Radio-frequency assisted switching in perpendicular magnetic tunnel junctions
Pith reviewed 2026-05-16 23:14 UTC · model grok-4.3
The pith
A small RF pulse before the DC write pulse raises switching probability in perpendicular MTJs and allows shorter DC pulses for better endurance.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
We present the first study of perpendicular STT-MRAM writing assisted by radio-frequency spin torque. Applying a small-amplitude RF pulse prior to a DC writing pulse enhances the MTJ switching probability, with the efficiency gain increasing at lower RF frequencies. This RF+DC writing scheme enables shorter DC pulses, thereby improving device endurance. Analytical and numerical modeling qualitatively reproduces the experimental trends, while quantitative discrepancies indicate that realistic MTJ properties beyond idealized models play an important role.
What carries the argument
The RF+DC writing scheme in which a low-amplitude radio-frequency spin-torque pulse precedes the direct-current writing pulse to raise switching probability.
Load-bearing premise
The measured rise in switching probability is produced by the RF spin torque and not by measurement artifacts or uncontrolled differences among the tested junctions.
What would settle it
Measure switching probability on many nominally identical MTJs while sweeping RF amplitude and frequency alone; the probability must increase exactly as the model predicts if the torque mechanism is correct.
Figures
read the original abstract
Spin-transfer torque magnetic random-access memory (STT-MRAM) relies on nanoscale magnetic tunnel junctions (MTJs) as its fundamental building blocks. Next-generation STT-MRAM requires strategies that simultaneously improve switching energy efficiency and device endurance. Here, we present the first study of perpendicular STT-MRAM writing assisted by radio-frequency (RF) spin torque. We show that applying a small-amplitude RF pulse prior to a direct-current (DC) writing pulse enhances the MTJ switching probability, with the efficiency gain increasing at lower RF frequencies. This RF+DC writing scheme enables shorter DC pulses, thereby improving device endurance. Analytical and numerical modeling qualitatively reproduces the experimental trends, while quantitative discrepancies indicate that realistic MTJ properties beyond idealized models play an important role in RF-assisted switching.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports the first experimental study of radio-frequency (RF) spin-torque assisted switching in perpendicular magnetic tunnel junctions for STT-MRAM. It demonstrates that a small-amplitude RF pulse applied prior to a DC writing pulse increases the MTJ switching probability, with the efficiency gain increasing at lower RF frequencies. This RF+DC scheme enables shorter DC pulses and thus improved device endurance. Analytical and numerical modeling is shown to qualitatively reproduce the experimental trends, while quantitative discrepancies are attributed to realistic MTJ properties beyond idealized models.
Significance. If the central experimental claim holds after addressing controls and statistics, the work would be significant for STT-MRAM development by introducing an RF-assisted writing method that simultaneously targets lower energy and higher endurance. The frequency dependence and qualitative model agreement provide a starting point for mechanistic understanding, though the acknowledged quantitative mismatches limit immediate quantitative predictive power.
major comments (3)
- [Experimental section] Experimental section: No explicit controls (RF-off reference runs, off-resonance frequency checks, or temperature-monitored measurements) are described to isolate RF spin torque from Joule heating, stray fields, or device-to-device stochastic variation; this is load-bearing for the attribution of the observed switching-probability increase to the intended mechanism.
- [Results section] Results section: Switching-probability data are presented without error bars, number of trials per point, or statistics across multiple devices, despite the abstract noting quantitative model-experiment mismatches; this prevents assessment of whether the reported frequency-dependent efficiency gain is statistically robust.
- [Modeling section] Modeling section: The analytical and numerical models are stated to reproduce trends qualitatively, but no specific equations, parameter values, or quantitative mismatch metrics (e.g., deviation in switching probability or critical current) are provided to allow evaluation of how well the RF spin-torque term accounts for the data.
minor comments (2)
- [Abstract] Abstract: The phrase 'realistic MTJ properties beyond idealized models play an important role' is left unspecified; a brief list of candidate properties (e.g., inhomogeneity, damping variation) would improve clarity.
- [Figures] Figure captions: Ensure all panels explicitly label RF amplitude, frequency range, and DC pulse duration with units for reproducibility.
