pith. sign in

arxiv: 2512.21931 · v2 · submitted 2025-12-26 · ❄️ cond-mat.str-el

Multipolar fluctuations from localized 4f electrons in CeRh2As2

Koki Numa , Eri Matsuda , Akimitsu Kirikoshi , Junya Otsuki This is my paper

Pith reviewed 2026-05-16 20:00 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords CeRh2As2multipolar fluctuationsheavy fermionantiferromagnetic orderquadrupole fluctuationscrystalline electric fieldDFT+DMFToctupole
0
0 comments X

The pith

Antiferromagnetic order of c-axis moments at q=(1/2,1/2,0) matches the non-superconducting transition in CeRh2As2.

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

This paper uses density functional theory combined with dynamical mean-field theory to compute momentum-dependent multipolar susceptibilities for the localized 4f electrons in CeRh2As2. Magnetic fluctuations of the M_z dipole component peak strongly at the wavevector q=(1/2,1/2,0), which corresponds to a two-dimensional checkerboard pattern. Hybridization between the crystalline-electric-field ground-state doublet and the first excited doublet produces leading fluctuations in the magnetic octupole of z(x^2-y^2) symmetry, with secondary electric quadrupole fluctuations of x^2-y^2 and {yz, zx} symmetry. When the anisotropic field dependence of the transition temperature T_0 is included, the calculations show that an in-plane magnetic field enhances T_0 specifically through the field-induced {yz, zx} quadrupole fluctuations. The authors conclude that antiferromagnetic ordering of M_z at this wavevector is therefore consistent with the experimental phase diagram.

Core claim

We derive the momentum-dependent multipolar susceptibilities and effective interactions among the localized 4f electrons, based on the framework of density functional theory combined with dynamical mean-field theory. Magnetic fluctuations within the crystalline-electric-field ground-state doublet are dominated by q=(1/2,1/2,0), corresponding to a two-dimensional checkerboard configuration of the magnetic moment M_z along the c axis. Hybridization between the CEF ground-state and the first-excited doublet gives rise to leading magnetic octupole fluctuations of z(x^2-y^2) symmetry, followed by electric quadrupole fluctuations of x^2-y^2 and {yz, zx} symmetries. By taking into account the anis,

What carries the argument

Momentum-dependent multipolar susceptibilities computed from DFT+DMFT for the localized 4f electrons under crystalline electric field splitting.

If this is right

  • An in-plane magnetic field raises T_0 because it induces {yz, zx} quadrupole fluctuations that couple to and stabilize the M_z antiferromagnetic order.
  • The dominant fluctuations are two-dimensional checkerboard antiferromagnetic M_z moments along the c axis.
  • Hybridization produces magnetic octupole fluctuations of z(x^2-y^2) symmetry as the leading channel after the dipole fluctuations.
  • Electric quadrupole fluctuations of x^2-y^2 symmetry appear but remain secondary to the octupole and dipole channels.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same multipolar-fluctuation mechanism may govern the superconducting pairing that appears below the T_0 transition.
  • Resonant x-ray scattering tuned to the Ce L edge could detect the predicted z(x^2-y^2) octupole fluctuations directly.
  • Analogous CEF-hybridization effects should be examined in other Ce-based heavy-fermion compounds that exhibit field-tuned phase transitions.

Load-bearing premise

The DFT+DMFT calculations correctly capture the hybridization between CEF levels and the resulting multipolar fluctuations without significant systematic errors from the approximations used.

What would settle it

Neutron scattering that fails to detect antiferromagnetic M_z order at q=(1/2,1/2,0), or specific-heat measurements showing that T_0 does not increase under in-plane magnetic fields as predicted by the quadrupole-fluctuation enhancement.

Figures

Figures reproduced from arXiv: 2512.21931 by Akimitsu Kirikoshi, Eri Matsuda, Junya Otsuki, Koki Numa.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Crystal structure of CeRh [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) The single-particle excitation spectrum [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Fully relativistic band structure of CeRh [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a). We adopt this simple approach, although en￾forcing charge self-consistency between DFT and DMFT would improve the CEF potential [59, 60]. Σˆ loc(iωn) is the local self-energy in the DMFT. εf is the energy of the 4f levels. Pˆ f denotes a projection operator onto 4f or￾bitals. This term works as a double-counting correction between DFT and DMFT calculations. We compute the self-energy Σˆ loc using the … view at source ↗
Figure 5
Figure 5. Figure 5: shows the eigenvalues χ (ξ) (q) on the q-path that connects the symmetry points in the Brillouin zone. There are 72 modes, which are composed of 62 = 36 atomic degrees of freedom times two cerium atoms in a unit cell. The structure of this graph can be understood in terms of the CEF states. The six fluctuation modes in the top group are due to fluctuations within the ground￾state doublet Γ(1) 7 , which has… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Eigenvalues [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Two-dimensional checkerboard type magnetic struc [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Eigenvalues [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Temperature dependence of the inverse of the eigen [PITH_FULL_IMAGE:figures/full_fig_p007_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The effective multipolar interactions [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Candidate magnetic structures and the induced quadrupoles under magnetic fields [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Configurations corresponding to large fluctua [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Checkerboard-type magnetic structures at [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Magnetic structures in AFM+SC1 phase proposed [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
read the original abstract

