmer, and J. Wrachtrup, “Optical detection of a single rare-earth ion in a crystal,” Nat. Commun. 3, 1029 (2012)

    2012

  4. [4]

    Rare-earth-doped materials for applications in quantum information storage and signal processing,

    Charles W. Thiel, Thomas Böttger, and R. L. Cone, “Rare-earth-doped materials for applications in quantum information storage and signal processing,” J. Lumin. 131, 353–361 (2011). 5

    work page 2011

  5. [5]

    Emerging rare-earth doped material platforms for quantum nanophotonics,

    Tian Zhong and Philippe Goldner, “Emerging rare-earth doped material platforms for quantum nanophotonics,” Nanophotonics 8, 2003–2015 (2019)

    2019

  6. [6]

    Erbium-implanted ma- terials for quantum communication applications,

    Paul Stevenson, Christopher M. Phenicie, Isaiah Gray, Sebastian P. Horvath, Sacha Welinski, Austin M. Fer- renti, Alban Ferrier, Philippe Goldner, Sujit Das, Ra- mamoorthy Ramesh, Robert J. Cava, Nathalie P. de Leon, and Jeff D. Thompson, “Erbium-implanted ma- terials for quantum communication applications,” Phys. Rev. B 105, 224106 (2022)

    work page 2022

  7. [7]

    Nanocavity-mediated purcell enhancement of Er in TiO2 thin films grown via atomic layer deposition,

    Cheng Ji, Michael T. Solomon, Gregory D. Grant, Koichi Tanaka, Muchuan Hua, Jianguo Wen, Sagar Ku- mar Seth, Connor P. Horn, Ignas Masiulionis, Man- ish Kumar Singh, Sean E. Sullivan, F. Joseph Heremans, David D. Awschalom, Supratik Guha, and Alan M. Di- bos, “Nanocavity-mediated purcell enhancement of Er in TiO2 thin films grown via atomic layer depositi...

    2024

  8. [8]

    These atomic parame- ters are extracted from Ref

    in two particles Hamiltonian [26, 29], where T i are the adjustable parameters, which are obtained fromab initio method or fitting experimental data [17, 30], and ti are three-particle operators. These atomic parame- ters are extracted from Ref. [17]. Further,Mh (h = 0, 2, 4) contains spin-spin and spin-other-orbit relativistic corrections, known as Marvi...

    work page

Show all 66 references
  1. [9]

    Rare-earth doped trans- parent ceramics for spectral filtering and quantum infor- mation processing,

    Nathalie Kunkel, Alban Ferrier, Charles W. Thiel, Mar- iola O. Ramírez, Luisa E. Bausá, Rufus L. Cone, Akio Ikesue, and Philippe Goldner, “Rare-earth doped trans- parent ceramics for spectral filtering and quantum infor- mation processing,” APL Mater.3, 096103 (2015)

    2015

  2. [10]

    Recent developments in rare-earth doped materials for optoelectronics,

    A. J. Kenyon, “Recent developments in rare-earth doped materials for optoelectronics,” Prog. Quantum Electron. 26, 225–284 (2002)

    2002

  3. [11]

    Guokui Liu and Bernard Jacquier,Spectroscopic Proper- ties of Rare Earths in Optical Materials (Springer, 2005)

    2005

  4. [12]

    Spectral and kinetic properties of Er 3+, Yb 3+:Yb3Al5O12 crystals at high temperatures,

    Boris Ivanovich Galagan, Boris I. Denker, Vyacheslav V. Osiko, and Sergei E. Sverchkov, “Spectral and kinetic properties of Er 3+, Yb 3+:Yb3Al5O12 crystals at high temperatures,” Quantum Electron. 36, 595 (2006)

    2006

  5. [13]

    Optical decoherence studies of yttrium oxyorthosilicate Y2SiO5 codopedwithEr 3+ andEu 3+ foropticalsignalprocessing and quantum information applications at 1.5 microns,

    C. W. Thiel, W. R. Babbitt, and R. L. Cone, “Optical decoherence studies of yttrium oxyorthosilicate Y2SiO5 codopedwithEr 3+ andEu 3+ foropticalsignalprocessing and quantum information applications at 1.5 microns,” Phys. Rev. B85, 174302 (2012)

    2012

  6. [14]