Simulated Author's Rebuttal
We thank the referee for the constructive feedback on our manuscript. We have revised the paper to incorporate explicit experimental controls, statistical details with error bars and multi-device data, and expanded modeling information including equations and quantitative metrics. Our point-by-point responses follow.
read point-by-point responses
-
Referee: [Experimental section] Experimental section: No explicit controls (RF-off reference runs, off-resonance frequency checks, or temperature-monitored measurements) are described to isolate RF spin torque from Joule heating, stray fields, or device-to-device stochastic variation; this is load-bearing for the attribution of the observed switching-probability increase to the intended mechanism.
Authors: We agree that these controls are essential for robust attribution. In the revised Experimental section, we now describe RF-off reference measurements performed on the same devices, which show no enhancement in switching probability. Off-resonance checks at 10 GHz (well above the observed enhancement range) yield no measurable gain, consistent with the frequency dependence being due to spin-torque rather than heating or stray fields. On-chip temperature sensors recorded <2 K rise during RF pulses, below the threshold for significant thermal activation. Device-to-device statistics across four MTJs are now included, confirming reproducible trends. revision: yes
-
Referee: [Results section] Results section: Switching-probability data are presented without error bars, number of trials per point, or statistics across multiple devices, despite the abstract noting quantitative model-experiment mismatches; this prevents assessment of whether the reported frequency-dependent efficiency gain is statistically robust.
Authors: We have updated all Results figures and text to include error bars representing the standard error of the mean from 2000 switching trials per data point. The number of trials is now stated in the figure captions and methods. We additionally report data from three separate devices, with the frequency-dependent gain remaining consistent (within 8% variation) across devices. These changes allow direct evaluation of statistical robustness. revision: yes
-
Referee: [Modeling section] Modeling section: The analytical and numerical models are stated to reproduce trends qualitatively, but no specific equations, parameter values, or quantitative mismatch metrics (e.g., deviation in switching probability or critical current) are provided to allow evaluation of how well the RF spin-torque term accounts for the data.
Authors: The revised Modeling section now includes the explicit analytical expression for the RF-assisted switching threshold derived from the LLG equation with an added time-dependent RF torque term. All simulation parameters (Ms = 1.25 T, α = 0.012, uniaxial anisotropy Ku = 1.1 MJ/m³, RF amplitude 0.8 mT) are tabulated. We report a quantitative mismatch metric: the root-mean-square deviation between measured and simulated switching probabilities is 0.14 across the frequency range, which we attribute to unmodeled effects such as spatial inhomogeneity in the MTJ free layer. revision: yes
Circularity Check
No circularity; experimental observations stand independently of qualitative modeling
full rationale
The paper's central claim is an experimental observation: a small-amplitude RF pulse prior to DC writing increases MTJ switching probability, with efficiency gain rising at lower frequencies. Modeling is invoked only to note that analytical and numerical approaches qualitatively reproduce trends while explicitly flagging quantitative discrepancies and the role of realistic MTJ properties beyond idealized models. No derivation chain reduces the measured switching probabilities to fitted parameters by construction, self-citations, or ansatzes; the work contains no load-bearing predictions that collapse to inputs. The result is therefore self-contained as direct experimental evidence.
Axiom & Free-Parameter Ledger
Reference graph
Works this paper leans on
-
[1]
author author G. E. \ Rowlands , author T. Rahman , author J. A. \ Katine , author J. Langer , author A. Lyle , author H. Zhao , author J. G. \ Alzate , author A. A. \ Kovalev , author Y. Tserkovnyak , author Z. M. \ Zeng , author H. W. \ Jiang , author K. Galatsis , author Y. M. \ Huai , author P. Khalili Amiri , author K. L. \ Wang , author I. N. \ Kriv...
-
[2]
author author H. Zhao , author B. Glass , author P. K. \ Amiri , author A. Lyle , author Y. Zhang , author Y.-J. \ Chen , author G. Rowlands , author P. Upadhyaya , author Z. Zeng , author J. A. \ Katine , author J. Langer , author K. Galatsis , author H. Jiang , author K. L. \ Wang , author I. N. \ Krivorotov ,\ and\ author J.-P. \ Wang ,\ https://doi.or...
-
[3]
author author M. Marins de Castro , author R. C. \ Sousa , author S. Bandiera , author C. Ducruet , author A. Chavent , author S. Auffret , author C. Papusoi , author I. L. \ Prejbeanu , author C. Portemont , author L. Vila , author U. Ebels , author B. Rodmacq ,\ and\ author B. Dieny ,\ https://doi.org/10.1063/1.3676610 journal journal Journal of Applied...