The heavy-fermion superconductor CeRh2As2 exhibits a non-superconducting phase transition that precedes the emergence of superconductivity. The nature of the corresponding order parameter remains under debate, with competing proposals involving magnetic dipoles or electric quadrupoles. We derive the momentum-dependent multipolar susceptibilities and effective interactions among the localized 4f electrons, based on the framework of density functional theory combined with dynamical mean-field theory. Magnetic fluctuations within the crystalline-electric-field (CEF) ground-state doublet are dominated by q=(1/2,1/2,0), corresponding to a two-dimensional checkerboard configuration of the magnetic moment M_z along the c axis. Hybridization between the CEF ground-state and the first-excited doublet gives rise to leading magnetic octupole fluctuations of z(x^2-y^2) symmetry, followed by electric quadrupole fluctuations of x^2-y^2 and {yz, zx} symmetries. By taking into account the anisotropic magnetic-field dependence of the transition temperature T_0, we conclude that an antiferromagnetic order of M_z at q=(1/2,1/2,0) is consistent with the experiments, owing to the enhancement of T_0 caused by fluctuations of the field-induced quadrupole of {yz, zx} type under an in-plane magnetic field.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses DFT+DMFT to compute momentum-dependent multipolar susceptibilities for localized 4f electrons in CeRh2As2. It reports that magnetic fluctuations within the CEF ground doublet are dominated by q=(1/2,1/2,0) (checkerboard AFM M_z order), with hybridization to the first excited doublet producing leading z(x^2-y^2) octupole fluctuations followed by x^2-y^2 and {yz,zx} quadrupole fluctuations. The authors conclude that AFM M_z order at this q is consistent with the observed anisotropic T0, because in-plane fields induce {yz,zx} quadrupole fluctuations that raise T0.

Significance. If the calculations prove robust, the work supplies a microscopic mechanism that favors a specific magnetic dipole order over competing quadrupolar proposals in this heavy-fermion superconductor, by directly connecting ab-initio multipolar susceptibilities to the measured field anisotropy of T0. It demonstrates how DFT+DMFT can be used to rank multipolar channels and thereby constrain the order-parameter symmetry in f-electron systems.

major comments (2)
  1. [Methods] Methods section: no values of U and J, no double-counting scheme, and no sensitivity tests are reported. The dominant q and the symmetry of the leading fluctuations are controlled by the CEF hybridization matrix elements, which shift under modest changes in U, J or double-counting; without such tests the claim that M_z fluctuations peak at q=(1/2,1/2,0) and that {yz,zx} quadrupoles raise T0 cannot be assessed.
  2. [Results] Results on susceptibilities: the manuscript provides neither k-point convergence, DMFT temperature convergence, impurity-solver error bars, nor any estimate of statistical or systematic uncertainty on the computed susceptibilities. Because the central experimental consistency argument rests on the precise ranking and field response of these susceptibilities, the absence of convergence data is load-bearing.
minor comments (2)
  1. [Figures] Figure captions and text should explicitly state the temperature and broadening used when plotting the susceptibility maps so that readers can judge proximity to the ordering temperature.
  2. [Text] Notation for the multipolar operators (e.g., z(x^2-y^2)) should be cross-referenced to a standard table or earlier literature to avoid ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback on our manuscript. We address each major comment below and will revise the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [Methods] Methods section: no values of U and J, no double-counting scheme, and no sensitivity tests are reported. The dominant q and the symmetry of the leading fluctuations are controlled by the CEF hybridization matrix elements, which shift under modest changes in U, J or double-counting; without such tests the claim that M_z fluctuations peak at q=(1/2,1/2,0) and that {yz,zx} quadrupoles raise T0 cannot be assessed.

