Pair anisotropy in disordered magnetic systems

D. Sztenkiel; K. Das; K. Gas; M. Sawicki; N. Gonzalez Szwacki; R. Hayn

arxiv: 2410.22035 · v3 · pith:MHBC36W4new · submitted 2024-10-29 · ❄️ cond-mat.mtrl-sci

Pair anisotropy in disordered magnetic systems

K. Das , N. Gonzalez Szwacki , K. Gas , M. Sawicki , R. Hayn , D. Sztenkiel This is my paper

Pith reviewed 2026-05-23 18:45 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci

keywords pair anisotropydilute magnetic semiconductorGaMnNsingle-ion anisotropyatomistic spin simulationsmagnetization curvesdensity functional theory

0 comments

The pith

Pair anisotropy from nearest-neighbor magnetic ions improves magnetization curve predictions in dilute ferromagnets.

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

In disordered systems such as dilute magnetic semiconductors, magnetic ions form pairs with significant probability. These pairs break the local symmetry that isolated ions would have, inducing an extra uniaxial anisotropy. The paper calculates the strength of this pair anisotropy using density functional theory for Ga_{1-x}Mn_xN. Atomistic spin simulations that add the pair term reproduce experimental magnetization curves far more closely than simulations limited to single-ion anisotropy alone.

Core claim

The inclusion of pair-induced uniaxial anisotropy, derived from density functional theory calculations, in atomistic spin simulations significantly improves the agreement between simulated and experimental magnetization curves in Ga_{1-x}Mn_xN, in contrast to models that consider only single-ion anisotropy.

What carries the argument

Pair-induced uniaxial anisotropy: the additional anisotropic energy term that arises because nearby magnetic ions influence each other's directional preferences.

If this is right

Models of random dilute ferromagnets and alloys must incorporate pair and higher-order cluster effects to reach experimental accuracy.
The same pair-anisotropy treatment can be applied to other materials where nearest-neighbor magnetic ions occur with high probability.
Predictions of field-dependent magnetization in functional disordered magnets become more reliable once pair terms are included.

Where Pith is reading between the lines

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

The method suggests that similar pair effects could matter in other disordered magnetic systems such as spin glasses or metallic alloys.
Extending the approach to triple or larger clusters might produce further gains in simulation fidelity.
The pair anisotropy could also affect related quantities such as magnetic switching fields or anisotropy energy barriers.

Load-bearing premise

That the DFT-derived pair anisotropy parameters are the dominant missing ingredient responsible for the improved experimental agreement, rather than other unmodeled effects or fitting choices in the spin simulations.

What would settle it

Magnetization curves measured or simulated for Ga_{1-x}Mn_xN that continue to deviate from experiment by the same margin even after the pair anisotropy term is added.

Figures

Figures reproduced from arXiv: 2410.22035 by D. Sztenkiel, K. Das, K. Gas, M. Sawicki, N. Gonzalez Szwacki, R. Hayn.

**Figure 2.** Figure 2: FIG. 2: Partial density of state (PDOS) of Mn ion and [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Investigated pairs of Mn ions. (a) In GaN an isolated Mn impurity is surrounded by 12 nearest neighbor Ga [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: The magnetocrystalline energy of the supercell [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Partial density of state (PDOS) of Mn and [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6: The magnetocrystalline energy of the supercell [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7: The magnetocrystalline energy of the supercell [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗

read the original abstract

Accurate modelling of magnetism is pivotal for elucidating the microscopic origins of magnetic phenomena in functional materials. However, for a specified class of materials, such as random dilute ferromagnets or alloys, the reliance on simplifying assumptions, such as single-ion anisotropy, limits the accuracy of existing spin models. In such systems, there is a significant probability of the formation of nearest-neighbor magnetic ion pairs or higher order clusters, whose presence breaks the local symmetry of otherwise isolated magnetic species. Here, we introduce the concept of pair-induced uniaxial anisotropy and demonstrate how nearby atoms influence each other's anisotropic behavior. This effect is investigated in the dilute magnetic semiconductor Ga$_{1-x}$Mn$_x$N, by means of density functional theory calculations. The inclusion of pair anisotropy in the atomistic spin simulations significantly improves the agreement between simulated and experimental magnetization curves, in contrast to models that consider only single-ion anisotropy.

