Observation of dual magnonic and phononic bandgaps in bi-componentnanostructured crystalsV. L. Zhang, F. S. Ma, H. H. Pan, C. S. Lin, H. S. Lim et al. Citation: Appl. Phys. Lett. 100, 163118 (2012); doi: 10.1063/1.4705301 View online: http://dx.doi.org/10.1063/1.4705301 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v100/i16 Published by the American Institute of Physics. Related ArticlesA new pulsed laser deposition technique: Scanning multi-component pulsed laser deposition method Rev. Sci. Instrum. 83, 043901 (2012) Smallest separation of nanorods from physical vapor deposition Appl. Phys. Lett. 100, 141605 (2012) Exchange anisotropy in the nanostructured MnAl system Appl. Phys. Lett. 100, 112408 (2012) Microstructure study of pinning sites of highly (0001) textured Sm(Co,Cu)5 thin films grown on Ru underlayer J. Appl. Phys. 111, 07B730 (2012) Spin-torque diode spectrum of ferromagnetically coupled (FeB/CoFe)/Ru/(CoFe/FeB) synthetic free layer J. Appl. Phys. 111, 07C917 (2012) Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors

Observation of dual magnonic and phononic bandgaps in bi-componentnanostructured crystals

V. L. Zhang,1 F. S. Ma,1 H. H. Pan,1 C. S. Lin,1 H. S. Lim,1 S. C. Ng,1 M. H. Kuok,1,a)

S. Jain,2,b) and A. O. Adeyeye2,c)

1Department of Physics, National University of Singapore, Singapore 1175422Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576

(Received 20 December 2011; accepted 6 April 2012; published online 19 April 2012)

We report on the experimental observation of dual magnonic and phononic bandgaps in

bi-component nanostructured crystals. The dispersion relations of linear periodic arrays of alternating

Fe (or Ni) and Ni80Fe20 nanostripes on a SiO2/Si substrate, mapped by Brillouin spectroscopy,

feature distinct bandgaps. Calculations of the magnon and phonon dispersions yield good agreement

with experiments. No magnon-phonon interaction is detected for the modes observed, making the

structures studied a potential platform for the separate and simultaneous processing of information

carried by hypersonic magnons and phonons, with no undesirable cross-talk between them. VC 2012American Institute of Physics. [http://dx.doi.org/10.1063/1.4705301]

While numerous studies have been conducted on pho-

tonics,1 relatively little is known about its magnetic and

acoustic analogues, referred to, respectively, as magnonics

and phononics. However the latter two, which aim to control

and manipulate the propagation of information-carrying spin

waves (magnons) and acoustic waves (phonons) in magnonic

and phononic crystals, respectively, are rapidly emerging

fields.2–8 It is the energy bandgaps, a basic property of these

crystals, which endow them with this functionality. Also, as

the wavelengths of magnons and phonons are very much

shorter than those of photons of the same frequency, mag-

nonic and phononic crystals lend themselves to miniaturiza-

tion more readily than do photonic crystals. Besides being of

great fundamental scientific interest, magnonic and phononic

crystals hold enormous application potential, such as in the

fabrication of nanoscale microwave devices.7,8

Photonic crystals are periodic composites comprising

two or more materials of different refractive indices, as

opposed to different elastic properties for phononic crystals.

With the advancement in nanofabrication techniques, meta-

materials with dual photonic and phononic frequency bandg-

aps have recently been realized. These photonic-phononic

crystals, which are also called phoxonic crystals,9,10 are

attracting great interest as they are expected to possess both

the attributes and functionalities arising from the bandgap

structures of their component excitations. For instance, with

their dual photonic and phononic bandgaps, phoxonic crys-

tals permit the simultaneous control of photon and phonon

propagation. Among such systems that have been investi-

gated are silica-opal thin films6 and three-dimensional (3D)

lattices of gold spheres in an epoxy matrix.10

Another possible class of materials with dual-excitation

bandgaps is the magnonic-phononic crystals. These metama-

terials, which we will term magphonic crystals (MPCs), ex-

hibit simultaneous magnonic and phononic bandgaps. Unlike

the phoxonic crystal, information on its analogue, the mag-

phonic crystal is very scarce. In 2008, Nikitov et al.11 theo-

retically studied the acoustic waves in 2D periodic layered

structures of magnetic films and suggested that these layered

structures may be considered as magphonic crystals. No ex-

perimental work on these crystals has, to date, been reported.