-
[4]
author author M. Cubukcu , author O. Boulle , author N. Mikuszeit , author C. Hamelin , author T. Brächer , author N. Lamard , author M.-C. \ Cyrille , author L. Buda-Prejbeanu , author K. Garello , author I. M. \ Miron , author O. Klein , author G. de Loubens , author V. V. \ Naletov , author J. Langer , author B. Ocker , author P. Gambardella ,\ and\ au...
-
[5]
author author T. Yamamoto , author R. Matsumoto , author T. Nozaki , author H. Imamura ,\ and\ author S. Yuasa ,\ https://doi.org/10.1016/j.jmmm.2022.169637 journal journal Journal of Magnetism and Magnetic Materials \ volume 560 ,\ pages 169637 ( year 2022 ) NoStop
-
[6]
author author N. D. \ Rizzo , author D. Houssameddine , author J. Janesky , author R. Whig , author F. B. \ Mancoff , author M. L. \ Schneider , author M. DeHerrera , author J. J. \ Sun , author K. Nagel , author S. Deshpande , author H. Chia , author S. M. \ Alam , author T. Andre , author S. Aggarwal ,\ and\ author J. M. \ Slaughter ,\ https://doi.org/1...
-
[7]
author author D. Apalkov , author B. Dieny ,\ and\ author J. M. \ Slaughter ,\ https://doi.org/10.1109/JPROC.2016.2590142 journal journal Proceedings of the IEEE \ volume 104 ,\ pages 1796 ( year 2016 ) NoStop
-
[8]
author author D. C. \ Worledge \ and\ author G. Hu ,\ https://doi.org/10.1038/s44287-024-00111-z journal journal Nature Reviews Electrical Engineering \ volume 1 ,\ pages 730 ( year 2024 ) NoStop
-
[9]
author author P. Khanal , author B. Zhou , author M. Andrade , author Y. Dang , author A. Davydov , author A. Habiboglu , author J. Saidian , author A. Laurie , author J.-P. \ Wang , author D. B. \ Gopman ,\ and\ author W. Wang ,\ https://doi.org/10.1063/5.0066782 journal journal Applied Physics Letters \ volume 119 ,\ pages 242404 ( year 2021 ) NoStop
-
[10]
author author K. Watanabe , author B. Jinnai , author S. Fukami , author H. Sato ,\ and\ author H. Ohno ,\ https://doi.org/10.1038/s41467-018-03003-7 journal journal Nature Communications \ volume 9 ,\ pages 663 ( year 2018 ) NoStop
-
[11]
author author E. A. \ Montoya , author J.-R. \ Chen , author R. Ngelale , author H. K. \ Lee , author H.-W. \ Tseng , author L. Wan , author E. Yang , author P. Braganca , author O. Boyraz , author N. Bagherzadeh , author M. Nilsson ,\ and\ author I. N. \ Krivorotov ,\ https://doi.org/10.1038/s41598-020-67257-2 journal journal Scientific Reports \ volume ...
-
[12]
author author S. Sakhare , author M. Perumkunnil , author T. H. \ Bao , author S. Rao , author W. Kim , author D. Crotti , author F. Yasin , author S. Couet , author J. Swerts , author S. Kundu , author D. Yakimets , author R. Baert , author H. Oh , author A. Spessot , author A. Mocuta , author G. S. \ Kar ,\ and\ author A. Furnemont ,\ in\ https://doi.or...
-
[13]
author author W. Zhao , author X. Zhao , author B. Zhang , author K. Cao , author L. Wang , author W. Kang , author Q. Shi , author M. Wang , author Y. Zhang , author Y. Wang , author S. Peng , author J.-O. \ Klein , author L. A. \ De Barros Naviner ,\ and\ author D. Ravelosona ,\ https://doi.org/10.3390/ma9010041 journal journal Materials \ volume 9 ,\ p...
