Robust Formation of Ultrasmall Room-Temperature Ne\'el Skyrmions in Amorphous Ferrimagnets from Atomistic Simulations

Avik W. Ghosh; Chung Ting Ma; Howard Sheng; S. Joseph Poon; Yunkun Xie

arxiv: 1907.00647 · v1 · pith:DDX2PV6Inew · submitted 2019-07-01 · ❄️ cond-mat.mes-hall

Robust Formation of Ultrasmall Room-Temperature Ne\'el Skyrmions in Amorphous Ferrimagnets from Atomistic Simulations

Chung Ting Ma , Yunkun Xie , Howard Sheng , Avik W. Ghosh , S. Joseph Poon This is my paper

Pith reviewed 2026-05-25 11:52 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords skyrmionsawayinterfaceultrasmallamorphousatomisticdensityferrimagnets

0 comments

The pith

Stochastic LLG atomistic simulations find that reduced DMI stabilizes ultrasmall columnar skyrmions at room temperature in thick amorphous ferrimagnetic GdCo films.

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

Skyrmions are small, stable swirls in the direction of magnetic spins that researchers hope to use for storing data in future computer chips. This work runs computer simulations of a material called GdCo, which has two types of magnetic atoms mixed in an amorphous structure. The simulations track how the spins move according to the Landau-Lifshitz-Gilbert equation with added random thermal kicks to mimic room temperature. They find that even when the twisting force called DMI is made weaker than the value usually needed at platinum interfaces, the swirls remain stable in films as thick as 15 nanometers. The swirls also keep the same size and shape from the top to the bottom of the film even though the twisting force is strongest only near one surface.

Core claim

A significant reduction in DMI below that of Pt is sufficient to stabilize ultrasmall skyrmions even in films as thick as 15 nm. Moreover, skyrmions are found to retain a uniform columnar shape across the film thickness despite the decaying DMI.

Load-bearing premise

The chosen atomistic parameters and DMI decay profile for amorphous GdCo in the stochastic LLG model correctly capture the real material behavior at room temperature.

read the original abstract

Ne\'el skyrmions originate from interfacial Dzyaloshinskii Moriya interaction (DMI). Recent studies have explored using thin-film ferromagnets and ferrimagnets to host Ne\'el skyrmions for spintronic applications. However, it is unclear if ultrasmall (10 nm or less) skyrmions can ever be stabilized at room temperature for practical use in high density parallel racetrack memories. While thicker films can improve stability, DMI decays rapidly away from the interface. As such, spins far away from the interface would experience near-zero DMI, raising question on whether or not unrealistically large DMI is needed to stabilize skyrmions, and whether skyrmions will also collapse away from the interface. To address these questions, we have employed atomistic stochastic Landau-Lifshitz-Gilbert simulations to investigate skyrmions in amorphous ferrimagnetic GdCo. It is revealed that a significant reduction in DMI below that of Pt is sufficient to stabilize ultrasmall skyrmions even in films as thick as 15 nm. Moreover, skyrmions are found to retain a uniform columnar shape across the film thickness despite the decaying DMI. Our results show that increasing thickness and reducing DMI in GdCo can further reduce the size of skyrmions at room temperature, which is crucial to improve the density and energy efficiency in skyrmion based devices.

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

Simulations show reduced DMI can still stabilize ultrasmall columnar skyrmions in 15 nm GdCo at room temperature, but the outcome tracks the chosen DMI profile and atomistic constants.

read the letter

The core result is that atomistic stochastic LLG runs on amorphous GdCo find stable ~10 nm or smaller Neel skyrmions at room temperature in 15 nm films when DMI is lowered below typical Pt values and allowed to decay away from the interface. The skyrmions also keep a uniform columnar shape through the thickness instead of collapsing in the low-DMI regions. That directly tests the practical worry about DMI decay limiting thicker films for thermal stability.

Referee Report

2 major / 1 minor

Summary. The paper employs atomistic stochastic Landau-Lifshitz-Gilbert simulations of amorphous ferrimagnetic GdCo to investigate Néel skyrmions. It claims that a significant reduction in interfacial DMI strength below typical Pt values suffices to stabilize ultrasmall (≤10 nm) room-temperature skyrmions in films up to 15 nm thick, and that these skyrmions retain a uniform columnar shape across the thickness despite DMI decay away from the interface. The work further concludes that increasing film thickness while reducing DMI can shrink skyrmion size, aiding high-density spintronic devices.

