Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Spin Hall effect in 3d ferromagnetic metals for field-free switching of perpendicular magnetization: A first-principles investigation

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper argues that ferromagnetic metals can replace heavy metals as spin current sources for spin-orbit torque switching, with an out-of-plane spin polarization that removes the need for an external magnetic field.

desk verdict A solid, useful first-principles study of spin Hall effects in 3d ferromagnets, with a big MnAl(101) prediction that rests on a bulk tensor rotation and an idealized interface; worth serious refereeing but the device-level claims need toning down. read the letter →

arxiv 2501.00737 v1 pith:JXTILJ7B submitted 2025-01-01 cond-mat.mtrl-sci

Fanxing Zheng , Jianting Dong , Yizhuo Song , Meng Zhu , Xinlu Li , Jia Zhang This is my paper · ORCID
classification cond-mat.mtrl-sci PACS 72.25.Ba75.76.+j
keywords spinHalleffectspin-orbittorquefield-freeswitchingperpendicularmagnetizationL10-MnAlferromagneticmetalsfirst-principlestransportKubo-Bastinformalism
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

The paper tries to establish that ferromagnetic metals can replace heavy metals as spin current sources for spin-orbit torque switching of perpendicular magnetization. It computes two mechanisms from first principles: the spin-orbit-coupling-driven spin Hall effect in Fe, Co, Ni, and their alloys, which yields spin Hall conductivities around $1000\,(\hbar/2e)(\Omega\,\text{cm})^{-1}$ at room temperature but small spin Hall angles of 0.01–0.02, and a non-relativistic spin Hall effect in L10-MnAl(101) that reaches conductivities of order $10^4$ with a spin Hall angle near 0.25. The reason this matters is that the out-of-plane spin polarization produced by a ferromagnetic source breaks the mirror symmetry that forces heavy-metal devices to require an external in-plane field, so perpendicular magnetization can be switched deterministically with no applied field. The authors demonstrate such switching by solving the Landau–Lifshitz–Gilbert equation with the calculated torques, identifying L10-MnAl(101) as the most energy-efficient of the studied sources.

What carries the argument

The load-bearing object is the third-rank spin conductivity tensor $\sigma^s_{\mu\nu}$ together with its symmetry constraints. For cubic ferromagnets the argument splits the tensor into time-reversal odd (Todd) and time-reversal even (Teven) parts and derives scaling laws, $\sigma^z_{zx} \propto M(T)\sigma_{xx}$ and $\sigma^y_{zx} \propto \sigma_{xx}^2$, that connect the magnetic spin Hall effect to magnetization and disorder. For MnAl the mechanism is a tensor rotation: the (001) plane's longitudinal anisotropic spin conductivity, which is nonzero even without spin-orbit coupling, is rotated to the (101) plane through Eqs. (2)–(4), turning the anisotropy $\tilde{\sigma}^z_{zz} - \tilde{\sigma}^z_{xx}$ into off-diagonal spin Hall terms proportional to $\sin\phi\cos\phi$. The paper then feeds the resulting conductivities into the Landau–Lifshitz–Gilbert equation with a damping-like torque that contains an out-of-plane spin component, and solves for the magnetization dynamics to demonstrate switching.

