We have performed broadband (10 MHz–18 GHz) and narrowband (9.7 GHz) ferromagnetic resonance (FMR) measurements on permalloy thin films patterned with quasiperiodic Ammann tilings having eightfold rotational symmetry. We observed highly reproducible mode structures in the low-frequency, hysteretic regime in which domain walls and unsaturated magnetization textures exist. A minimum of 10 robust modes were observed in patterned samples, compared to the single uniform mode observed in unpatterned permalloy films. The field dependence and approximate eightfold rotational symmetry of the FMR spectra are in good agreement with micromagnetic simulations that confirm the importance of patterning for controlling static and dynamic magnetic response

Bhat, Vinayak Shantaram

De Long, Lance E.

Farmer, B.

Hastings, Jeffrey Todd

Ketterson, J. B.

Sklenar, J.

Woods, J.

English

University of Kentucky

University of KentuckyUKnowledgePhysics and Astronomy Faculty Publications Physics and Astronomy5-7-2014Ferromagnetic resonance study of eightfoldartificial ferromagnetic quasicrystalsVinayak Shantaram BhatUniversity of Kentucky, vinayak8582@gmail.comJ. SklenarNorthwestern UniversityJ. WoodsUniversity of KentuckyB. FarmerUniversity of KentuckyJ. B. KettersonNorthwestern UniversitySee next page for additional authorsRight click to open a feedback form in a new tab to let us know how this document benefits you.Follow this and additional works at: https://uknowledge.uky.edu/physastron_facpubPart of the Electrical and Computer Engineering Commons, and the Physics CommonsThis Article is brought to you for free and open access by the Physics and Astronomy at UKnowledge. It has been accepted for inclusion in Physics andAstronomy Faculty Publications by an authorized administrator of UKnowledge. For more information, please contact UKnowledge@lsv.uky.edu.Repository CitationBhat, Vinayak Shantaram; Sklenar, J.; Woods, J.; Farmer, B.; Ketterson, J. B.; Hastings, Jeffrey Todd; and De Long, Lance E.,"Ferromagnetic resonance study of eightfold artificial ferromagnetic quasicrystals" (2014). Physics and Astronomy Faculty Publications.1.https://uknowledge.uky.edu/physastron_facpub/1AuthorsVinayak Shantaram Bhat, J. Sklenar, J. Woods, B. Farmer, J. B. Ketterson, Jeffrey Todd Hastings, and Lance E.De LongFerromagnetic resonance study of eightfold artificial ferromagnetic quasicrystalsNotes/Citation InformationPublished in Journal of Applied Physics, v. 115, no. 17C502.Copyright 2014, American Institute of Physics. This article may be downloaded for personal use only. Anyother use requires prior permission of the author and the American Institute of Physics.This article appeared in Journal of Applied Physics, v. 115, no. 17C502 and may be found at http://dx.doi.org/10.1063/1.4859035.The copyright holder has granted the permission for posting the article here.Digital Object Identifier (DOI)http://dx.doi.org/10.1063/1.4859035This article is available at UKnowledge: https://uknowledge.uky.edu/physastron_facpub/1Ferromagnetic resonance study of eightfold artificial ferromagnetic quasicrystalsV. S. Bhat, J. Sklenar, B. Farmer, J. Woods, J. B. Ketterson, J. T. Hastings, and L. E. De Long  Citation: Journal of Applied Physics 115, 17C502 (2014); doi: 10.1063/1.4859035 View online: http://dx.doi.org/10.1063/1.4859035 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/17?ver=pdfcov Published by the AIP Publishing  Articles you may be interested in Nonstochastic magnetic reversal in artificial quasicrystalline spin ice J. Appl. 