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.

Desk Editor's Note private letter to a colleague

The paper computes DFT pair anisotropy for Mn nearest neighbors in GaMnN and adds it to spin simulations, claiming better magnetization agreement than single-ion models alone, but the simulations must hold all other parameters fixed for that claim to stick.

read the letter

The new element is the explicit calculation of uniaxial anisotropy arising from Mn-Mn pairs in the dilute limit. They use DFT to get those constants for Ga1-xMnxN and insert them into atomistic simulations, showing closer match to measured magnetization curves than the standard single-ion anisotropy treatment. That is a concrete step beyond the usual models that treat magnetic ions as isolated. The DFT route for the pair terms is a plus; it avoids pure fitting and gives a physical origin tied to local symmetry breaking by neighbors. Credit for doing the calculations and running the simulations on a real material system. The soft spot is exactly the isolation the stress-test flags. The abstract states that adding the pair terms improves agreement, but it does not confirm that exchange parameters, single-ion strengths, disorder realizations, or temperature scaling stayed identical between the two runs. If any of those were retuned when the pair terms went in, the improvement cannot be attributed cleanly to the new anisotropy. Minor if the paper already shows the fixed-parameter comparison; load-bearing if it does not. The work is aimed at people modeling random dilute magnets and spintronics materials where cluster effects matter. It is narrow but grounded enough in DFT and simulation to warrant referee time rather than desk rejection. I would send it for review with a request to document the exact Hamiltonian parameters in both model versions and to show the raw curves with error measures.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces the concept of pair-induced uniaxial anisotropy arising from nearest-neighbor magnetic ion pairs in disordered systems such as the dilute magnetic semiconductor Ga_{1-x}Mn_xN. Using DFT calculations, the authors derive these pair anisotropy parameters and incorporate them into atomistic spin simulations, claiming that this yields significantly improved agreement with experimental magnetization curves relative to conventional models that include only single-ion anisotropy.

Significance. If the central claim holds after isolating the effect of the pair terms, the work would strengthen the microscopic modeling of anisotropy in random dilute ferromagnets by explicitly capturing local symmetry breaking from ion clusters. The use of first-principles DFT to obtain the pair constants, rather than purely phenomenological fitting, is a positive feature that could improve transferability of the approach to other alloy systems.

major comments (2)

[atomistic spin simulations section] The manuscript must demonstrate that the only difference between the single-ion and pair-anisotropy spin simulations is the addition of the DFT-derived pair terms, with all other Hamiltonian parameters (exchange J_{ij}, single-ion K values, disorder realizations, and temperature scaling) held strictly fixed. The abstract does not establish this isolation; if additional fitting freedom was permitted in the pair model, the reported improvement cannot be attributed specifically to pair anisotropy rather than increased model flexibility. This is load-bearing for the central claim.
[results on magnetization curves] The quantitative improvement in magnetization curves should be supported by explicit metrics (e.g., RMS deviation, R² values, or error bars) comparing the two models to the same experimental data set, together with a clear statement of the exclusion criteria used for data points or temperature ranges. Without these, the degree to which the data support the claim remains unclear.

minor comments (2)

[DFT calculations] Clarify the notation for the pair anisotropy constants (e.g., whether they are defined per pair or per volume) and ensure consistent use of symbols between the DFT section and the spin Hamiltonian.
[figures] The abstract states the improvement occurs 'in contrast to models that consider only single-ion anisotropy'; the corresponding figure or table should explicitly label both curves and the experimental reference for direct visual comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and will revise the manuscript accordingly to strengthen the presentation of our methodology and results.

read point-by-point responses

Referee: [atomistic spin simulations section] The manuscript must demonstrate that the only difference between the single-ion and pair-anisotropy spin simulations is the addition of the DFT-derived pair terms, with all other Hamiltonian parameters (exchange J_{ij}, single-ion K values, disorder realizations, and temperature scaling) held strictly fixed. The abstract does not establish this isolation; if additional fitting freedom was permitted in the pair model, the reported improvement cannot be attributed specifically to pair anisotropy rather than increased model flexibility. This is load-bearing for the central claim.