In this letter, we report on the experimental observation

of dual magnonic and phononic band structures in nanostruc-

tured crystals. Each of the structures studied is composed of

a 1D periodic array of nanostripes of two alternating ferro-

magnetic materials deposited on a SiO2/Si substrate. The fre-

quency band structures of spin and acoustic waves in the

artificial crystals were measured by Brillouin light scattering,

an excellent technique for probing these waves in nanostruc-

tured materials.3–5,12,13 Numerical calculations of the mag-

non dispersions with Hoffmann boundary conditions

imposed at the interfaces between nanostripes, and the pho-

non dispersions within the finite element framework were

also performed.

The nanostructured crystals studied, which we will refer

to as the Fe/Py and Ni/Py MPCs, were fabricated as follows.

Briefly, a 30 nm-thick 1D periodic array of alternating Fe (or

Ni) and permalloy (Py, Ni80Fe20) stripes, of lattice constant

a¼ 500 nm, was synthesized on a 800 nm-thick SiO2/Si(001)

wafer using high-resolution electron beam lithography and

lift-off techniques.3 Each of the stripes is 250 nm wide and

100 lm long.

The Brillouin measurements were performed in the

180�-backscattering geometry, with the scattering plane nor-

mal to the sample surface and the magnon or phonon wave-

vector q along the periodicity direction of the artificial

crystal (Fig. 1(a)). The k¼ 514.5 nm radiation of an argon-

ion laser was used to excite the spectra, and the scattered

light was frequency analyzed with a (3 þ 3)-pass tandem

Fabry-Perot interferometer, which was equipped with a sili-

con avalanche diode detector. Prior to the spectral scans, the

samples were first saturated in a 0.7-T field applied along the

symmetry axes of the stripes (z direction in Fig. 2(c)), which

was then gradually reduced to zero. Brillouin spectra of mag-

netic excitations were recorded in p-s polarization, while

a)Electronic mail: phykmh@nus.edu.sg.b)Current address: Materials Science Division, Argonne National Labora-

tory, 9700 South Cass Ave., Argonne, Illinois 60439, USA.c)Electronic mail: eleaao@nus.edu.sg.

0003-6951/2012/100(16)/163118/4/$30.00 VC 2012 American Institute of Physics100, 163118-1

APPLIED PHYSICS LETTERS 100, 163118 (2012)

acoustic excitations in p-p polarization. Dispersion relations

of the spin and acoustic waves were mapped by varying the

laser light incidence angle h, up to the third Brillouin zone

(BZ), i.e., over the magnon or phonon wavevector range q(¼ 4psinh/k) from 0 to 2.6p/a.

We will first discuss the experimental and computational

results obtained for the Fe/Py MPC. Exemplary polarized

Brillouin spectra recorded under zero magnetic field, at BZ

boundaries q¼p/a and 2p/a are displayed in Figs. 1(b) and

1(c). Unlike p-p Brillouin spectra, the p-s ones are dependent

on applied magnetic field and are thus attributed to scattering

from magnons. Magnon and phonon mode frequencies

obtained from spectral fits using Lorentzian functions were

plotted against wavevector to yield dispersion relations

shown in Figs. 2(a) and 2(b). The dispersion relations exhibit

respective sets of magnonic and phononic forbidden bands

within which no spin waves and elastic waves can propagate.

The measured magnonic band structure, displayed in

Fig. 2(a), features a prominent 2.8 GHz bandgap centered at

10.7 GHz and a smaller 1.0 GHz one centered at 12.8 GHz.

Dispersion relations and dynamic magnetization profiles of

the spin waves were calculated by solving the linearized

Landau-Lifshitz equations and Maxwell’s equations in the

magnetostatic limit, based on a finite element approach, with

Hoffmann boundary conditions14 imposed at the Fe-Py inter-

faces. The computational unit cell, depicted in Fig. 2(c), was

used with the Bloch-Floquet theorem applied along the peri-

odicity direction. Magnetic parameters used in the calcula-

tions are the saturation magnetization MS¼ 7.22� 105 A/m,

exchange stiffness constant A¼ 1.08� 10�11 J/m, gyromag-

netic ratio c¼ 186 GHz/T for Py, and MS¼ 1.75� 106 A/m,

A¼ 2.10� 10�11 J/m, c¼ 193 GHz/T for Fe. These values

were obtained from Brillouin measurements of spin waves

on 30 nm-thick Py and Fe reference films. Fig. 2(a) shows

that our calculations agree well with the measured spin wave

dispersions. Numerically simulated dynamic magnetization

profiles of the observed spin wave modes, for wavevectors

q¼p/a and 2p/a, are displayed in Fig. 2(c). They illustrate

the respective resonant and forced magnetization precessions

in the Py and Fe stripes, characteristic of the dispersion of

the lowest-energy magnons.15

The measured phonon dispersion presented in Fig. 2(b)