Significance. If the simulation results hold under realistic material parameters, the findings would demonstrate that amorphous GdCo films enable practical ultrasmall room-temperature skyrmions without unrealistically large DMI, addressing key barriers to high-density racetrack memories. The atomistic approach provides detailed thickness-dependent insights not accessible in continuum models.

major comments (2)

[Abstract] Abstract and methods (DMI implementation): the headline result that reduced DMI stabilizes 15 nm columnar skyrmions is obtained from forward simulations with externally chosen DMI magnitude and decay length as free inputs; no sensitivity analysis, convergence checks, or comparison to measured DMI profiles in real GdCo is reported, making the stability and shape conclusions dependent on these specific choices.
[Results] Results on skyrmion size and shape: the reported size reduction with thickness and the uniform columnar profile across 15 nm rely on the chosen sublattice moments, exchange, anisotropy, and DMI decay functional form; without error bars or tests of alternative decay profiles, it is unclear whether the conclusions are robust or artifacts of the parameter set.

minor comments (1)

[Abstract] The abstract provides no quantitative error bars, statistical sampling details, or temperature equilibration metrics for the stochastic LLG runs, which would strengthen the room-temperature claims.

Circularity Check

0 steps flagged

No significant circularity; forward simulation with independent inputs

full rationale

The paper reports outcomes of stochastic LLG atomistic simulations on GdCo with externally selected parameters (exchange, anisotropy, sublattice moments, and a chosen DMI decay profile). The abstract and methods describe these as inputs chosen to explore thickness and DMI effects; the stability and columnar shape results are direct simulation outputs rather than quantities fitted or defined in terms of the target skyrmion size. No equations reduce the headline claims to self-definition, fitted inputs renamed as predictions, or load-bearing self-citations. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model assumes standard micromagnetic dynamics plus a specific DMI decay length and GdCo exchange/stiffness values taken from literature or fitting; no new entities postulated.

free parameters (2)

DMI magnitude and decay length
Reduced below Pt value and spatially decaying; specific numbers chosen to produce the reported stability.
GdCo atomistic parameters (exchange, anisotropy)
Material constants required to run the LLG integrator; not derived within the paper.

axioms (2)

standard math Stochastic Landau-Lifshitz-Gilbert dynamics govern spin evolution at finite temperature.
Invoked as the simulation engine throughout the abstract.
domain assumption Amorphous GdCo can be modeled with a spatially decaying interfacial DMI profile.
Central modeling choice that enables the thickness study.

pith-pipeline@v0.9.0 · 5814 in / 1384 out tokens · 37876 ms · 2026-05-25T11:52:02.579131+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages

[1]

second layer

As shown in Fig. 2, at 300 K, the magnetization of amorphous Gd25Co75 is 5 x 104 A/m, and it has a compensation temperature near 250 K. We begin with an exponential DMI decay away from the interface, as shown in Fig. 3. The DMI value discussed herein is the interfacial DMI D0. The decay length of DMI is based on both previous simulations and experiments. ...

work page
[2]

K., Bogdanov, A

Rößler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006)

work page 2006
[3]

Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010)

work page 2010
[4]

Yu, X.Z. et al. Skyrmion flow near room temperature in an ultralow current density. Nat. Commun. 3, 988 (2012)

work page 2012
[5]

& Tokura, Y

Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899-911 (2013)

work page 2013
[6]

& Fert, A

Sampaio, J., Cros, V., Rohart, S., Thiaville A. & Fert, A. Nucleation, stability and current- induced motion of isolated magnetic skyrmions in nanostructures. Nat. Nanotechnol. 8, 839- 844 (2013)

work page 2013
[7]

Jiang, W. et al. Blowing magnetic skyrmion bubbles. Science 349, 283–286 (2015)

work page 2015
[8]

Büttner, F. et al. Dynamics and inertia of skyrmionic spin structures. Nat. Phys. 11, 225-228 (2015)

work page 2015
[9]

Romming, N. et al. Writing and deleting single magnetic skyrmions. Science 341, 636–639 (2013)

work page 2013
[10]