What would settle it

A spin-torque ferromagnetic resonance or harmonic Hall measurement on an epitaxial L10-MnAl(101) bilayer: if the measured damping-like SOT efficiency comes out far below 0.25, or if the torque does not follow the predicted $\sin\phi\cos\phi$ variation across MnAl films grown on different plane orientations, the bulk-rotation picture is wrong. A slab-geometry first-principles transport calculation that includes surface states and interface disorder would give the same verdict.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that ferromagnets produce usable out-of-plane (Sz) spin currents by two routes. In cubic 3d metals, magnetization parallel to the current breaks the mirror planes and generates a magnetic, spin-orbit-driven spin Hall component $\sigma^z_{zx}$ of order $1000\,(\hbar/2e)(\Omega\,\text{cm})^{-1}$ at 300 K, scaling linearly with magnetization and longitudinal conductivity, yet the accompanying spin Hall angle is only about 0.01–0.02 because of the high longitudinal conductance. In tetragonal L10-MnAl, the longitudinal spin conductivity is strongly anisotropic, with $\tilde{\sigma}^z_{zz} \approx 1.2\times10^5$ versus $\tilde{\sigma}^z_{xx} \approx 3.3\times10^4\,(\hbar/2e)(\Omega\,\text{cm})^{-1}$, and rotating the crystal plane from (001) to (101) converts this anisotropy into off-diagonal spin Hall conductivities of about $3\times10^4$ with a spin Hall angle near 0.25 that persists up to 400 K. With these values, the LLG equation gives deterministic, field-free switching of perpendicular magnetization, with L10-MnAl(101) requiring the lowest switching current density and threshold power density among the materials compared.

Load-bearing premise

Everything hinges on the assumption that the bulk MnAl(001) conductivity tensor, rotated to the (101) plane, describes what a real thin-film device does, together with a perfectly transparent interface in the switching analysis; if surface states, quantum confinement, or interface scattering alter the transport anisotropy or reduce spin transmission, the 0.25 spin Hall angle and the switching efficiency will drop.

Editorial extensions

If this is right

  • Fe, Co, Ni, and their FexCo1−x and NixFe1−x alloys can switch perpendicular magnetization without an external field, at switching current densities near $10^8\,\text{A}/\text{cm}^2$, comparable to conventional heavy-metal systems but without the field requirement.
  • L10-MnAl(101), with a spin Hall angle near 0.25, brings the switching current down to the order of $10^7\,\text{A}/\text{cm}^2$ and shows the lowest threshold power density among the studied sources, placing it ahead of the antiferromagnet and alloy references.
  • The MnAl spin Hall angle stays close to 0.25 from low temperature up to 400 K, so the non-relativistic mechanism is not degraded by thermal disorder the way the spin-orbit-driven angles are.
  • Heavy-element ferromagnets such as Fe50Pt50 sit between the two extremes, with a spin Hall angle of about 0.1 and a low power density, suggesting alloying 3d magnets with 5d elements as a tuning knob.
  • The linear and quadratic scaling laws for the Todd and Teven spin Hall conductivities give a predictive rule for how these torques behave with temperature and composition across alloy families.

Reading between the lines

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

  • The $\sin\phi\cos\phi$ rotation law of Eq. (4) is a design rule the paper applies only to the (101) plane: the same recipe should work for any ferromagnet with strong longitudinal spin-conductivity anisotropy, so screening tetragonal magnets such as the Mn-Ga, Fe-Pt, and Mn-Bi families for large $\tilde{\sigma}^z_{zz} - \tilde{\sigma}^z_{xx}$ could reveal materials with comparable or larger effect
  • The 0.25 spin Hall angle assumes perfect interface transparency, so real MnAl(101)/ferromagnet stacks will lose efficiency to interface spin-mixing conductance and disorder; the paper's number is an upper bound to test against, not a device guarantee.
  • An explicit experimental probe of the mechanism is the growth-angle dependence: measuring the SOT efficiency on MnAl films cut at several vicinal angles should follow $\sin\phi\cos\phi$, which would separate the non-relativistic contribution from conventional spin-orbit-driven torque.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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. The paper reports first-principles KKR-GF calculations of the spin Hall effect in 3d ferromagnetic metals and alloys (Fe, Co, Ni, FeCo, NiFe) and in L10-MnAl. For Fe, Co, Ni and their alloys, the authors compute SOC-driven spin Hall conductivities with out-of-plane spin polarization on the order of 1000 (ℏ/2e)(Ω cm)^−1 and spin Hall angles of 0.01–0.02 at room temperature. For L10-MnAl, they argue that a non-relativistic spin Hall effect arises from anisotropic longitudinal spin conductivity; by rotating the bulk (001) spin conductivity tensor to the (101) orientation, they predict spin Hall conductivities around 3×10^4 (ℏ/2e)(Ω cm)^−1 and a spin Hall angle around 0.25 at 300 K. An LLG model is used to show that these ferromagnetic spin sources can switch perpendicular magnetization field-free, with MnAl(101) giving the lowest switching current density and power density.

