We demonstrate, at room temperature, the strong coupling of the fundamental and non-uniform magnetostatic modes of an yttrium iron garnet ferrimagnetic sphere to the electromagnetic modes of a co-axial cavity. The well-defined field profile within the cavity yields a specific coupling strength for each magnetostatic mode. We experimentally measure the coupling strength for the different magnetostatic modes and, by calculating the expected coupling strengths, we are able to identify the modes themselves.
References
1.
C.
Kittel
, “Interpretation of anomalous Larmor frequencies in ferromagnetic resonance experiment
,” Phys. Rev.
71
, 270
–271
(1947
).2.
C.
Kittel
, “On the theory of ferromagnetic resonance absorption
,” Phys. Rev.
73
, 155
–161
(1948
).3.
L. R.
Walker
, “Magnetostatic modes in ferromagnetic resonance
,” Phys. Rev.
105
, 390
–399
(1957
).4.
P. C.
Fletcher
and R. O.
Bell
, “Ferrimagnetic resonance modes in spheres
,” J. Appl. Phys.
30
, 687
(1959
).5.
C.
Kittel
, “Excitation of spin waves in a ferromagnet by a uniform rf field
,” Phys. Rev.
110
, 1295
–1297
(1958
).6.
M. H.
Seavey
and P. E.
Tannenwald
, “Direct observation of spin-wave resonance
,” Phys. Rev. Lett.
1
, 168
–169
(1958
).7.
Y. V.
Khivintsev
, L.
Reisman
, J.
Lovejoy
, R.
Adam
, C. M.
Schneider
, R. E.
Camley
, and Z. J.
Celinski
, “Spin wave resonance excitation in ferromagnetic films using planar waveguide structures
,” J. Appl. Phys.
108
, 023907
(2010
).8.
M.
Goryachev
, W. G.
Farr
, D. L.
Creedon
, Y.
Fan
, M.
Kostylev
, and M. E.
Tobar
, “High-cooperativity cavity QED with magnons at microwave frequencies
,” Phys. Rev. Appl.
2
, 054002
(2014
).9.
J. R.
Eshbach
, “Spin-wave propagation and the magnetoelastic interaction in yttrium iron garnet
,” Phys. Rev. Lett.
8
, 357
–359
(1962
).10.
M.
Tsoi
, A. G. M.
Jansen
, J.
Bass
, W.
Chiang
, V.
Tsoi
, and P.
Wyder
, “Generation and detection of phase-coherent current-driven magnons in magnetic multilayers
,” Nature
406
, 46
–48
(2000
).11.
A. V.
Chumak
, A. A.
Serga
, and B.
Hillebrands
, “Magnon transistor for all-magnon data processing
,” Nat. Commun.
5
, 4700
(2014
).12.
O. O.
Soykal
and M. E.
Flatté
, “Strong field interactions between a nanomagnet and a photonic cavity
,” Phys. Rev. Lett.
104
, 077202
(2010
).13.
O. O.
Soykal
and M. E.
Flatté
, “Size dependence of strong coupling between nanomagnets and photonic cavities
,” Phys. Rev. B
82
, 104413
(2010
).14.
X.
Zhang
, C.-l.
Zou
, L.
Jiang
, and H. X.
Tang
, “Strongly coupled magnons and cavity microwave photons
,” Phys. Rev. Lett.
113
, 156401
(2014
).
[PubMed]
15.
H.
Huebl
, C. W.
Zollitsch
, J.
Lotze
, F.
Hocke
, M.
Greifenstein
, A.
Marx
, R.
Gross
, and S. T. B.
Goennenwein
, “High cooperativity in coupled microwave resonator ferrimagnetic insulator hybrids
,” Phys. Rev. Lett.
111
, 127003
(2013
).16.
Y.
Tabuchi
, S.
Ishino
, T.
Ishikawa
, R.
Yamazaki
, K.
Usami
, and Y.
Nakamura
, “Hybridizing ferromagnetic magnons and microwave photons in the quantum limit
,” Phys. Rev. Lett.
113
, 083603
(2014
).17.
E. G.
Spencer
, R. C.
Lecraw
, and A. M.
Clogston
, “Low-temperature line-width maximum in yttrium iron garnet
,” Phys. Rev. Lett.
3
, 32
–33
(1959
).18.
Ferrisphere, Inc., Flanders, New Jersey.
19.
C.
Bilzer
, T.
Devolder
, P.
Crozat
, C.
Chappert
, S.
Cardoso
, and P. P.
Freitas
, “Vector network analyzer ferromagnetic resonance of thin films on coplanar waveguides: Comparison of different evaluation methods
,” J. Appl. Phys.
101
, 074505
(2007
).20.
S. S.
Kalarickal
, P.
Krivosik
, M.
Wu
, C. E.
Patton
, M. L.
Schneider
, P.
Kabos
, T. J.
Silva
, and J. P.
Nibarger
, “Ferromagnetic resonance linewidth in metallic thin films: Comparison of measurement methods
,” J. Appl. Phys.
99
, 093909
(2006
).21.
For some modes, the resonance equation admits more than one solution, which is generally labelled with a third index. As none of the modes we explicitly discuss here have multiple resonances, for simplicity we omit this index.
22.
P. T.
Kristensen
, C.
Van Vlack
, and S.
Hughes
, “Generalized effective mode volume for leaky optical cavities
,” Opt. Lett.
37
, 1649
(2012
).23.
A. A.
Clerk
, M. H.
Devoret
, S. M.
Girvin
, F.
Marquardt
, and R. J.
Schoelkopf
, “Introduction to quantum noise, measurement, and amplification
,” Rev. Mod. Phys.
82
, 1155
–1208
(2010
).© 2015 AIP Publishing LLC.
2015
AIP Publishing LLC
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