Electronic phase separation at LaAlO3/SrTiO3 interfaces tunable by oxygen deficiency

A. Chikina; C. A. F. Vaz; D. Bracher; F. Bisti; F. Lechermann; F. Miletto Granozio; M.-A. Husanu; M. Caputo; T. Schmitt; V. N. Strocov

REVIEW 2 major objections 5 minor 5 references

Electronic phase separation at LaAlO3/SrTiO3 interfaces tunable by oxygen deficiency

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read At oxygen-deficient LaAlO3/SrTiO3 interfaces, growing oxygen vacancies increases the total mobile-electron signal but leaves the Fermi momenta of the $d_{xy}$ and $d_{yz}$ bands constant, which the paper reads as electronic phase…

desk verdict First SX-ARPES evidence of phase separation at the LAO/STO interface: constant kF with growing spectral weight is a solid observation, and the paper deserves peer review despite a real matrix-element control gap. read the letter →

arxiv 1908.06321 v1 pith:ZV4UMAQC submitted 2019-08-17 cond-mat.mtrl-sci cond-mat.mes-hall

V. N. Strocov , A. Chikina , M. Caputo , M.-A. Husanu , F. Bisti , D. Bracher , T. Schmitt , F. Miletto Granozio

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C. A. F. Vaz F. Lechermann

This is my paper · ORCID

classification cond-mat.mtrl-scicond-mat.mes-hall

keywords electronicphaseseparationLaAlO3/SrTiO3interfaceoxygenvacanciessoft-X-rayARPESresonantphotoemissionLuttingercountoxidetwo-dimensionalelectrongas

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 sets out to establish that the LaAlO3/SrTiO3 interface, the standard workhorse of oxide electronics, is electronically phase-separated: its mobile electrons live in conducting puddles of fixed local electronic structure surrounded by an insulating host, and the fraction of the interface that conducts can be tuned by oxygen deficiency. The authors use soft-X-ray angle-resolved photoemission with resonant Ti L-edge excitation to follow what happens as intense X-rays progressively create oxygen vacancies in the SrTiO3. They find that the total spectroscopic weight of the mobile electron system grows by roughly a factor of 3.3 while the Fermi momenta of the $d_{xy}$ and $d_{yz}$ bands, and therefore the Luttinger counts, stay constant. The only way both can be true is that the extra electrons are not filling the existing bands; instead, the conducting puddles expand laterally, from about 30% of the interface toward 100%. If correct, this reconciles why transport always sees fewer carriers than band theory predicts and supplies a microscopic picture for the coexisting ferromagnetic and superconducting regions at these interfaces.

What carries the argument

The central observable is a comparison between two counts of electrons. The total mobile-electron concentration $n_s^{\rm tot}$ is read from the angle-integrated resonant photoemission weight $W_{\rm MES}$ of the $t_{2g}$ band, while the local mobile-electron density inside each conducting region is read from the Luttinger count $n_s^{\rm Lutt}$ — the number of carriers per unit area enclosed by the Fermi surface — extracted from $k_F$ by locating the maxima of the negative gradient $-dI_F/d|k|$ of the Fermi-surface intensity. Electronic phase separation is identified when $W_{\rm MES}$ grows while $k_F$, and hence $n_s^{\rm Lutt}$, does not. The supporting theoretical machinery is the effective nearest-neighbor pair interaction $J_{\rm eff} = \frac{1}{4}(E_{AA} - 2E_{AB} + E_{BB})$ on the square lattice of interface oxygen sites; its negative value means that oxygen vacancies attract each other and cluster, and this clustering is what separates the mobile-electron puddles from the vacancy-rich insulating regions.

What would settle it

Measure the same irradiation series with a non-resonant photon energy away from the Ti L edge and normalize the mobile-electron weight to the Ti 2p core-level intensity; if the normalized intensity no longer grows with irradiation while $k_F$ stays constant, the apparent rise in $n_s^{\rm tot}$ is a resonance artifact and the electronic-phase-separation inference loses its experimental foundation. Independently, scanning tunneling spectroscopy could look for the predicted two-phase pattern: metallic patches with a fixed Fermi surface surrounded by insulating regions.

