The wave solutions of the Landau–Lifshitz equation (spin waves) are characterized by some of the most complex and peculiar dispersion relations among all waves. For example, the spin-wave (“magnonic”) dispersion can range from the parabolic law (typical for a quantum-mechanical electron) at short wavelengths to the nonanalytical linear type (typical for light and acoustic phonons) at long wavelengths. Moreover, the long-wavelength magnonic dispersion has a gap and is inherently anisotropic, being naturally negative for a range of relative orientations between the effective field and the spin-wave wave vector. Nonuniformities in the effective field and magnetization configurations enable the guiding and steering of spin waves in a deliberate manner and therefore represent landscapes of graded refractive index (graded magnonic index). By analogy to the fields of graded-index photonics and transformation optics, the studies of spin waves in graded magnonic landscapes can be united under the umbrella of the graded-index magnonics theme and are reviewed here with focus on the challenges and opportunities ahead of this exciting research direction.
References
1.
V. V.
Kruglyak
, S. O.
Demokritov
, and D.
Grundler
, J. Phys. D: Appl. Phys.
43
, 264001
(2010
), and references therein.2.
A. I.
Akhiezer
, V. G.
Baryakhtar
, and S. V.
Peletminskii
, Spin Waves
(North-Holland
, Amsterdam
, 1968
).3.
A. G.
Gurevich
and G. A.
Melkov
, Magnetization Oscillations and Waves
(Chemical Rubber Corp.
, New York
, 1996
).4.
5.
A. V.
Vashkovskii
, A. V.
Stalmakhov
, and D. G.
Shakhnazaryan
, Izv. Vyssh. Uchebn. Zaved., Fiz.
31
, 67
(1988
).6.
7.
A. V.
Vashkovskii
and E. G.
Lokk
, Phys.-Usp.
47
, 601
(2004
).8.
S.-K.
Kim
, S.
Choi
, K.-S.
Lee
, D.-S.
Han
, D.-E.
Jung
, and Y.-S.
Choi
, Appl. Phys. Lett.
92
, 212501
(2008
).9.
T.
Schneider
, A. A.
Serga
, A. V.
Chumak
, C. W.
Sandweg
, S.
Trudel
, S.
Wolff
, M. P.
Kostylev
, V. S.
Tiberkevich
, A. N.
Slavin
, and B.
Hillebrands
, Phys. Rev. Lett.
104
, 197203
(2010
).10.
C. S.
Davies
, A.
Francis
, A. V.
Sadovnikov
, S. V.
Chertopalov
, M. T.
Bryan
, S. V.
Grishin
, D. A.
Allwood
, Y. P.
Sharaevskii
, S. A.
Nikitov
, and V. V.
Kruglyak
, Phys. Rev. B
92
, 020408
(2015
).11.
12.
J. B.
Pendry
, A. I.
Fernandez-Dominguez
, Y.
Luo
, and R.
Zhao
, Nat. Phys.
9
, 518
(2013
).13.
See http://www.itrs.net/Links/2013ITRS/Summary2013.htm for International Technology Roadmap for Semiconductors (ITRS), Emerging Research Devices (2013) (last accessed January 31,
2015
).14.
Y. I.
Gorobets
and S. A.
Reshetnyak
, Tech. Phys.
43
, 188
(1998
).15.
16.
E. H.
Lock
, Phys.-Usp.
51
, 375
(2008
).17.
S.-K.
Kim
, J. Phys. D: Appl. Phys.
43
, 264004
(2010
), and references therein.18.
M.
Dvornik
, Y.
Au
, and V. V.
Kruglyak
, Top. Appl. Phys.
125
, 101
(2013
), and references therein.19.
M.
Donahue
and D.
Porter
, Interagency Report No. NISTIR 6376, NIST, Gaithersburg, MD (1999
).20.
R. W.
Damon
and J. R.
Eshbach
, J. Phys. Chem. Solids
19
, 308
(1961
).21.
A. V.
Vashkovsky
and E. H.
Lock
, Phys.-Usp.
49
, 389
(2006
), and references therein.22.
B. A.
Kalinikos
and A. N.
Slavin
, J. Phys. C
19
, 7013
(1986
).23.
The Permalloy samples considered here were assumed to have Ms = 800 G and A = 1.3 μerg/cm.
24.
V.
Veerakumar
and R. E.
Camley
, Phys. Rev. B
74
, 214401
(2006
).25.
Y.
Au
, M.
Dvornik
, T.
Davison
, E.
Ahmad
, P. S.
Keatley
, A.