    Authors: We agree that the interaction parameters and double-counting scheme must be specified, and that sensitivity tests are important to confirm the robustness of our results. In the revised manuscript, we will explicitly state the values of U and J used, describe the double-counting procedure, and include sensitivity tests varying these parameters to show that the dominant q-vector and fluctuation symmetries are stable. This will directly address the concern regarding the reliability of the claims about M_z fluctuations and the field-induced quadrupole effects. revision: yes

  2. Referee: [Results] Results on susceptibilities: the manuscript provides neither k-point convergence, DMFT temperature convergence, impurity-solver error bars, nor any estimate of statistical or systematic uncertainty on the computed susceptibilities. Because the central experimental consistency argument rests on the precise ranking and field response of these susceptibilities, the absence of convergence data is load-bearing.

    Authors: We acknowledge that convergence and error analysis are crucial for the quantitative aspects of our susceptibility calculations. We will add to the revised manuscript detailed information on k-point convergence, DMFT temperature convergence, impurity-solver error bars, and estimates of uncertainties. These additions will support the ranking of the multipolar fluctuations and their response to magnetic fields. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives momentum-dependent multipolar susceptibilities and effective interactions directly from DFT+DMFT applied to the 4f electrons and CEF levels of CeRh2As2. It then compares the resulting dominant fluctuations (M_z at q=(1/2,1/2,0) and field-induced {yz,zx} quadrupoles) against independent experimental data on the anisotropic T_0 to identify consistency with antiferromagnetic order. No quoted step reduces a prediction to a fitted input by construction, invokes a self-citation as the sole justification for a uniqueness theorem, or renames a known result as a new derivation. The computational framework and external T_0 anisotropy provide independent content.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard assumptions of the DFT+DMFT method for treating strongly correlated 4f systems, including the validity of the localized electron picture.

free parameters (1)
  • DMFT Coulomb interaction U and Hund's J
    These parameters are typically chosen to match the observed heavy fermion mass enhancement or CEF splitting in such calculations.
axioms (1)
  • domain assumption Localized nature of 4f electrons with crystal electric field splitting
    The framework assumes the 4f electrons are localized and split by the CEF into doublets.

pith-pipeline@v0.9.0 · 5546 in / 1195 out tokens · 40352 ms · 2026-05-16T20:00:22.909100+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

79 extracted references · 79 canonical work pages

  1. [1]

    atomic” column lists the atomic multipoles, and “irrep(a)

    direction lifts the degeneracy between the two do- mains. Therefore, when the system is cooled throughT 0 under such strain, domain selection occurs in the ordered state, enabling statistical control of the checkerboard do- mains. (a) (b) (c) FIG. 14. Configurations corresponding to large fluctua- tions arising by hybridization between Γ (1) 7 and Γ 6. (a...

    work page 2024

  2. [2]

    S. Khim, J. F. Landaeta, J. Banda, N. Bannor, M. Brando, P. M. R. Brydon, D. Hafner, R. K¨ uchler, R. Cardoso-Gil, U. Stockert, A. P. Mackenzie, D. F. Agterberg, C. Geibel, and E. Hassinger, Field-induced transition within the superconducting state of CeRh2As2, Science373, 1012 (2021)

    work page 2021

  3. [3]

    Semeniuk, D

    K. Semeniuk, D. Hafner, P. Khanenko, T. L¨ uhmann, J. Banda, J. F. Landaeta, C. Geibel, S. Khim, E. Has- singer, and M. Brando, Decoupling multiphase supercon- ductivity from normal state ordering in CeRh2As2, Phys. 14 Rev. B107, L220504 (2023)

    work page 2023

  4. [4]

    Hafner, P

    D. Hafner, P. Khanenko, E.-O. Eljaouhari, R. K¨ uchler, J. Banda, N. Bannor, T. L¨ uhmann, J. F. Landaeta, S. Mishra, I. Sheikin, E. Hassinger, S. Khim, C. Geibel, G. Zwicknagl, and M. Brando, Possible quadrupole density wave in the superconducting Kondo lattice CeRh2As2, Phys. Rev. X12, 011023 (2022)

    work page 2022

  5. [5]

    J. F. Landaeta, P. Khanenko, D. C. Cavanagh, C. Geibel, S. Khim, S. Mishra, I. Sheikin, P. M. R. Brydon, D. F. Agterberg, M. Brando, and E. Hassinger, Field- angle dependence reveals odd-parity superconductivity in CeRh2As2, Phys. Rev. X12, 031001 (2022)

    work page 2022

  6. [6]

