A simple kinetic approach based on approximate solution of the Fokker–Planck equation for magnetic moment orientations is developed for the calculation of the hysteresis loop of a superparamagnetic nanoparticle assembly with predominantly uniaxial magnetic anisotropy. The hysteresis loops of the oriented assembly have been obtained in the intermediate to high damping limit as a function of temperature at various angles that the applied magnetic field makes with the particle easy anisotropy axis. An analytic approximation is given for the effective energy barriers separating energy wells. The evolution of the hysteresis loop as a function of temperature is shown to take place between the ultimate Stoner–Wohlfarth loop and the equilibrium magnetization curve. Analytical estimates for the coercive force and the blocking temperature are obtained both for ordered and randomly oriented assemblies of uniaxial particles.
REFERENCES
1.
2.
3.
C. C.
Berry
and A. S. G.
Curtis
, J. Phys. D
36
, R198
(2003
).4.
D.
Weller
and A.
Moser
, IEEE Trans. Magn.
35
, 4423
(1999
).5.
C. P.
Bean
and J. D.
Livingston
, J. Appl. Phys.
30
, S120
(1959
).6.
E. F.
Kneller
and F. E.
Luborsky
, J. Appl. Phys.
34
, 656
(1963
).7.
R. H.
Victora
, Phys. Rev. Lett.
63
, 457
(1989
).8.
N. H.
Bertram
and H. J.
Richter
, J. Appl. Phys.
85
, 4991
(1999
).9.
10.
A. M.
Afanas’ev
, M. A.
Chuev
, and J.
Hesse
, Phys. Rev. B
56
, 5489
(1997
).11.
C.
Yang
, J. M.
Sivertsen
, and J. H.
Judy
, IEEE Trans. Magn.
34
, 1606
(1998
).12.
A. M.
Afanas’ev
, M. A.
Chuev
, and J.
Hesse
, Sov. Phys. JETP
89
, 533
(1999
).13.
M. A.
Chuev
and J.
Hesse
, J. Phys.: Condens. Matter
19
, 506201
(2007
).14.
R. W.
Chantrell
, D.
Weller
, T. J.
Klemmer
, S.
Sun
, and E. E.
Fullerton
, J. Appl. Phys.
91
, 6866
(2002
).15.
H. F.
Du
and A.
Du
, J. Appl. Phys.
99
, 104306
(2006
).16.
W. F.
Brown
, Jr., Phys. Rev.
130
, 1677
(1963
).17.
18.
J. L.
Garcia-Palacios
and F. J.
Lazaro
, Phys. Rev. B
58
, 14937
(1998
).19.
I.
Klik
and L.
Gunther
, J. Stat. Phys.
60
, 473
(1990
).20.
I.
Klik
and L.
Gunther
, J. Appl. Phys.
67
, 4505
(1990
).21.
W. T.
Coffey
, D. S. F.
Crothers
, Yu. P.
Kalmykov
, and J. T.
Waldron
, Phys. Rev. B
51
, 15947
(1995
).22.
W. T.
Coffey
, D. S. F.
Crothers
, J. L.
Dormann
, L. J.
Geoghegan
, Yu. P.
Kalmykov
, J. T.
Waldron
, and A. W.
Wickstead
, Phys. Rev. B
52
, 15951
(1995
).23.
L. J.
Geoghegan
, W. T.
Coffey
, and B.
Mulligan
, Adv. Chem. Phys.
100
, 475
(1997
).24.
W. T.
Coffey
, D. S. F.
Crothers
, J. L.
Dormann
, L. J.
Geoghegan
, and E. C.
Kennedy
, Phys. Rev. B
58
, 3249
(1998
).25.
W. T.
Coffey
, D. S. F.
Crothers
, J. L.
Dormann
, Yu. P.
Kalmykov
, E. C.
Kennedy
, and W.
Wernsdorfer
, Phys. Rev. Lett.
80
, 5655
(1998
).26.
D. A.
Garanin
, E. C.
Kennedy
, D. S. F.
Crothers
, and W. T.
Coffey
, Phys. Rev. E
60
, 6499
(1999
).27.
W. T.
Coffey
, D. A.
Garanin
, H.
Kachkachi
, and D. J.
McCarthy
, J. Magn. Magn. Mater.
221
, 110
(2000
).28.
P. M.
Déjardin
, D. S. F.
Crothers
, W. T.
Coffey
, and D. J.
McCarthy
, Phys. Rev. E
63
, 021102
(2001
).29.
W. T.
Coffey
, D. S. F.
Crothers
, Yu. P.
Kalmykov
, and S. V.
Titov
, Phys. Rev. B
64
, 012411
(2001
).30.
W. T.
Coffey
, Yu. P.
Kalmykov
, and J. T.
Waldron
, The Langevin Equation
, 2nd ed. (World Scientific
, Singapore
, 2004
), Chap. 9.31.
Yu. P.
Kalmykov
, J. Appl. Phys.
96
, 1138
(2004
).32.
W. T.
Coffey
, Yu. P.
Kalmykov
, S. V.
Titov
, and B. P.
Mulligan
, Phys. Rev. E
73
, 061101
(2006
).33.
Yu. P.
Kalmykov
, W. T.
Coffey
, and S. V.
Titov
, Phys. Solid State
47
, 272
(2005
).34.
Yu. P.
Kalmykov
, W. T.
Coffey
, B.
Ouari
, and S. V.
Titov
, J. Magn. Magn. Mater.
292
, 372
(2005
).35.
Yu. P.
Kalmykov
and B.
Ouari
, Phys. Rev. B
71
, 094410
(2005
).36.
B.
Ouari
and Yu. P.
Kalmykov
, J. Appl. Phys.
100
, 123912
(2006
).37.
H. J.
Suh
, C.
Heo
, C. Y.
You
, W.
Kim
, T. D.
Lee
, and K. J.
Lee
, Phys. Rev. B
78
, 064430
(2008
).38.
N. A.
Usov
and Yu. B.
Grebenshchikov
, J. Appl. Phys.
105
, 043904
(2009
).39.
N. A.
Usov
and Yu. B.
Grebenshchikov
, in Magnetic Nanoparticles
, edited by S. P.
Gubin
, (Wiley-VCH
, Weinheim
, 2009
), Chap. 8.40.
E. C.
Stoner
and E. P.
Wohlfarth
, Philos. Trans. R. Soc. London, Ser. A
240
, 599
(1948
).41.
J. L.
Dormann
, F.
D’Orazio
, F.
Lucari
, E.
Tronc
, P.
Prene
, J. P.
Jolivet
, D.
Fiorani
, R.
Cherkaoui
, and M.
Nogues
, Phys. Rev. B
53
, 14291
(1996
).42.
W. H.
Press
, B. P.
Flannery
, S. A.
Teukolsky
, and W. T.
Vetterling
, Numerical Recipes
(Cambridge University Press
, Cambridge
, 1986
).43.
M.
Abramowitz
and I. A.
Stegun
, Handbook of Mathematical Functions
(National Bureau of Standards
, Washington, D.C.
, 1964
).44.
G. F.
Goya
, T. S.
Serquo
, F. C.
Fonseca
, and M. P.
Morales
, J. Appl. Phys.
94
, 3520
(2003
).45.
P.
Dutta
, A.
Manivannan
, M. S.
Seehra
, N.
Shah
, and G. P.
Huffman
, Phys. Rev. B
70
, 174428
(2004
).46.
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