    Coherent spin dynamics of ytterbium ions in yttrium orthosilicate,

    Hee-Jin Lim, Sacha Welinski, Alban Ferrier, Philippe Goldner, and J. J. L. Morton, “Coherent spin dynamics of ytterbium ions in yttrium orthosilicate,” Phys. Rev. B 97, 064409 (2018)

    2018

  7. [15]

    Coherent spin control at the quantum level in an ensemble-based optical memory,

    Pierre Jobez, Cyril Laplane, Nuala Timoney, Nicolas Gisin, Alban Ferrier, Philippe Goldner, and Mikael Afzelius, “Coherent spin control at the quantum level in an ensemble-based optical memory,” Phys. Rev. Lett. 114, 230502 (2015)

    2015

  8. [16]

    Distinguishing erbium dopants in Y2O3 by site symmetry: Ab initio theory of two spin- photon interfaces,

    Churna Bhandari, Cüneyt Şahin, Durga Paudyal, and Michael E. Flatté, “Distinguishing erbium dopants in Y2O3 by site symmetry: Ab initio theory of two spin- photon interfaces,” Phys. Rev. Mater.7, 126201 (2023)

    2023

  9. [17]

    Synthesis and lumi- nescence properties of erbium-doped Y2O3 nanotubes,

    Yuanbing Mao, Jian Y. Huang, Roman Ostroumov, Kang L. Wang, and Jane P. Chang, “Synthesis and lumi- nescence properties of erbium-doped Y2O3 nanotubes,” J. Phys. Chem. C112, 2278–2285 (2008)

    2008

  10. [18]

    Group theory: Application to the physics of con- densed matter,

    Mildred S. Dresselhaus, Gene Dresselhaus, and Ado Jo- rio, “Group theory: Application to the physics of con- densed matter,” (2007)

    2007

  11. [19]

    A systematic analysis of the spectra of the lan- thanides doped into single crystal LaF3,

    W. T. Carnall, G. L. Goodman, K. Rajnak, and R. S. Rana, “A systematic analysis of the spectra of the lan- thanides doped into single crystal LaF3,” J. Chem. Phys. 90, 3443–3457 (1989)

    1989

  12. [20]

    Vacuum ultraviolet spectra and crys- tal field analysis of YAlO3 doped with Nd3+ and Er3+,

    Chang-kui Duan, Peter A. Tanner, Vladimir N. Makhov, and Marco Kirm, “Vacuum ultraviolet spectra and crys- tal field analysis of YAlO3 doped with Nd3+ and Er3+,” Phys. Rev. B75, 195130 (2007)

    2007

  13. [21]

    Crystal field and magnetism of Pr 3+ and Nd3+ ions in orthorhombic perovskites,

    P. Novák, K. Knížek, M. Maryško, Z. Jirák, and J. Kuneš, “Crystal field and magnetism of Pr 3+ and Nd3+ ions in orthorhombic perovskites,” J. Phys. Con- dens. Matter 25, 446001 (2013)

    2013

  14. [22]

    Crystalfieldparam- eters with Wannier functions: Application to rare-earth aluminates,

    P.Novák, K.Knížek, andJ.Kuneš,“Crystalfieldparam- eters with Wannier functions: Application to rare-earth aluminates,” Phys. Rev. B87, 205139 (2013)

    2013

  15. [23]

    Crystal fields of lithium rare-earth tetrafluorides and multiplet split- ting of the +3 rare-earth ions,

    Leila Mollabashi and S. Jalali-Asadabadi, “Crystal fields of lithium rare-earth tetrafluorides and multiplet split- ting of the +3 rare-earth ions,” Phy. Rev. B102, 045120 (2020)

    2020

  16. [24]

    Density functional theory calculation of crystal-field energy levels for Yb3+ in the Cs2NaYbF6 crystal,

    Lixin Ning and Gian Paolo Brivio, “Density functional theory calculation of crystal-field energy levels for Yb3+ in the Cs2NaYbF6 crystal,” Phys. Rev. B 75, 235126 (2007)

    2007

  17. [25]

    qlanth: A hamiltonian for the lanthanides

    Juan David Lizarazo Ferro, “qlanth: A hamiltonian for the lanthanides.” San Francisco (CA): GitHub (2024)