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Extended reading notes

Core claim

At oxygen-deficient LaAlO3/SrTiO3 interfaces, X-ray irradiation increases the concentration of oxygen vacancies and, with it, the total spectral weight of the mobile $t_{2g}$ electron system; yet the Fermi momenta of the $d_{xy}$ and $d_{yz}$ bands remain constant through the entire irradiation range, with the $d_{yz}$ Fermi momentum near $0.4$ Å$^{-1}$. Since these Fermi momenta determine the Luttinger counts, the local band filling in the conducting regions is unchanged even as the total number of mobile electrons grows. The paper interprets this as electronic phase separation: the mobile electrons accumulate in quasi-3D conducting puddles with fixed electronic structure embedded in an insulating host, so irradiation inflates the lateral conducting fraction rather than the local density. Supporting calculations using a binary-alloy cluster expansion give a negative effective pair interaction between oxygen vacancies ($J_{\rm eff} = -143$ meV in DFT and $-155$ meV in DFT+DMFT), indicating that vacancies cluster, and the distinct orbital character of the localized $e_g$ states near vacancies repels the itinerant $t_{2g}$ electrons, pushing the puddles into relatively defect-free regions. The same Luttinger-count-versus-transport comparison applied to stoichiometric samples implies that the intrinsic interface also phase-separates, with a lateral conducting fraction of order 70%.

Load-bearing premise

The load-bearing premise is that the angle-integrated ARPES intensity of the mobile-electron band faithfully measures the total number of mobile electrons; if the growth of oxygen vacancies changes the Ti L-edge resonance or photoemission matrix elements, the apparent intensity could rise while the electron count stays flat, and a constant $k_F$ would then mean only that band filling does not change.

Editorial extensions

If this is right

At oxygen-deficient LAO/STO interfaces, the lateral conducting fraction rises from about 30% toward 100% as oxygen vacancies are added, since the mobile-electron weight grows by a factor of 3.3 while the local band filling stays constant.
The stoichiometric interface is also phase-separated: the ARPES Luttinger count of roughly $7\times10^{13}$ e/cm$^2$ versus Hall densities of $4$–$6\times10^{13}$ e/cm$^2$ implies a lateral conducting fraction of about 70%.
Transport measurements will systematically read lower carrier densities than the local Fermi-surface count because they average over insulating regions, resolving a long-standing shortfall between predicted and measured interfacial carrier densities.
At high vacancy concentrations, newly doped electrons preferentially go into localized in-gap $e_g$ states rather than into the mobile $t_{2g}$ system, so continued oxygen deficiency becomes progressively less efficient at adding mobile carriers.
The oxygen-deficiency tunability of the conducting fraction offers a way to pattern conductive and magnetic regions into oxide devices, for example by X-ray or electron-beam lithography, and opens the possibility of networks of ferromagnetic Josephson junctions.

Reading between the lines

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

An extension the paper does not perform: scanning tunneling spectroscopy across the interface should resolve two distinct electronic signatures — regions with the fixed $d_{xy}$/$d_{yz}$ Fermi surface and regions showing only the in-gap state — whose relative areas track the irradiation dose; a continuous gradation of local density would contradict the sharp-puddle picture.
If the puddle picture is correct, high-field quantum oscillations from the buried electron gas should show Fermi-surface frequencies independent of oxygen deficiency while the Hall density increases, providing a clean cross-check of constant local band filling.
The negative $J_{\rm eff}$ implies the puddle morphology is not a fixed material property: external knobs that change the magnetism of the localized $e_g$ electrons, such as strain or magnetic field, should alter vacancy clustering and hence the conducting fraction.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Bottom line: this is the first SX-ARPES observation on the LAO/STO interface itself showing constant Fermi momenta while the mobile-electron spectral weight grows by ~3.3x under X-ray irradiation. The kF constancy is shown across two Brillouin zones using a gradient method, and the intensity increase appears at both the L3 and L2 resonances, which favor different d-orbital characters. That is a solid, genuinely new experimental result.

