The mean field approximation is used to study the phase states and phase transitions in ultrathin ferromagnetic films with S = 1 and a combination of easy-plane and tilted anisotropies and mechanical boundary conditions. Depending on the relationship among the material parameters, the system can exist in an angular ferromagnetic phase, a quadrupole phase, or a spatially inhomogeneous state. The spectra of elementary excitations and the stability curves are determined for these phases. An analysis of the stability curves makes it possible to construct a phase diagram for the system.
REFERENCES
1.
M.
Farle
, B.
Mirwald-Schulz
, A. N.
Anisimov
, W.
Platow
, and K.
Baberschke
, Phys. Rev. B
55
, 3708
(1997
).2.
3.
4.
F.
Schedin
, L.
Hewitt
, P.
Morrall
, V. N.
Petrov
, G.
Thornton
, S.
Case
, M. F.
Thomas
, and V. M.
Uzdin
, Phys. Rev. B
58
, 11861
(1998
).5.
E. M.
Gyorgy
, A.
Rosencwaig
, E. I.
Blount
, W. J.
Tabor
, and M. E.
Lines
, Appl. Phys. Lett.
18
, 479
(1971
).6.
A. R.
Prokopov
, S. V.
Dubinko
, A. O.
Khrebtov
, and M. N.
Gremina
, Fiz. Tverd. Tela
39
, 1415
(1997
).7.
L. Ya.
Arifov
, Yu. A.
Fridman
, V. I.
Butrim
, and O. A.
Kosmacheva
, Fiz. Nizk. Temp.
27
, 860
(2001
)L. Ya.
Arifov
, Yu. A.
Fridman
, V. I.
Butrim
, and O. A.
Kosmacheva
, [Low Temp. Phys.
27
, 636
(2001
)].8.
9.
V. V.
Randoshkin
, M. Yu.
Gusev
, Yu. F.
Kozlov
, and N. S.
Neustroev
, Zh. Tekh. Fiz.
70
, 118
(2000
).10.
M. J.
Donahue
, L. H.
Bennet
, R. D.
McMichael
, L. J.
Swartzendruber
, A. J.
Shapiro
, V. I.
Nikitenko
, V. S.
Gornakov
, L. M.
Dedukh
, A. F.
Khapikov
, V. N.
Matveev
, and V. I.
Levashov
, J. Appl. Phys.
79
, 5315
(1996
).11.
C. L.
Dennis
, R. P.
Borges
, L. D.
Buda
, U.
Ebels
, J. F.
Gregg
, M.
Hehn
, E.
Jouguelet
, K.
Ounadjela
, I.
Petej
, I. L.
Prejbeanu
, and M. J.
Thornton
, J. Phys.: Condens. Matter
14
, R1175
(2002
).12.
J. M.
Shaw
, W. H.
Rippard
, S. E.
Russek
, T.
Reith
, and C. M.
Falco
, J. Appl. Phys.
101
, 023909
(2007
).13.
O.
Hellwig
, A.
Berger
, T.
Thomson
, E.
Dobisz
, Z. Z.
Bandic
, H.
Yang
, D. S.
Kercher
, and E. E.
Fullerton
, Appl. Phys. Lett.
90
, 162516
(2007
).14.
C.
Bunce
, J.
Wu
, G.
Ju
, B.
Lu
, D.
Hinzke
, N.
Kazantseva
, U.
Nowak
, and R. W.
Chantrell
, Phys. Rev. B
81
, 174428
(2010
).15.
A. I.
Akhiezer
, V. G.
Baryakhtar
, and S. V.
Peletminskii
, Zh. Eksp. Teor. Fiz.
35
, 228
(1958
).16.
E. A.
Turov
and V. G.
Shavrov
, Usp. Fiz. Nauk
140
, 429
(1983
).17.
18.
V. G.
Baryakhtar
, I. M.
Vitebskii
, N. M.
Lavrinenko
, and V. L.
Sobolev
, Zh. Eksp. Teor. Fiz.
23
, 2664
(1986
).19.
20.
21.
V. G.
Baryakhtar
and E. A.
Turov
, Electronic Structure and Electronic Properties of Metals and Alloys
(Naukova dumka
, Kiev
, 1988
), p. 39
[in Russian].22.
23.
Yu. A.
Fridman
, D. V.
Spirin
, and Ph. N.
Klevets
, Phys. Status Solidi B
232
, 264
(2002
).24.
R. P.
Erickson
and D. L.
Mills
, Phys. Rev. B
46
, 861
(1992
).25.
26.
Yu. A.
Fridman
, D. A.
Matunin
, Ph. N.
Klevets
, and O. A.
Kosmachev
, J. Magn. Magn. Mater.
321
, 3782
(2009
).27.
R.
Antos
, Y.
Otani
, and J.
