Magnetic Structures in Nonmag-/MAG-/Nonmag-Netic Sandwiches
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7= -Jm2 Y cos(yoi-
N-1
a-
K!,
Z sin 2 p0+ Ka(sin
2
V, +
sin 2
YN).
(1)
i=1i=2
The first term on the right-hand side of the above expression covers the exchange coupling energy between the classical spin-vectors on the nearest-neighboring layers. The remaining. terms are for the in-plane shape anisotropy K(, and the vertical interface anisotropy KI, respectively, where the dashes denote the difference between the present quantities and those in standard experimental notations. 227 Mat. Res. Soc. Symp. Proc. Vol. 384 01995 Materials Research Society
N
K' transition metal
K'
FOM 5s
A• Ký K'
2
Figure 1: Discrete model[4]. The stable spin configuration is determined by minimizing the energy functional (1). In the present discrete model, no analytic results can be expected. For numnerical calculation in this section, we take .Jini = 1 and ot = 1(lattice constant).
Fixing the magnetic constants, we have found a spin-reorientation transition from the perpendicular uniform configuration to a nonuniform one, as the number of layers is increased from N = 2. A further transition is observed, where the nonuniform configuration is switched into the in-plane uniform one. The phase diagram of the spin configuration, shown as dashed arrows for IK = 0.10, with the number of layers and the surface anisotopy as variables is depicted in Fig.2, for two different values of volume anisotropy. The phase boundaries consist of steps, as the result of the discrete variance of the thickness, namely the number of layers. The locations of the phase boundaries depend sensitively on the value of volume anisotropv.
N 12 10 8
6
6'
....
. . .:
:
,
..
"....... .
. ." .
..
..
.... .... .... ... ... ...
. . .
,4 2
K "i.O.y
-..
00 0
0.2
0.4
0.6
0.8
1.0 KS
Figure 2: Phase diagram of the spin configuration with fixed volume anisotropics[4]. We have calculated the magnetic configuration in systems of N = 4 - 20 and various values of K,' and iCv, and tried to rearrange the data into a single diagram. We then arrive at the conclusion that if one takes the variables as (N- AN) K' and K/V A- as in Fig.3 where AN = 2.2 is selected to obtain the best plotting, all the phase boundaries, such as those shown in Fig.2, fall into two smooth curves[4]. This fact implies the presence of the following scaling relations among the film thickness, the anisotropies and the exchange I, Jm1. coupling in the spin-reorientation transitions: (N - AN) KI,/(Jm2) and I!/ CONTINUOUS MODEL In this section, we introduce the continuum approach and present the essential results.
228
N-2.2 'V-,.!
V
2 2.5 2.0
.--1.56 ..
1.5 1.0
.
0.5
,."•0.5.0
• i
~~~v
so... =...Oropy
• "
K''.0.04 K''-0.08
•
0
.
1
2
K,'
K'-O 10
3
4 /-,
Figure 3: Scaled phase diagrams[4]. Consider a ferromagnetic layer with thickness 2a: On the surfaces there exist perpendicular anisotropies IK,, within the film the anisotropy A7, is in the film plane, and the exchangc stiffness A is ferromagnetic and finite. We assume that the magnetization is uniform in
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