reveals first, second, and third bandgaps with respective

widths of 0.4, 0.6, and 0.6 GHz. The phonon dispersion rela-

tions and mode displacement profiles were calculated within

the framework of the finite element approach with the

Bloch-Floquet theorem applied along the periodicity direc-

tion. We considered a 1D 30 nm-thick periodic array of

FIG. 1. (a) Schematics of Brillouin light scattering geometry showing the

light incident angle h, incident and scattered photon wavevectors ki and ks,

magnon/phonon wavevector q. Polarized Brillouin spectra of the Fe/Py

MPC measured at (b) first Brillouin zone boundary (q¼p/a, a¼ 500 nm)

and (c) second Brillouin zone boundary (q¼ 2p/a). Spectra were fitted with

Lorentzian functions (dashed curves), and the resultant fitted spectra are

shown as solid curves.

FIG. 2. Dispersion relations of (a) mag-

nons and (b) phonons in the Fe/Py MPC.

The magnon/phonon wavevector q is

along the direction of periodicity (x-

direction). Experimental and theoretical

data are denoted by symbols and contin-

uous curves, respectively. Measured

bandgaps are indicated by shaded bands

and Brillouin zone boundaries by verti-

cal dashed lines. (c) y-components of the

dynamic magnetizations of observed

magnon modes. (d) y-components of the

displacements of observed phonon

modes. The dynamic magnetization and

displacement profiles are color-coded, as

indicated by the scale bar.

163118-2 Zhang et al. Appl. Phys. Lett. 100, 163118 (2012)

alternating Fe and Py stripes in contact with an 800 nm-thick

silica sub-layer atop a 4 lm-thick Si substrate. The computa-

tional unit cell used is depicted in Fig. 2(d). The top layer of

the 500 nm-wide cell comprises a 124.5 nm-wide Fe stripe, a

249.5 nm-wide Py stripe, a 1 nm-wide gap, and a 125 nm-

wide Fe stripe. A gap of width of the order of 1 nm was intro-

duced in the simulations, as misalignment during the two-

step lithographic process would result in such a gap at alter-

nate Fe/Py interfaces. As this gap width is shorter than the

exchange length of the ferromagnetic materials, its presence

does not significantly affect the calculated magnon disper-

sion. Although the interactions at the Py-Fe interfaces are

exchange-dipolar in character, for the dimensions of the

arrays studied, the nature of the spin waves is predominantly

magnetostatic, i.e., dipolar-dominated.16 Parameters used in

the numerical calculations for Fe, Py, SiO2, and Si are

Young’s moduli¼ 211, 180, 73, and 169 GPa, Poisson

ratios¼ 0.29, 0.3, 0.17, and 0.064, mass densities¼ 7870,

8600, 2200, and 2330 kg/m3, respectively.17–20 The simu-

lated phonon dispersion relation, presented in Fig. 2(b), cap-

tures the features of the Brillouin measured one. Mode

displacement profiles for q¼p/a and 2p/a, displayed in Fig.

2(d), exhibit characteristics of Rayleigh waves (RW).