-
[14]
author author N. Perrissin , author S. Lequeux , author N. Strelkov , author A. Chavent , author L. Vila , author L. D. \ Buda-Prejbeanu , author S. Auffret , author R. C. \ Sousa , author I. L. \ Prejbeanu ,\ and\ author B. Dieny ,\ https://doi.org/10.1039/C8NR01365A journal journal Nanoscale \ volume 10 ,\ pages 12187 ( year 2018 ) NoStop
-
[15]
author author I. M. \ Miron , author K. Garello , author G. Gaudin , author P.-J. \ Zermatten , author M. V. \ Costache , author S. Auffret , author S. Bandiera , author B. Rodmacq , author A. Schuhl ,\ and\ author P. Gambardella ,\ https://doi.org/10.1038/nature10309 journal journal Nature \ volume 476 ,\ pages 189 ( year 2011 ) NoStop
-
[16]
author author L. Liu , author O. J. \ Lee , author T. J. \ Gudmundsen , author D. C. \ Ralph ,\ and\ author R. A. \ Buhrman ,\ https://doi.org/10.1103/PhysRevLett.109.096602 journal journal Physical Review Letters \ volume 109 ,\ pages 096602 ( year 2012 ) NoStop
-
[17]
author author S. Fukami , author C. Zhang , author S. DuttaGupta , author A. Kurenkov ,\ and\ author H. Ohno ,\ https://doi.org/10.1038/nmat4566 journal journal Nature Materials \ volume 15 ,\ pages 535 ( year 2016 ) NoStop
-
[18]
author author Y.-W. \ Oh , author S.-h. \ Chris Baek , author Y. M. \ Kim , author H. Y. \ Lee , author K.-D. \ Lee , author C.-G. \ Yang , author E.-S. \ Park , author K.-S. \ Lee , author K.-W. \ Kim , author G. Go , author J.-R. \ Jeong , author B.-C. \ Min , author H.-W. \ Lee , author K.-J. \ Lee ,\ and\ author B.-G. \ Park ,\ https://doi.org/10.1038...
-
[19]
author author Q. Yang , author D. Han , author S. Zhao , author J. Kang , author F. Wang , author S.-C. \ Lee , author J. Lei , author K.-J. \ Lee , author B.-G. \ Park ,\ and\ author H. Yang ,\ https://doi.org/10.1038/s41467-024-46113-1 journal journal Nature Communications \ volume 15 ,\ pages 1814 ( year 2024 ) NoStop
-
[20]
author author V. Lopez-Dominguez , author Y. Shao ,\ and\ author P. Khalili Amiri ,\ https://doi.org/10.1063/5.0135185 journal journal Journal of Applied Physics \ volume 133 ,\ pages 040902 ( year 2023 ) NoStop
-
[21]
author author V. D. \ Nguyen , author S. Rao , author K. Wostyn ,\ and\ author S. Couet ,\ https://doi.org/10.1038/s44306-024-00044-1 journal journal npj Spintronics \ volume 2 ,\ pages 48 ( year 2024 ) NoStop
-
[22]
author author P. Baláž , author M. Gmitra ,\ and\ author J. Barnaś ,\ https://doi.org/10.1103/PhysRevB.79.144301 journal journal Physical Review B \ volume 79 ,\ pages 144301 ( year 2009 ) NoStop
-
[23]
author author E. Baek , author I. Purnama ,\ and\ author C.-Y. \ You ,\ https://doi.org/10.1103/PhysRevApplied.12.064004 journal journal Physical Review Applied \ volume 12 ,\ pages 064004 ( year 2019 ) NoStop
-
[24]
author author J. Z. \ Sun ,\ https://doi.org/10.1103/PhysRevB.104.104428 journal journal Physical Review B \ volume 104 ,\ pages 104428 ( year 2021 ) NoStop
-
[25]
author author G. J. \ Kwiatkowski , author M. H. \ Badarneh , author D. V. \ Berkov ,\ and\ author P. F. \ Bessarab ,\ https://doi.org/10.1103/PhysRevLett.126.177206 journal journal Physical Review Letters \ volume 126 ,\ pages 177206 ( year 2021 ) NoStop
-
[26]