    2024

  18. [26]

    Magneticdipole and electric quadrupole transitions in the trivalent lan- thanide series: Calculated emission rates and oscillator strengths,

    ChristopherM.DodsonandRashidZia,“Magneticdipole and electric quadrupole transitions in the trivalent lan- thanide series: Calculated emission rates and oscillator strengths,” Phys. Rev. B86, 125102 (2012)

    2012

  19. [27]

    Orthogonalized oper- ators for the f shell,

    B. R. Judd and H. Crosswhite, “Orthogonalized oper- ators for the f shell,” J. Opt. Soc. Am. B 1, 255–260 (1984)

    1984

  20. [28]

    Configuration interac- tion effects in lN configurations,

    K. Rajnak and B. G. Wybourne, “Configuration interac- tion effects in lN configurations,” Phys. Rev. 132, 280 (1963)

    1963

  21. [29]

    Configuration interaction in Mn II,

    R. E. Trees, “Configuration interaction in Mn II,” Phys. Rev. 83, 756 (1951)

    1951

  22. [30]

    Wybourne, Spectroscopic properties of rare earths (Interscience, 1965)

    Brian G. Wybourne, Spectroscopic properties of rare earths (Interscience, 1965)

    1965

  23. [31]

    Three-particle operators for equivalent elec- trons,

    B. R. Judd, “Three-particle operators for equivalent elec- trons,” Phys. Rev.141, 4 (1966)

    1966

  24. [32]

    W. T. Carnall, Hannah Crosswhite, and Henry Milton Crosswhite, Energy level structure and transition proba- bilities in the spectra of the trivalent lanthanides in LaF 3, Tech.Rep.ANL-78-XX-95(ChemistryDivision, Argonne National Laboratory, and Department of Physics, The Johns...

    1978

  25. [33]

    Mutual magnetic interactions of elec- trons,

    H. H. Marvin, “Mutual magnetic interactions of elec- trons,” Phys. Rev.71, 102 (1947)

    1947

  26. [34]

    Atomic screening constants from SCF functions. II. atoms with 37 to 86 electrons,

    Enrico Clementi, D. L. Raimondi, and William P. Rein- hardt, “Atomic screening constants from SCF functions. II. atoms with 37 to 86 electrons,” J. Chem. Phys. 47, 1300–1307 (1967)

    1967

  27. [35]

    wan- nier90: A tool for obtaining maximally-localised Wan- nier functions,

    Arash A. Mostofi, Jonathan R. Yates, Young-Su Lee, Ivo Souza, David Vanderbilt, and Nicola Marzari, “wan- nier90: A tool for obtaining maximally-localised Wan- nier functions,” Comput. Phys. Commun.178, 685–699 (2008)

    2008

  28. [36]

    Lanthanide ion- izationenergiesandthesub-shellbreak.Part 2.Thethird and fourth ionization energies,

    David A. Johnson and Peter G. Nelson, “Lanthanide ion- izationenergiesandthesub-shellbreak.Part 2.Thethird and fourth ionization energies,” J. Phys. Chem. Ref. Data 46, 013109 (2017)

    2017

  29. [37]

    Ionization energies of lanthanides,

    Peter F. Lang and Barry C. Smith, “Ionization energies of lanthanides,” J. Chem. Educ.87, 875–881 (2010)

    2010

  30. [38]

    Ab Initio crystal field theory: Erbium in oxide 6 hosts for quantum applications,

    Yogendra Limbu, Yueguang Shi, Joseph Sink, Tharnier O. Puel, Durga Paudyal, and Michael E. Flatté, “Ab Initio crystal field theory: Erbium in oxide 6 hosts for quantum applications,” Submitted to Phys. Rev. B (2024)

    2024

  31. [39]

    Ab-initio simulations of materials using VASP: Density-functional theory and beyond,

    Jürgen Hafner, “Ab-initio simulations of materials using VASP: Density-functional theory and beyond,” J. Com- put. Chem. 29, 2044–2078 (2008)

    2008

  32. [40]

    Efficiency of ab- initio total energy calculations for metals and semicon- ductors using a plane-wave basis set,

    Georg Kresse and Jürgen Furthmüller, “Efficiency of ab- initio total energy calculations for metals and semicon- ductors using a plane-wave basis set,” Comput. Mater. Sci. 6, 15–50 (1996)