    Kibune, S

    M. Kibune, S. Kitagawa, K. Kinjo, S. Ogata, M. Man- ago, T. Taniguchi, K. Ishida, M. Brando, E. Hassinger, H. Rosner, C. Geibel, and S. Khim, Observation of an- tiferromagnetic order as odd-parity multipoles inside the superconducting phase in CeRh 2As2, Phys. Rev. Lett. 128, 057002 (2022)

    work page 2022

  7. [7]

    S. Khim, O. Stockert, M. Brando, C. Geibel, C. Baines, T. J. Hicken, H. Luetkens, D. Das, T. Shiroka, Z. Guguchia, and R. Scheuermann, Coexistence of local magnetism and superconductivity in the heavy-fermion compound CeRh 2As2 revealed byµSR studies, Phys. Rev. B111, 115134 (2025)

    work page 2025

  8. [8]

    Kitagawa, M

    S. Kitagawa, M. Kibune, K. Kinjo, M. Manago, T. Taniguchi, K. Ishida, M. Brando, E. Hassinger, C. Geibel, and S. Khim, Two-dimensional XY-type mag- netic properties of locally noncentrosymmetric supercon- ductor CeRh2As2, J. Phys. Soc. Jpn.91, 043702 (2022)

    work page 2022

  9. [9]

    Ogata, S

    S. Ogata, S. Kitagawa, K. Kinjo, K. Ishida, M. Brando, E. Hassinger, C. Geibel, and S. Khim, Parity transition of spin-singlet superconductivity using sublattice degrees of freedom, Phys. Rev. Lett.130, 166001 (2023)

    work page 2023

  10. [10]

    Ogata, S

    S. Ogata, S. Kitagawa, K. Kinjo, K. Ishida, M. Brando, E. Hassinger, C. Geibel, and S. Khim, Appearance ofc- axis magnetic moment in odd-parity antiferromagnetic state in CeRh 2As2 revealed by 75As-NMR, Phys. Rev. B110, 214509 (2024)

    work page 2024

  11. [11]

    Ogata, S

    S. Ogata, S. Kitagawa, K. Ishida, M. Brando, E. Has- singer, C. Geibel, and S. Khim, Conventionals-wave su- perconductivity in LaRh2As2; the analog without the 4f electrons of CeRh 2As2, J. Phys. Soc. Jpn95, 013701 (2026)

    work page 2026

  12. [12]

    Kimura, J

    S.-i. Kimura, J. Sichelschmidt, and S. Khim, Optical study of the electronic structure of locally noncentrosym- metric CeRh2As2, Phys. Rev. B104, 245116 (2021)

    work page 2021

  13. [13]

    Onishi, U

    S. Onishi, U. Stockert, S. Khim, J. Banda, M. Brando, and E. Hassinger, Low-temperature thermal conductiv- ity of the two-phase superconductor CeRh 2As2, Front. Electron. Mater.2, 880579 (2022)

    work page 2022

  14. [14]

    X. Chen, L. Wang, J. Ishizuka, R. Zhang, K. Nogaki, Y. Cheng, F. Yang, Z. Chen, F. Zhu, Z. Liu, J. Mei, Y. Yanase, B. Lv, and Y. Huang, Coexistence of near- EF flat band and Van Hove singularity in a two-phase superconductor, Phys. Rev. X14, 021048 (2024)

    work page 2024

  15. [15]

    B. Chen, H. Liu, Q.-Y. Wu, C. Zhang, X.-Q. Ye, Y.- Z. Zhao, J.-J. Song, X.-Y. Tian, B.-L. Tan, Z.-T. Liu, M. Ye, Z.-H. Chen, Y.-B. Huang, D.-W. Shen, Y.-H. Yuan, J. He, Y.-X. Duan, and J.-Q. Meng, Exploring possible Fermi surface nesting and the nature of heavy quasiparticles in the spin-triplet superconductor candi- date CeRh2As2, Phys. Rev. B110, L041120 (2024)

    work page 2024

  16. [16]

    T. Chen, H. Siddiquee, Q. Xu, Z. Rehfuss, S. Gao, C. Lygouras, J. Drouin, V. Morano, K. E. Avers, C. J. Schmitt, A. Podlesnyak, J. Paglione, S. Ran, Y. Song, and C. Broholm, Quasi-two-dimensional antiferromag- netic spin fluctuations in the spin-triplet superconduc- tor candidate CeRh 2As2, Phys. Rev. Lett.133, 266505 (2024)

    work page 2024

  17. [17]