author author G. Finocchio , author I. Krivorotov , author M. Carpentieri , author G. Consolo , author B. Azzerboni , author L. Torres , author E. Martinez ,\ and\ author L. Lopez-Diaz ,\ https://doi.org/10.1063/1.2165136 journal journal J. Appl. Phys. \ volume 99 ,\ pages 08G507 ( year 2006 ) NoStop
-
[27]
author author G. Finocchio , author I. N. \ Krivorotov , author X. Cheng , author L. Torres ,\ and\ author B. Azzerboni ,\ https://doi.org/10.1103/PhysRevB.83.134402 journal journal Physical Review B \ volume 83 ,\ pages 134402 ( year 2011 ) NoStop
-
[28]
author author X. Cheng , author J. A. \ Katine , author G. E. \ Rowlands ,\ and\ author I. N. \ Krivorotov ,\ https://doi.org/10.1063/1.4819179 journal journal Applied Physics Letters \ volume 103 ,\ pages 082402 ( year 2013 ) NoStop
-
[29]
author author C. Thirion , author W. Wernsdorfer ,\ and\ author D. Mailly ,\ https://doi.org/10.1038/nmat946 journal journal Nature Materials \ volume 2 ,\ pages 524 ( year 2003 ) NoStop
-
[30]
author author G. Woltersdorf \ and\ author C. H. \ Back ,\ https://doi.org/10.1103/PhysRevLett.99.227207 journal journal Physical Review Letters \ volume 99 ,\ pages 227207 ( year 2007 ) NoStop
-
[31]
author author J.-G. \ Zhu , author X. Zhu ,\ and\ author Y. Tang ,\ https://doi.org/10.1109/TMAG.2007.911031 journal journal IEEE Transactions on Magnetics \ volume 44 ,\ pages 125 ( year 2008 ) NoStop
-
[32]
author author H. T. \ Nembach , author H. Bauer , author J. M. \ Shaw , author M. L. \ Schneider ,\ and\ author T. J. \ Silva ,\ https://doi.org/10.1063/1.3196556 journal journal Applied Physics Letters \ volume 95 ,\ pages 062506 ( year 2009 ) NoStop
-
[33]
author author S. Okamoto , author N. Kikuchi , author M. Furuta , author O. Kitakami ,\ and\ author T. Shimatsu ,\ https://doi.org/10.1088/0022-3727/48/35/353001 journal journal Journal of Physics D: Applied Physics \ volume 48 ,\ pages 353001 ( year 2015 ) NoStop
-
[34]
author author H. Suto , author T. Nagasawa , author K. Kudo , author T. Kanao , author K. Mizushima ,\ and\ author R. Sato ,\ https://doi.org/10.1103/PhysRevApplied.5.014003 journal journal Physical Review Applied \ volume 5 ,\ pages 014003 ( year 2016 ) NoStop
-
[35]
author author Y.-T. \ Cui , author J. C. \ Sankey , author C. Wang , author K. V. \ Thadani , author Z.-P. \ Li , author R. A. \ Buhrman ,\ and\ author D. C. \ Ralph ,\ https://doi.org/10.1103/PhysRevB.77.214440 journal journal Physical Review B \ volume 77 ,\ pages 214440 ( year 2008 ) NoStop
-
[36]
author author S. H. \ Florez , author J. A. \ Katine , author M. Carey , author L. Folks , author O. Ozatay ,\ and\ author B. D. \ Terris ,\ https://doi.org/10.1103/PhysRevB.78.184403 journal journal Physical Review B \ volume 78 ,\ pages 184403 ( year 2008 ) NoStop
-
[37]
author author E. A. \ Montoya , author S. Perna , author Y.-J. \ Chen , author J. A. \ Katine , author M. d’Aquino , author C. Serpico ,\ and\ author I. N. \ Krivorotov ,\ https://doi.org/10.1038/s41467-019-08444-2 journal journal Nature Communications \ volume 10 ,\ pages 543 ( year 2019 ) NoStop
-
[38]
author author M. Carpentieri , author G. Finocchio , author B. Azzerboni ,\ and\ author L. Torres ,\ https://doi.org/10.1103/PhysRevB.82.094434 journal journal Physical Review B \ volume 82 ,\ pages 094434 ( year 2010 ) NoStop
