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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: [email protected])Current address: Materials Science Division, Argonne National Labora-
tory, 9700 South Cass Ave., Argonne, Illinois 60439, USA.c)Electronic mail: [email protected].
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.
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