Significance. If the results hold, the paper provides a systematic first-principles benchmark of spin Hall properties in 3d ferromagnets and identifies a promising non-relativistic spin Hall mechanism in anisotropic ferromagnets for field-free SOT switching. The computational setup (KKR-GF, Kubo-Bastin, CPA, dense k-meshes) is standard and the calculated resistivities agree well with experimental values, lending credibility to the transport calculations for Fe, Co, Ni, and their alloys. The identification of two distinct spin Hall mechanisms and the explicit symmetry analysis are useful contributions. However, the central quantitative claim for L10-MnAl(101) rests on a bulk tensor rotation and an idealized LLG switching model; these assumptions are not validated against thin-film or interface effects.

major comments (3)
  1. [Section C, Eqs. (2)–(4) and Fig. 5] The giant non-relativistic spin Hall conductivities for MnAl(101) are obtained by rotating the bulk (001) spin conductivity tensor using Eqs. (2)–(4). This assumes that the bulk longitudinal spin conductivities σ_xx^z and σ_zz^z remain unchanged in a thin-film (101) geometry, which neglects quantum confinement, surface states, and interface-induced symmetry lowering. Since the predicted spin Hall angle θ≈0.25 and the associated switching efficiency directly scale with the anisotropy σ_xx^z − σ_zz^z, the device-level claims are not yet supported. The authors should either perform thin-film or supercell transport calculations that include the (101) surface, or clearly restate the result as a bulk-rotation estimate and temper the switching-efficiency conclusions accordingly.
  2. [Section D, Jsw formula and Fig. 6] The switching current density is evaluated as Jsw = (2e/ℏ)τ_DL/(t_z θ_D), using bulk spin Hall angles and implicitly assuming perfect interface transparency and zero spin memory loss. For a ferromagnetic spin source in contact with a second ferromagnetic layer, interfacial spin-dependent reflection, spin memory loss, and the reduced effective spin current transmitted into the free layer can substantially increase the required current density. The quantitative Jsw and power-density comparisons in Fig. 6(e) are therefore optimistic upper bounds. The authors should state this limitation explicitly and, if possible, incorporate interface parameters or compare with experimental SOT efficiencies in similar ferromagnetic bilayers.
  3. [Section B, Fig. 3 and accompanying text] The scaling relations σ_zx^z ∝ M(T)σ_xx and σ_zx^y ∝ a σ_xx^2 are described as "universal" for ferromagnetic materials, but they are presented as empirical fits to the present calculations without a derivation. If this universality is intended to support predictions for other materials, the authors should provide a more formal argument (e.g., based on the Boltzmann equation or the skew-scattering side-jump decomposition) or soften the claim to an observed trend within the studied alloy set.
minor comments (5)
  1. [Abstract and main text] The spin Hall angle for MnAl(101) is quoted as "around 0.25" in the abstract and Section D, but the values θ_x=0.25 and θ_z=0.19 in Fig. 5(d) imply a magnitude θ_D=sqrt(0.25^2+0.19^2)≈0.31. The inconsistency should be resolved.
  2. [Equation (2)] The rotation matrix in Eq. (2) is garbled in the manuscript text; it should be typeset clearly so that the transformation R and the sign conventions in Eq. (4) can be verified.
  3. [Table I] The tensor entries in Table I are difficult to parse because of formatting, particularly the distinction between Todd and Teven components. A cleaner presentation with explicit 3×3 matrices would improve readability.
  4. [Section D] The LLG equation (5) is written with a torque term (m×s) for the field-like torque and (m×(m×s)) for the damping-like torque, but the derivation of the effective field B_M from K_eff is stated without the standard factor of 2; please check the convention against the cited literature.
  5. [Introduction] The acronym "ABSTRCT" appears in the abstract; this typo should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: spin Hall conductivities are computed ab initio and the MnAl(101) result follows from an explicit tensor transformation of independently calculated longitudinal spin conductivities.