Shibata
, J. Phys. Soc. Jpn.
77
, 031004
(2008
).28.
V. G.
Baryakhtar
, B. A.
Ivanov
, and M. V.
Chetkin
, Usp. Fiz. Nauk
146
, 417
(1985
).29.
Yu. A.
Fridman
, Ph. N.
Klevets
, and D. V.
Spirin
, Phys. Status Solidi B
241
, 1106
(2004
).30.
Yu. A.
Fridman
, Ph. N.
Klevets
, and D. V.
Spirin
, New Developments in Ferromagnetism Research
(Nova Science
, New York
, 2005
), p. 291
.31.
32.
33.
34.
35.
36.
37.
38.
V. M.
Kalita
, I. M.
Ivanova
, and V. M.
Loktev
, [Low Temp. Phys.
28
, 475
(2002
)].39.
Y. A.
Fridman
, O. A.
Kosmachev
, and P. N.
Klevets
, Eur. Phys. J. B
81
, 185
(2011
).40.
41.
42.
B. A.
Ivanov
and A. K.
Kolezhuk
, Phys. Rev. B
68
, 052401
(2003
).43.
B. A.
Ivanov
, R. S.
Khymyn
, and A. K.
Kolezhuk
, Phys. Rev. Lett.
100
, 047203
(2008
).44.
V. G.
Bar’yakhtar
, V. I.
Butrim
, A. K.
Kolezhuk
, and B. A.
Ivanov
, Phys. Rev. B
87
, 224407
(2013
).45.
T. A.
Toth
, A. M.
Launchli
, F.
Mila
, and K.
Penc
, Phys. Rev. B
85
, 140403
(2012
).46.
T.
Moria
, Phys. Rev.
117
, 635
(1960
).47.
E. L.
Nagaev
, Magnets with Complex Exchange Interactions
(Nauka
, Moscow
, 1988
) [in Russian].48.
B. A.
Ivanov
, A. K.
Kolezhuk
, and G. M.
Wysin
, Phys. Rev. Lett.
76
, 511
(1996
).49.
E. G.
Galkina
, A. Yu.
Galkin
, B. A.
Ivanov
, and Franco
Nori
, Phys. Rev. B
81
, 184413
(2010
).50.
B. A.
Ivanov
and R. S.
Khimin
, [Low Temp. Phys.
34
, 182
(2008
)].51.
V. I.
Butrim
, B. A.
Ivanov
, A. S.
Kuznetsov
, and R. S.
Khimin
, Fiz. Nizk. Temp.
34
, 1266
(2008
)V. I.
Butrim
, B. A.
Ivanov
, A. S.
Kuznetsov
, and R. S.
Khimin
, [Low Temp. Phys.
34
, 997
(2008
)].52.
F.
Michaud
and F.
Mila
, Phys. Rev. B
88
, 094435
(2013
).53.
A.
Smerald
and N.
Shannon
, Phys. Rev. B
88
, 184430
(2013
).54.
Yu. A.
Fridman
, O. A.
Kosmachev
, and Ph. N.
Klevets
, J. Magn. Magn. Mater.
320
, 435
(2008
).55.
K.
Stevens
, Proc. Phys. Soc. A
65
, 209
(1952
).56.
57.
58.
L. D.
Landau
and E. M.
Lifshitz
, Statistical Physics, Part I
(Nauka
, Moscow
, 1976
), p. 583
[in Russian].59.
V. G.
Baryakhtar
, V. N.
Krivoruchko
, and D. A.
Yablonskii
, Green Functions in the Theory of Magnetism
(Naukova dumka
, Kiev
, 1984
), p. 336
[in Russian].60.
61.
V. V.
Valkov
, T. A.
Valkova
, and S. G.
Ovchinnikov
, Zh. Eksp. Teor. Fiz.
88
, 550
(1985
).62.
63.
Yu. A.
Fridman
, F. N.
Klevets
, and G. A.
Gorelikov
, Zh. Eksp. Teor. Fiz.
141
, 748
(2012
).64.
Yu. A.
Fridman
, F. N.
Klevets
, G. A.
Gorelikov
, and A. G.
Meleshko
, Zh. Eksp. Teor. Fiz.
142
, 1155
(2012
).65.
E. A.
Turov
, A. A.
Lugovoi
, V. D.
Buchelnikov
, Yu. A.
Kuzavko
, V. G.
Shavrov
, and O. V.
Yan
, Preprint No. 86/4, Institute of Metals Physics, Academy of Sciences of the USSR, Sverdlovsk, 25 (1986
).66.
K. P.
Belov
, Rare-Earth Magnets and Their Applications
(Nauka
, Moscow
, 1980
), p. 239
[in Russian].© 2014 AIP Publishing LLC.
2014
AIP Publishing LLC
You do not currently have access to this content.