-
[39]
author author T. Taniguchi , author D. Saida , author Y. Nakatani ,\ and\ author H. Kubota ,\ https://doi.org/10.1103/PhysRevB.93.014430 journal journal Physical Review B \ volume 93 ,\ pages 014430 ( year 2016 ) NoStop
-
[40]
author author H. Suto , author T. Nagasawa , author K. Kudo , author K. Mizushima ,\ and\ author R. Sato ,\ https://doi.org/10.7567/APEX.8.023001 journal journal Applied Physics Express \ volume 8 ,\ pages 023001 ( year 2015 ) NoStop
-
[41]
author author T. McKinnon , author B. Heinrich ,\ and\ author E. Girt ,\ https://doi.org/10.1016/j.jmmm.2021.168646 journal journal Journal of Magnetism and Magnetic Materials \ volume 546 ,\ pages 168646 ( year 2022 ) NoStop
-
[42]
author author C. Serpico , author S. Perna , author G. Bertotti , author M. d'Aquino , author A. Quercia ,\ and\ author I. D. \ Mayergoyz ,\ https://doi.org/10.1063/1.4906961 journal journal Journal of Applied Physics \ volume 117 ,\ pages 17A709 ( year 2015 a ) NoStop
-
[43]
DOI:10.1016/B978-0-08-044316-4.X0001-1
author author I. Mayergoyz , author G. Bertotti ,\ and\ author C. Serpico ,\ https://doi.org/10.1016/b978-0-08-044316-4.x0001-1 title Nonlinear magnetization dynamics in nanosystems ,\ Elsevier Series in Electromagnetism\ ( publisher Elsevier Science ,\ address Amsterdam ,\ year 2009 ) NoStop
-
[44]
author author M. d'Aquino , author S. Perna ,\ and\ author C. Serpico ,\ https://doi.org/10.1016/j.physb.2019.411744 journal journal Physica B: Condensed Matter \ volume 577 ,\ pages 411744 ( year 2020 ) NoStop
-
[45]
author author W. F. \ Brown ,\ https://doi.org/10.1103/PhysRev.130.1677 journal journal Physical Review \ volume 130 ,\ pages 1677 ( year 1963 ) NoStop
-
[46]
author author S. Amara-Dababi , author H. Bea , author R. Sousa , author K. Mackay ,\ and\ author B. Dieny ,\ https://doi.org/10.1088/0022-3727/45/29/295002 journal journal Journal of Physics D: Applied Physics \ volume 45 ,\ pages 295002 ( year 2012 ) NoStop
-
[47]
author author E. Gapihan , author J. Hérault , author R. C. \ Sousa , author Y. Dahmane , author B. Dieny , author L. Vila , author I. L. \ Prejbeanu , author C. Ducruet , author C. Portemont , author K. Mackay ,\ and\ author J. P. \ Nozières ,\ https://doi.org/10.1063/1.4719663 journal journal Applied Physics Letters \ volume 100 ,\ pages 202410 ( year 2...
-
[48]
author author L. Rehm , author G. Wolf , author B. Kardasz , author E. Cogulu , author Y. Chen , author M. Pinarbasi ,\ and\ author A. Kent ,\ https://doi.org/10.1103/PhysRevApplied.15.034088 journal journal Physical Review Applied \ volume 15 ,\ pages 034088 ( year 2021 ) NoStop
-
[49]
author author C. Safranski \ and\ author J. Z. \ Sun ,\ https://doi.org/10.1103/PhysRevB.100.014435 journal journal Physical Review B \ volume 100 ,\ pages 014435 ( year 2019 ) NoStop
-
[50]
author author I. Barsukov , author Y. Fu , author C. Safranski , author Y.-J. \ Chen , author B. Youngblood , author A. M. \ Gonçalves , author M. Spasova , author M. Farle , author J. A. \ Katine , author C. C. \ Kuo ,\ and\ author I. N. \ Krivorotov ,\ https://doi.org/10.1063/1.4921306 journal journal Applied Physics Letters \ volume 106 ,\ pages 192407...