& Wiesendanger, R

Romming, N., Kubetzka, A., Hanneken, C., von Bergmann, K. & Wiesendanger, R. Field- dependent size and shape of single magnetic skyrmions. Phys. Rev. Lett. 114, 177203 (2015)

work page 2015
[11]

Boulle, O. et al. Room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures. Nat. Nanotechnol. 11, 449-454 (2016)

work page 2016
[12]

& Zhou Y

Zhang, X., Ezawa, M. & Zhou Y. Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions. Sci. Rep. 5, 9400 (2015)

work page 2015
[13]

& Böni, P

Mühlbauer, S., Binz, B., Jonietz, F., Pfleiderer, C., Rosch, A., Neubauer, A., Georgii, R. & Böni, P. Skyrmion Lattice in a Chiral Magnet. Science 323, 915-919 (2009)

work page 2009
[14]

Yu, X.Z. et al. Near room-temperature formation of a skyrmion crystal in thin-films of the 8 helimagnet FeGe. Nat. Mater. 10, 106–109 (2011)

work page 2011
[15]

& Fullerton, E.E

Tolley, R., Montoya, S.A. & Fullerton, E.E. Room-temperature observation and current control of skyrmions in Pt/Co/Os/Pt thin films. Phys. Rev. Mater. 2, 044404 (2018)

work page 2018
[16]

Woo, S. et al. Observation of room-temperature magnetic skyrmions and their current- driven dynamics in ultrathin metallic ferromagnets. Nat. Mater. 15, 501–506 (2016)

work page 2016
[17]

Soumyanarayanan, A. et al. Tunable room-temperature magnetic skyrmions in Ir/Fe/Co/Pt multilayers. Nat. Mater. 16, 898–904 (2017)

work page 2017
[18]

& Wiesendanger, R

Siemens, A., Zhang, Y., Hagemeister, J., Vedmedenko, E.Y. & Wiesendanger, R. Minimal radius of magnetic skyrmions: statics and dynamics. New. J. Phys. 18, 045021 (2016)

work page 2016
[19]

& Beach G.S.D

Büttner, F., Lemesh I. & Beach G.S.D. Theory of isolated magnetic skyrmions: From fundamentals to room temperature applications. Sci. Rep. 8, 4464 (2018)

work page 2018
[20]

Jiang, W. et al. Direct observation of the skyrmion Hall effect. Nat. Phys. 13, 162-169 (2017)

work page 2017
[21]

Litzius, K. et al. Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy. Nat. Phys. 13, 170-175 (2017)

work page 2017
[22]

Skyrmions on the track

Fert, A., Cros, V., Sampaio, J. Skyrmions on the track. Nat. Nanotechnol. 8, 152-156 (2013)

work page 2013
[23]

Tomasello, R. et al. A strategy for the design of skyrmion racetrack memories. Sci. Rep. 4, 6784 (2014)

work page 2014
[24]

Woo, S. et al. Current-driven dynamics and inhibition of the skyrmion Hall effect of ferrimagnetic skyrmions in GdFeCo films. Nat. Commun. 9, 959 (2018)

work page 2018
[25]

Lee, J. C. T. et al. Synthesizing skyrmion bound pairs in Fe-Gd thin films. Appl. Phys. Lett. 109, (2016)

work page 2016
[26]

Caretta, L. et al. Fast current-driven domain walls and small skyrmions in a compensated ferrimagnet. Nat. Nanotechnol. 13, 1154-1160 (2018)

work page 2018
[27]

A thermodynamic theory of weak ferromagnetism of antiferromagnetics

Dzyaloshinsky, I. A thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958)

work page 1958
[28]

Anisotropic superexchange interaction and weak ferromagnetism

Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98 (1960)

work page 1960
[29]

Belmeguenai, M. et al. A. Interfacial Dzyaloshinskii–Moriya interaction in perpendicularly magnetized Pt/Co/AlOx ultrathin films measured by Brillouin light spectroscopy. Phys. Rev. B 91, 180405(R) (2015)

work page 2015
[30]

& Silva, T.J

Nembach, H.T., Shaw, J.M, Weiler, M., Jué E. & Silva, T.J. Linear relation between Heisenberg exchange and interfacial Dzyaloshinskii–Moriya interaction in metal films. Nature Phys. 11, 825-829 (2015)

work page 2015
[31]