    1996

  33. [41]

    Projector augmented-wave method,

    Peter E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B50, 17953 (1994)

    1994

  34. [42]

    As- sessment of the Perdew–Burke–Ernzerhof exchange- correlation functional,

    Matthias Ernzerhof and Gustavo E. Scuseria, “As- sessment of the Perdew–Burke–Ernzerhof exchange- correlation functional,” J. Chem. Phys.110, 5029–5036 (1999)

    1999

  35. [43]

    Concentration of vacancies at metal-oxide surfaces: Case study of MgO (100),

    Norina A. Richter, Sabrina Sicolo, Sergey V. Levchenko, Joachim Sauer, and Matthias Scheffler, “Concentration of vacancies at metal-oxide surfaces: Case study of MgO (100),” Phys. Rev. Lett.111, 045502 (2013)

    2013

  36. [44]

    Density-functional study ofthestructureandstabilityofZnOsurfaces,

    B. Meyer and Dominik Marx, “Density-functional study ofthestructureandstabilityofZnOsurfaces,” Phys.Rev. B 67, 035403 (2003)

    2003

  37. [45]

    Electronic structure, growth mechanism and photoluminescence of CaWO4 crystals,

    L. S. Cavalcante, V. M. Longo, J. C. Sczancoski, M. A. P. Almeida, A. A. Batista, José Arana Varela, Marcelo Or- naghi Orlandi, Elson Longo, and M. Siu Li, “Electronic structure, growth mechanism and photoluminescence of CaWO4 crystals,” CrystEngComm 14, 853–868 (2012)

    2012

  38. [46]

    Electronic band structures of the scheelite materials CaMoO4, CaWO4, PbMoO4, and PbWO4,

    Yaoju Zhang, N. A. W. Holzwarth, and R. T. Williams, “Electronic band structures of the scheelite materials CaMoO4, CaWO4, PbMoO4, and PbWO4,” Phys. Rev. B 57, 12738 (1998)

    1998

  39. [47]

    Density func- tional theory study of dopants in polycrystalline TiO2,

    Wolfgang Körner and Christian Elsässer, “Density func- tional theory study of dopants in polycrystalline TiO2,” Phys. Rev. B83, 205315 (2011)

    2011

  40. [48]

    One- and two-photon excited lumines- cence and band-gap assignment in CaWO4,

    V. B. Mikhailik, H. Kraus, D. Wahl, M. Itoh, M. Koike, and I. K. Bailiff, “One- and two-photon excited lumines- cence and band-gap assignment in CaWO4,” Phys. Rev. B 69, 205110 (2004)

    2004

  41. [49]

    Optical absorp- tion of divalent metal tungstates: correlation between the band-gap energy and the cation ionic radius,

    R. Lacomba-Perales, J. Ruiz-Fuertes, D. Errandonea, D. Martínez-García, and A. Segura, “Optical absorp- tion of divalent metal tungstates: correlation between the band-gap energy and the cation ionic radius,” EPL 83, 37002 (2008)

    2008

  42. [50]

    Is the band gap of pristine TiO2 nar- rowed by anion- and cation-doping of titanium dioxide in second-generation photocatalysts?

    Nick Serpone, “Is the band gap of pristine TiO2 nar- rowed by anion- and cation-doping of titanium dioxide in second-generation photocatalysts?” J. Phys. Chem. B 110, 24287–24293 (2006)

    2006

  43. [51]

    Exciton thermoreflectance of MgO and CaO,

    R. C. Whited, Christopher J. Flaten, and W. C. Walker, “Exciton thermoreflectance of MgO and CaO,” Solid State Commun. 13, 1903–1905 (1973)

    1973

  44. [52]

    On the optical band gap of zinc oxide,

    Vedentam Srikant and David R. Clarke, “On the optical band gap of zinc oxide,” J. Appl. Phys.83, 5447–5451 (1998)

    1998

  45. [53]

    Spin-lattice re- laxation in aΓ8 quartet: Er3+ in MgO,

    M. Borg, R. Buisson, and C. Jacolin, “Spin-lattice re- laxation in aΓ8 quartet: Er3+ in MgO,” Phys. Rev. B1, 1917 (1970)

    1970

  46. [54]

