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Observation of Shubnikov-de Haas Oscillations, Non-trivial Berry Phase, Planar Hall and Anisotropic Magnetoresistance at the conducting interface of EuO-KTaO$_3$

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The conducting EuO-KTaO3 interface hosts two Rashba-split Fermi surfaces, and both carry a nontrivial pi Berry phase.

desk verdict First SdH at a KTO interface, but the high-frequency Berry phase leans on a 3D correction that the angle-dependence data don't actually prove. read the letter →

arxiv 1908.04977 v1 pith:KT536XEE submitted 2019-08-14 cond-mat.mes-hall

Nand Kumar , Neha Wadehra , Ruchi Tomar , Sushanta Dattagupta , Sanjeev Kumar , S. Chakraverty This is my paper · ORCID
classification cond-mat.mes-hall
keywords Shubnikov-deHaasoscillationsRashbaeffectBerryphaseEuO-KTaO3interfaceweakantilocalizationplanarHallanisotropicmagnetoresistanceoxidetwo-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 reports the first observation of Shubnikov-de Haas oscillations at a conducting EuO-KTaO3 interface and uses them to argue that the interface hosts a Rashba-type two-dimensional electron gas. Two oscillation frequencies, 90 T and 50 T, are identified as the outer and inner Fermi surfaces of Rashba spin-split bands. Both surfaces give Landau-fan intercepts consistent with a pi Berry phase, meaning each cyclotron orbit encloses the Dirac point of the Rashba Hamiltonian. Independent observations of weak antilocalization, planar Hall effect, and anisotropic magnetoresistance support strong spin-orbit coupling. If correct, this makes oxide interfaces based on KTaO3 a promising platform for spin-orbit physics and spintronics.

What carries the argument

The central object is the Landau fan diagram, a plot of Landau index n against 1/B, whose intercept is read through the Lifshitz-Onsager relation A(hbar/eB) = 2pi(n + 1/2 - phi_B/2pi + delta). The offset delta is taken as 0 for a 2D Fermi surface and -1/8 for a 3D Fermi surface, which converts the measured intercept into the Berry phase phi_B. The paper combines this with the Iordanskii-Lyanda-Geller-Pikus formula for weak antilocalization to extract the spin-precession length and the Rashba strength parameter, and with in-plane magnetoresistance measurements to identify the planar Hall and anisotropic magnetoresistance signatures.

What would settle it

A direct test is angle-resolved photoemission on the same interface: if the two SdH surfaces are the inner and outer branches of a Rashba-split band, the measured dispersion should show two spin-split bands meeting at a Dirac point near the Fermi level with opposite chiral spin textures, whereas a single parabolic band would rule out the pi Berry phase interpretation.

Watch

Extended reading notes

Core claim

The paper claims that the EuO-KTaO3 interface conducts through two Fermi surfaces whose Shubnikov-de Haas oscillations have frequencies of 90 T and 50 T. From the temperature dependence of the oscillation amplitudes, the effective masses are about 0.59 m_e for the high-frequency surface and 1.0 m_e for the low-frequency one. Landau-fan extrapolation gives intercepts of 0.5 and -0.6; assigning delta = 0 to the 2D 50-T surface and delta = -1/8 to the 3D 90-T surface, both yield a Berry phase of pi. The paper interprets this as both cyclotron orbits enclosing the Dirac point of Rashba-split bands, draws a three-band diagram with a Rashba wavevector near 0.01-0.012 reciprocal angstroms, and reports planar Hall and anisotropic magnetoresistance that change from two-fold to four-fold as the in-plane field increases.

Load-bearing premise

The central claim depends on calling the 50-T oscillation a 2D Fermi surface and the 90-T oscillation a 3D Fermi surface based on how their amplitudes change with sample tilt; if the angle dependence is only amplitude loss for a quasi-2D sheet, the offset used in the Landau fan and the resulting Berry phase for the high-frequency surface would change.

Editorial extensions

If this is right

  • The two SdH frequencies imply two Fermi-surface areas, 8.3 x 10^-3 Å^-2 and 4.6 x 10^-3 Å^-2, consistent with inner and outer Rashba-split bands.
  • A pi Berry phase on both surfaces means each orbit encloses the Dirac point, so the interface is a Rashba-type 2DEG rather than a trivial parabolic-band conductor.
  • The weak-antilocalization fit gives a spin-precession length near 9 nm and a Rashba parameter of about 8.6 x 10^-12 eV m, which is high for an all-oxide system.
  • The observed two-fold AMR that becomes four-fold at higher fields, together with oscillatory planar Hall effect, connects this oxide interface to the transport signatures seen in topological materials.