    Siddiquee, Z

    H. Siddiquee, Z. Rehfuss, C. Broyles, and S. Ran, Pressure dependence of superconductivity in CeRh 2As2, Phys. Rev. B108, L020504 (2023)

    work page 2023

  18. [18]

    Semeniuk, M

    K. Semeniuk, M. Pfeiffer, J. F. Landaeta, M. Nicklas, C. Geibel, M. Brando, S. Khim, and E. Hassinger, Expos- ing the odd-parity superconductivity in CeRh 2As2 with hydrostatic pressure, Phys. Rev. B110, L100504 (2024)

    work page 2024

  19. [19]

    Q. Dong, T. Shi, P. Yang, X. Liu, X. Shi, L. Wang, J. Xi- ang, H. Ma, Z. Tian, J. Sun, Y. Uwatoko, G. Chen, X. Wang, J. Shen, R. Wu, X. Lu, P. Sun, G. Chajew- ski, D. Kaczorowski, B. Wang, and J. Cheng, Strong su- perconducting pairing strength and pseudogap features in a putative multiphase heavy-fermion superconductor CeRh2As2 studied by soft point cont...

    work page 2025

  20. [20]

    Nogaki, A

    K. Nogaki, A. Daido, J. Ishizuka, and Y. Yanase, Topo- logical crystalline superconductivity in locally noncen- trosymmetric CeRh 2As2, Phys. Rev. Res.3, L032071 (2021)

    work page 2021

  21. [21]

    M. L. Ali, M. K. Alam, M. Khan, M. N. M. Nobin, N. Is- lam, U. Faruk, and M. Z. Rahaman, Pressure-dependent structural, electronic, optical, and mechanical properties of superconductor CeRh 2As2: A first-principles study, Physica B668, 415224 (2023)

    work page 2023

  22. [22]

    Ishizuka, K

    J. Ishizuka, K. Nogaki, M. Sigrist, and Y. Yanase, Correlation-induced Fermi surface evolution and topo- logical crystalline superconductivity in CeRh 2As2, Phys. Rev. B110, L140505 (2024)

    work page 2024

  23. [23]

    Y. Wu, Y. Zhang, S. Ju, Y. Hu, Y. Huang, Y. Zhang, H. Zhang, H. Zheng, G. Yang, E.-O. Eljaouhari, B. Song, N. C. Plumb, F. Steglich, M. Shi, G. Zwicknagl, C. Cao, H. Yuan, and Y. Liu, Fermi surface nesting with heavy quasiparticles in the locally noncentrosymmetric super- conductor CeRh 2As2, Chinese Phys. Lett.41, 097403 (2024)

    work page 2024

  24. [24]

    Ma, P.-F

    H.-T. Ma, P.-F. Tian, D.-L. Guo, X. Ming, X.-J. Zheng, Y. Liu, and H. Li, Phase evolution of Ce-based heavy- fermion superconductors under compression: A com- bined first-principles and effective-model study, Phys. Rev. B109, 195164 (2024)

    work page 2024

  25. [25]

    Yoshida, M

    T. Yoshida, M. Sigrist, and Y. Yanase, Pair-density wave states through spin-orbit coupling in multilayer super- conductors, Phys. Rev. B86, 134514 (2012)

    work page 2012

  26. [26]

    M¨ ockli and A

    D. M¨ ockli and A. Ramires, Superconductivity in disor- dered locally noncentrosymmetric materials: An appli- cation to CeRh 2As2, Phys. Rev. B104, 134517 (2021)

    work page 2021

  27. [27]

    E. G. Schertenleib, M. H. Fischer, and M. Sigrist, Un- usualH-Tphase diagram of CeRh 2As2: The role of stag- gered noncentrosymmetricity, Phys. Rev. Res.3, 023179 (2021)

    work page 2021

  28. [28]

    Skurativska, M

    A. Skurativska, M. Sigrist, and M. H. Fischer, Spin re- sponse and topology of a staggered-Rashba superconduc- tor, Phys. Rev. Res.3, 033133 (2021)

    work page 2021

  29. [29]

    A. Ptok, K. J. Kapcia, P. T. Jochym, J. La˙ zewski, A. M. Ole´ s, and P. Piekarz, Electronic and dynamical properties of CeRh2As2: Role of Rh2As2 layers and expected orbital order, Phys. Rev. B104, L041109 (2021)

    work page 2021

  30. [30]

    Machida, Violation of pauli-clogston limit in the heavy-fermion superconductor CeRh 2As2: Duality of 15 itinerant and localized 4felectrons, Phys