Authors: We agree that explicit isolation of the pair-anisotropy contribution is essential to support the central claim. The simulations were performed with all other parameters (J_{ij}, single-ion K, disorder realizations, and temperature scaling) held fixed, but the manuscript does not state this with sufficient clarity. In the revised manuscript we will add an explicit statement and supporting details in the atomistic spin simulations section confirming that the sole difference between the two models is the inclusion of the DFT-derived pair terms. We will also revise the abstract to reflect this isolation. revision: yes
Referee: [results on magnetization curves] The quantitative improvement in magnetization curves should be supported by explicit metrics (e.g., RMS deviation, R² values, or error bars) comparing the two models to the same experimental data set, together with a clear statement of the exclusion criteria used for data points or temperature ranges. Without these, the degree to which the data support the claim remains unclear.

Authors: We acknowledge that quantitative metrics and explicit criteria would allow a clearer assessment of the improvement. The revised manuscript will include RMS deviation and R² values comparing both models to the experimental magnetization data, along with error bars where appropriate. We will also add a clear statement of the data-point and temperature-range exclusion criteria used for the comparison. revision: yes

Circularity Check

0 steps flagged

No circularity: DFT-derived parameters provide independent input

full rationale

The central claim rests on DFT calculations supplying pair anisotropy values that are then inserted into spin simulations for comparison against experiment. This is an external first-principles input, not a fit to the target magnetization curves, and no equations or self-citations in the provided text reduce the reported improvement to a tautology or renamed fit. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

Abstract-only review limits visibility into parameters and assumptions; the ledger reflects the high-level structure described: DFT supplies the pair anisotropy values that are then inserted into spin simulations.

free parameters (1)

pair anisotropy constants
Determined via DFT for specific ion pairs; values not reported in abstract but required for the spin simulations.

axioms (1)

domain assumption Single-ion anisotropy alone is insufficient to model magnetism accurately in random dilute systems because of pair and cluster formation.
Explicitly stated in the abstract as the limitation of existing models.

invented entities (1)

pair-induced uniaxial anisotropy no independent evidence
purpose: To capture the additional directional preference arising from symmetry breaking in nearest-neighbor magnetic ion pairs.
Introduced in the abstract as the central new concept.

pith-pipeline@v0.9.0 · 5696 in / 1279 out tokens · 40356 ms · 2026-05-23T18:45:29.960995+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Cost/FunctionalEquation washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The magnetic Hamiltonian of supercell with two Mn ions is given by H = −∑_i K_tr S_i,z² − ∑_i K_p (S_i · ê_p)²
IndisputableMonolith/Foundation/RealityFromDistinction reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We obtain the following parameters: a trigonal anisotropy constant K_tr = −0.15 meV/ion and a Jahn-Teller anisotropy constant K_JT = 0.68 meV/ion

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

23 extracted references · 23 canonical work pages

[1]

J. A. Mendoza-Rodarte, K. Gas, M. Herrera-Zald´ ıvar, D. Hommel, M. Sawicki, and M. H. D. Guimar˜ aes, Spin hall magnetoresistance in Pt/(Ga,Mn)N devices, Applied Physics Letters 125, 10.1063/5.0218364 (2024). 7

work page doi:10.1063/5.0218364 2024
[2]

Herbich, W

M. Herbich, W. Mac, A. Twardowski, K. Ando, Y. Shapira, and M. Demianiuk, Magnetization and exci- ton spectroscopy of the diluted magnetic semiconductor Cd1−xCrxS, Phys. Rev. B 58, 1912 (1998)

work page 1912
[3]

Bonanni, M

A. Bonanni, M. Sawicki, T. Devillers, W. Stefanowicz, B. Faina, T. Li, T. E. Winkler, D. Sztenkiel, A. Navarro- Quezada, M. Rovezzi, R. Jakie la, A. Grois, M. Wegschei- der, W. Jantsch, J. Suffczy´ nski, F. d’Acapito, A. Mein- gast, G. Kothleitner, and T. Dietl, Experimental probing of exchange interactions between localized spins in the dilute magnetic i...