Reading between the lines

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

  • If the proposed band diagram is correct, spin-resolved photoemission or nonlocal spin-transport measurements on the same interface should detect spin-momentum locking with opposite spin textures on the two Rashba branches.
  • The 90-T carrier classified as 3D might instead be a second 2D subband with a larger wavefunction extent; angle-dependent SdH on cleaner, higher-mobility samples could distinguish these cases directly.
  • Because EuO is ferromagnetic, the Berry phase and the Rashba splitting could in principle be tuned by rotating the magnetization, offering a testable magnetic-field and temperature protocol across the EuO Curie temperature.
  • A natural extension is to vary the EuO thickness or growth conditions to move the Fermi level across the Dirac point; if the picture holds, the Berry phase should switch from pi to 0 when only one spin-split band is occupied.
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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

3 major / 5 minor

Summary. This manuscript reports magnetotransport experiments on the conducting interface of EuO-KTaO3 (KTO). The authors observe Shubnikov-de Haas (SdH) oscillations with two frequencies, approximately 50 T and 90 T, and use temperature-dependent amplitudes to extract effective masses. From Landau fan diagrams, they obtain intercepts of 0.5 and -0.6 for the low- and high-frequency components, respectively. Interpreting the 50 T (low-field) oscillations as 2D (delta=0) and the 90 T (high-field) oscillations as 3D (delta=1/8), they conclude that both Fermi surfaces carry a non-trivial pi Berry phase, implying that both enclose a Dirac point. Additional data show weak antilocalization, planar Hall effect, anisotropic magnetoresistance, and a proposed Rashba-split band diagram based on Hall and SdH carrier densities, WAL fitting, and a consistency check between two values of the Rashba wavevector k_o.

Significance. If the claim is correct, this is the first observation of SdH oscillations and a non-trivial Berry phase at any KTO-based conducting interface, providing evidence for a Rashba-type 2DEG with two spin-split Fermi surfaces that enclose a Dirac point. The combination of WAL, PHE, and AMR in an oxide system with ferromagnetism is also of interest. The manuscript follows the standard Lifshitz-Onsager methodology, and the agreement between k_o from the SdH analysis and from the WAL fit is a legitimate consistency check rather than a circular step. However, the central Berry phase claim for the 90 T component rests on a 3D classification that is only qualitatively supported, and the limited field range of the SdH data leaves the intercept extrapolation vulnerable to large uncertainty. The experimental observation of SdH oscillations is a solid contribution, but the interpretation needs additional verification before the Dirac-point conclusion can be accepted.