Vansteenkiste
, B.
Van Waeyenberge
, and V. V.
Kruglyak
, Phys. Rev. Lett.
110
, 097201
(2013
).26.
R.
Gieniusz
, H.
Ulrichs
, V. D.
Bessonov
, U.
Guzowska
, A. I.
Stognii
, and A.
Maziewski
, Appl. Phys. Lett.
102
, 102409
(2013
).27.
K.-S.
Lee
and S.-K.
Kim
, J. Appl. Phys.
104
, 053909
(2008
).28.
A.
Khitun
, M.
Bao
, and K. L.
Wang
, J. Phys. D: Appl. Phys.
43
, 264005
(2010
).29.
S. S.
Mukherjee
, J. H.
Kwon
, M.
Jamali
, M.
Hayashi
, and H.
Yang
, Phys. Rev. B
85
, 224408
(2012
).30.
D.-E.
Jeong
, D.-S.
Han
, S.
Choi
, and S.-K.
Kim
, SPIN
1
, 27
(2011
).31.
J.
Jorzick
, S. O.
Demokritov
, B.
Hillebrands
, M.
Bailleul
, C.
Fermon
, K. Y.
Guslienko
, A. N.
Slavin
, D. V.
Berkov
, and N. L.
Gorn
, Phys. Rev. Lett.
88
, 47204
(2002
).32.
J. P.
Park
, P.
Eames
, D. M.
Engebretson
, J.
Berezovsky
, and P. A.
Crowell
, Phys. Rev. Lett.
89
, 277201
(2002
).33.
V. V.
Kruglyak
, A.
Barman
, R. J.
Hicken
, J. R.
Childress
, and J. A.
Katine
, Phys. Rev. B
71
, 220409
(2005
).34.
M.
Dvornik
, P. V.
Bondarenko
, B. A.
Ivanov
, and V. V.
Kruglyak
, J. Appl. Phys.
109
, 07B912
(2011
).35.
V. E.
Demidov
, S. O.
Demokritov
, K.
Rott
, P.
Krzysteczko
, and G.
Reiss
, Appl. Phys. Lett.
92
, 232503
(2008
).36.
X. J.
Xing
, S. W.
Li
, X. H.
Huang
, and Z. G.
Wang
, AIP Adv.
3
, 032144
(2013
).37.
M.
Krawczyk
, J. Phys.: Conf. Ser.
200
, 072056
(2010
).38.
V. E.
Demidov
, J.
Jersch
, S. O.
Demokritov
, K.
Rott
, P.
Krzysteczko
, and G.
Reiss
, Phys. Rev. B
79
, 054417
(2009
).39.
C.
Bayer
, J. P.
Park
, H.
Wang
, M.
Yan
, C. E.
Campbell
, and P. A.
Crowell
, Phys. Rev. B
69
, 134401
(2004
).40.
G.
Duerr
, K.
Thurner
, J.
Topp
, R.
Huber
, and D.
Grundler
, Phys. Rev. Lett.
108
, 227202
(2012
).41.
V. E.
Demidov
, M. P.
Kostylev
, K.
Rott
, J.
Münchenberger
, G.
Reiss
, and S. O.
Demokritov
, Appl. Phys. Lett.
99
, 082507
(2011
).42.
E.
Schlömann
, J. Appl. Phys.
35
, 159
(1964
).43.
Y.
Au
, T.
Davison
, E.
Ahmed
, P. S.
Keatley
, R. J.
Hicken
, and V. V.
Kruglyak
, Appl. Phys. Lett.
98
, 122506
(2011
).44.
M.
Arikan
, Y.
Au
, G.
Vasile
, S.
Ingvarsson
, and V. V.
Kruglyak
, J. Phys. D: Appl. Phys.
46
, 135003
(2013
).45.
P.
Gruszecki
, J.
Romero-Vivas
, Y. S.
Dadoenkova
, N. N.
Dadoenkova
, I. L.
Lyubchanskii
, and M.
Krawczyk
, Appl. Phys. Lett.
105
, 242406
(2014
).46.
G.
Duerr
, R.
Huber
, and D.
Grundler
, J. Phys.: Condens. Matter
24
, 024218
(2012
), and references therein.47.
X.
Xing
, W.
Yin
, and Z.
Wang
, J. Phys. D: Appl. Phys.
48
, 215004
(2015
).48.
A. V.
Sadovnikov
, C. S.
Davies
, S. V.
Grishin
, V. V.
Kruglyak
, D. V.
Romanenko
, Y. P.