full rationale

The central quantities are computed ab initio: the SOC-driven spin Hall conductivities of Fe, Co, Ni and alloys come from KKR-based Kubo-Bastin transport calculations, benchmarked against experimental resistivities and magnetic moments; they are not fitted to the target spin Hall values. The MnAl non-relativistic spin Hall conductivity is obtained by applying the tensor transformation in Eqs. (2)–(4) to the independently computed longitudinal spin conductivities σ^z_xx and σ^z_zz; this is a symmetry-imposed algebraic consequence, not a restatement of the input, and the large off-diagonal values follow from the calculated anisotropy of the longitudinal spin conductivities. The LLG switching analysis uses literature parameters for CoFeB and the computed spin Hall angles to solve Eq. (5); the switching current density and power density are derived outputs, not fitted inputs. The scaling relations in Fig. 3 are fits to the calculated outputs, not inputs to the calculation. Self-citations [24,45] are used only for comparison values (Fe50Pt50, Mn3Pt/Mn3Ir) and do not carry a load-bearing premise. No step reduces a prediction to its own inputs by construction.

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

No free parameters were fitted to obtain the reported spin Hall conductivities; the main numerical values come from first-principles Kubo-Bastin calculations. The LLG switching current density uses CoFeB parameters from the literature (alpha=0.02, Keff=1e6 erg/cm3, Ms=800 emu/cm3, tz=1 nm), which are inputs, not fitted. The main assumptions concern DFT/CPA accuracy, the tensor rotation for MnAl(101), and ideal interface transparency in the LLG model.

assumptions (6)
  • domain assumption Multiple-scattering KKR-GF with lmax=3 and Kubo-Bastin linear response gives quantitatively reliable spin Hall conductivities.
    Computational Method section; lmax truncation and 10^7 k-points are assumed converged, but no convergence tests are reported.
  • domain assumption CPA with temperature-dependent disorder from experimental M(T) captures phonon and spin disorder scattering.
    Used for resistivity and spin Hall conductivity temperature dependence; validated only by resistivity comparison for Fe.
  • domain assumption LDA/PBE exchange-correlation is accurate for 3d transition metals and MnAl.
    Standard for these systems, but no beyond-DFT checks are provided.
  • standard math The spin conductivity transforms as a third-rank tensor under coordinate rotation in the non-relativistic limit.
    Used in Eq. (3) to rotate MnAl(001) results to the (101) plane; valid for nonrelativistic spin current.
  • domain assumption LLG with damping-like torque, no field-like torque, and perfect interface transparency models the SOT switching device.
    Section D; interface quality and spin-mixing conductance are not modeled.
  • domain assumption Bulk infinite-crystal conductivity applies to a MnAl(101) thin film.
    Used to evaluate the (101) plane; ignores surface states and quantum confinement.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Spin Hall effect in 3d ferromagnetic metals for field-free switching of perpendicular magnetization: A first-principles investigation." pith.science (2026). https://pith.science/paper/JXTILJ7B

@misc{pith2026250100737,
  author       = {Pith},
  title        = {Pith review of: Spin Hall effect in 3d ferromagnetic metals for field-free switching of perpendicular magnetization: A first-principles investigation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JXTILJ7B}},
  note         = {Machine review of arXiv:2501.00737}
}
read the original abstract