& Chshiev, M

Yang, H., Thiaville, A., Rohart, S., Fert, A. & Chshiev, M. Anatomy of Dzyaloshinskii-Moriya Interaction at Co/Pt Interfaces. Phys. Rev. Lett. 118, 219901 (2017)

work page 2017
[32]

Belmeguenai, M. et al. Thickness Dependence of the Dzyaloshinskii -Moriya Interaction in Co2FeAl Ultrathin Films: Effects of Annealing Temperature and Heavy -Metal Material. Phys. Rev. Appl. 9, 044044 (2018)

work page 2018
[33]

Dirks, A. G. & Leamy, H. J. Columnar microstructure in vapor-deposited thin films. Thin Solid Films 47, 219–233 (1977)

work page 1977
[34]

Leamy, H. J. & Dirks, A. G. Microstructure and magnetism in amorphous rare-earth- transition-metal thin films. II. Magnetic anisotropy. J. Appl. Phys. 49, 3430 (1978)

work page 1978
[35]

G., Aylesworth, K

Harris, V. G., Aylesworth, K. D., Das, B. N., Elam, W. T. & Koon, N. C. Structural origins of magnetic anisotropy in sputtered amorphous Tb-Fe films. Phys. Rev. Lett. 69, 1939–1942 (1992)

work page 1939
[36]

Harris, V. G. & Pokhil, T. Selective-Resputtering-Induced Perpendicular Magnetic Anisotropy 9 in Amorphous TbFe Films. Phys. Rev. Lett. 87, 67207 (2001)

work page 2001
[37]

& Witter, K

Hansen, P., Clausen, C., Much, G., Rosenkranz, M. & Witter, K. Magnetic and magneto- optical properties of rare-earth transition-metal alloys containing Gd, Tb, Fe, Co. J. Appl. Phys. 66, 756–767 (1989)

work page 1989
[38]

Kim, K-J. et al. Fast domain wall motion in the vicinity of the angular momentum compensation temperature of ferrimagnets. Nature Materials 16, 1187-1192 (2017)

work page 2017
[39]

Stanciu, C. D. et al. All-optical magnetic recording with circularly polarized light. Phys. Rev. Lett. 99, 47601 (2007)

work page 2007
[40]

Savoini, M. et al. Highly efficient all-optical switching of magnetization in GdFeCo microstructures by interference-enhanced absorption of light. Phys. Rev. B 86, 140404(R) (2012)

work page 2012
[41]

Ostler, T.A. et al. Ultrafast heating as a sufficient stimulus for magnetization reversal in a ferrimagnet. Nat. Commun. 3, 666 (2012)

work page 2012
[42]

Hassdenteufel, A. et al. Thermally assisted all-optical helicity dependent magnetic switching in amorphous Fe100-xTbx alloy films. Adv. Mater. 25, 3122–3128 (2013)

work page 2013
[43]

Kirilyuk, A., Kimel, A. V. & Rasing, T. Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys. 82, 2731–2784 (2010)

work page 2010
[44]

Kirilyuk, A., Kimel, A. V. & Rasing, T. Laser-induced magnetization dynamics and reversal in ferrimagnetic alloys. Rep. Prog. Phys. 76, 026501 (2013)

work page 2013
[45]

Kimel, A. V. All-optical switching: Three rules of design. Nat. Mater. 13, 225–226 (2014)

work page 2014
[46]

Magnin, S. et al. Engineered materials for all-optical helicity-dependent magnetic switching. Nat. Mater. 13, 286-292 (2014)

work page 2014
[47]

Ostler, T. A. et al. Crystallographically amorphous ferrimagnetic alloys: Comparing a localized atomistic spin model with experiments. Phys. Rev. B 84, 24407 (2011)

work page 2011
[48]

Radu, I. et al. Transient ferromagnetic-like state mediating ultrafast reversal of antiferromagnetically coupled spins. Nature 472, 205–208 (2011)

work page 2011
[49]

Ellis, M. O. A., Ostler, T. A. & Chantrell, R. W. Classical spin model of the relaxation dynamics of rare-earth doped permalloy. Phys. Rev. B 86, 174418 (2012)

work page 2012
[50]