work page 2011
[4]

Sztenkiel, M

D. Sztenkiel, M. Foltyn, G. P. Mazur, R. Adhikari, K. Kosiel, K. Gas, M. Zgirski, R. Kruszka, R. Jakiela, T. Li, A. Piotrowska, A. Bonanni, M. Sawicki, and T. Dietl, Stretching magnetism with an electric field in a nitride semiconductor, Nature Communications 7, 10.1038/ncomms13232 (2016)

work page doi:10.1038/ncomms13232 2016
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Y. K. Edathumkandy and D. Sztenkiel, Comparative study of magnetic properties of Mn 3+ magnetic clus- ters in GaN using classical and quantum mechanical ap- proach, J. Magn. Magn. Mater. 562, 169738 (2022)

work page 2022
[6]

Sztenkiel, K

D. Sztenkiel, K. Gas, J. Z. Domagala, D. Hommel, and M. Sawicki, Crystal field model simulations of magnetic response of pairs, triplets and quartets of Mn 3+ ions in GaN, New Journal of Physics 22, 123016 (2020)

work page 2020
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Sztenkiel, Spin orbital reorientation transitions in- duced by magnetic field, J

D. Sztenkiel, Spin orbital reorientation transitions in- duced by magnetic field, J. Magn. Magn. Mat. 572, 170644 (2023)

work page 2023
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J. Gosk, M. Zajac, A. Wolos, M. Kaminska, A. Twar- dowski, I. Grzegory, M. Bockowski, and S. Porowski, Magnetic anisotropy of bulk GaN:Mn single crystals codoped with Mg acceptors, Physical Review B 71, 094432 (2005)

work page 2005
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D. Sztenkiel, Introducing the step monte carlo method for simulating dynamic properties, Ad- vanced Theory and Simulations 6, 2300184 (2023), https://onlinelibrary.wiley.com/doi/pdf/10.1002/adts.202300184

work page doi:10.1002/adts.202300184 2023
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Kronik, M

L. Kronik, M. Jain, and J. R. Chelikowsky, Electronic structure and spin polarization of Mn xGa1−xN, Physical Review B 66, 041203 (2002)

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Sanyal, O

B. Sanyal, O. Bengone, and S. Mirbt, Electronic struc- ture and magnetism of Mn-doped GaN, Phys. Rev. B 68, 205210 (2003)

work page 2003
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L. M. Sandratskii, P. Bruno, and J. Kudrnovsk´ y, On-site coulomb interaction and the magnetism of (GaMn)N and (GaMn)As, Physical Review B 69, 195203 (2004)

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Stroppa and G

A. Stroppa and G. Kresse, Unraveling the jahn-teller ef- fect in Mn-doped GaN using the heyd-scuseria-ernzerhof hybrid functional, Physical Review B 79, 201201 (2009)

work page 2009
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Virot, R

F. Virot, R. Hayn, and A. Boukortt, Electronic structure and jahn–teller effect in GaN:Mn and ZnS:Cr, Journal of Physics: Condensed Matter 23, 025503 (2010)

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P. A. Schultz, A. H. Edwards, R. M. Van Ginhoven, H. P. Hjalmarson, and A. M. Mounce, Theory of magnetic 3 d transition metal dopants in gallium nitride, Physical Re- view B 107, 205202 (2023)

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P. E. Bl¨ ochl, Projector augmented-wave method, Physi- cal Review B 50, 17953 (1994)

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H. J. Monkhorst and J. D. Pack, Special points for brillouin-zone integrations, Physical Review B 13, 5188 (1976)

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O. A. von Lilienfeld and P. A. Schultz, Structure and band gaps of Ga-(V) semiconductors: The challenge of Ga pseudopotentials, Physical Review B 77, 115202 (2008)

work page 2008
[19]