Ferromagnetic metals, with the potential to generate spin current with unconventional spin polarization via the spin Hall effect, offer promising opportunities for field-free switching of perpendicular magnetization and for the spin-orbit torque devices. In this study, we investigate two distinct spin Hall mechanisms in 3d ferromagnetic metals including spin-orbit coupling driven spin Hall effect in Fe, Co, Ni and their alloys, and non-relativistic spin Hall effect arising from anisotropic spin-polarized transport by taking L10-MnAl as an example. By employing first-principles calculations, we examine the temperature and alloy composition dependence of spin Hall conductivity in Fe, Co, Ni and their alloys. Our results reveal that the spin Hall conductivities with out-of-plane spin polarization in 3d ferromagnetic metals are at the order of 1000 \frac{\hbar}{2e} \left( \Omega \, \text{cm} \right)^{-1} at 300 K, but with a relatively low spin Hall angles around 0.01~0.02 due to the large longitudinal conductivity. For L10-MnAl(101), the non-relativistic spin Hall conductivity can reach up to 10000\frac{\hbar}{2e} \left( \Omega \, \text{cm} \right)^{-1}, with a giant spin Hall angle around 0.25 at room temperature. By analyzing the magnetization switching process, we demonstrate deterministic switching of perpendicular magnetization without an external magnetic field by using 3d ferromagnetic metals as spin current sources. Our work may provide an unambiguous understanding on spin Hall effect in ferromagnetic metals and pave the way for their potential applications in related spintronic devices.

Figures

Figures reproduced from arXiv: 2501.00737 by the authors.

Figure 1
Figure 1. FIG. 1. Illustration of typical symmetry and spin current generated by spin Hall effect in [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The calculated temperature dependent (a) longitudinal resistivity ρ [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The calculated spin Hall conductivity [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The calculated composition dependent (a) spin Hall conductivity [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Atomic structure of MnAl(001) and the Cartersian coordinated system. The colored [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Spin current symmetries generated by GdFeCo ferrimagnet across its magnetisation compensation temperature

    cond-mat.mes-hall 2025-11 conditional novelty 6.0 of 10

    GdFeCo's spin Hall and spin anomalous Hall torques retain their signs through the magnetization compensation temperature, with opposite signs and distinct proposed sublattice origins.

Reference graph

Works this paper leans on

55 extracted references · 49 canonical work pages · cited by 1 Pith paper

  1. [1]

    S. A. Wolf, D. D. Awschalom, R. A. Buhrman et al., Science 294,1488 (2001)

    work page 2001

  2. [2]

    Žutić, J

    I. Žutić, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004)

    2004

  3. [3]

    Manchon, H

    A. Manchon, H. C. Koo, J. Nitta, S. M. Frolov and R. A. Duine, Nat. Mater. 14, 871 (2015)

    work page 2015

  4. [4]

    A. V . Larionov and L. E. Golub, Phys. Rev. B 78, 033302 (2008)

    work page 2008

  5. [5]

    X. Qian, J. Liu, L. Fu, and J. Li, Science 346, 1344 (2014)

    2014

  6. [6]

    Sinova, S

    J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, Rev. Mod. Phys. 87, 1213 (2015)

    2015

  7. [7]

    Lee and K.-J

    S.-W. Lee and K.-J. Lee, Proc. IEEE 104, 1831 (2016)

    work page 2016

  8. [8]

    K. Ando, S. Takahashi, K. Harii, K. Sasage, J. Ieda, S. Maekawa, and E. Saitoh, Phys. Rev. Lett. 101, 036601 (2008)

    work page 2008

Show all 55 references
  1. [9]

    L. Liu, O. -J. Lee, T. J. Gudmundsen, D. C. Ralph, and R. A. Buhrman, Phys. Rev. Lett. 109, 096602 (2012)

    2012

  2. [10]

    Liu, C.-F

    L. Liu, C.-F. Pai, Y . Li, H. W. Tseng, D. C. Ralph, and R. A. Buhrman, Science 336, 555 (2012)

    2012

  3. [11]

    Prenat, K

    G. Prenat, K. Jabeur, P. Vanhauwaert, et al., IEEE Trans. Multi-Scale Comput. Syst. 2, 49 (2016)

    2016

  4. [12]

    Manchon, J

    A. Manchon, J. Železný, I. M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello, and P. Gambardella, Rev. Mod. Phys. 91, 035004 (2019)

    2019

  5. [13]

