We report the experimental observation in thin films of the hybridization of the uniform ferromagnetic resonance mode with nonuniform magnons as a result of the two-magnon scattering mechanism, leading to a frequency-pulling effect on the ferromagnetic resonance. This effect, when not properly accounted for, leads to a discrepancy in the dependence of the ferromagnetic resonance field on frequency for different field orientations. The frequency-pulling effect is the complement of the broadening of the ferromagnetic resonance line shape by two-magnon scattering and can be calculated using the same parameters. By accounting for the two-magnon frequency shifts through these means, consistency is achieved in fitting data from in-plane and perpendicular-to-plane resonance conditions.

1.
D. C.
Ralph
and
M. D.
Stiles
, “
Spin transfer torques
,”
J. Magn. Magn. Mater.
320
,
1190
(
2008
).
2.
J.
Sinova
,
S. O.
Valenzuela
,
J.
Wunderlich
,
C. H.
Back
, and
T.
Jungwirth
, “
Spin Hall effects
,”
Rev. Mod. Phys.
87
,
1213
(
2015
).
3.
A.
Manchon
,
J.
Železný
,
I. M.
Miron
,
T.
Jungwirth
,
J.
Sinova
,
A.
Thiaville
,
K.
Garello
, and
P.
Gambardella
, “
Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems
,”
Rev. Mod. Phys.
91
,
035004
(
2019
).
4.
F.
Hellman
,
A.
Hoffmann
,
Y.
Tserkovnyak
,
G. S. D.
Beach
,
E. E.
Fullerton
,
C.
Leighton
,
A. H.
MacDonald
,
D. C.
Ralph
,
D. A.
Arena
,
H. A.
Dürr
,
P.
Fischer
,
J.
Grollier
,
J. P.
Heremans
,
T.
Jungwirth
,
A. V.
Kimel
,
B.
Koopmans
,
I. N.
Krivorotov
,
S. J.
May
,
A. K.
Petford-Long
,
J. M.
Rondinelli
,
N.
Samarth
,
I. K.
Schuller
,
A. N.
Slavin
,
M. D.
Stiles
,
O.
Tchernyshyov
,
A.
Thiaville
, and
B. L.
Zink
, “
Interface-induced phenomena in magnetism
,”
Rev. Mod. Phys.
89
,
025006
(
2017
).
5.
J.-M.
Beaujour
,
D.
Ravelosona
,
I.
Tudosa
,
E. E.
Fullerton
, and
A. D.
Kent
, “
Ferromagnetic resonance linewidth in ultrathin films with perpendicular magnetic anisotropy
,”
Phys. Rev. B
80
,
180415
(
2009
).
6.
L.
Chen
,
S.
Mankovsky
,
S.
Wimmer
,
M. A. W.
Schoen
,
H. S.
Körner
,
M.
Kronseder
,
D.
Schuh
,
D.
Bougeard
,
H.
Ebert
,
D.
Weiss
, and
C. H.
Back
, “
Emergence of anisotropic Gilbert damping in ultrathin Fe layers on GaAs(001)
,”
Nat. Phys.
14
,
490
(
2018
).
7.
R.
Arias
and
D. L.
Mills
, “
Extrinsic contributions to the ferromagnetic resonance response of ultrathin films
,”
Phys. Rev. B
60
,
7395
(
1999
).
8.
R. D.
McMichael
and
P.
Krivosik
, “
Classical model of extrinsic ferromagnetic resonance linewidth in ultrathin films
,”
IEEE Trans. Magn.
40
,
2
(
2004
).
9.
P.
Krivosik
,
N.
Mo
,
S.
Kalarickal
, and
C. E.
Patton
, “
Hamiltonian formalism for two magnon scattering microwave relaxation: Theory and applications
,”
J. Appl. Phys.
101
,
083901
(
2007
).
10.
W. K.
Peria
,
T. A.
Peterson
,
A. P.
McFadden
,
T.
Qu
,
C.
Liu
,
C. J.
Palmstrøm
, and
P. A.
Crowell
, “
Interplay of large two-magnon ferromagnetic resonance linewidths and low Gilbert damping in Heusler thin films
,”
Phys. Rev. B
101
,
134430
(
2020
).
11.
M.
Farle
, “
Ferromagnetic resonance of ultrathin metallic layers
,”
Rep. Prog. Phys.
61
,
755
(
1998
).
12.
A. E.
Clark
,
M.
Wun-Fogle
,
J. B.
Restorff
,
K. W.
Dennis
,
T. A.
Lograsso
, and
R. W.
McCallum
, “
Temperature dependence of the magnetic anisotropy and magnetostriction of Fe100x Gax (x = 8.6, 16.6, 28.5)
,”
J. Appl. Phys.
97
,
10M316
(
2005
).
13.
D. B.
Gopman
,
V.
Sampath
,
H.
Ahmad
,
S.
Bandyopadhyay
, and
J.
Atulasimha
, “
Static and dynamic magnetic properties of sputtered Fe-Ga thin films
,”
IEEE Trans. Magn.
53
,
1
(
2017
).
14.
M. J.
Hurben
and
C. E.
Patton
, “
Theory of two magnon scattering microwave relaxation and ferromagnetic resonance linewidth in magnetic thin films
,”
J. Appl. Phys.
83
,
4344
(
1998
).
15.
A. Y.
Dobin
and
R. H.
Victora
, “
Surface roughness induced extrinsic damping in thin magnetic films
,”
Phys. Rev. Lett.
92
,
257204
(
2004
).
16.
G.
Woltersdorf
and
B.
Heinrich
, “
Two-magnon scattering in a self-assembled nanoscale network of misfit dislocations
,”
Phys. Rev. B
69
,
184417
(
2004
).
17.
S. S.
Kalarickal
,
P.
Krivosik
,
J.
Das
,
K. S.
Kim
, and
C. E.
Patton
, “
Microwave damping in polycrystalline Fe-Ti-N films: Physical mechanisms and correlations with composition and structure
,”
Phys. Rev. B
77
,
054427
(
2008
).
18.
A.
Azevedo
,
A. B.
Oliveira
,
F. M.
de Aguiar
, and
S. M.
Rezende
, “
Extrinsic contributions to spin-wave damping and renormalization in thin Ni50Fe50 films
,”
Phys. Rev. B
62
,
5331
(
2000
).
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