K. Gas, J. Z. Domagala, R. Jakiela, G. Kunert, P. Dluzewski, E. Piskorska-Hommel, W. Paszkow- icz, D. Sztenkiel, M. J. Winiarski, D. Kowalska, R. Szukiewicz, T. Baraniecki, A. Miszczuk, D. Hommel, and M. Sawicki, Impact of substrate temperature on mag- netic properties of plasma-assisted molecular beam epi- taxy grown (Ga,Mn)N, J. Alloys and Compounds 747...

work page 2018
[20]

Sztenkiel, K

D. Sztenkiel, K. Gas, N. G. Szwacki, M. Foltyn, C. Sliwa, T. Wojciechowski, J. Z. Domagala, D. Hommel, M. Saw- icki, and T. Dietl, Electric field manipulation of mag- netization in an insulating dilute ferromagnet through piezoelectromagnetic coupling (2024)

work page 2024
[21]

Hobbs, G

D. Hobbs, G. Kresse, and J. Hafner, Fully unconstrained noncollinear magnetism within the projector augmented- wave method, Physical Review B 62, 11556 (2000)

work page 2000
[22]

Dietl, H

T. Dietl, H. Ohno, F. Matsukura, J. Cibert, and D. Fer- rand, Zener model description of ferromagnetism in zinc-blende magnetic semiconductors, Science 287, 1019 (2000)

work page 2000
[23]

D. D. Awschalom and M. E. Flatt´ e, Challenges for semi- conductor spintronics, Nature Physics 3, 153 (2007)

work page 2007

[1] [1]

J. A. Mendoza-Rodarte, K. Gas, M. Herrera-Zald´ ıvar, D. Hommel, M. Sawicki, and M. H. D. Guimar˜ aes, Spin hall magnetoresistance in Pt/(Ga,Mn)N devices, Applied Physics Letters 125, 10.1063/5.0218364 (2024). 7

work page doi:10.1063/5.0218364 2024

[2] [2]

Herbich, W

M. Herbich, W. Mac, A. Twardowski, K. Ando, Y. Shapira, and M. Demianiuk, Magnetization and exci- ton spectroscopy of the diluted magnetic semiconductor Cd1−xCrxS, Phys. Rev. B 58, 1912 (1998)

work page 1912

[3] [3]

Bonanni, M

A. Bonanni, M. Sawicki, T. Devillers, W. Stefanowicz, B. Faina, T. Li, T. E. Winkler, D. Sztenkiel, A. Navarro- Quezada, M. Rovezzi, R. Jakie la, A. Grois, M. Wegschei- der, W. Jantsch, J. Suffczy´ nski, F. d’Acapito, A. Mein- gast, G. Kothleitner, and T. Dietl, Experimental probing of exchange interactions between localized spins in the dilute magnetic i...

work page 2011

[4] [4]

Sztenkiel, M

D. Sztenkiel, M. Foltyn, G. P. Mazur, R. Adhikari, K. Kosiel, K. Gas, M. Zgirski, R. Kruszka, R. Jakiela, T. Li, A. Piotrowska, A. Bonanni, M. Sawicki, and T. Dietl, Stretching magnetism with an electric field in a nitride semiconductor, Nature Communications 7, 10.1038/ncomms13232 (2016)

work page doi:10.1038/ncomms13232 2016

[5] [5]

Y. K. Edathumkandy and D. Sztenkiel, Comparative study of magnetic properties of Mn 3+ magnetic clus- ters in GaN using classical and quantum mechanical ap- proach, J. Magn. Magn. Mater. 562, 169738 (2022)

work page 2022

[6] [6]

Sztenkiel, K

D. Sztenkiel, K. Gas, J. Z. Domagala, D. Hommel, and M. Sawicki, Crystal field model simulations of magnetic response of pairs, triplets and quartets of Mn 3+ ions in GaN, New Journal of Physics 22, 123016 (2020)

work page 2020

[7] [7]

Sztenkiel, Spin orbital reorientation transitions in- duced by magnetic field, J

D. Sztenkiel, Spin orbital reorientation transitions in- duced by magnetic field, J. Magn. Magn. Mat. 572, 170644 (2023)

work page 2023

[8] [8]