Evans, R. F. L. et al. Atomistic spin model simulations of magnetic nanomaterials. J. Phys. Condens. Matter 26, 103202 (2014)

work page 2014
[51]

& Chubykalo-Fesenko O

Atxitia, U., Nieves, P. & Chubykalo-Fesenko O. Landau-Lifshitz-Bloch equation for ferrimagnetic materials. Phys. Rev. B 86, 104414 (2012)

work page 2012
[52]

Chen, G. et al. Tailoring the chirality of magnetic domain walls by interface engineering. Nat. Commun. 4, 2671 (2013)

work page 2013
[53]

Hrabec, A. et al. Measuring and tailoring the Dzyaloshinskii-Moriya interaction in perpendicularly magnetized thin films. Phys. Rev. B 90, 020402(R) (2014)

work page 2014
[54]

Stashkevich, A.A. et al. Experimental study of spin-wave dispersion in Py/Pt film structures in the presence of an interface Dzyaloshinskii-Moriya interaction. Phys. Rev. B 91, 214409 (2015)

work page 2015
[55]

Ma, X. et al. Interfacial control of Dzyaloshinskii-Moriya interaction in heavy metal/ferromagnetic metal thin film heterostructures. Phys. Rev. B 94, 180408(R) (2016)

work page 2016
[56]

Tacchi, S. et al. Interfacial Dzyaloshinskii-Moriya Interaction in Pt/CoFeB Films: Effect of the Heavy-Metal Thickness. Phys. Rev. Lett. 118, 147201 (2017)

work page 2017
[57]

Cho, J. et al. The sign of the interfacial Dzyaloshinskii –Moriyainteraction in ultrathin amorphous and polycrystalline magnetic films. J. Phys. D: Appl. Phys. 50, 425004 (2017)

work page 2017
[58]

& Szunyogh, L

Simon, E., Rózsa, L., Palotás, K. & Szunyogh, L. Magnetism of a Co monolayer on Pt(111) capped by overlayers of 5d elements: A spin-model study. Phys. Rev. B 97, 134405 (2018). 10

work page 2018
[59]

Atomic packing and short-to- medium-range order in metallic glasses

Sheng, H.W., Luo, W.K., Alamgir, F.M., Bai, J.M., & Ma, E. Atomic packing and short-to- medium-range order in metallic glasses. Nature 439, 419-425 (2006)

work page 2006
[60]

Antiferromagnetic Skyrmion: Stability, Creation and Manipulation

Zhang, X., Zhou, Y., & Ezawa, M. Antiferromagnetic Skyrmion: Stability, Creation and Manipulation. Sci. Rep. 6, 24795 (2016)

work page 2016
[61]

A., Static and Dynamical Properties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature

Baker, J., & Tretiakov, O. A., Static and Dynamical Properties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature. Phys. Rev. Lett. 116, 147203 (2016)

work page 2016
[62]

Kim, K-J. et al. Fast domain wall motion in the vicinity of the angular momentum compensation temperature of ferrimagnets. Nature Materials 16, 1187-1192 (2017). Acknowledgements: This work was supported by the DARPA Topological Excitations in Electronics (TEE) program (grant D18AP00009). The content of the information does not necessarily reflect the pos...

work page 2017

[1] [1]

second layer

As shown in Fig. 2, at 300 K, the magnetization of amorphous Gd25Co75 is 5 x 104 A/m, and it has a compensation temperature near 250 K. We begin with an exponential DMI decay away from the interface, as shown in Fig. 3. The DMI value discussed herein is the interfacial DMI D0. The decay length of DMI is based on both previous simulations and experiments. ...

work page

[2] [2]

K., Bogdanov, A

Rößler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006)

work page 2006

[3] [3]

Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010)

work page 2010

[4] [4]

Yu, X.Z. et al. Skyrmion flow near room temperature in an ultralow current density. Nat. Commun. 3, 988 (2012)

work page 2012

[5] [5]

& Tokura, Y

Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899-911 (2013)

work page 2013

[6] [6]

& Fert, A

Sampaio, J., Cros, V., Rohart, S., Thiaville A. & Fert, A. Nucleation, stability and current- induced motion of isolated magnetic skyrmions in nanostructures. Nat. Nanotechnol. 8, 839- 844 (2013)

work page 2013

[7] [7]