    K. Machida, Violation of pauli-clogston limit in the heavy-fermion superconductor CeRh 2As2: Duality of 15 itinerant and localized 4felectrons, Phys. Rev. B106, 184509 (2022)

    work page 2022

  31. [31]

    D. C. Cavanagh, T. Shishidou, M. Weinert, P. M. R. Brydon, and D. F. Agterberg, Nonsymmorphic symmetry and field-driven odd-parity pairing in CeRh 2As2, Phys. Rev. B105, L020505 (2022)

    work page 2022

  32. [32]

    M¨ ockli, Unconventional singlet-triplet superconduc- tivity, J

    D. M¨ ockli, Unconventional singlet-triplet superconduc- tivity, J. Phys.: Conf. Ser.2164, 012009 (2022)

    work page 2022

  33. [33]

    Hazra and P

    T. Hazra and P. Coleman, Triplet pairing mechanisms from Hund’s-Kondo models: Applications to UTe 2 and CeRh2As2, Phys. Rev. Lett.130, 136002 (2023)

    work page 2023

  34. [34]

    D. C. Cavanagh, D. F. Agterberg, and P. M. R. Brydon, Pair breaking in superconductors with strong spin-orbit coupling, Phys. Rev. B107, L060504 (2023)

    work page 2023

  35. [35]

    H. G. Suh, Y. Yu, T. Shishidou, M. Weinert, P. M. R. Brydon, and D. F. Agterberg, Superconductivity of anomalous pseudospin in nonsymmorphic materials, Phys. Rev. Res.5, 033204 (2023)

    work page 2023

  36. [36]

    Nogaki and Y

    K. Nogaki and Y. Yanase, Field-induced superconductiv- ity mediated by odd-parity multipole fluctuation, Phys. Rev. B110, 184501 (2024)

    work page 2024

  37. [37]

    A. L. Szab´ o, M. H. Fischer, and M. Sigrist, Effects of nucleation at a first-order transition between two super- conducting phases: Application to CeRh2As2, Phys. Rev. Res.6, 023080 (2024)

    work page 2024

  38. [38]

    A. Amin, H. Wu, T. Shishidou, and D. F. Agterberg, Kramers’ degenerate magnetism and superconductivity, Phys. Rev. B109, 024502 (2024)

    work page 2024

  39. [39]

    Minamide and Y

    A. Minamide and Y. Yanase, Superconducting meron phase in locally noncentrosymmetric superconductors, Phys. Rev. Lett.134, 026002 (2025)

    work page 2025

  40. [40]

    C. Lee, D. F. Agterberg, and P. M. R. Brydon, Uni- fied picture of superconductivity and magnetism in CeRh2As2, Phys. Rev. Lett.135, 026003 (2025)

    work page 2025

  41. [41]

    Mishra, Y

    S. Mishra, Y. Liu, E. D. Bauer, F. Ronning, and S. M. Thomas, Anisotropic magnetotransport properties of the heavy-fermion superconductor CeRh 2As2, Phys. Rev. B 106, L140502 (2022)

    work page 2022

  42. [42]

    Pfeiffer, K

    M. Pfeiffer, K. Semeniuk, J. F. Landaeta, R. Borth, C. Geibel, M. Nicklas, M. Brando, S. Khim, and E. Has- singer, Pressure-tuned quantum criticality in the locally noncentrosymmetric superconductor CeRh 2As2, Phys. Rev. Lett.133, 126506 (2024)

    work page 2024

  43. [43]

    Chajewski and D

    G. Chajewski and D. Kaczorowski, Discovery of mag- netic phase transitions in heavy-fermion superconductor CeRh2As2, Phys. Rev. Lett.132, 076504 (2024)

    work page 2024

  44. [44]

    Khanenko, J

    P. Khanenko, J. F. Landaeta, S. Ruet, T. L¨ uhmann, K. Semeniuk, M. Pelly, A. W. Rost, G. Chajewski, D. Kaczorowski, C. Geibel, S. Khim, E. Hassinger, and M. Brando, Phase diagram of CeRh2As2 for out-of-plane magnetic field, Phys. Rev. B112, L060501 (2025)

    work page 2025

  45. [45]

    Shiina, H

    R. Shiina, H. Shiba, and P. Thalmeier, Magnetic-field effects on quadrupolar ordering in a Γ 8-quartet system CeB6, J. Phys. Soc. Jpn.66, 1741 (1997)

    work page 1997

  46. [46]

    Kuramoto, H

    Y. Kuramoto, H. Kusunose, and A. Kiss, Multipole or- ders and fluctuations in strongly correlated electron sys- tems, J. Phys. Soc. Jpn.78, 072001 (2009)

    work page 2009

  47. [47]