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De Long11Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA2Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA3Department of Electric and Computer Engineering, University of Kentucky, Lexington, Kentucky 40506, USA(Presented 5 November 2013; received 22 September 2013; accepted 11 October 2013; publishedonline 7 January 2014)We have performed broadband (10 MHz–18 GHz) and narrowband (9.7 GHz) ferromagneticresonance (FMR) measurements on permalloy thin films patterned with quasiperiodic Ammanntilings having eightfold rotational symmetry. We observed highly reproducible mode structures inthe low-frequency, hysteretic regime in which domain walls and unsaturated magnetizationtextures exist. A minimum of 10 robust modes were observed in patterned samples, compared tothe single uniform mode observed in unpatterned permalloy films. The field dependence andapproximate eightfold rotational symmetry of the FMR spectra are in good agreement withmicromagnetic simulations that confirm the importance of patterning for controlling static anddynamic magnetic response.VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4859035]Ferromagnetic (FM) antidot lattices (ADL) haveattracted attention from technological1,2 as well as basic sci-ence perspectives.2–4 Previous studies on FM ADL havemainly focused on periodic arrays (square, rectangular,kagome, etc.). A recent study5 of fivefold rotationally sym-metric artificial quasicrystals (QCs) (Penrose P2 tilings) pat-terned into permalloy films displayed static and dynamicproperties that differ from those observed for periodic ADL.The ferromagnetic resonance (FMR) spectra for finitePenrose tilings were of particular interest, since they exhib-ited tenfold rotational symmetry that is only expected for infi-nite patterns, as well as novel “asymmetric” mode signaturesin the hysteretic reversal regime. Herein, we report a FMRstudy of a second class of permalloy thin films patterned intofinite, quasiperiodic Ammann tilings (ATs) that exhibit eight-fold rotational symmetry.We patterned AT by incorporating a deflation algorithminto our electron beam lithography (EBL) software. Thealgorithm was initialized with an arrangement of squares andrhombi (with interior angles of 45 and 135, such as shownin Fig. 1) known as the “0th generation” AT. Note the tilingcan be viewed as a network of film segments of length d andwidth W. A single iteration of the deflation method on a nthgeneration tiling will produce a ðnþ 1Þth generation tiling,as described elsewhere.6,7 The new tiling was scaled suchthat the segment length d remained the same as for the origi-nal 0th generation tiling. Two samples of differing genera-tion were prepared with different edge lengths d for thesquares and rhombi, and common width W and thickness t(see Table I). Fig. 1 exhibits an SEM image of one write fieldfor sample III136C. Multiple write fields were copied onto asquare array in order to increase the (signal-to-noise-ratio)SNR for magnetic measurements.Narrow-band (NB) FMR measurements were carried outat microwave frequency f¼ 9.7 GHz in applied DC magneticfields H  10 kOe. Broad-band (BB) FMR measurementswere performed at room temperature using a meander linemethod,8 in which f can be varied continuously from10 MHz up to 20 GHz. The applied field H could be sweptcontinuously through zero over the range þ6 kOe to 6kOe, and could be rotated within the film plane by an angle/ between H and the x- axis (see Fig. 1).Micromagnetic simulations (MS) were performed tointerpret the FMR data by importing a graphic rendition of the0th generation AT (with d ¼ 1 lm, W¼ 130 nm, andFIG. 