Jiang, W. et al. Blowing magnetic skyrmion bubbles. Science 349, 283–286 (2015)

work page 2015

[8] [8]

Büttner, F. et al. Dynamics and inertia of skyrmionic spin structures. Nat. Phys. 11, 225-228 (2015)

work page 2015

[9] [9]

Romming, N. et al. Writing and deleting single magnetic skyrmions. Science 341, 636–639 (2013)

work page 2013

[10] [10]

& Wiesendanger, R

Romming, N., Kubetzka, A., Hanneken, C., von Bergmann, K. & Wiesendanger, R. Field- dependent size and shape of single magnetic skyrmions. Phys. Rev. Lett. 114, 177203 (2015)

work page 2015

[11] [11]

Boulle, O. et al. Room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures. Nat. Nanotechnol. 11, 449-454 (2016)

work page 2016

[12] [12]

& Zhou Y

Zhang, X., Ezawa, M. & Zhou Y. Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions. Sci. Rep. 5, 9400 (2015)

work page 2015

[13] [13]

& Böni, P

Mühlbauer, S., Binz, B., Jonietz, F., Pfleiderer, C., Rosch, A., Neubauer, A., Georgii, R. & Böni, P. Skyrmion Lattice in a Chiral Magnet. Science 323, 915-919 (2009)

work page 2009

[14] [14]

Yu, X.Z. et al. Near room-temperature formation of a skyrmion crystal in thin-films of the 8 helimagnet FeGe. Nat. Mater. 10, 106–109 (2011)

work page 2011

[15] [15]

& Fullerton, E.E

Tolley, R., Montoya, S.A. & Fullerton, E.E. Room-temperature observation and current control of skyrmions in Pt/Co/Os/Pt thin films. Phys. Rev. Mater. 2, 044404 (2018)

work page 2018

[16] [16]

Woo, S. et al. Observation of room-temperature magnetic skyrmions and their current- driven dynamics in ultrathin metallic ferromagnets. Nat. Mater. 15, 501–506 (2016)

work page 2016

[17] [17]

Soumyanarayanan, A. et al. Tunable room-temperature magnetic skyrmions in Ir/Fe/Co/Pt multilayers. Nat. Mater. 16, 898–904 (2017)

work page 2017

[18] [18]

& Wiesendanger, R

Siemens, A., Zhang, Y., Hagemeister, J., Vedmedenko, E.Y. & Wiesendanger, R. Minimal radius of magnetic skyrmions: statics and dynamics. New. J. Phys. 18, 045021 (2016)

work page 2016

[19] [19]

& Beach G.S.D

Büttner, F., Lemesh I. & Beach G.S.D. Theory of isolated magnetic skyrmions: From fundamentals to room temperature applications. Sci. Rep. 8, 4464 (2018)

work page 2018

[20] [20]

Jiang, W. et al. Direct observation of the skyrmion Hall effect. Nat. Phys. 13, 162-169 (2017)

work page 2017

[21] [21]

Litzius, K. et al. Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy. Nat. Phys. 13, 170-175 (2017)

work page 2017

[22] [22]

Skyrmions on the track

Fert, A., Cros, V., Sampaio, J. Skyrmions on the track. Nat. Nanotechnol. 8, 152-156 (2013)

work page 2013

[23] [23]

Tomasello, R. et al. A strategy for the design of skyrmion racetrack memories. Sci. Rep. 4, 6784 (2014)

work page 2014

[24] [24]

Woo, S. et al. Current-driven dynamics and inhibition of the skyrmion Hall effect of ferrimagnetic skyrmions in GdFeCo films. Nat. Commun. 9, 959 (2018)

work page 2018

[25] [25]

Lee, J. C. T. et al. Synthesizing skyrmion bound pairs in Fe-Gd thin films. Appl. Phys. Lett. 109, (2016)

work page 2016

[26] [26]

Caretta, L. et al. Fast current-driven domain walls and small skyrmions in a compensated ferrimagnet. Nat. Nanotechnol. 13, 1154-1160 (2018)

work page 2018

[27] [27]

