Paper Citation Record · LEDGER

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence

As of 18 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 3 inbound Pith citation observations for arXiv:2512.22108.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2512.22108 v2

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measured 46 of 46 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-03T14:00:06.144234Z

measured 49 of 49 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T14:00:06.027470Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-10T22:07:38.434807Z

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Outbound references

Observation 8b8c9672-6038-404b-92d5-46e19ee81bb3 · outbound

This paper cites Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.027470Z

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Observation 9b53143e-ace7-480d-8f40-92d70542fb9b · outbound

This paper cites The spin torques given by equations (9) and (10) are equal to zero.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence The spin torques given by equations (9) and (10) are equal to zero

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.032050Z

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Observation 2330185a-0a71-43a0-8d9e-4f4403f9953b · outbound

This paper cites The dispersion dependence (35) contains two types of solutions.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence The dispersion dependence (35) contains two types of solutions

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.034858Z

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Observation 45feafcf-480b-4eb5-aa0e-ba3282ec3822 · outbound

This paper cites These conditions satisfy equations (9), (10), (28), (29), and (34), where each term is equal to zero.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence These conditions satisfy equations (9), (10), (28), (29), and (34), where each term is equal to zero

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.037769Z

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Observation e3b4c2cb-7a54-46e5-a00b-741846582aba · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.040571Z

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Observation bf17bdf3-3f60-455a-88e1-4feeb8f596cc · outbound

This paper cites In this case the ﬁrst term in equation (9) has nonzero projection on the z-direction.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence In this case the ﬁrst term in equation (9) has nonzero projection on the z-direction

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.043209Z

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Observation b5b17abc-f8f9-43dc-a2f8-1c3ed9365207 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.045930Z

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Observation 46bb833c-8e93-403f-bde5-d32c80dfc475 · outbound

This paper cites Fiebig, ”Revival of the magnetoelectric eﬀect”, J.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Fiebig, ”Revival of the magnetoelectric eﬀect”, J

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.048619Z

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Observation eb10e59c-019c-4c0f-bc76-8c60aa24d80b · outbound

This paper cites Nagaosa, ”Theory of multiferroic behavior in cycloid al helimagnets”, J.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Nagaosa, ”Theory of multiferroic behavior in cycloid al helimagnets”, J

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.051167Z

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Observation fac87e04-f2a2-4fdc-9cc9-8deb99598f40 · outbound

This paper cites Tokura, S.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Tokura, S

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.053765Z

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Observation 3a99069a-b511-4114-be09-7454f9ac68d5 · outbound

This paper cites Dong, J.-M.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Dong, J.-M

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.056401Z

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Observation 58f1ad63-7a09-4d17-b9d6-b812f8de2b41 · outbound

This paper cites Mostovoy, ”Multiferroics: diﬀerent routes to magne- toelectric coupling”, npj Spintronics, 2 18 (2024).

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Mostovoy, ”Multiferroics: diﬀerent routes to magne- toelectric coupling”, npj Spintronics, 2 18 (2024)

Reference 12

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Observation e6d3e5c2-5437-4f19-8bb4-6aa0c01aee6d · outbound

This paper cites Katsura, N.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Katsura, N

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.062177Z

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Observation 2374eb8f-81f1-4997-a152-27ae80f979e5 · outbound

This paper cites G.Bar’yakhtar, V.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence G.Bar’yakhtar, V

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.064673Z

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Observation 9f89fcc1-cec4-4878-ac4a-39b9e6afa5cf · outbound

This paper cites Mostovoy, ”Ferroelectricity in Spiral Magnets”, Phy s.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Mostovoy, ”Ferroelectricity in Spiral Magnets”, Phy s

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.067251Z

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Observation b9743b21-1755-4551-82e8-8f8c832bb4c2 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.069669Z

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Observation 3e4d34b8-c5a6-440c-b1c6-7c9c99fc7736 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.072367Z