What the paper does well: it makes a sharp distinction between total concentration (from spectral weight) and per-puddle concentration (from kF). The EPS reading—puddles with fixed local band structure inflating in lateral fraction—is the natural explanation, and the DFT-based J_eff clustering calculation is a credible supporting mechanism (though not load-bearing). The PEEM upper bound of 500 Å is a nice honest addition.

Where it is soft: the load-bearing step is that W_MES tracks n_s^tot. The stress-test note is right that irradiation-driven changes in Ti3+ fraction (~30% in the top layer) could change the Ti L-edge resonance and matrix elements at fixed photon energies, mimicking an intensity increase without any real increase in carrier number. The paper does not fully close this. The Supplement 3 ratio to Ti 2p uses the same resonant MES and therefore does not control for it. Having the effect at two photon energies helps but does not rule out a Ti3+-driven cross-section change. Missing error bars on W_MES and kF also weaken the quantitative LCF estimates. The LCF claims—30% for the fresh OD sample and ~70% for stoichiometric samples—are order-of-magnitude, not precise numbers, and the stoichiometric extrapolation is the most speculative part of the paper. The reliance on incomplete self-citation [22] for the vacancy location and depth is a real annoyance for the reader.

But the central experimental fact is not in question: on the same sample, under irradiation, kF stays put while spectral weight rises. That is a strong constraint on any theory of oxygen-vacancy doping at this interface, independent of the EPS interpretation.

Who this is for: anyone working on LAO/STO, oxide interfaces, or electronic phase separation in correlated oxides. It deserves a serious referee. I would ask for a control with off-resonant or non-resonant photon energies if feasible, explicit uncertainty analysis on kF, and either published data or more details on the [22] results. None of these are likely to overturn the main observation.

Referee Report

2 major / 5 minor

Summary. The manuscript reports soft-X-ray angle-resolved photoemission measurements on oxygen-deficient LaAlO3/SrTiO3 heterostructures in which X-ray irradiation is used to create oxygen vacancies. Angle-integrated resonant photoemission shows that the Ti3+ core-level, in-gap state, and mobile-electron (MES) spectral weights grow with irradiation time; the MES weight grows by a factor of about 3.3. Momentum-resolved images show that the Fermi momenta of the d_xy and d_yz bands remain constant at about 0.4 Å-1 over the same range. The authors interpret this combination as electronic phase separation: the mobile electrons live in conducting puddles with a fixed local band structure, and irradiation increases the lateral conducting fraction from an initial value estimated at about 30% toward saturation. Supporting DFT and DFT+DMFT calculations give a negative effective pair interaction between oxygen vacancies, indicating clustering, and PEEM places an upper limit of 500 Å on any Ti3+ clusters. The paper also compares the stoichiometric-interface Luttinger count with Hall data to estimate a lateral conducting fraction of order 70%.

Significance. The experiment is significant because, if the intensity-to-concentration calibration is valid, it provides direct ARPES-based evidence for electronic phase separation at the LAO/STO interface and a quantitative, irradiation-tuned estimate of the conducting fraction. The constant-kF observation itself is robust: it is shown for both d_xy and d_yz bands, measured across two Brillouin zones, and extracted with a gradient method that is relatively insensitive to matrix-element distortions. The DFT-based J_eff calculation is a genuine ab initio input, and the PEEM control provides a useful upper bound on the vacancy-cluster size. The principal weakness is the calibration of the resonant MES intensity as a measure of the total mobile-electron concentration, which is addressable experimentally. The paper is therefore a strong candidate for publication after the calibration concern is resolved.

major comments (2)