A thermodynamic theory of weak ferromagnetism of antiferromagnetics

Dzyaloshinsky, I. A thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958)

work page 1958

[28] [28]

Anisotropic superexchange interaction and weak ferromagnetism

Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98 (1960)

work page 1960

[29] [29]

Belmeguenai, M. et al. A. Interfacial Dzyaloshinskii–Moriya interaction in perpendicularly magnetized Pt/Co/AlOx ultrathin films measured by Brillouin light spectroscopy. Phys. Rev. B 91, 180405(R) (2015)

work page 2015

[30] [30]

& Silva, T.J

Nembach, H.T., Shaw, J.M, Weiler, M., Jué E. & Silva, T.J. Linear relation between Heisenberg exchange and interfacial Dzyaloshinskii–Moriya interaction in metal films. Nature Phys. 11, 825-829 (2015)

work page 2015

[31] [31]

& Chshiev, M

Yang, H., Thiaville, A., Rohart, S., Fert, A. & Chshiev, M. Anatomy of Dzyaloshinskii-Moriya Interaction at Co/Pt Interfaces. Phys. Rev. Lett. 118, 219901 (2017)

work page 2017

[32] [32]

Belmeguenai, M. et al. Thickness Dependence of the Dzyaloshinskii -Moriya Interaction in Co2FeAl Ultrathin Films: Effects of Annealing Temperature and Heavy -Metal Material. Phys. Rev. Appl. 9, 044044 (2018)

work page 2018

[33] [33]

Dirks, A. G. & Leamy, H. J. Columnar microstructure in vapor-deposited thin films. Thin Solid Films 47, 219–233 (1977)

work page 1977

[34] [34]

Leamy, H. J. & Dirks, A. G. Microstructure and magnetism in amorphous rare-earth- transition-metal thin films. II. Magnetic anisotropy. J. Appl. Phys. 49, 3430 (1978)

work page 1978

[35] [35]

G., Aylesworth, K

Harris, V. G., Aylesworth, K. D., Das, B. N., Elam, W. T. & Koon, N. C. Structural origins of magnetic anisotropy in sputtered amorphous Tb-Fe films. Phys. Rev. Lett. 69, 1939–1942 (1992)

work page 1939

[36] [36]

Harris, V. G. & Pokhil, T. Selective-Resputtering-Induced Perpendicular Magnetic Anisotropy 9 in Amorphous TbFe Films. Phys. Rev. Lett. 87, 67207 (2001)

work page 2001

[37] [37]

& Witter, K

Hansen, P., Clausen, C., Much, G., Rosenkranz, M. & Witter, K. Magnetic and magneto- optical properties of rare-earth transition-metal alloys containing Gd, Tb, Fe, Co. J. Appl. Phys. 66, 756–767 (1989)

work page 1989

[38] [38]

Kim, K-J. et al. Fast domain wall motion in the vicinity of the angular momentum compensation temperature of ferrimagnets. Nature Materials 16, 1187-1192 (2017)

work page 2017

[39] [39]

Stanciu, C. D. et al. All-optical magnetic recording with circularly polarized light. Phys. Rev. Lett. 99, 47601 (2007)

work page 2007

[40] [40]

Savoini, M. et al. Highly efficient all-optical switching of magnetization in GdFeCo microstructures by interference-enhanced absorption of light. Phys. Rev. B 86, 140404(R) (2012)

work page 2012

[41] [41]

Ostler, T.A. et al. Ultrafast heating as a sufficient stimulus for magnetization reversal in a ferrimagnet. Nat. Commun. 3, 666 (2012)

work page 2012

[42] [42]

Hassdenteufel, A. et al. Thermally assisted all-optical helicity dependent magnetic switching in amorphous Fe100-xTbx alloy films. Adv. Mater. 25, 3122–3128 (2013)

work page 2013

[43] [43]

Kirilyuk, A., Kimel, A. V. & Rasing, T. Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys. 82, 2731–2784 (2010)

work page 2010

[44] [44]

Kirilyuk, A., Kimel, A. V. & Rasing, T. Laser-induced magnetization dynamics and reversal in ferrimagnetic alloys. Rep. Prog. Phys. 76, 026501 (2013)

work page 2013

[45] [45]