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Observation 9bc18778-8a5c-446f-a00d-0951796b4d21 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.074736Z

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Observation a4655df7-9726-4aee-92cc-0d7763615996 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.077051Z

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Observation b2bad505-ecf5-4c46-83ba-2d6851708dd7 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.079617Z

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Observation 0ecf4773-a6f8-4f6b-842b-e3e6a2680a6e · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.082186Z

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Observation cd878015-75c0-4559-9a4f-c018d4323f70 · outbound

This paper cites Zakeri, Y.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Zakeri, Y

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.084648Z

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Observation ac4ee37a-de60-46b1-809a-591363308032 · outbound

This paper cites Moon, S.-M.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Moon, S.-M

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.087045Z

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Observation 52052c8d-a102-4b92-8af9-d8e8666b87d0 · outbound

This paper cites Risinggard, I.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Risinggard, I

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.089473Z

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Observation 00d276f4-9995-4823-b860-4b6a689ece3b · outbound

This paper cites Regimes of optical transparency and instabilities of collinear dielectric ferromagnetic materials in the presence of the dynamic magnetoelectric effect.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Regimes of optical transparency and instabilities of collinear dielectric ferromagnetic materials in the presence of the dynamic magnetoelectric effect

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.091911Z

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Observation fbc1ec57-f3c6-4009-82b2-96db6a799e4e · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.094783Z

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Observation c66ee572-5d85-4c6f-8a0d-5058c5490c53 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.097197Z

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Observation a2a7a816-eb06-44e2-983d-d490ec8ebfd8 · outbound

This paper cites Pimenov, A.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Pimenov, A

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.099668Z

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Observation 38b39749-cd2c-48c7-961e-ef11d1f9d3e8 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.102032Z

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Observation 230748db-5bce-4d95-a2f5-93a550ebc676 · outbound

This paper cites Aupiais, M.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Aupiais, M

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.104449Z

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Observation b413875a-44cb-4479-8649-598c288ac0df · outbound

This paper cites Katsura, A.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Katsura, A

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.107001Z

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Observation 77402d68-2a28-41db-a600-46e20441b62d · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.109595Z

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Observation 3ef64a81-6d83-407a-9c99-2f7514a4e418 · outbound

This paper cites Hermenau, S.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Hermenau, S

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.111990Z

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Observation 32bc9b6c-e100-4d57-b6d5-8460df18ccb4 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.114534Z

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Observation acf3276d-49c8-41ec-a633-70389cb8c8bf · outbound

This paper cites Udvardi, L.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Udvardi, L

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.116939Z

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Observation c0ae0d2d-054a-4d75-bbbb-661ea3fd3061 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.119594Z

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Observation 5475814e-3ee2-447e-ab39-85968bc7ee91 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.121999Z

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Observation aa1f333c-4f72-4f4b-a9e2-6690d1d6a7db · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.124321Z

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Observation e7ce7e27-4f16-405a-a277-8bb004511fff · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.126808Z

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Observation e4c255db-a133-419a-8ca0-cf5282d7872f · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.129151Z

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Observation afc4d18d-7070-4947-bcf8-8f4f9bf8484a · outbound

This paper cites Sparavigna, A.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Sparavigna, A

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.131639Z

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Observation bc0b4adc-2ee8-4cb8-83b3-929700eab273 · outbound

This paper cites Cheong, M.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Cheong, M

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.134097Z

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Observation b2f9749d-7d93-42c0-9b13-d855a59988f5 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.136846Z

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Observation 17871706-9372-494e-bc83-d5346abf91da · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.139554Z

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Observation a411c5ae-a253-4aff-927a-898eb440f5ab · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.141914Z

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Observation 836f8e73-027b-43a7-afad-0cc5bdbd0dd4 · outbound

This paper cites an unresolved cited work.

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence Unresolved cited work

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-03T14:00:06.144234Z

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Pith citing papers

Observation 8b8c9672-6038-404b-92d5-46e19ee81bb3 · inbound