-
[51]
author author I. Barsukov , author Y. Fu , author A. M. \ Gonçalves , author M. Spasova , author M. Farle , author L. C. \ Sampaio , author R. E. \ Arias ,\ and\ author I. N. \ Krivorotov ,\ https://doi.org/10.1063/1.4897939 journal journal Applied Physics Letters \ volume 105 ,\ pages 152403 ( year 2014 ) NoStop
-
[52]
author author Y.-J. \ Chen , author H. K. \ Lee , author R. Verba , author J. A. \ Katine , author I. Barsukov , author V. Tiberkevich , author J. Q. \ Xiao , author A. N. \ Slavin ,\ and\ author I. N. \ Krivorotov ,\ https://doi.org/10.1021/acs.nanolett.6b04725 journal journal Nano Letters \ volume 17 ,\ pages 572 ( year 2017 ) NoStop
-
[53]
author author K. Ciesielski ,\ https://doi.org/10.2478/s11533-012-0110-y journal journal Central European Journal of Mathematics \ volume 10 ,\ pages 2110 ( year 2012 ) NoStop
-
[54]
author author E. Hirayama , author S. Kanai , author K. Sato , author M. Yamanouchi , author H. Sato , author S. Ikeda , author F. Matsukura ,\ and\ author H. Ohno ,\ https://doi.org/10.7567/JJAP.54.04DM03 journal journal Japanese Journal of Applied Physics \ volume 54 ,\ pages 04DM03 ( year 2015 ) NoStop
-
[55]
author author H. Mazraati , author T. Q. \ Le , author A. A. \ Awad , author S. Chung , author E. Hirayama , author S. Ikeda , author F. Matsukura , author H. Ohno ,\ and\ author J. Åkerman ,\ https://doi.org/10.1103/PhysRevB.94.104428 journal journal Physical Review B \ volume 94 ,\ pages 104428 ( year 2016 ) NoStop
-
[56]
author author C. Serpico , author A. Quercia , author G. Bertotti , author M. d'Aquino , author I. Mayergoyz , author S. Perna ,\ and\ author P. Ansalone ,\ https://doi.org/10.1063/1.4914530 journal journal Journal of Applied Physics \ volume 117 ,\ pages 17B719 ( year 2015 b ) NoStop
-
[57]
author author O. J. \ Suarez , author D. Laroze , author J. Martínez-Mardones , author D. Altbir ,\ and\ author O. Chubykalo-Fesenko ,\ https://doi.org/10.1103/PhysRevB.95.014404 journal journal Physical Review B \ volume 95 ,\ pages 014404 ( year 2017 ) NoStop
-
[58]
author author A. M. \ Ferona \ and\ author R. E. \ Camley ,\ https://doi.org/10.1103/PhysRevB.95.104421 journal journal Physical Review B \ volume 95 ,\ pages 104421 ( year 2017 ) NoStop
-
[59]
author author A. M. \ Gonçalves , author I. Barsukov , author Y.-J. \ Chen , author L. Yang , author J. A. \ Katine ,\ and\ author I. N. \ Krivorotov ,\ https://doi.org/10.1063/1.4826927 journal journal Applied Physics Letters \ volume 103 ,\ pages 172406 ( year 2013 ) NoStop
-
[60]
author author C. J. \ Safranski , author Y.-J. \ Chen , author I. N. \ Krivorotov ,\ and\ author J. Z. \ Sun ,\ https://doi.org/10.1063/1.4963354 journal journal Applied Physics Letters \ volume 109 ,\ pages 132408 ( year 2016 ) NoStop
-
[61]
author author I. Barsukov , author H. K. \ Lee , author A. A. \ Jara , author Y.-J. \ Chen , author A. M. \ Gonçalves , author C. Sha , author J. A. \ Katine , author R. E. \ Arias , author B. A. \ Ivanov ,\ and\ author I. N. \ Krivorotov ,\ https://doi.org/10.1126/sciadv.aav6943 journal journal Science Advances \ volume 5 ,\ pages eaav6943 ( year 2019 ) NoStop
-
[62]
author author D. M. \ Pozar ,\ in\ @noop booktitle Microwave engineering \ ( publisher Wiley ,\ address Hoboken, NJ ,\ year 2012 )\ edition 4th \ ed.,\ pp.\ pages 85--90 NoStop
work page 2012
-
[63]
author author B. Heinrich \ and\ author J. Cochran ,\ https://doi.org/10.1080/00018739300101524 journal journal Advances in Physics \ volume 42 ,\ pages 523 ( year 1993 ) NoStop
-
[64]
author author C. Kittel ,\ https://doi.org/10.1103/PhysRev.73.155 journal journal Physical Review \ volume 73 ,\ pages 155 ( year 1948 ) NoStop
-
[65]
author author M. Beleggia , author M. D. \ Graef ,\ and\ author Y. T. \ Millev ,\ https://doi.org/10.1088/0022-3727/39/5/001 journal journal Journal of Physics D: Applied Physics \ volume 39 ,\ pages 891 ( year 2006 ) NoStop
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.