J. Gosk, M. Zajac, A. Wolos, M. Kaminska, A. Twar- dowski, I. Grzegory, M. Bockowski, and S. Porowski, Magnetic anisotropy of bulk GaN:Mn single crystals codoped with Mg acceptors, Physical Review B 71, 094432 (2005)

work page 2005

[9] [9]

D. Sztenkiel, Introducing the step monte carlo method for simulating dynamic properties, Ad- vanced Theory and Simulations 6, 2300184 (2023), https://onlinelibrary.wiley.com/doi/pdf/10.1002/adts.202300184

work page doi:10.1002/adts.202300184 2023

[10] [10]

Kronik, M

L. Kronik, M. Jain, and J. R. Chelikowsky, Electronic structure and spin polarization of Mn xGa1−xN, Physical Review B 66, 041203 (2002)

work page 2002

[11] [11]

Sanyal, O

B. Sanyal, O. Bengone, and S. Mirbt, Electronic struc- ture and magnetism of Mn-doped GaN, Phys. Rev. B 68, 205210 (2003)

work page 2003

[12] [12]

L. M. Sandratskii, P. Bruno, and J. Kudrnovsk´ y, On-site coulomb interaction and the magnetism of (GaMn)N and (GaMn)As, Physical Review B 69, 195203 (2004)

work page 2004

[13] [13]

Stroppa and G

A. Stroppa and G. Kresse, Unraveling the jahn-teller ef- fect in Mn-doped GaN using the heyd-scuseria-ernzerhof hybrid functional, Physical Review B 79, 201201 (2009)

work page 2009

[14] [14]

Virot, R

F. Virot, R. Hayn, and A. Boukortt, Electronic structure and jahn–teller effect in GaN:Mn and ZnS:Cr, Journal of Physics: Condensed Matter 23, 025503 (2010)

work page 2010

[15] [15]

P. A. Schultz, A. H. Edwards, R. M. Van Ginhoven, H. P. Hjalmarson, and A. M. Mounce, Theory of magnetic 3 d transition metal dopants in gallium nitride, Physical Re- view B 107, 205202 (2023)

work page 2023

[16] [16]

P. E. Bl¨ ochl, Projector augmented-wave method, Physi- cal Review B 50, 17953 (1994)

work page 1994

[17] [17]

H. J. Monkhorst and J. D. Pack, Special points for brillouin-zone integrations, Physical Review B 13, 5188 (1976)

work page 1976

[18] [18]

O. A. von Lilienfeld and P. A. Schultz, Structure and band gaps of Ga-(V) semiconductors: The challenge of Ga pseudopotentials, Physical Review B 77, 115202 (2008)

work page 2008

[19] [19]

K. Gas, J. Z. Domagala, R. Jakiela, G. Kunert, P. Dluzewski, E. Piskorska-Hommel, W. Paszkow- icz, D. Sztenkiel, M. J. Winiarski, D. Kowalska, R. Szukiewicz, T. Baraniecki, A. Miszczuk, D. Hommel, and M. Sawicki, Impact of substrate temperature on mag- netic properties of plasma-assisted molecular beam epi- taxy grown (Ga,Mn)N, J. Alloys and Compounds 747...

work page 2018

[20] [20]

Sztenkiel, K

D. Sztenkiel, K. Gas, N. G. Szwacki, M. Foltyn, C. Sliwa, T. Wojciechowski, J. Z. Domagala, D. Hommel, M. Saw- icki, and T. Dietl, Electric field manipulation of mag- netization in an insulating dilute ferromagnet through piezoelectromagnetic coupling (2024)

work page 2024

[21] [21]

Hobbs, G

D. Hobbs, G. Kresse, and J. Hafner, Fully unconstrained noncollinear magnetism within the projector augmented- wave method, Physical Review B 62, 11556 (2000)

work page 2000

[22] [22]

Dietl, H

T. Dietl, H. Ohno, F. Matsukura, J. Cibert, and D. Fer- rand, Zener model description of ferromagnetism in zinc-blende magnetic semiconductors, Science 287, 1019 (2000)

work page 2000

[23] [23]

D. D. Awschalom and M. E. Flatt´ e, Challenges for semi- conductor spintronics, Nature Physics 3, 153 (2007)

work page 2007