Optimization study of the nanostructure of hard/soft magnetic multilayers
Matteo Amato
Dipartimento di Fisica, Universita ` di Firenze, Largo Enrico Fermi 2, I-50125 Firenze, Italy
Maria Gloria Pini
Istituto di Elettronica Quantistica, Consiglio Nazionale delle Ricerche, Via Panciatichi 56/30, I-50127 Firenze, Italy
Angelo Rettori
Dipartimento di Fisica, Universita ` di Firenze and Istituto Nazionale di Fisica della Materia, Unita ` di Firenze,
Largo Enrico Fermi 2, I-50125 Firenze, Italy
Received 16 November 1998
We present numerical simulations, based on a mean-field calculation of the equilibrium configuration, for
the magnetization reversal process in magnetic multilayers consisting of a hard h phase with large anisotropy,
exchange coupled to a soft s phase with large magnetization. Starting from a trilayer made of 50h /100s /50h
layers, and using realistic Hamiltonian parameters pertinent to epitaxial Sm-Co/Fe films, we separately inves-
tigate the effect of i increasing nanostructuration, while maintaining constant the overall hard/soft ratio, and
ii decreasing the thickness of the hard phase, while keeping constant that of the soft phase. We find that the
exchange-bias field and the coercive field strongly increase upon increasing nanostructuration and that the
maximum energy product ( BH)
max
rapidly tends to the ideal value (2 M
sat
)
2
. In contrast, upon reducing the
thickness of the hard phase in a trilayer, the exchange-bias field and the coercive field remain nearly constant.
Thus, combining both effects in an opportune way, we are able to determine the most convenient composition
in order to obtain a permanent exchange-spring magnet with high performance, i.e., very high ( BH)
max
.
S0163-18299902729-0
I. INTRODUCTION
In recent years, the search for high performance perma-
nent magnetic materials
1,2
has received strong impetus since
the concept of the exchange-spring magnet was introduced.
3
The idea is to assemble a composite magnet consisting of
two suitably dispersed and mutually exchange-coupled
phases: a hard h phase, which provides a high coercive
field, and a soft s phase, with a high saturation magnetiza-
tion. The exchange coupling between the two phases gives
origin to a typical reversible behavior of the demagnetization
curve, hence the name exchange-spring magnet. In this way,
one can obtain an enhancement of remanence with respect to
a magnet made of the pure hard phase, so that high-energy
products ( BH )
max
can be reached:
4
for example, in
Sm
2
Fe
17
N
3
/Fe
65
Co
35
multilayers with a volume fraction of
only 9% of the hard phase, Skomski and Coey predicted a
( BH )
max
as high as 137 MGOe i.e., more than twice the
value obtained by a laboratory-scale Nd
2
Fe
14
B magnet
5
.
The fine distribution of the two phases on a nanometric scale
can be achieved by several techniques: melt spinning,
6,7
me-
chanical alloying,
8,9
etc. Multilayer exchange-spring mag-
nets, which can be obtained by ultrahigh vacuum vapor
deposition
10
or sputtering,
11–18
are particularly appealing
from the theoretical point of view because the thicknesses of
the hard and soft phases are easily controllable, thus leading
to a simple and well-defined structure. Moreover, they are
becoming more and more interesting even for applications,
owing to the possibility of being integrated in electronic
devices.
19
In this paper, we present a theoretical study of the mag-
netization reversal process in a two-phase multilayer. Our
work was stimulated by recent experimental results and nu-
merical simulations in high-quality epitaxial hard/soft Sm-
Co/transition metal TMTM=Fe, Co bilayers,
16,17
grown
via dc magnetron sputtering.
15
To calculate the equilibrium
configuration for a multilayer, we use a mean-field method
recently developed.
20,21
Starting from a trilayer made of
50h /100s /50h layers, we separately investigate the effect of
the following.
i Increasing nanostructuration, while maintaining con-
stant the total number of layers and the overall hard/soft
ratio, in order to obtain higher exchange-bias and coercive
fields.
ii Decreasing the thickness of the hard phase, while
keeping constant that of the soft phase, so that a higher satu-
ration magnetization can be obtained.
Our aim is to determine the optimal composition in order to
obtain a permanent exchange-spring magnet with high per-
formance. In particular, for a Sm-Co/Fe film with opportune
nanostructuration and reduction of the hard phase actually, a
10h +33s +10h +34s +10h +33s +10h heptalayer, we pre-
dict that a very high maximum energy product, ( BH )
max
74 MGOe, can be obtained. The paper is organized as
follows. In Sec. II we present the model and the mean-field
theoretical framework. In Sec. III the results of our calcula-
tion are displayed and discussed. Finally, in Sec. IV we draw
the conclusions.
PHYSICAL REVIEW B 1 AUGUST 1999-I VOLUME 60, NUMBER 5
PRB 60 0163-1829/99/605/34147/$15.00 3414 ©1999 The American Physical Society