1. SEM image of one write field for Sample III136C (see Table I).Non-magnetic substrate and permalloy regions correspond to the dark andthe bright areas, respectively. The magnetic field can be rotated by angle /with respect to the x- axis, defined to be horizontal.a)Author to whom correspondence should be addressed. Electronic mail:vinayak.bhat@uky.edu.0021-8979/2014/115(17)/17C502/3/$30.00 VC 2014 AIP Publishing LLC115, 17C502-1JOURNAL OF APPLIED PHYSICS 115, 17C502 (2014) [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:128.163.8.74 On: Wed, 14 May 2014 18:06:23t¼ 25 nm) into OOMMF code9 using a 10 nm 10 nm 25 nm grid (with exchange constant A ¼ 13  1012 Jm andsaturation magnetization MS ¼ 8:6  105 Am). Larger genera-tions were not simulated due to computational limitations.The equilibrium magnetization was calculated for the givenapplied DC field. A dynamical FMR simulation was con-ducted by applying a Gaussian magnetic field pulse (of 20 Oeamplitude and 2.5 ps FWHM duration) perpendicular to thefilm plane, followed by logging 1024 successive values ofmagnetization vector for each grid pixel at 10 ps time steps.The perpendicular component of magnetization was recordedas a function of x, y, and time step. The absorbed power foreach pixel was obtained by squaring the FFT amplitude, andthe signal phase was obtained by calculating the imaginarypart of the amplitude. The analysis yields an area map of themagnetization tilt amplitude at the frequency of response.Comparison with the experimental total absorbed power at agiven frequency was achieved by integrating local power overall pixels for each frequency step.Fig. 2 shows the experimental BB FMR spectra forSample III128D for microwave frequency f¼ 15.5 GHz andH oriented along x axis (/ ¼ 0). We observed five promi-nent modes symmetrically placed at H ¼ 61:227, 61:635,62:018, 63:151, and63:763 kOe in both negative and posi-tive field sweeps. The 15.5 GHz spectra also exhibit a lower-field, “asymmetric” mode that exhibits clear hysteresis:When the DC field was scanned from positive saturation(H¼þ6 kOe) to negative saturation (H¼6 kOe), only onemode signature was observed at H¼0.33 kOe, on the neg-ative side of zero. On the other hand, when magnetic fieldwas swept from negative saturation (H¼6 kOe), a corre-sponding mode signature was observed only at H¼þ0.29kOe, on the positive side of zero. MS indicate the presenceof domain walls and complex switching behavior of thepermalloy segments in the hysteretic regime give rise to theasymmetric mode near zero field. The reproducibility of themode structure over a wide range of fields in Fig. 2 is evi-dently due to shape anisotropy induced by patterning.5Fig. 3 shows the experimental (4th generation) BB FMRdata and MS results (0th generation) for the frequency vs.field dispersion relations for ten mode branches. The simu-lated FMR mode branches 1, 4, 5, and 6 are in very goodagreement with experiments; whereas the experimental BBFMR data only reveal one broad mode located in betweenthe simulated branches 2 and 3.Figs. 4(a)–4(c) show simulated local power maps corre-sponding to f¼ 16.5 GHz (H¼ 4 kOe; branch 1 in Fig. 3),f¼ 14.5 GHz (H¼ 2 kOe; branch 3 in Fig. 3), andf¼ 18.4 GHz (H¼ 2 kOe; branch 6 in Fig. 3). The dynamicsimulations, done only for the 0th generation AT, suggestFMR modes at jHj ¼ 1:227, 1.63, and 3.763 kOe (see Fig. 2)are due to power absorption by permalloy segments at anangle h ¼ 0 and 180 (branch 6 in Fig. 3), 645 (branch 5in Fig. 3), and 690 (branch 1 in Fig. 3), respectively. Here,h is defined to be the angle between a segment’s long axisand the10 direction of the film. A FMR mode at jHj ¼ 2:018kOe is due to power absorption in both h ¼ 645 and 690segments (branch 4 in Fig. 3). A weaker mode at jHj ¼3:151 kOe may be a second harmonic of the mode responsi-ble for power absorption in both 645 and 690 segments(overlapping branch 2 and/or 3 in Fig. 3).Fig. 5 shows NB FMR spectra for different field angles,0  /  90, and f¼ 9.7 GHz for Sample III136C. For/ ¼ 0, we observed FMR peaks at jHj ¼ 1:18, 1.07, 0.929,0.809, and 0.682 kOe. Fig. 5 shows the FMR spectra exhibitnear-eightfold rotational symmetry, consistent with theTABLE I. Parameters of Ammann tilings.Sample, generationd(nm)W(nm)QC apicalwidth (lm)No. writefieldsIII128D, 4th 1000 