[Electronic phase separation / X-ray irradiation dynamics (Fig. 3; Supplemental 3)] The central inference that n_s^tot increases rests entirely on the assumption that W_MES, the angle-integrated resonant ARPES intensity at hv = 460.4 and 466.4 eV, is a faithful measure of the number of mobile MES electrons. As the authors note, X-ray irradiation converts about 30% of the Ti ions in the top TiO2 layer to Ti3+. At fixed photon energies on the Ti L3/L2 edges, the resonant enhancement and final-state screening for the t2g-derived MES can change with growing Ti3+ concentration; if the matrix element grows by a factor near 3.3, the observed W_MES increase would be produced with no change in n_s^tot, and the constant k_F would simply mean an unchanged band population. The two-resonance consistency is suggestive but does not control for this, because both photon energies lie on the Ti L-edge. Please provide an off-resonant measurement, a lineshape-based estimate of the matrix-element change, or another independent calibration of n_s^tot; the MES/Ti2p ratio in Supplemental 3 normalizes to a core level but still uses the same resonant MES intensity and therefore does not by itself settle the question.
[Identification of EPS (paragraph beginning 'The depth extension...' and Supplemental 3)] The quantitative LCF estimates, which are a headline result, inherit the W_MES normalization and additional assumptions. The main-text analysis sets the initial LCF at about 30% by assuming that the large-t_irr endpoint corresponds to LCF = 100%, while the Supplemental 3 Ti2p-normalized analysis gives about 40%; these two estimates differ by roughly 33%. The manuscript gives no uncertainty analysis for either estimate. Please provide error bars, quantify the sensitivity to the saturation-at-100% assumption, and state the LCF range consistent with both methods.

minor comments (5)

[References] Reference [22] is listed as 'Strocov et al., (2019)' without a full citation; this must be completed before publication.
[Introduction] In the Introduction, the phrase 'a a dimensionality transformation' contains a duplicated article and should be corrected.
[Fig. 3(a) and Fig. 3(b)] The spectral-weight curves are normalized to their maximum values, but no error bars or statistical uncertainties are shown; since the factor 3.3 and the MES/IGS buildup ratio are used quantitatively, the precision of these quantities should be stated.
[Identification of EPS (Fig. 4, paragraph on k_F statistics)] The text notes that the d_yz k_F is uncertain 'in the region of very small t_irr where the ARPES signal is yet small'; because the small-t_irr limit determines the claimed initial LCF of about 30%, this caveat should be quantified rather than stated qualitatively.
[Supplemental 4] The PEEM statement that Ti3+ puddles are 'less than the instrumental lateral resolution of 500 Å' should be phrased as an upper bound set by resolution, and the text should state explicitly that the measurement cannot distinguish smaller clusters from a uniform Ti3+ distribution.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the central EPS inference rests on two independent measurements (W_MES intensity growth and constant k_F), and the LCF estimate is a conservative normalization, not a fitted prediction.

full rationale

Walking the derivation chain: the paper infers an increase of the total MES concentration n_s^tot from the angle-integrated resonant-ARPES weight W_MES, and a constant local Luttinger count n_s^Lutt from the k_F values obtained via the -dI_F/d|k| gradient method. These are two independent experimental observables; neither is defined in terms of the other, and the EPS interpretation is presented as the reconciliation of their discrepancy, not as an equation that reduces to its own input. The LCF estimate uses W_MES curves normalized to their maximal-t_irr value and combines the observed factor ~3.3 with the statement that the LCF 'by definition can not exceed 100%' to obtain a ~30% upper bound at small oxygen deficiency. This is a conservative calibration/bound, not a fitted parameter renamed as a prediction. The J_eff clustering analysis is computed from DFT and DFT+DMFT supercell energies through J_eff = 1/4(E_AA - 2E_AB + E_BB), a standard cluster-expansion construction; the resulting negative J_eff is an ab initio output, not fitted to the ARPES intensities or to the EPS conclusion. Self-citations such as [18,19,29,41] supply prior experimental band parameters, ResPE behavior, and computational details; they are used as data/method references, not as a load-bearing uniqueness argument that defines the present claim. The skeptical concern that irradiation-driven changes in Ti L-edge resonance or matrix elements could increase W_MES without increasing electron number is a real measurement-validity confound, but it is not circularity: it does not make the paper's derivation equivalent to its inputs by construction. No step was found where an equation is self-definitional, a fitted input is called a prediction, or a conclusion is forced by a self-citation chain. The paper is therefore judged to have no significant circularity.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests mainly on the proportionality between ARPES intensity and electron concentration, and on the layering model of V_Os near the surface with deep MES penetration. These are externally supported but not fully demonstrated within this paper. No invented entities or fitted model parameters beyond the LCF saturation normalization.