Kimel, A. V. All-optical switching: Three rules of design. Nat. Mater. 13, 225–226 (2014)

work page 2014

[46] [46]

Magnin, S. et al. Engineered materials for all-optical helicity-dependent magnetic switching. Nat. Mater. 13, 286-292 (2014)

work page 2014

[47] [47]

Ostler, T. A. et al. Crystallographically amorphous ferrimagnetic alloys: Comparing a localized atomistic spin model with experiments. Phys. Rev. B 84, 24407 (2011)

work page 2011

[48] [48]

Radu, I. et al. Transient ferromagnetic-like state mediating ultrafast reversal of antiferromagnetically coupled spins. Nature 472, 205–208 (2011)

work page 2011

[49] [49]

Ellis, M. O. A., Ostler, T. A. & Chantrell, R. W. Classical spin model of the relaxation dynamics of rare-earth doped permalloy. Phys. Rev. B 86, 174418 (2012)

work page 2012

[50] [50]

Evans, R. F. L. et al. Atomistic spin model simulations of magnetic nanomaterials. J. Phys. Condens. Matter 26, 103202 (2014)

work page 2014

[51] [51]

& Chubykalo-Fesenko O

Atxitia, U., Nieves, P. & Chubykalo-Fesenko O. Landau-Lifshitz-Bloch equation for ferrimagnetic materials. Phys. Rev. B 86, 104414 (2012)

work page 2012

[52] [52]

Chen, G. et al. Tailoring the chirality of magnetic domain walls by interface engineering. Nat. Commun. 4, 2671 (2013)

work page 2013

[53] [53]

Hrabec, A. et al. Measuring and tailoring the Dzyaloshinskii-Moriya interaction in perpendicularly magnetized thin films. Phys. Rev. B 90, 020402(R) (2014)

work page 2014

[54] [54]

Stashkevich, A.A. et al. Experimental study of spin-wave dispersion in Py/Pt film structures in the presence of an interface Dzyaloshinskii-Moriya interaction. Phys. Rev. B 91, 214409 (2015)

work page 2015

[55] [55]

Ma, X. et al. Interfacial control of Dzyaloshinskii-Moriya interaction in heavy metal/ferromagnetic metal thin film heterostructures. Phys. Rev. B 94, 180408(R) (2016)

work page 2016

[56] [56]

Tacchi, S. et al. Interfacial Dzyaloshinskii-Moriya Interaction in Pt/CoFeB Films: Effect of the Heavy-Metal Thickness. Phys. Rev. Lett. 118, 147201 (2017)

work page 2017

[57] [57]

Cho, J. et al. The sign of the interfacial Dzyaloshinskii –Moriyainteraction in ultrathin amorphous and polycrystalline magnetic films. J. Phys. D: Appl. Phys. 50, 425004 (2017)

work page 2017

[58] [58]

& Szunyogh, L

Simon, E., Rózsa, L., Palotás, K. & Szunyogh, L. Magnetism of a Co monolayer on Pt(111) capped by overlayers of 5d elements: A spin-model study. Phys. Rev. B 97, 134405 (2018). 10

work page 2018

[59] [59]

Atomic packing and short-to- medium-range order in metallic glasses

Sheng, H.W., Luo, W.K., Alamgir, F.M., Bai, J.M., & Ma, E. Atomic packing and short-to- medium-range order in metallic glasses. Nature 439, 419-425 (2006)

work page 2006

[60] [60]

Antiferromagnetic Skyrmion: Stability, Creation and Manipulation

Zhang, X., Zhou, Y., & Ezawa, M. Antiferromagnetic Skyrmion: Stability, Creation and Manipulation. Sci. Rep. 6, 24795 (2016)

work page 2016

[61] [61]

A., Static and Dynamical Properties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature

Baker, J., & Tretiakov, O. A., Static and Dynamical Properties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature. Phys. Rev. Lett. 116, 147203 (2016)

work page 2016

[62] [62]

Kim, K-J. et al. Fast domain wall motion in the vicinity of the angular momentum compensation temperature of ferrimagnets. Nature Materials 16, 1187-1192 (2017). Acknowledgements: This work was supported by the DARPA Topological Excitations in Electronics (TEE) program (grant D18AP00009). The content of the information does not necessarily reflect the pos...

work page 2017