Source-linked AI summary
Numerical extraction of de Haas - van Alphen frequencies from calculated band energies
P. M. C. Rourke, S. R. Julian
TL;DR
The paper addresses the difficulty of extracting observable dHvA orbits and effective masses from complicated calculated band structures, where publicly available comparison methods were scarce. It introduces an interpolated k-space super-cell approach that slices the Fermi surface, identifies and matches orbits, and determines extremal quantities. Applied to UPt3, the algorithm found previously missed frequencies that improve agreement with experiment and provide new evidence for itinerant 5f electrons.
Problem
Extracting dHvA orbits from complicated calculated band structures is difficult, and publicly available methods for comparing calculations with quantum-oscillation experiments were scarce.
Method
The algorithm builds a heavily interpolated k-space super cell, slices it perpendicular to the magnetic field, locates and matches Fermi-surface orbits, and determines extremal frequencies and effective masses.
Results
New frequencies in calculated UPt3 bands were located that had not previously been found and that increase agreement between the model and experiment.
Takeaways & Limitations
The new frequencies provide evidence for the itinerant nature of the 5f electrons in UPt3.
Takeaways & Limitations
A documented earlier method requires prior knowledge of extremal orbit centers, while Eq. 10 is valid only for extremal orbits whose energy gradient lies within the slice.
Abstract
from arXiv · showhide
A new algorithm for extracting de Haas-van Alphen frequencies and effective masses from calculated band energies is presented. The algorithm creates an interpolated k-space "super cell," which is broken into slices perpendicular to the desired magnetic field direction. Fermi surface orbits are located within each slice, and de Haas-van Alphen frequencies and effective masses are calculated. Orbits are then matched across slices, and extremal orbits determined. This technique has been successful in locating extremal orbits not previously noticed in the complicated topology of existing UPt3 band-structure data; these new orbits agree with experimental de Haas-van Alphen measurements on this material, and solidify the case for a fully-itinerant model of UPt3.
1 Introduction
The paper frames dHvA measurements as probes of Fermi-surface topology and effective masses, while emphasizing that predicting observable orbits from complicated calculated band structures is difficult and previously lacked broadly available tools.
- The Fermi surface separates occupied from unoccupied k-space states, and its shape strongly influences metallic electronic properties.
- Magnetic fields confine k-space states to Landau tubes, whose depopulation as they leave the Fermi surface produces oscillations periodic in 1/H.
- dHvA frequencies correspond to extremal cross-sectional areas perpendicular to the magnetic field, while temperature damping reveals effective masses around those orbits.
- Only extremal closed orbits produce dHvA frequencies; complicated surfaces may also contain open or near-open orbits that complicate interpretation.
- Extracting predicted dHvA orbits is non-trivial because real compounds can have open, near-open, nested, and non-central orbits.
- Earlier documented methods worked best when extremal orbit centers were already known, whereas complicated Fermi surfaces can contain visually unobvious extremal orbits.
2 Numerical method
The method constructs an interpolated, field-aligned k-space super cell, detects Fermi-surface orbits on perpendicular slices, and identifies extremal orbits automatically. It calculates orbit properties while tracking them across slices and accommodates arbitrary reciprocal-unit-cell geometries.
- Overview: The algorithm automatically extracts extremal orbits, effective masses, and density-of-states contributions from calculated Fermi surfaces without manual guidance.It reads BXSF band-energy grids produced by electronic-structure calculations.
- 2.2 k-space super cell construction: A cubic super cell aligned with the magnetic field is constructed, mapped to the reciprocal unit cell, and populated with interpolated band energies.Third-order Lagrange interpolation on a 4 × 4 × 4-point grid determines energies at super-cell grid points.
- 2.3 Fermi surface orbit detection: For each detected orbit, the program computes cross-sectional area, effective mass, and electron or hole character from interpolated Fermi-surface points and energy slopes.Fermi-surface points are linearly interpolated between neighboring grid points, and slopes are resolved into orthogonal components.
- 2.5–2.6 Orbit matching and extremal selection: Orbits are matched between adjacent slices so they can be associated with Fermi-surface sheets, after which extremal orbits are selected.Orbit data from similar orbits on separate sheets are averaged before output.
- 2.2 k-space super cell construction: The super-cell construction supports arbitrary reciprocal lattice vectors, including nonorthogonal vectors, and uses a cube sized to track zone-crossing orbits.The cube sides are defined as 4× the longest reciprocal lattice vector.
- 2.3 Fermi surface orbit detection: The super cell is divided into one-grid-point-thick perpendicular slices, where Fermi-surface outlines are located by scanning the two-dimensional k-point arrays.Orbits crossing the super-cell boundaries are treated as open and ignored.
3 Results
The algorithm accurately extracts dHvA frequencies and effective masses from test Fermi surfaces, then identifies previously overlooked extremal orbits in UPt3 that match experimental frequencies.
- Test Fermi surfaces: The barrel test reproduced the first four Yamaji angles at 49.5°, 69.6°, 76.6°, and 80.1°, where belly and neck frequencies meet.These angles correspond to cross-sectional areas becoming independent of k_z.
- Test Fermi surfaces: For the barrel at φ > 0°, extracted frequencies differed from the approximate analytical curve by up to 3%, likely reflecting the curve’s inexact nature.The ideal barrel dependence lacks an exact equation in this angular regime.
- UPt3: Applied to UPt3, the algorithm confirmed known orbits and found new extremal orbits corresponding to previously unexplained experimental frequencies, including η.The η frequency likely corresponds to orbit II or alternatively orbit III in Fig. 2.
- UPt3: The calculated UPt3 frequencies showed good agreement with measured frequency-angle variation, while differences in overall frequency magnitude remained typical for heavy-fermion materials.Flat bands make Fermi-surface size sensitive to small Fermi-energy shifts.
- UPt3: Locating the previously missing UPt3 orbits brought the traditional band-structure calculation closer to experiment and helped resolve the controversy over itinerant uranium 5f electrons.The new orbits were also confirmed by an independent extraction method when their Brillouin-zone locations were supplied.
4 Conclusion
The paper introduces a robust approach for extracting quantum-oscillation frequencies and effective masses from calculated band energies, including in complicated Fermi surfaces. Applied to UPt3, it found previously missed frequencies that improved agreement between model and experiment and provided evidence for itinerant 5f electrons.
- The program uses a large, heavily interpolated k-space super cell to characterize complicated Fermi surfaces and locate all extremal orbits.The approach exploits desktop computing power to improve robustness on complex topologies.
- Applied to UPt3, the algorithm located new frequencies that had not previously been found on the calculated Fermi surface.
- The new frequencies increase agreement between the UPt3 model and experiment, providing new evidence for itinerant 5f electrons.