major comments (3)
  1. [Fig. 1(b) and Fig. 2(f)] The assignment of delta = 1/8 for the 90 T (high-field) oscillation is the only basis for converting its fan intercept (-0.6) into a pi Berry phase. The sole support for a 3D Fermi surface is the qualitative statement that the high-field oscillations persist up to theta = 90 degrees, while no angle-resolved FFT or plot of F(theta) is provided. Without this, a quasi-2D pocket with finite k_z dispersion would yield delta = 0, and the same intercept would give phi_B = 1.2 pi, not pi. Moreover, calling the 90 T pocket 3D is in tension with the paper's own interpretation of both SdH frequencies as the inner and outer Fermi surfaces of a Rashba-split 2DEG. This load-bearing classification must be independently verified, for example by angle-dependent frequency analysis showing F constant versus theta over multiple angles.
  2. [Fig. 2(f) and surrounding text] The Landau fan extrapolation for the 90 T component is based on very few oscillations. The text explicitly identifies the high-field oscillations with B > 10 T, i.e., 1/B < 0.1 T^-1, and the data extend only to 14 T, giving a 1/B window of about 0.07-0.10 T^-1. With a frequency of 90 T, this corresponds to fewer than three full oscillations, so the intercept -0.6 cannot be determined with the precision required to discriminate between phi_B = pi and phi_B = 1.2 pi. The manuscript should quantify the uncertainty in the intercepts (e.g., from the linear fits or from including/excluding points) and should discuss how many Landau levels are actually resolved. As it stands, the pi-Berry-phase claim for the high-frequency band is not robust.
  3. [Eq. (3) and Fig. 3(a)] The ILP weak-antilocalization fit is used to extract B_SO approximately 2.3 T, which is then converted into a Rashba parameter and a k_o value used to support the band diagram. The text correctly notes that ILP theory applies in the diffusive regime B < hbar/(2 e l_m^2), estimated here as 0.5 T, yet the fit yields B_SO = 2.3 T and presumably extends over a much wider field range (Fig. 3(a) shows data to 14 T). The validity of the fit beyond its stated regime is not addressed, and this undermines the reliability of B_SO, the spin-precession length, and the k_o consistency check. The authors should either restrict the fit to the diffusive regime or justify the use of ILP beyond it.
minor comments (5)
  1. [Band diagram section (Fig. 3(b))] The Hall carrier density (5e13 cm^-2) is assigned entirely to band 1, while bands 2 and 3 are assigned the smaller SdH densities. Because the Hall coefficient is a mobility-weighted average over all conducting bands, this assignment is not justified without a multi-band Hall analysis; this affects the proposed band offsets and the stated agreement with ARPES.
  2. [Throughout] There are numerous typographical and grammatical errors, including 'polyonomial', 'Similiarly', 'Thn', and irregular reference formatting (e.g., 'author H.F. Legg'). These do not affect the science but should be corrected.
  3. [Eq. (2)] The sign convention linking the fitted intercept to phi_B and delta is stated ambiguously. The text first defines the intercept as (phi_B/2pi +/- delta) and then quotes values 0.5 and -0.6; to make the analysis reproducible, the authors should write explicitly the linear form n vs. 1/B from which the intercept is taken and show how phi_B is obtained from the fitted intercept for each delta value.
  4. [Fig. 1(a) and Fig. 2(c)-(d)] The effective mass values are given as (0.60 +/- 0.001) m_e etc., but it is unclear how the uncertainties were obtained and whether they correspond to the scatter of fits at different fields; clarify the error estimation.
  5. [Fig. 4] The abstract and Fig. 4 caption say 'two fold' planar Hall and AMR, but the text states that the AMR changes from two-fold to four-fold with increasing field. Please reconcile these statements.

Circularity Check

0 steps flagged · score 2.0 of 10

No circularity: Berry phase follows from standard Onsager analysis; self-citations are context only.

full rationale

The Berry-phase claim is produced by applying the standard Lifshitz-Onsager quantization rule, Eq. (2), to the measured Landau-index fan diagram in Fig. 2(f); no parameter is fitted to a pre-chosen Berry phase. The low-frequency intercept (0.5) gives phi_B/2pi = 0.5 with delta = 0, and the high-frequency intercept (-0.6) is converted with the assumed 3D correction delta = +/-1/8 to phi_B/2pi ~ 0.6 - 0.125 = 0.475 ~ 0.5. This is a textbook conversion, not a circular reduction. The delta = 1/8 assignment rests on the angle-dependence classification in Fig. 1(b), which is an empirical judgment that could be challenged: if the 90-T component were instead quasi-2D, the same intercept would give phi_B ~ 1.2pi. However, a questionable dimensionality classification is a correctness risk, not definitional circularity. The k_o comparison between the SdH-derived band geometry and the WAL fitting is a consistency check, not a fitted input. Self-citations (refs. 20, 24, 43) supply material context and a prior Berry-phase interpretation, but they are accompanied by independent references (refs. 6, 28, 44) and standard formulas; they do not carry the derivation. No step reduces by construction to its own input.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central claims rest on standard quantum-oscillation theory, a Rashba-Hamiltonian interpretation, and several fitting and modeling choices. The most consequential choices are the delta phase correction from the 2D/3D classification, the use of Hall density as a single-band density, and the WAL fit beyond its stated diffusive limit. No new physical entities are introduced.

