Relaxation process from photoinduced states of double-step spin-crossover systems
using a kinetic two-sublattice Ising-like model including intra-site coupling
Shinichiro Mouri* and Koichiro Tanaka
†
Department of Physics, Kyoto University, Kitashirakawa Oiwaketyo, Sakyo-ku, Kyoto 606-8502, Japan
Sébastien Bonhommeau
Laboratoire de Chimie de Coordination (LCC/CNRS/UPR8241), Centre National de la Recherche Scientifique, 205, Route de Narbonne,
31077 Toulouse, France
and Laboratoire de Physique des Solides de Toulouse, UMR 5477 CNRS, 118 Route de Narbonne, F-31062 Toulouse Cedex, France
Nawel Ould Moussa, Gábor Molnár, and Azzedine Bousseksou
‡
Laboratoire de Chimie de Coordination (LCC/CNRS/UPR8241), Centre National de la Recherche Scientifique, 205,
Route de Narbonne, 31077 Toulouse, France
Received 7 September 2007; revised manuscript received 24 September 2008; published 18 November 2008
A two-sublattice kinetic mean-field Ising-like model is proposed to describe the relaxation process from
photo-induced metastable states in double-step spin-crossover complexes. Its originality lies in the rigorous
treatment of intra-site coupling that yields dynamical equations by using additionally the Glauber stochastic
treatment of master equations. The numerical resolution of these equations permits one to extract not only the
high-spin fraction but also the intra-site correlation and the symmetry-breaking parameter which are hidden
order parameters in these systems. Our simulation can demonstrate interesting relaxation behavior. As the
result of synergy of inter- and intra-site interactions, double-step relaxation curves can be obtained in most
cases. When decreasing the magnitude of interactions, one-step sigmoidal relaxation or stretched exponential
relaxations appear. Asymmetry between A and B sublattices may even induce curious dynamics such as triple
steplike behavior that is also observed for weak fluctuations in the initial configuration. For stronger fluctua-
tions the system relaxes to an ordered metastable state instead of reaching the ground state. This model is
finally applied to genuine systems, namely, the binuclear spin-crossover complex FebtNCS
2
2
bpym and
the polymeric spin-crossover compound FepmdAgCN
2
Ag
2
CN
3
that exhibit both a two steps thermal
spin transition. The relaxation curves are then conveniently reproduced considering weak-interaction param-
eters whose possible origins will be highlighted.
DOI: 10.1103/PhysRevB.78.174308 PACS numbers: 75.30.Wx, 64.60.My
I. INTRODUCTION
Photo-induced phase transitions PIPTRefs. 1 and 2
are highly cooperative structural and electronic phenomena
in solid state. They consist of populating nonequilibrium
states by irradiating a system initially in its ground state.
Once the photoexcitation is over, the material tends to relax
from this photogenerated state. Several treatments that are
proposed to interpret relaxation processes take advantage of
the kinetic Ising-like model based on a stochastic approach
developed by Boukheddaden and co-workers.
3–8
In particu-
lar, such a model turns out to be appropriate to allow for
relaxations following light-induced excited spin state trap-
ping LIESST effect in ironII spin-crossover complexes
from a low-spin LS state
1
A
1
to a metastable high-spin
HS state
5
T
2
.
9,10
It accounts especially well for sigmoidal
self-accelerated relaxation decays occurring in rather
strongly cooperative systems. This kinetic Ising-like model
has also the advantage to give a microscopic view of coop-
erative interactions, which is not the case in the empirical
rate-equation model proposed by Hauser et al.,
11
even
though it can reproduce the typical relaxation dynamics of
ironII spin-crossover complexes monoexponential and
stretched exponential relaxations notably.
In this paper, we are going to focus on spin-crossover
compounds showing double-step thermal spin transition. The
two-sublattice Ising-like model suggested by Bousseksou et
al.
12,13
is one of the best models used to explain the static
behavior of their thermal spin conversion. In the frame of
this approach, the double-step conversion is caused by the
synergistic effect of ferromagneticlike and antiferromagneti-
clike interactions thought to be at the origin of the unusual
photo-induced properties that are sometimes observed in
these materials. Two interesting examples are the binuclear
spin-crossover complex FebtNCS
2
2
bpym and the
polymeric mononuclear spin-crossover complex
FepmdAgCN
2
Ag
2
CN
3
. In the former, a double-step
spin conversion from the HS-HS state to the LS-LS state via
the HS-LS state occurs, and it is possible to populate selec-
tively the HS-LS state using an infrared laser irradiation and
the HS-HS state with a red laser excitation from the LS-LS
state.
14–17
In the latter, the double-step relaxation behavior is
also observed but only the pure HS state can be
photogenerated.
18
In order to shed different light on the re-
laxations of double-step spin-crossover compounds, we ex-
tend in this paper the aforementioned kinetic Ising-like
model to the study of relaxation processes from photo-
induced states in double-step spin-crossover complexes by
including local intra-site couplings.
In Sec. II, a different theoretical model based on micro-
scopic Ising-like Hamiltonian including local antiferromag-
PHYSICAL REVIEW B 78, 174308 2008
1098-0121/2008/7817/17430811 ©2008 The American Physical Society 174308-1