Magnetic Concentration Phase Transitions in Ultrathin Films
Afremov Leonid
1, a
and Il`yushin Ilia
2, b
School of Natural Science, Far-Easter Federal University, Vladivostok, Russia
a
afremovl@mail.dvgu.ru,
b
futted@gmail.com
Keywords: size effects, Curie temperature, ultrathin films, magnetic phase transition,
concentration phase transition, percolation threshold.
Abstract. Modeling study of magnetic and concentration phase transition in ultrathin films of
diluted magnet has been carried out under approximation of random interaction between atomic
magnetic moments of nearest neighbors and within the framework of Ising model. The dependence
of Curie temperature on concentration of magnetic atoms was formed. It is shown that with
increasing of thickness of ultrathin film the critical concentration of transition from unordered to
ordered magnetic state decreases down to the value equal to the percolation threshold.
Introduction
One of the tasks of Physics of nanomaterials is development of new magnetic materials with
targeted properties. Therefore, along with experimental studies, nanotechnologists need methods
for theoretical modeling of magnetic properties of nanomaterials. The method proposed below can
be used within the framework of single formal description for calculating of saturation
magnetization, Curie temperature and critical concentration of magnetic phase transition in
ultrathin films. Moreover, the formal description allows modeling of magnetic properties of
nanoparticles with any type of ordering: whether they are ferromagnetic, antiferromagnetic or
ferrimagnetic materials. In diluted magnets the critical temperature of magnetic phase transition
depends on concentration of magnetic atoms. The two critical processes proceed here, near the point
of phase transition, simultaneously: the beginning of magnetic ordering and the geometrical process
of percolation, related with changing of general number of interatomic bonds. Notably,
notwithstanding the association of these processes, the critical proceeding each of them can be
different. If non-magnetic atoms don’t affect the distribution of magnetic atoms, than the processes
of magnetic ordering and percolation coincide [1].
Model
• ultrathin film consist of monolayers of diluted magnet, the concentration of magnetic
atoms in which is ;
• interaction fields ℎ between spin magnetic moments of the atoms are distributed randomly,
and direct exchange interaction is realized only between the nearest neighbors ;
• spin magnetic moments are oriented along an axis (approximation of the Ising model).
For forming of distribution function for random interaction fields ℎ and average magnetic moment
let us use the formal description, which has been stated in details in the works [2 - 4]. In
approximation of the model introduced above, the equations defining average magnetic moments in
each monolayer can be reduced as follow:
=
1 −
1
−
1 +
1 −
1 +
1 −
2
∗
tanh !
"
,
$
%,
Advanced Materials Research Vol. 683 (2013) pp 69-72
Online available since 2013/Apr/24 at www.scientific.net
© (2013) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMR.683.69
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,
www.ttp.net. (ID: 95.154.72.68, Far-Easter Federal University, Vladivostok, Russian Federation-03/02/14,03:20:36)