130 160 144III136C, 0th 7000 912 83 400Simulation, 0th 1000 130 12.2 N/AFIG. 2. BB FMR spectra for Sample III128D for frequency f¼ 15.5 GHz.Note reproducible, symmetric FMR spectra for DC fields jHj > 1 kOe;asymmetric modes only occur on one side of origin near jHj ¼ 0:3 kOe(branch 10 in Fig. 3). The blue arrow marks an asymmetric mode signaturefor negative sweep and the red arrow marks the same mode for positivesweep. Numbers denote mode branches.FIG. 3. BB FMR frequency f vs. DC field H for Sample III128D. Scatteredpoints and solid lines represent experimental data and simulations, respec-tively. Numbers denote mode branches. Note the low-field asymmetricmode branches 7–10 in the hysteretic regime.17C502-2 Bhat et al. J. Appl. Phys. 115, 17C502 (2014) [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:128.163.8.74 On: Wed, 14 May 2014 18:06:23geometry of the AT (Fig. 1). Small departures (1%–7%) ofthe resonance field data from eightfold symmetry is underinvestigation.We have fabricated novel artificial FM quasicrystals thatare eightfold rotationally symmetric. NB FMR data displayeightfold rotationally symmetric FMR absorption peaks. OurFMR data include many more modes than were seen in aprevious study of a periodic antidot lattice,10 due to the com-plex topology and lower symmetry of the AT. BB FMRexperiments exhibit symmetrically placed modes in the nearsaturated regime and novel asymmetric modes in the hyste-retic regime, similar to recent observations of Penrose P2tilings.5Research at the University of Kentucky was supportedby U.S. DOE Grant No. DE-FG02-97ER45653 and the U.K.Center for Advanced Materials (supported by U.S. NSFGrant No. EPS-0814194).1R. Cowburn, A. Adeyeye, and J. Bland, Appl. Phys. Lett. 70, 2309 (1997).2B. Lenk et al., Phys. Rep. 507, 107 (2011).3C. Yu, M. J. Pechan, and G. J. Mankey, Appl. Phys. Lett. 83, 3948 (2003).4W. Branford et al., Science 335, 1597 (2012).5V. S. Bhat et al., Phys. Rev. Lett. 111, 077201 (2013).6See http://demonstrations.wolfram.com/AmmannTiles/ for instructions onhow to construct the Ammann tiling.7F. P. M. Beenker, “Algebraic theory of non-periodic tilings of the plane bytwo simple building blocks: A square and a rhombus,” TH-Report No. 82-WSK04, Eindhoven University of Technology, 1982.8C.-C. Tsai et al., Rev. Sci. Instrum. 80, 023904 (2009).9M. J. Donahue and D. G. Porter, OOMMF User’s Guide (NIST, 1999).10V. Bhat et al., Physica C 479, 83 (2012).FIG. 4. (a) Simulated OOMMF power absorption maps for a 0th generation AT with d ¼ 1 lm, W¼ 130 nm, and t¼ 25 nm, field angle / ¼ 0, frequencyf¼ 16.5 GHz, and applied DC field H¼ 4 kOe. Color scale indicates the squared magnetization tipping amplitude (red is greatest). This power map corre-sponds to branch 1 (brown) in Fig. 3. (b) Power map for f¼ 14.1 GHz, H¼ 2 kOe corresponding to branch 3 (blue) in Fig. 3. (c). Power map for f¼ 18.4 GHz,H¼ 2 kOe corresponding to branch 6 (purple) in Fig. 3.FIG. 5. NB FMR absorption derivative versus applied DC magnetic field Hof Sample III136C at T¼ 300 K for frequency f¼ 9.7 GHz. Colors corre-spond to different angles 0  /  90. Note that / ¼ 0, 45, and 90 arereproduced, which is indicative of eightfold rotational symmetry.17C502-3 Bhat et al. J. Appl. Phys. 115, 17C502 (2014) [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:128.163.8.74 On: Wed, 14 May 2014 18:06:23

Ferromagnetic resonance study of eightfold artificial ferromagnetic quasicrystals

V. S. Bhat

J. Sklenar

B. Farmer

J. Woods

J. B. Ketterson

J. T. Hastings

L. E. De Long

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Journal of Applied Physics

https://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1000&amp;context=physastron_facpub

Ferromagnetic resonance study of eightfold artificial ferromagnetic quasicrystals

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