Sharaevskii
, and S. A.
Nikitov
, Appl. Phys. Lett.
106
, 192406
(2015
).49.
V. S.
Tkachenko
, A. N.
Kuchko
, M.
Dvornik
, and V. V.
Kruglyak
, Appl. Phys. Lett.
101
, 152402
(2012
).50.
V. S.
Tkachenko
, A. N.
Kuchko
, and V. V.
Kruglyak
, [Low Temp. Phys.
39
, 163
(2013
)].51.
I.
Dzyaloshinsky
, J. Phys. Chem. Solids
4
, 241
(1958
).52.
D. D.
Sheka
, V. P.
Kravchuk
, and Y.
Gaididei
, J. Phys. A
48
, 125202
(2015
).53.
R.
Hertel
, W.
Wulfhekel
, and J.
Kirschner
, Phys. Rev. Lett.
93
, 257202
(2004
).54.
C.
Bayer
, H.
Schultheiss
, B.
Hillebrands
, and R.
Stamps
, IEEE Trans. Magn.
41
, 3094
(2005
).55.
S.
Macke
and D.
Goll
, J. Phys.: Conf. Ser.
200
, 042015
(2010
).56.
K. Y.
Guslienko
, B. A.
Ivanov
, V.
Novosad
, Y.
Otani
, H.
Shima
, and K.
Fukamichi
, J. Appl. Phys.
91
, 8037
(2002
).57.
B. A.
Ivanov
and C. E.
Zaspel
, J. Appl. Phys.
95
, 7444
(2004
).58.
C.
Ragusa
, M.
Carpentieri
, F.
Celegato
, P.
Tiberto
, E.
Enrico
, L.
Boarino
, and G.
Finocchio
, IEEE Trans. Magn.
47
, 2498
(2011
).59.
K. Y.
Guslienko
, G. N.
Kakazei
, Y. V.
Kobljanskyj
, G. A.
Melkov
, V.
Novosad
, and A. N.
Slavin
, New J. Phys.
16
, 063044
(2014
).60.
C.
Patschureck
, K.
Lenz
, M. O.
Liedke
, M. U.
Lutz
, T.
Strache
, I.
Mönch
, R.
Schäfer
, L.
Schultz
, and J.
McCord
, Phys. Rev. B
86
, 054426
(2012
).61.
C.
Hamann
, R.
Mattheis
, I.
Mönch
, J.
Fassbender
, L.
Schultz
, and J.
McCord
, New J. Phys.
16
, 023010
(2014
).62.
C.
Schütte
and M.
Garst
, Phys. Rev. B
90
, 094423
(2014
).63.
M.
Mochizuki
, X. Z.
Yu
, S.
Seki
, N.
Kanazawa
, W.
Koshibae
, J.
Zang
, M.
Mostovoy
, Y.
Tokura
, and N.
Nagaosa
, Nat. Mater.
13
, 241
(2014
).64.
65.
66.
67.
S. A.
Nikitov
, P.
Tailhades
, and C. S.
Tsai
, J. Magn. Magn. Mater.
236
, 320
(2001
).68.
S.
Neusser
, B.
Botters
, and D.
Grundler
, Phys. Rev. B
78
, 054406
(2008
).69.
S.
Tacchi
, B.
Botters
, M.
Madami
, J. W.
Klos
, M. L.
Sokolovskyy
, M.
Krawczyk
, G.
Gubbiotti
, G.
Carlotti
, A. O.
Adeyeye
, S.
Neusser
, and D.
Grundler
, Phys. Rev. B
86
, 014417
(2012
).70.
T.
Schwarze
and D.
Grundler
, Appl. Phys. Lett.
102
, 222412
(2013
).71.
M.
Krawczyk
, S.
Mamica
, M.
Mruczkiewicz
, J. W.
Klos
, S.
Tacchi
, M.
Madami
, G.
Gubbiotti
, G.
Duerr
, and D.
Grundler
, J. Phys. D: Appl. Phys.
46
, 495003
(2013
).72.
A. Y.
Galkin
, B. A.
Ivanov
, and C. E.
Zaspel
, Phys. Rev. B
74
, 144419
(2006
).73.
A. A.
Awad
, G. R.
Aranda
, D.
Dieleman
, K. Y.
Guslienko
, G. N.
Kakazei
, B. A.
Ivanov
, and F. G.
Aliev
, Appl. Phys. Lett.
97
, 132501
(2010
).74.
X.-G.
Wang
, G.-H.
Guo
, Z.-X.
Li
, D.-W.