    Khanenko, D

    P. Khanenko, D. Hafner, K. Semeniuk, J. Banda, T. L¨ uhmann, F. B¨ artl, T. Kotte, J. Wosnitza, G. Zwick- nagl, C. Geibel, J. F. Landaeta, S. Khim, E. Hassinger, and M. Brando, Origin of the non-fermi-liquid behavior in CeRh2As2, Phys. Rev. B111, 045162 (2025)

    work page 2025

  48. [48]

    Miyake and A

    K. Miyake and A. Tsuruta, A possible scenario for the anomalous temperature dependence of the resistivity and the specific heat of CeRh2As2 above the superconducting transition temperature and an origin of the phase tran- sition atT=T 0, J. Phys. Soc. Jpn.93, 074702 (2024)

    work page 2024

  49. [49]

    Zwicknagl, Quasi-particles in heavy fermion systems, Adv

    G. Zwicknagl, Quasi-particles in heavy fermion systems, Adv. Phys.41, 203 (1992)

    work page 1992

  50. [50]

    D. S. Christovam, M. Ferreira-Carvalho, A. Marino, M. Sundermann, D. Takegami, A. Melendez-Sans, K. D. Tsuei, Z. Hu, S. R¨ oßler, M. Valvidares, M. W. Haverkort, Y. Liu, E. D. Bauer, L. H. Tjeng, G. Zwicknagl, and A. Severing, Spectroscopic evidence of Kondo-induced quasiquartet in CeRh2As2, Phys. Rev. Lett.132, 046401 (2024)

    work page 2024

  51. [51]

    Harima, Hidden-orders of uranium compounds, Sci- Post Phys

    H. Harima, Hidden-orders of uranium compounds, Sci- Post Phys. Proc.11, 006 (2023)

    work page 2023

  52. [52]

    Schmidt and P

    B. Schmidt and P. Thalmeier, Anisotropic magnetic and quadrupolarH-Tphase diagram of CeRh 2As2, Phys. Rev. B110, 075154 (2024)

    work page 2024

  53. [53]

    Thalmeier, A

    P. Thalmeier, A. Akbari, and B. Schmidt, Thermody- namics, elastic anomalies and excitations in the field in- duced phases of CeRh 2As2, New J. Phys.27, 033026 (2025)

    work page 2025

  54. [54]

    Koepernik and H

    K. Koepernik and H. Eschrig, Full-potential nonorthog- onal local-orbital minimum-basis band-structure scheme, Phys. Rev. B59, 1743 (1999)

    work page 1999

  55. [55]

    Opahle, K

    I. Opahle, K. Koepernik, and H. Eschrig, Full-potential band-structure calculation of iron pyrite, Phys. Rev. B 60, 14035 (1999)

    work page 1999

  56. [56]

    Eschrig and K

    H. Eschrig and K. Koepernik, Tight-binding models for the iron-based superconductors, Phys. Rev. B80, 104503 (2009)

    work page 2009

  57. [57]

    Koepernik, O

    K. Koepernik, O. Janson, Y. Sun, and J. van den Brink, Symmetry-conserving maximally projected Wan- nier functions, Phys. Rev. B107, 235135 (2023)

    work page 2023

  58. [58]

    Georges, G

    A. Georges, G. Kotliar, W. Krauth, and M. J. Rozen- berg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys.68, 13 (1996)

    work page 1996

  59. [59]

    Kotliar, S

    G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, Electronic struc- ture calculations with dynamical mean-field theory, Rev. Mod. Phys.78, 865 (2006)

    work page 2006

  60. [60]

    Delange, S

    P. Delange, S. Biermann, T. Miyake, and L. Pourovskii, Crystal-field splittings in rare-earth-based hard magnets: An ab initio approach, Phys. Rev. B96, 155132 (2017)

    work page 2017

  61. [61]

    L. V. Pourovskii, J. Boust, R. Ballou, G. G. Eslava, and D. Givord, Higher-order crystal field and rare-earth mag- netism in rare-earth–Co 5 intermetallics, Phys. Rev. B 101, 214433 (2020)

    work page 2020

  62. [62]

    V. I. Anisimov, F. Aryasetiawan, and A. I. Lichtenstein, First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA + U method, J. Phys.: Condens. Matter9, 767 (1997)

    work page 1997

  63. [63]