    Orbit-lattice interaction in Γ8 quartets. I. determination of the coupling parameters for Er3+:MgO and Dy3+:CaF2 from EPR under uniaxial stress,

    J. M. Baker and G. Currell, “Orbit-lattice interaction in Γ8 quartets. I. determination of the coupling parameters for Er3+:MgO and Dy3+:CaF2 from EPR under uniaxial stress,” J. Phys. C: Solid State Phys.9, 3819 (1976)

    1976

  47. [55]

    Optical spectrum and magnetic properties of Er3+ in CaWO4,

    Bernal G. Enrique, “Optical spectrum and magnetic properties of Er3+ in CaWO4,” J. Chem. Phys.55, 2538– 2549 (1971)

    1971

  48. [56]

    Optical spectrum of triply ionized erbium in calcium tungstate,

    Donald E. Wortman, “Optical spectrum of triply ionized erbium in calcium tungstate,” J. Chem. Phys.54, 314– 321 (1971)

    1971

  49. [57]

    Crystal field effect in YbMnO3,

    M. Diviš, J. Hölsä, M. Lastusaari, A. P. Litvinchuk, and V. Nekvasil, “Crystal field effect in YbMnO3,” J. Alloys Compd. 451, 662–665 (2008)

    2008

  50. [58]

    Dominant co-exposed {1 0 1}/{1 1 1} facet of Er-doped rutile TiO2 film via hy- drothermal doping,

    N. K. A. Hamed, N. Nafarizal, M. K. Ahmad, A. B. Faridah, and M. Shimomura, “Dominant co-exposed {1 0 1}/{1 1 1} facet of Er-doped rutile TiO2 film via hy- drothermal doping,” Mater. Lett.336, 133864 (2023)

    2023

  51. [59]

    Neutron spectroscopic determination of the crystalline electric field in HoBa2Cu3O7−δ,

    A. Furrer, P. Brüesch, and P. Unternährer, “Neutron spectroscopic determination of the crystalline electric field in HoBa2Cu3O7−δ,” Phys. Rev. B38, 4616 (1988)

    1988

  52. [60]

    A new class of materials for Bloembergen- type masers,

    B. Bleaney, “A new class of materials for Bloembergen- type masers,” Proc. Phys. Soc.73, 937 (1959)

    1959

  53. [61]

    Energy levels of rare earth ions in cu- bic crystal fields,

    J. A. White, “Energy levels of rare earth ions in cu- bic crystal fields,” J. Phys. Chem. Solids23, 1787–1793 (1962)

    1962

  54. [62]

    Superposition model of the orbit-lattice interaction. II. analysis of strain results for Er3+:MgO,

    S. C. Chen and D. J. Newman, “Superposition model of the orbit-lattice interaction. II. analysis of strain results for Er3+:MgO,” J. Phys. C: Solid State Phys.17, 3045 (1984)

    1984

  55. [63]

    C. J. Bradley and A. P. Cracknell, The Mathemati- cal Theory of Symmetry in Solids (Oxford: Clarendon, 1972)

    1972

  56. [64]

    Crys- tal field properties of f-electron states in RBa2Cu3O7 for R = Ho, Nd and Pr,

    G. L. Goodman, C. K. Loong, and L. Soderholm, “Crys- tal field properties of f-electron states in RBa2Cu3O7 for R = Ho, Nd and Pr,” J. Phys.: Condens. Matter3, 49 (1991)

    1991

  57. [65]

    Narrow optical line widths in erbium im- planted in TiO2,

    Christopher M. Phenicie, Paul Stevenson, Sacha Welin- ski, Brendon C. Rose, Abraham T. Asfaw, Robert J. Cava, Stephen A. Lyon, Nathalie P. De Leon, and Jeff D. Thompson, “Narrow optical line widths in erbium im- planted in TiO2,” Nano Lett.19, 8928–8933 (2019)

    2019

  58. [66]

    Ab initio calculations of erbium crystal field splittings in oxide hosts: role of the4f radial wave function,

    Y. Limbu, Y. Shi, J. Sink, T. O. Puel, D. Paudyal, and M. E. Flatté, “Ab initio calculations of erbium crystal field splittings in oxide hosts: role of the4f radial wave function,” (2025), unpublished

    2025

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.