Lee, Han, and Kim Reply:In [1], we reported our finding on the physical origin of wide band-gap openings in planar nanostrips, as derived by application of periodic width modulations in the magnetic waveguides. K. Di et al. in their Comment [2], however, argue that the band gap can be reduced remarkably by applying a linear combination of symmetric and antisymmetric fields [see ‘‘AþB’’ in the inset of Fig.1(a)]. They also insist that they could find a complete set of magnonic bands based on all of the mode symmetries. However, their work does not constitute grounds for judging our method ‘‘wrong’’ and our conclu- sions ‘‘erroneous.’’ Moreover, the excitation field alluded to in the Comment is not sufficiently general to obtain the complete set of magnonic band structures, but rather re- mains specific. The grounds of these conclusions, drawn from our further work, are the following.
In Fig.1(b), the superposition of the two blue and red dispersion curves obtained independently from symmetric (‘‘B’’) and antisymmetric (‘‘A’’) excitation fields, respec- tively, agrees with the dispersion (green) curves obtained from the superposition of those two excitation fields (AþB). This indicates that the modes excited indepen- dently from the symmetric and antisymmetric fields are not coupled. Thus, the change of the position and width of the band gaps in the dispersion curves for consideration of the AþBfield is due only to the existence of additional modes driven by the asymmetric field [2]. Consequently, our results driven by the symmetric field (B) are physically correct. In Fig.1(b), the bands of the antisymmetric modes are located in between the bands of the symmetric modes, which effects a significant band-gap decrease. However, we recently found that, even with respect to both the symmetric and antisymmetric modes, wide band gaps on the order of 10 GHz can be produced simply by changing the periodicity of the width-modulated waveguides, as shown in Fig.1(c). Our proposed magnonic crystals still offer wide band gaps on the order of 10 GHz and they are applicable to spin-wave filters [3].
TheAþBfield used in the Comment [2] is not general to obtain complete magnonic bands. Figure2(a)shows the dispersion curves for spin waves in asingle-width nano- strip from the A, B, and AþB excitation fields. The symmetric field excites the first lowest (m¼1) mode, but the antisymmetric field the second lowest (m¼2) mode. The superposition of the two fields excites the two lowest modes, as seen in Fig. 2(b). Moreover, a very specific field exerted only at one spot (marked by black, 1:51:510 nm3 in size and positioned at y¼ 19:5 nm) excites an additional third width mode (m¼3) as well as both the two lowest modes [see Fig.2(c)]. This off-centered spot position is chosen to avoid excitation of only the symmetric width modes for the case where the symmetric field is applied at the center position ofy¼0. In conclusion, although the AþB field used in the Comment [2] is not general to obtain complete magnonic
bands, consideration of symmetric and antisymmetric ex- citation fields and their superposition enables the study of additional antisymmetric modes in width-modulated nanostrips.
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science, ICT & Future Planning (Grant No. 2013003460).
Ki-Suk Lee,1Dong-Soo Han,2and Sang-Koog Kim2,*
1School of Mechanical and Advanced Materials Engineering KIST-UNIST Ulsan Center for Convergent Materials Ulsan National Institute of Science and Technology Ulsan 689-798, Republic of Korea
2Department of Materials Science and Engineering National Creative Research Initiative Center for Spin Dynamics & Spin-Wave Devices
and Nanospinics Laboratory
Research Institute of Advanced Materials Seoul National University
Seoul 151-744, Republic of Korea
Received 1 March 2013; published 2 October 2013 DOI:10.1103/PhysRevLett.111.149702
PACS numbers: 75.40.Gb, 75.30.Ds, 75.40.Mg
2.5µm
y= 19.5 nm 10 nm x
z y (a)
kx(P/2π) fsw(GHz)
[P1 (nm), P2 (nm)] = [9, 9]
(b) (c) [7.5, 7.5] [6, 6]
B A
A+B A B
B A
B A
B A
B B B
B 30 60 90
0
30 60 90
0
0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1
kx(P/2π) fsw(GHz)
FIG. 1 (color online). (a) Geometry and dimensions of width- modulated nanostrip. Sinc field pulses were applied to the1:5 3010 nm3 central area (dark blue). The inset shows four different excitation fields as indicated. (b),(c) Dispersion curves of spin wave modes in width-modulated strips of indicated values of [P1,P2], as obtained from FFTs of temporalMz=Ms oscillations along thexaxis at positiony¼19:5 nmto observe both the symmetric and antisymmetirc width modes.
kx(nm-1) kx(nm-1)
fsw(GHz)
m= 1 m= 2
m= 1 m= 2
) c ( )
a (
fsw(GHz)
B A
A + B
m= 3
m= 1 m= 2 Spot
30 60 90
0
30 60 90
0 0.2 0 0.2 00 0.2
kx(nm-1) fsw(GHz)
(b)
30 60 90
0
FIG. 2 (color online). Dispersion curves for 30 nm single- width nanostrip excited by (a) A, B, (b) AþB, and (c) Spot fields.
PRL111,149702 (2013) P H Y S I C A L R E V I E W L E T T E R S week ending 4 OCTOBER 2013
0031-9007=13=111(14)=149702(2) 149702-1 Ó2013 American Physical Society
*Corresponding author.
[1] K.-S. Lee, D.-S. Han, and S.-K. Kim,Phys. Rev. Lett.102, 127202 (2009).
[2] K. Di et al., preceding Comment, Phys. Rev. Lett. 111, 149701 (2013).
[3] S.-K. Kim, K.-S. Lee, and D.-S. Han,Appl. Phys. Lett.95, 082507 (2009).
PRL111,149702 (2013) P H Y S I C A L R E V I E W L E T T E R S week ending 4 OCTOBER 2013
149702-2