free parameters (7)
  • Effective mass of 90 T oscillation = 0.59 m_e
    Fitted from temperature dependence of SdH amplitude via Lifshitz-Kosevich formula (Fig. 2c,d); used in Rashba parameter calculation.
  • Effective mass of 50 T oscillation = ~1.0 m_e
    Fitted from temperature dependence of SdH amplitude; used to assign bands and for Fermi energy estimates.
  • m* for band 1 = 0.3 m_e
    Taken from prior literature (ref. 53) to convert Hall density into Fermi energy E_F = 0.36 eV; the value is not derived in this paper.
  • B_phi from WAL fit = 5e-2 T
    Fitted ILP parameter for inelastic scattering; used to estimate phase coherence length of 176 nm.
  • B_SO from WAL fit = 2.3 T
    Fitted ILP parameter for spin-orbit scattering; converted into spin-precession length 9 nm and Rashba constant 8.6e-12 eVm.
  • Landau fan intercept for 50 T oscillation = 0.5
    Linear extrapolation of Landau index vs 1/B; yields pi Berry phase for a 2D Fermi surface with delta = 0.
  • Landau fan intercept for 90 T oscillation = -0.6
    Linear extrapolation of Landau index vs 1/B; with delta = 1/8 gives pi Berry phase for a 3D Fermi surface.
assumptions (6)
  • standard math Landau-Onsager quantization with phase correction delta = 0 (2D) or 1/8 (3D) applies to the SdH oscillations.
    Used in Eq. (2) to convert Landau fan intercepts into Berry phase.
  • domain assumption The two FFT frequencies 50 T and 90 T correspond to two distinct closed Fermi surfaces without significant beating between them.
    This is the basis for analyzing each component separately; if they were interference from one anisotropic surface, the Berry phase assignment would change.
  • domain assumption Angle dependence classifies 50 T as 2D and 90 T as 3D.
    The text concludes 2D from dying oscillations and 3D from persistence to theta = 90 degrees, an unusual criterion; delta is chosen accordingly.
  • domain assumption Rashba Hamiltonian has a Dirac point at k = 0 and each spin-split Fermi surface encloses it, giving Berry phase pi.
    Imported from Rashba theory (refs 6,28) to interpret the pi phase as Rashba spin-split bands.
  • ad hoc to paper Hall carrier density can be assigned to a single parabolic band (band 1) while SdH bands 2 and 3 are added separately.
    The band diagram treats n_Hall = 5e13 cm^-2 as band-1 density and adds 2.3e12 and 9.8e11 cm^-2 for the SdH bands; no self-consistent multi-band Hall analysis is provided.
  • ad hoc to paper ILP weak-antilocalization formula is valid over the fit range used to obtain BSO = 2.3 T.
    The paper itself notes ILP applies for B < 0.5 T, yet BSO is 2.3 T; the validity of extrapolating the theory to that field range is not addressed.

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Pith. "Pith review of Observation of Shubnikov-de Haas Oscillations, Non-trivial Berry Phase, Planar Hall and Anisotropic Magnetoresistance at the conducting interface of EuO-KTaO$_3$." pith.science (2026). https://pith.science/paper/KT536XEE

@misc{pith2026190804977,
  author       = {Pith},
  title        = {Pith review of: Observation of Shubnikov-de Haas Oscillations, Non-trivial Berry Phase, Planar Hall and Anisotropic Magnetoresistance at the conducting interface of EuO-KTaO$_3$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KT536XEE}},
  note         = {Machine review of arXiv:1908.04977}
}
abstract

The momentum dependent splitting of spin-bands in an electronic system is known as the "Rashba effect". Systems with the "Rashba effect" possess a Dirac point in momentum space. An electron in a cyclotron orbit enclosing that Dirac point in the reciprocal space gains a "Berry phase". We report here the Shubnikov-de-Haas oscillations (SdH) at the conducting interface of EuO-KTaO$_3$ (KTO). Observed SdH oscillations suggest the presence of two Fermi surfaces. For both the Fermi surfaces, we have seen the presence of a non-trivial "Berry phase" suggesting that the surfaces enclose the "Dirac point". Thus the Berry phase originates from the inner and outer Fermi surfaces of the Rashba spin-split bands. As in topological insulators, two fold planar Hall and anisotropic magnetoresistance have also been observed in EuO-KTO. Analyzing the SdH, Hall and magnetoresistance data, we have drawn a possible band diagram near the Fermi surface.

Figures

Figures reproduced from arXiv: 1908.04977 by the authors.

Figure 1
Figure 1. (Color online) (a) ∆Rxx as a function of applied magnetic field at different temperatures. Orange and green circles represent high and low magnetic field oscillations re￾spectively. The inset shows the FFT spectrum for oscillations at 1.8 K. (b) Angle dependent ∆Rxx as a function of applied magnetic field. The schematic shows the measurement geom￾etry. ture as shown by the temperature dependent sheet resis￾tivity me… view at source ↗
Figure 2
Figure 2. (Color online) (a) and (b) ∆Rxx as a function of 1/B at different temperatures for high and low frequency respectively. (c) and (d) Temperature dependence of oscillation amplitudes at 90 and 50 T respectively. The calculated effective masses for different field values at different temperatures are shown. (e) The m*/me values as a function of 1/B for low and high fields. (f) Landau index plot for two frequecies. Clos… view at source ↗
Figure 3
Figure 3. (Color online) (a) Magnetoconductance plot of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: (Color online) (a) Schematic of the measurement [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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Pith tools

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