Wang
, Y.-Z.
Nie
, and W.
Tang
, Eur. Phys. Lett.
109
, 37008
(2015
).75.
A. M.
Kosevich
, B. A.
Ivanov
, and A. S.
Kovalev
, Phys. Rep.
194
, 117
(1990
), and references therein.76.
R. K.
Dumas
, E.
Iacocca
, S.
Bonetti
, S. R.
Sani
, S. M.
Mohseni
, A.
Eklund
, J.
Persson
, O.
Heinonen
, and J.
Åkerman
, Phys. Rev. Lett.
110
, 257202
(2013
).77.
S.
Nikitov
, Y.
Filimonov
, S.
Vysotsky
, Y.
Khivintsev
, and E.
Pavlov
, in IEEE International Ultrasonics Symposium Proceedings
(2012
), p. 1240
.78.
O.
Prikhod'ko
, O. S.
Sukhorukova
, S. V.
Tarasenko
, and V. G.
Shavrov
, JETP Lett.
100
, 319
(2014
).79.
V. G.
Baryakhtar
, B. A.
Ivanov
, T. K.
Soboleva
, and A. L.
Sukstanskii
, Zh. Eksp. Teor. Fiz.
64
, 857
(1986
).80.
V. G.
Baryakhtar
and A. G.
Danilevich
, [Low Temp. Phys.
39
, 993
(2013
)], and references therein.81.
M.
Krawczyk
and D.
Grundler
, J. Phys.: Condens. Matter
26
, 123202
(2014
), and references therein.82.
S. O.
Demokritov
, A. A.
Serga
, A.
Andre
, V. E.
Demidov
, M. P.
Kostylev
, B.
Hillebrands
, and A. N.
Slavin
, Phys. Rev. Lett.
93
, 047201
(2004
).83.
H.-J.
Chia
, F.
Guo
, L. M.
Belova
, and R. D.
McMichael
, Phys. Rev. Lett.
108
, 087206
(2012
).84.
A. B.
Ustinov
and B. A.
Kalinikos
, Tech. Phys. Lett.
40
, 568
(2014
).85.
V. E.
Demidov
, S.
Urazhdin
, A. B.
Rinkevich
, G.
Reiss
, and S. O.
Demokritov
, Appl. Phys. Lett.
104
, 152402
(2014
).86.
G. E. W.
Bauer
, E.
Saitoh
, and B. J.
van Wees
, Nat. Mater.
11
, 391
(2012
).87.
T.
Satoh
, Y.
Terui
, R.
Moriya
, B. A.
Ivanov
, K.
Ando
, E.
Saitoh
, T.
Shimura
, and K.
Kuroda
, Nat. Photonics
6
, 662
(2012
).88.
O.
Kolokoltsev
, N.
Qureshi
, E.
Mejia-Uriarte
, and C. L.
Ordonez-Romero
, J. Appl. Phys.
112
, 013902
(2012
).89.
A. V.
Chumak
, A. D.
Karenowska
, A. A.
Serga
, and B.
Hillebrands
, Top. Appl. Phys.
125
, 243
(2013
), and references therein.90.
A. A.
Nikitin
, A. B.
Ustinov
, A. A.
Semenov
, A. V.
Chumak
, A. A.
Serga
, V. I.
Vasyuchka
, E.
Lahderanta
, B. A.
Kalinikos
, and B.
Hillebrands
, Appl. Phys. Lett.
106
, 102405
(2015
).91.
92.
S. V.
Vasiliev
, V. V.
Kruglyak
, M. L.
Sokolovskii
, and A. N.
Kuchko
, J. Appl. Phys.
101
, 113919
(2007
).93.
P.
Gawronski
, K. J.
Merazzo
, O.
Chubykalo-Fesenko
, R. P.
del Real
, and M.
Vazquez
, Nanotechnology
25
, 475703
(2014
).94.
V. E.
Demidov
, S.
Urazhdin
, A.
Zholud
, A. V.
Sadovnikov
, and S. O.
Demokritov
, Appl. Phys. Lett.
106
, 022403
(2015
).95.
B. A.
Ivanov
, [Low Temp. Phys.
31
, 635
(2005
)], and references therein.96.
L. J.
Heyderman
and R. L.
Stamps
, J. Phys.: Condens. Matter
36
, 363201
(2014
), and references therein.97.
B. A.
Ivanov
, [Low Temp. Phys.
40
, 91
(2014
)], and references therein.© 2015 AIP Publishing LLC.
2015
AIP Publishing LLC
You do not currently have access to this content.