Simulations of acoustic waves on the unpatterned refer-

ence samples, Py/SiO2/Si and Fe/SiO2/Si, based on the com-

putational unit cell shown in Fig. 3(b), have also been

performed. As the results for both samples are very similar,

only those of the former are presented in Fig. 3(a). The simu-

lated displacement profiles of the Rayleigh and Sezawa

modes for q¼ 1.25p/a are shown in Fig. 3(c).21 The blue and

red solid lines represent the respective calculated dispersions

of the Rayleigh and Sezawa modes of the reference sample,

while the blue and red dashed lines, those of their corre-

sponding folded modes. It is to be noted that the measured

dispersion of the Rayleigh modes, denoted by squares, agrees

well with simulations. The experimental Brillouin data for

the Fe/Py MPC, represented by dots in Fig. 3(a), reveal two

Bragg bandgaps (shown as green bands). These bandgaps,

whose widths increase with BZ number, arise from the zone

folding of the RW dispersions and avoided crossings at the

BZ boundaries.22 Interestingly, an additional bandgap viz. a

hybrid bandgap (shown as a red band), opens up within the

second BZ at q � 1.25p/a. The formation of this gap has its

origin in the hybridization and avoided crossings of the Ray-

leigh and zone-folded Sezawa modes.23

As Fig. 4 reveals, the Ni/Py sample also possesses si-

multaneous magnonic and phononic bandgaps. Numerical

calculations of the dispersion relations of spin and acoustic

waves in this sample parallel those performed for the Fe/Py

MPC. Magnetic parameters used in the calculations are

MS¼ 3.21� 105 A/m, A¼ 0.68� 10�11 J/m, c¼ 196 GHz/T,

values obtained from Brillouin measurements of spin waves

on a 30 nm-thick Ni reference film. Values of the Young’s

modulus, Poisson ratio, and density of Ni used in the calcula-

tions are 186 GPa, 0.29, and 8900 kg/m3, respectively.24 The

observed first and second magnonic bandgaps of 2.8 and

1.0 GHz for the Fe/Py MPC are larger than the corresponding

ones of 1.3 and 0.8 GHz observed for the Ni/Py MPC.

Krawczyk and Puszkarski predicted that low magnetic con-

trast would result in narrow magnonic bandgap widths.25 As

the magnetic contrast between Fe and Py is higher than that

between Ni and Py, our observations support their

prediction.

In stark contrast to the energetically well-separated band

structures for spin and acoustic waves in the Fe/Py MPC

under zero applied magnetic field, those of the Ni/Py MPC

FIG. 3. (a) Phonon dispersion relations. Experimental Fe/Py MPC data are

represented by dots. Squares denote the measured Rayleigh mode dispersion

on the unpatterned Py/SiO2/Si reference sample. Blue and red solid lines rep-

resent the simulated Rayleigh and Sezawa wave dispersions for the reference

sample, while blue and red dashed lines their corresponding folded disper-

sions. Measured Bragg and hybrid bandgaps are represented by green and

pink bands, respectively, and BZ boundaries by dotted-dashed lines. (b) Com-

putational unit cell of the reference sample. (c) y-displacements of Rayleigh

and Sezawa modes of the reference sample for wavevector q¼ 1.25p/a. The

displacements are color-coded, based on the same scale bar shown in Fig. 2.

FIG. 4. Magnon and phonon dispersion relations of Ni/Py MPC. Experi-

mental and theoretical data are denoted by symbols and continuous curves,

respectively. Measured bandgaps are represented by shaded bands and Bril-

louin zone boundaries by vertical dashed lines.

163118-3 Zhang et al. Appl. Phys. Lett. 100, 163118 (2012)

overlap completely. This is partly because the frequencies of

the lowest-energy magnonic branches are mainly determined

by the stripes with the lower magnetic parameters. Hence,

the observed dispersions of the lowest-energy magnons of

the Fe/Py MPC are characterized by the respective resonant

and forced magnetization precessions in its Py and Fe stripes,

while those of the Ni/Py MPC, by the respective resonant

and forced magnetization precessions in its Ni and Py

stripes.26 As the magnetic parameters of Ni are lower than

those of Py, the magnon frequencies in the latter MPC are

lower than those of the former. Another reason is that the

phononic band structures of both MPCs are almost identical,

a consequence of the very similar elastic parameters of their

constituent ferromagnetic materials.

It is noteworthy that, for both MPCs, while application

of a magnetic field radically modifies their magnon disper-

sion spectra, their corresponding phonon ones are found to

be independent of magnetic field, suggesting the absence of

magnon-phonon interactions. This has important implica-

tions for potential applications. For instance, information

carried by magnons and phonons could be separately and

simultaneously processed in devices based on such mag-

phonic crystals, with no undesirable cross-talk between the

two excitations. Additionally, the magnonic bandgaps in

such devices can be tuned by the application of a magnetic

field, independently of the phononic bandgaps.

For the samples studied, the band structure of magnons

is dependent only on the magnetic properties of the constitu-

ent ferromagnetic materials. In the case of phonons, we

found that the phononic band structure strongly depends on

the elastic properties of the SiO2/Si substrate. Thus mag-

phonic crystals, exhibiting the same magnonic band structure

but different phononic ones, can be engineered by selecting

the same pair of constituent magnetic materials but different

underlying substrate materials for fabrication. Conversely, if

MPCs possessing the same phononic band structure, but dif-

ferent magnonic ones are desired, then different pairs of con-

stituent magnetic materials atop the same support substrate

are to be selected.

