A phase difference with a practical consequence
The preprint reports a relative phase difference of 0.39π between quantum oscillations seen in magnetization and in a strain-sensor signal used to track the ac magnetostrictive coefficient in YbMnBi2. That is reasonably close to the expected π/2 shift, or a quarter cycle. The result gives researchers a calibration rule for interpreting this response, but it does not produce a unique numerical Berry phase.
The study’s central question was whether the response-specific phase offset could be calibrated by directly comparing ac magnetostrictive oscillations with magnetization oscillations from the same material. The expectation under test was a plus-or-minus π/2 difference, with the sign set by how the extremal electron orbit changes under stress. Here, phase means the relative timing of the two oscillating responses as the magnetic field changes. That timing matters because the paper says a response-phase correction must come before inferring the phase of the underlying cyclotron orbit.
How the signals were compared
All of the primary measurements came from one YbMnBi2 single crystal, reported as 2.8 × 1.5 × 0.2 mm3. The same crystal supplied the magnetization, magnetostrictive-coefficient and thermopower data, keeping the comparison tied to one specimen. Magnetization was recorded in a PPMS with a vibrating-sample magnetometer, while the ac magnetostrictive measurement was made in a 14-T cryostat. The latter used a composite magnetoelectric PMN-PT strain sensor, a 1 Oe ac field and lock-in detection. Because the coupling factor was not known precisely, the measured voltage, VME, was treated as a frequency-and-phase proxy rather than an absolute magnetostrictive coefficient.
Once smooth backgrounds were removed, fast Fourier transform analysis found one fundamental frequency in each response: 159.2 T for magnetization and 156.8 T for the ME signal. The closely similar values provided the basis for comparing the oscillations’ phase in the field-dependent analysis. The visibility thresholds were different: ME oscillations appeared above approximately 4 T, while magnetization oscillations required fields above approximately 6 T. In the measurements reported, the ME signal therefore had the lower observed onset field.
The temperature dependence of the ME oscillation was also used to estimate the cyclotron mass, an effective mass tied to the orbit producing the oscillation. An LK thermal-damping fit at a fixed field of 12.4 T gave m* = 0.22m0. The paper places that value alongside 0.24m0 from magnetotransport.
Why the phase still needs correction
Phase extraction was itself handled cautiously. For an oscillation frequency of about 160 T, the lowest accessible Landau index remained above 10. That made extrapolating the data toward zero index substantially uncertain, so the authors extracted the phases directly by fitting the oscillatory waveforms with Lifshitz–Kosevich, or LK, expressions.
Under the common positive-amplitude convention, the fitted phase was 0.49π for magnetization and 0.88π for the ME voltage. Their difference was 0.39π, close to π/2 but not identical to it. The authors attribute the deviation in their phase fit to the restricted field window and to slowly varying terms that were not included. The finding is therefore best read as an approximate quadrature relationship: the two responses are shifted by nearly, rather than exactly, a quarter cycle.
The practical message is a correction rule. Before a cyclotron-orbit phase is inferred from ac magnetostrictive oscillations, the paper says a plus-or-minus π/2 response-phase correction should be applied, with its sign fixed by the stress derivative of the extremal Fermi surface. This separates the phase of the measurement response from the phase researchers want to interpret.
That calibration does not settle the Berry-phase question. The paper does not assign a unique numerical value because the orbital-moment contribution is unknown, while the sign of the relevant stress response or of the orbit’s stress derivative can introduce an additional π shift. Independent constraints on orbital, spin, effective-g and stress-related contributions would be needed before a numerical Berry phase could be assigned. The preprint consequently presents a calibrated relative phase, not a standalone topological conclusion.
A useful check with clear limits
A separate angular check offered limited support for phase stability. At 6.5 K, thermopower oscillations persisted as the field direction was varied from -10° to 15°. The fitted frequency changed by roughly 159.3 to 161 T, an angular minimum indicated an approximately 2.5° zero-angle offset, and the fitted phase remained nearly constant. No metamagnetic transition was observed up to 14 T, and the authors concluded that a few degrees of misalignment did not measurably alter the phase.
The scope of that check is narrow. Controlled rotation was difficult, and thermopower—not simultaneous rotation of magnetization and the ME measurement—was used for the angular test. The central comparison still rests on one crystal, with no independent sample replication reported. In addition, the unknown strain-transfer factor means the voltage proxy cannot provide the absolute ac magnetostrictive coefficient. These limits make the result a calibration for the reported setup rather than a general rule already demonstrated across samples and measurement geometries.
The document is identified as arXiv:2608.25656v1, dated 26 August 2026, with the manuscript marked 27 August 2026. No journal or peer-review status is reported in the supplied record. For now, its main contribution is a way to align two response phases before attempting a more ambitious interpretation of quantum-oscillation data.
Paper data and sources
Original title: Phase calibration of quantum oscillations in the magnetostrictive coefficient using the topological antiferromagnet YbMnBi$_2$
Authors: Qin Deng, Long Zhang, Zeyu Li et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
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