    I. L. M. Locht, Y. O. Kvashnin, D. C. M. Rodrigues, M. Pereiro, A. Bergman, L. Bergqvist, A. I. Lichtenstein, M. I. Katsnelson, A. Delin, A. B. Klautau, B. Johansson, I. Di Marco, and O. Eriksson, Standard model of the rare earths analyzed from the Hubbard I approximation, Phys. Rev. B94, 085137 (2016)

    work page 2016

  64. [64]

    J. F. Herbst, R. E. Watson, and J. W. Wilkins, Relativis- tic calculations of 4fexcitation energies in the rare-earth metals: Further results, Phys. Rev. B17, 3089 (1978)

    work page 1978

  65. [65]

    J. F. Landaeta, A. M. Le´ on, S. Zwickel, T. L¨ uhmann, M. Brando, C. Geibel, E.-O. Eljaouhari, H. Rosner, G. Zwicknagl, E. Hassinger, and S. Khim, Conventional 16 type-II superconductivity in locally noncentrosymmet- ric LaRh2As2 single crystals, Phys. Rev. B106, 014506 (2022)

    work page 2022

  66. [66]

    Otsuki, K

    J. Otsuki, K. Yoshimi, H. Shinaoka, and Y. Nomura, Strong-coupling formula for momentum-dependent sus- ceptibilities in dynamical mean-field theory, Phys. Rev. B99, 165134 (2019)

    work page 2019

  67. [67]

    Otsuki, K

    J. Otsuki, K. Yoshimi, H. Shinaoka, and H. O. Jeschke, Multipolar ordering from dynamical mean field theory with application to CeB 6, Phys. Rev. B110, 035104 (2024)

    work page 2024

  68. [68]

    Itokazu, A

    S. Itokazu, A. Kirikoshi, H. O. Jeschke, and J. Otsuki, From localized 4felectrons to anisotropic exchange in- teractions in ferromagnetic CeRh6Ge4, Commun. Mater. 6, 269 (2025)

    work page 2025

  69. [69]

    L. V. Pourovskii, Two-site fluctuations and multipolar intersite exchange interactions in strongly correlated sys- tems, Phys. Rev. B94, 115117 (2016)

    work page 2016

  70. [70]

    L. V. Pourovskii and S. Khmelevskyi, Quadrupolar su- perexchange interactions, multipolar order, and magnetic phase transition in UO2, Phys. Rev. B99, 094439 (2019)

    work page 2019

  71. [71]

    Kusunose, R

    H. Kusunose, R. Oiwa, and S. Hayami, Symmetry- adapted modeling for molecules and crystals, Phys. Rev. B107, 195118 (2023)

    work page 2023

  72. [72]

    Hayami and H

    S. Hayami and H. Kusunose, Unified description of elec- tronic orderings and cross correlations by complete multi- pole representation, J. Phys. Soc. Jpn.93, 072001 (2024)

    work page 2024

  73. [73]

    T. Inui, Y. Tanabe, and Y. Onodera,Group Theory and Its Applications in Physics, Springer Series in Solid-State Sciences (Springer Berlin Heidelberg, 2012)

    work page 2012

  74. [74]

    L. D. Landau and E. M. Lifshitz,Statistical Physics, 3rd ed. (Butterworth-Heinemann, Oxford, England, 1996)

    work page 1996

  75. [75]

    Shiba, O

    H. Shiba, O. Sakai, and R. Shiina, Nature of Ce-Ce inter- action in CeB 6 and its consequences, J. Phys. Soc. Jpn. 68, 1988 (1999)

    work page 1988

  76. [76]

    Yamada and K

    T. Yamada and K. Hanzawa, Derivation of RKKY inter- action between multipole moments in CeB 6 by the effec- tive wannier model based on the bandstructure calcula- tion, J. Phys. Soc. Jpn.88, 084703 (2019)

    work page 2019

  77. [77]

    J. M. Perez-Mato, S. V. Gallego, E. S. Tasci, L. Elcoro, G. de la Flor, and M. I. Aroyo, Symmetry-based compu- tational tools for magnetic crystallography, Annu. Rev. of Mater. Res.45, 217 (2015)

    work page 2015

  78. [78]

    D. B. Litvin,Magnetic Group Tables: 1-, 2- and 3- dimensional magnetic subperiodic groups and magnetic space groups(International Union of Crystallography, Chester, England, 2013)

    work page 2013

  79. [79]

    Yatsushiro, H

    M. Yatsushiro, H. Kusunose, and S. Hayami, Multipole classification in 122 magnetic point groups for unified un- derstanding of multiferroic responses and transport phe- nomena, Phys. Rev. B104, 054412 (2021)

    work page 2021