free parameters (1)

LCF at saturation (normalization reference) = 100%
The relative ARPES MES intensity is normalized so that the maximum irradiation state corresponds to 100% lateral conducting fraction; used to derive initial LCF ~30% (Fig. 3) and ~40% (Supplemental 3). This is a chosen scaling, not a measured absolute value.

assumptions (4)

domain assumption The integrated ARPES intensity of a band is proportional to the number of electrons in the probed volume, with matrix elements constant across irradiation.
Invoked when W_MES is taken as a measure of n_s^tot in 'X-ray irradiation dynamics'. Not corrected for Ti3+ resonant enhancement changes.
standard math The Fermi surface area (Luttinger count) determines the local 2D/3D carrier density in the MES.
Standard Luttinger theorem, used to convert measured kF to n_s^Lutt.
domain assumption V_Os generated by soft X-rays are predominantly in the top TiO2 layer, while the MES extends >100 Å into STO, so ARPES intensity is proportional to lateral puddle fraction.
Based on SIMS and out-of-plane dispersion in refs [21,22]; needed for LCF interpretation.
domain assumption The cluster expansion with nearest-neighbor pair interactions on a square lattice captures the sign of V_O interactions.
Used to derive J_eff from three supercell energies; finite-size and long-range effects neglected, as acknowledged.

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Cite this review

Pith. "Pith review of Electronic phase separation at LaAlO3/SrTiO3 interfaces tunable by oxygen deficiency." pith.science (2026). https://pith.science/paper/ZV4UMAQC

@misc{pith2026190806321,
  author       = {Pith},
  title        = {Pith review of: Electronic phase separation at LaAlO3/SrTiO3 interfaces tunable by oxygen deficiency},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZV4UMAQC}},
  note         = {Machine review of arXiv:1908.06321}
}

read the original abstract

Electronic phase separation is crucial for the fascinating macroscopic properties of the LaAlO3/SrTiO3 (LAO/STO) paradigm oxide interface, including the coexistence of superconductivity and ferromagnetism. We investigate this phenomenon using angle-resolved photoelectron spectroscopy (ARPES) in the soft-X-ray energy range, where the enhanced probing depth combined with resonant photoexcitation allow access to fundamental electronic structure characteristics (momentum-resolved spectral function, dispersions and ordering of energy bands, Fermi surface) of buried interfaces. Our experiment uses X-ray irradiation of the LAO/STO interface to tune its oxygen deficiency, building up a dichotomic system where mobile weakly correlated Ti t2g-electrons co-exist with localized strongly correlated Ti eg-ones. The ARPES spectra dynamics under X-ray irradiation shows a gradual intensity increase under constant Luttinger count of the Fermi surface. This fact identifies electronic phase separation (EPS) where the mobile electrons accumulate in conducting puddles with fixed electronic structure embedded in an insulating host phase, and allows us to estimate the lateral fraction of these puddles. We discuss the physics of EPS invoking a theoretical picture of oxygen-vacancy clustering, promoted by the magnetism of the localized Ti eg-electrons, and repelling of the mobile t2g-electrons from these clusters. Our results on the irradiation-tuned EPS elucidate the intrinsic one taking place at the stoichiometric LAO/STO interfaces.

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Reference graph

Works this paper leans on

5 extracted references · 5 canonical work pages

[1]

X-ray induced energy shifts of the ARPES spectral structures The intensity evolution of the ARPES spectral structures under X-ray irradiation is accompanied by their energy shifts. Fig. S1 ( c ) compiles the E B -shifts of the Ti 4+ core-level peak, two VB-ones and IGS-one from their position at saturation, with the MES-peak pinned at E F ...

work page 2017
[2]

S2 ( a , b ) represent ARPES images of our OD-LAO/STO samples at small and large t irr , respectively, measured across two BZs

