1 Single Nanomagnet Behaviour: Surface and Finite-Size Effects
5
Fig. 1.1 Cubic system with pbc and thermal behavior of the magnetization for two sizes
Fig. 1.2 Cubic system with fbc and thermal behavior of the magnetization for pbc and fbc systems
M ∼ = 1 −
θ
2
W N ,
(1.1)
where
W N =
1
N
k
1
1 − λ k
, θ =
T
T MFA
c
(1.2)
and for a three-dimensional (d = 3) sc lattice λ k = (cos k x + cos k y + cos k z )/d. It
is important to note that W N in (1.2) for pbc and fbc differ only by the definition of
the discrete wave vectors [2, 3], since
k α =
2π n α /N , pbc
π n α /N , fbc
,
n α = 0, 1, . . . , N − 1
(1.3)
5
Fig. 1.1 Cubic system with pbc and thermal behavior of the magnetization for two sizes
Fig. 1.2 Cubic system with fbc and thermal behavior of the magnetization for pbc and fbc systems
M ∼ = 1 −
θ
2
W N ,
(1.1)
where
W N =
1
N
k
1
1 − λ k
, θ =
T
T MFA
c
(1.2)
and for a three-dimensional (d = 3) sc lattice λ k = (cos k x + cos k y + cos k z )/d. It
is important to note that W N in (1.2) for pbc and fbc differ only by the definition of
the discrete wave vectors [2, 3], since
k α =
2π n α /N , pbc
π n α /N , fbc
,
n α = 0, 1, . . . , N − 1
(1.3)