    X. Han, X. Wang, C. Wan, G. Yu, and X. Lv, Appl. Phys. Lett. 118, 120502 (2021)

    2021

  6. [14]

    Q. Shao, P. Li, L. Liu, et al., IEEE Trans. Magn. 57, 1 (2021)

    2021

  7. [15]

    B. F. Miao, S. Y . Huang, D. Qu, and C. L. Chien, Phys. Rev. Lett. 111, 066602 (2013)

    2013

  8. [16]

    Nagaosa, J

    N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Rev. Mod. Phys. 82, 1539 (2010)

    2010

  9. [17]

    Taniguchi, J

    T. Taniguchi, J. Grollier, and M. D. Stiles, Phys. Rev. Appl. 3, 044001 (2015)

    2015

  10. [18]

    Iihama, T

    S. Iihama, T. Taniguchi, K. Yakushiji, A. Fukushima, Y . Shiota, S. Tsunegi, R. Hiramatsu, S. Yuasa, Y . Suzuki, and H. Kubota, Nat. Electron. 1, 120 (2018)

    2018

  11. [19]

    J. D. Gibbons, D. MacNeill, R. A. Buhrman, and D. C. Ralph, Phys. Rev. Appl. 9, 064033 (2018)

    2018

  12. [20]

    T. Seki, S. Iihama, T. Taniguchi, and K. Takanashi, Phys. Rev. B 100, 144427 (2019)

    2019

  13. [21]

    S. C. Baek, V . P. Amin, Y . Oh, G. Go, S.-J. Lee, M. D. Stiles, B.-G. Park, and K.- J. Lee, Nat. Mater. 17, 509 (2018)

    2018

  14. [22]

    H. Wu, S. A. Razavi, Q. Shao, X. Li, K. L. Wong, Y . Liu, G. Yin, and K. L. Wang, Phys. Rev. B 99, 184403 (2019)

    2019

  15. [23]

    T. Y . Ma, C. H. Wan, X. Wang, W. L. Yang, C. Y . Guo, C. Fang, M. K. Zhao, J. Dong, Y . Zhang, and X. F. Han, Phys. Rev. B 101, 134417 (2020)

    2020

  16. [24]

    Zheng, M

    F. Zheng, M. Zhu, J. Dong, X. Li, Y . Zhou, K. Wu, and J. Zhang, Phys. Rev. B 109, 224401 (2024)

    2024

  17. [25]

    A. Mook, R. R. Neumann, A. Johansson, J. Henk, and I. Mertig, Phys. Rev. Res. 2, 023065 (2020)

    2020

  18. [26]

    Salemi and P

    L. Salemi and P. M. Oppeneer, Phys. Rev. B 106, 024410 (2022)

    2022

  19. [27]

    Kimata, H

    M. Kimata, H. Chen, K. Kondou, S. Sugimoto, P. K. Muduli, M. Ikhlas, Y . Omori, T. Tomita, A. H. MacDonald, S. Nakatsuji, and Y . Otani, Nature 565, 627 (2019)

    2019

  20. [28]

    M. Yang, L. Sun, Y . Zeng, et al., Nat. Commun. 15, 3201 (2024)

    2024

  21. [29]

    K. D. Belashchenko, Phys. Rev. B 109, 54409 (2024)

    2024

  22. [30]

    Ebert, D

    H. Ebert, D. Ködderitzsch, and J. Minár, Rep. Prog. Phys. 74, 096501 (2011)

    2011

  23. [31]

    Ebert et al., The Munich SPR-KKR Package, version 8.6, http://olymp.cup.uni- muenchen.de/ak/ebert/sprkkr (2017)

    H. Ebert et al., The Munich SPR-KKR Package, version 8.6, http://olymp.cup.uni- muenchen.de/ak/ebert/sprkkr (2017)

    2017

  24. [32]

    S. H. V osko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980)

    1980

  25. [33]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

    1996

  26. [34]