X-ray irradiation dynamics of band structure and Fermi surface in an extended k-space region Fig. S2 ( a , b ) represent ARPES images of our OD-LAO/STO samples at small and large t irr , respectively, measured across two BZs. Similarly to Fig. 4, these images show E ( k ) independent of t irr . ( c , d ) show the corres...

work page
[3]

In our ResPE map, Fig

Estimate of the LCF based on intensity ratio of the MES and Ti 2p signals A way to estimate the irradiation-dependent LCF in the OD-LAO/STO samples can be based on comparison of the MES spectral intensity to the Ti 2 p peak as the intensity reference. In our ResPE map, Fig. 1 ( a ), the Ti 2 p peaks excited by second-order light (photon energy 2 ...

work page 2016
[4]

The experiment was carried out at the SIM beamline of the Swiss Light Source which delivered a photon flux of ~10 14 ph/sec/0.01% within a spot of 100x200 μm 2

Microscopic investigation on the EPS at the LAO/STO interface Our X-ray irradiation dependent PEEM measurements aimed spatial resolution of the nucleation and clustering of the V O s as marked by the Ti 3+ ions. The experiment was carried out at the SIM beamline of the Swiss Light Source which delivered a photon flux of ~10 14 ph/sec/0.01% within ...

work page
[35]

Flechsig, F

U. Flechsig, F. Nolting, A. Fraile Rodríguez, J. Krempaský, C. Quitmann, T. Schmidt, S. Spielmann, D. Zimoch, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, in (AIP, 2010), pp. 319–322. [36] K. Szot, W. Speier, R. Carius, U. Zastrow, and W. Beyer, Physical Review Letters 88 , 075508 (2002). [37] J. Gabel, M. Zapf, P. Scheiderer, P. Schütz, L. Dudy,...

work page 2002

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

X-ray induced energy shifts of the ARPES spectral structures The intensity evolution of the ARPES spectral structures under X-ray irradiation is accompanied by their energy shifts. Fig. S1 ( c ) compiles the E B -shifts of the Ti 4+ core-level peak, two VB-ones and IGS-one from their position at saturation, with the MES-peak pinned at E F ...

work page 2017

[2] [2]

S2 ( a , b ) represent ARPES images of our OD-LAO/STO samples at small and large t irr , respectively, measured across two BZs

X-ray irradiation dynamics of band structure and Fermi surface in an extended k-space region Fig. S2 ( a , b ) represent ARPES images of our OD-LAO/STO samples at small and large t irr , respectively, measured across two BZs. Similarly to Fig. 4, these images show E ( k ) independent of t irr . ( c , d ) show the corres...

work page

[3] [3]

In our ResPE map, Fig

Estimate of the LCF based on intensity ratio of the MES and Ti 2p signals A way to estimate the irradiation-dependent LCF in the OD-LAO/STO samples can be based on comparison of the MES spectral intensity to the Ti 2 p peak as the intensity reference. In our ResPE map, Fig. 1 ( a ), the Ti 2 p peaks excited by second-order light (photon energy 2 ...

work page 2016

[4] [4]

The experiment was carried out at the SIM beamline of the Swiss Light Source which delivered a photon flux of ~10 14 ph/sec/0.01% within a spot of 100x200 μm 2

Microscopic investigation on the EPS at the LAO/STO interface Our X-ray irradiation dependent PEEM measurements aimed spatial resolution of the nucleation and clustering of the V O s as marked by the Ti 3+ ions. The experiment was carried out at the SIM beamline of the Swiss Light Source which delivered a photon flux of ~10 14 ph/sec/0.01% within ...

work page

[5] [35]

Flechsig, F

U. Flechsig, F. Nolting, A. Fraile Rodríguez, J. Krempaský, C. Quitmann, T. Schmidt, S. Spielmann, D. Zimoch, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, in (AIP, 2010), pp. 319–322. [36] K. Szot, W. Speier, R. Carius, U. Zastrow, and W. Beyer, Physical Review Letters 88 , 075508 (2002). [37] J. Gabel, M. Zapf, P. Scheiderer, P. Schütz, L. Dudy,...

work page 2002