In summary, we have demonstrated experimentally the

existence of simultaneous magnonic and phononic bandgaps

in linear arrays of Fe (or Ni) and permalloy nanostripes on

SiO2/Si substrates. As such structures, which we term mag-phonic crystals, possess additional functionalities over mag-

nonic and phononic crystals that rely on a single type of

excitation as the information carrier, they are potentially

more useful technologically. It is hoped that this study will

spur further interest in these metamaterials which are also of

great fundamental scientific interest.

Financial support by the Ministry of Education, Singa-

pore under Grant No. R144-000-282-112 is gratefully

acknowledged.

1J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).2B. Lenk, H. Ulrichs, F. Garbs, and M. Munzenberg, Phys. Rep. 507, 107

(2011).3Z. K. Wang, V. L. Zhang, H. S. Lim, S. C. Ng, M. H. Kuok, S. Jain, and

A. O. Adeyeye, ACS Nano 4, 643 (2010).4Z. K. Wang, V. L. Zhang, H. S. Lim, S. C. Ng, M. H. Kuok, S. Jain, and

A. O. Adeyeye, Appl. Phys. Lett. 94, 083112 (2009).5W. Cheng, J. Wang, U. Jonas, G. Fytas, and N. Stefanou, Nature Mater. 5,

830 (2006).6A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S.

Tamura, D. R. Yakovlev, and M. Bayer, Phys. Rev. Lett. 101, 033902

(2008).7S. Neusser and D. Grundler, Adv. Mater. 21, 2927 (2009).8Y. Pennec, J. O. Vasseur, B. Djafari-Rouhani, L. Dobrzynski, and P. A.

Deymier, Surf. Sci. Rep. 65, 229 (2010).9V. Laude, J.-C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani,

N. Papanikolaou, J. M. Escalante, and A. Martinez, Opt. Express 19, 9690

(2011).10N. Papanikolaou, I. E. Psarobas, and N. Stefanou, Appl. Phys. Lett. 96,

231917 (2010).11S. Nikitov, Y. Gulyaev, V. Grigorevsky, A. Grigorevsky, I. Lisenkov, and

R. Popov, J. Acoust. Soc. Am. 123, 3040 (2008).12Z. K. Wang, H. S. Lim, H. Y. Liu, S. C. Ng, M. H. Kuok, L. L. Tay, D. J.

Lockwood, M. G. Cottam, K. L. Hobbs, P. R. Larson, J. C. Keay, G. D.

Lian, and M. B. Johnson, Phys. Rev. Lett. 94, 137208 (2005).13J. Y. Sun, Z. K. Wang, H. S. Lim, S. C. Ng, M. H. Kuok, T. T. Tran, and

X. Lu, ACS Nano 4, 7692 (2010).14J. Barnas, “Spin waves in multilayers,” in Linear and Non-Linear Spin

Waves in Magnetic Films and Superlattices, edited by M. G. Cottam

(World Scientific, Singapore, 1994).15G. Gubbiotti, S. Tacchi, M. Madami, G. Carlotti, A. O. Adeyeye, and M.

Kostylev, J. Phys. D: Appl. Phys. 43, 264003 (2010).16M. L. Sokolovskyy and M. Krawczyk, J. Nanopart. Res. 13, 6085 (2011).17A. M. James and M. P. Lord, Index of Chemical and Physical Data (Mac-

millan, New York, 1992).18H. Deng, M. K. Minor, and J. A. Barnard, IEEE Trans. Magn. 32, 3702

(1996).19B. A. Auld, Acoustic Fields and Waves in Solids (Wiley, New York,

1973), Vol. 2.20W. A. Brantley, J. Appl. Phys. 44, 534 (1973).21M. G. Beghi, C. E. Bottani, P. M. Ossi, T. A. Lafford, and B. K. Tanner,

J. Appl. Phys. 81, 672 (1997).22J. R. Dutcher, S. Lee, B. Hillebrands, G. J. McLaughlin, B. G. Nickel, and

G. I. Stegeman, Phys. Rev. Lett. 68, 2464 (1992).23A. A. Maznev and A. G. Every, J. Appl. Phys. 106, 113531 (2009).24R. Jorna, D. Visser, V. Bortolani, and F. Nizzoli, J. Appl. Phys. 65, 718

(1989).25M. Krawczyk and H. Puszkarski, Phys. Rev. B 77, 054437 (2008).26C. S. Lin, H. S. Lim, Z. K. Wang, S. C. Ng, and M. H. Kuok, Appl. Phys.

Lett. 98, 022504 (2011).

163118-4 Zhang et al. Appl. Phys. Lett. 100, 163118 (2012)