    Ködderitzsch, K

    D. Ködderitzsch, K. Chadova, and H. Ebert, Phys. Rev. B 92, 184415 (2015)

    2015

  27. [35]

    Chadova, S

    K. Chadova, S. Mankovsky, J. Minár, and H. Ebert, Phys. Rev. B 95, 125109 (2017)

    2017

  28. [36]

    J. S. Faulkner and G. M. Stocks, Phys. Rev. B 21, 3222 (1980)

    1980

  29. [37]

    Ebert, S

    H. Ebert, S. Mankovsky, K. Chadova, S. Polesya, J. Minár, and D. Ködderitzsch, Phys. Rev. B 91, 165132 (2015)

    2015

  30. [38]

    Ködderitzsch, K

    D. Ködderitzsch, K. Chadova, J. Minár, and H. Ebert, New J. Phys. 15, 053009 (2013)

    2013

  31. [39]

    M. D. Kuz’ min, Phys. Rev. Lett. 94, 107204 (2005)

    2005

  32. [40]

    R. S. Sundar and S. C. Deevi, Int. Mater. Rev. 50, 157 (2005)

    2005

  33. [41]

    Yousuf, P

    M. Yousuf, P. Ch. Sahu, and K. G. Rajan, Phys. Rev. B 34, 8086 (1986)

    1986

  34. [42]

    Chadova, D

    K. Chadova, D. Ködderitzsch, J. Minár, H. Ebert, J. Kiss, S. W. D’Souza, L. Wollmann, C. Felser, and S. Chadov, Phys. Rev. B 93, 195102 (2016)

    2016

  35. [43]

    L. A. Hall, Survey of Electrical Resistivity Measurements on 16 Pure Metals in the Temperature Range 0 to 273 K, National Bureau of Standards, 1968

    1968

  36. [44]

    F. Wang, G. Shi, K.-W. Kim, et al., Nat. Mater. 23, 768 (2024)

    2024

  37. [45]

    M. Zhu, X. Li, F. Zheng, J. Dong, Y . Zhou, K. Wu, and J. Zhang, Phys. Rev. B 110, 54420 (2024)

    2024

  38. [46]

    Y . Pu, G. Shi, Q. Yang, D. Yang, F. Wang, C. Zhang, and H. Yang, Adv. Funct. Mater. 34, 2400143 (2024)

    2024

  39. [47]

    A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, APL Mater. 1, (2013)

    2013

  40. [48]

    Iihama, S

    S. Iihama, S. Mizukami, H. Naganuma, M. Oogane, Y . Ando, and T. Miyazaki, Phys. Rev. B 89, 174416 (2014)

    2014

  41. [49]

    Miron, K

    I. Miron, K. Garello, G. Gauydin, et al., Nature 476, 189 (2011)

    2011

  42. [50]

    Garello, I

    K. Garello, I. M. Miron, C. O. Avci, F. Freimuth, Y . Mokrousov, S. Blügel, S. Auffret, O. Boulle, G. Gaudin, and P. Gambardella, Nat. Nanotechnol. 8, 587 (2013)

    2013

  43. [51]

    C. Avci, K. Garello, A. Ghosh, et al., Nature Phys 11, 570 (2015)

    2015

  44. [52]

    Taslimi, M

    H. Taslimi, M. Heydarzadeh Sohi, S. Mehrizi, and M. Saremi, J. Mater. Sci. Mater. Electron. 26, 2962 (2015)

    2015

  45. [53]

    G. D. Samolyuk, S. Mu, A. F. May, B. C. Sales, S. Wimmer, S. Mankovsky, H. Ebert, and G. M. Stocks, Phys. Rev. B 98, 165141 (2018)

    2018

  46. [54]

    Dumpich, E

    G. Dumpich, E. F. Wassermann, V . Manns, W. Keune, S. Murayama, and Y . Miyako, J. Magn. Magn. Mater. 67, 55 (1987)

    1987

  47. [55]

    C. Jo, J. I. Lee, and Y . Jang, Chem. Mater. 17, 2667 (2005)

    2005

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.