Ising-Like Model of Nanosize Spin-Crossover Molecular Crystals
151
intensity of white fluctuations is at which hysteresis collapse is ε = 140. We keep this
intensity for the system with colored fluctuations in order to provide the qualitative
comparison of the impact of degree of autocorrelation on hysteresis width. As shown
in Fig. 2d, the hysteresis width for τ = 5 and τ = 50 is slightly changed. Therefore,
in the system with fluctuations, there are such conditions in which the action of fluctuations stimulates the manifestation of first-order phase transition and the shifting
of cooperativity threshold for the first-order phase transition toward lower values.
For the first-order phase transition, the fluctuations of external field provoke the
narrowing of the hysteresis loop despite the correlation properties. The hysteresis
loop for the system with time-correlated fluctuations envelops the one for system with
white Gaussian stochastic process. With narrowing the spectrum of fluctuations, the
hysteresis loop is narrowing but with much slower rate than for white fluctuations.
The opposite behavior is noticed with the rising of the autocorrelation time of OU
random process, i.e., the degree of correlation. For strongly correlated fluctuations,
the width of hysteresis loop rises with an increase in degree of correlation and, at
last, it may become wider than without fluctuations (deterministic system).
The relationship between microscopic Ising-like approach and macroscopic models was previously given in our paper [22], where analytical results obtained for classical macroscopic system and supported by numerical simulations show the same
trends of vanishing system’s bistability under the noise action.
The transition temperatures T up and T down are related to the heating and cooling
branches which are initiated from the low-temperature stable LS state and the hightemperature metastable HS state, respectively. Altogether, the competition between
energy of the molar entropy change ΔS = R ln g and octahedral ligand field splitting
energy Δ identifies the preferred (LS or HS) state but the breathing of crystal field
changes this situation significantly. If Δ is larger than k B T ln g (the strong ligand
field), the ground is electronic configuration t
6
2g associated to LS state; otherwise, the
t
4
2g e
2
g electronic configuration which correspond to HS state of iron(II) spin-crossover
system becomes ground. Our results demonstrate that the transition temperatures of
the system strongly depend on the breathing crystal field.
5 The Manifestation of Hysteresis in 3D SCO Nanocrystals
with Ferromagnetic and Antiferromagnetic Surface
The influence of surface molecule interaction on hysteretic behavior of whole 3D
SCO nanocrystal is evaluated via temperature transition graphs following the same
manner used in paper [23], additionally taking into account the possibility of fluctuations of external field. Therefore, the basic model of SCO with ferromagnetic and
antiferromagnetic surface from [23] has been adapted for nonzero fluctuation case
as is given in (6). In the present studies, the initial system has been prepared in firstorder phase transition mode that was reached by picking up the positive coupling
value of molecules inside the lattice at J
b
= 85.
151
intensity of white fluctuations is at which hysteresis collapse is ε = 140. We keep this
intensity for the system with colored fluctuations in order to provide the qualitative
comparison of the impact of degree of autocorrelation on hysteresis width. As shown
in Fig. 2d, the hysteresis width for τ = 5 and τ = 50 is slightly changed. Therefore,
in the system with fluctuations, there are such conditions in which the action of fluctuations stimulates the manifestation of first-order phase transition and the shifting
of cooperativity threshold for the first-order phase transition toward lower values.
For the first-order phase transition, the fluctuations of external field provoke the
narrowing of the hysteresis loop despite the correlation properties. The hysteresis
loop for the system with time-correlated fluctuations envelops the one for system with
white Gaussian stochastic process. With narrowing the spectrum of fluctuations, the
hysteresis loop is narrowing but with much slower rate than for white fluctuations.
The opposite behavior is noticed with the rising of the autocorrelation time of OU
random process, i.e., the degree of correlation. For strongly correlated fluctuations,
the width of hysteresis loop rises with an increase in degree of correlation and, at
last, it may become wider than without fluctuations (deterministic system).
The relationship between microscopic Ising-like approach and macroscopic models was previously given in our paper [22], where analytical results obtained for classical macroscopic system and supported by numerical simulations show the same
trends of vanishing system’s bistability under the noise action.
The transition temperatures T up and T down are related to the heating and cooling
branches which are initiated from the low-temperature stable LS state and the hightemperature metastable HS state, respectively. Altogether, the competition between
energy of the molar entropy change ΔS = R ln g and octahedral ligand field splitting
energy Δ identifies the preferred (LS or HS) state but the breathing of crystal field
changes this situation significantly. If Δ is larger than k B T ln g (the strong ligand
field), the ground is electronic configuration t
6
2g associated to LS state; otherwise, the
t
4
2g e
2
g electronic configuration which correspond to HS state of iron(II) spin-crossover
system becomes ground. Our results demonstrate that the transition temperatures of
the system strongly depend on the breathing crystal field.
5 The Manifestation of Hysteresis in 3D SCO Nanocrystals
with Ferromagnetic and Antiferromagnetic Surface
The influence of surface molecule interaction on hysteretic behavior of whole 3D
SCO nanocrystal is evaluated via temperature transition graphs following the same
manner used in paper [23], additionally taking into account the possibility of fluctuations of external field. Therefore, the basic model of SCO with ferromagnetic and
antiferromagnetic surface from [23] has been adapted for nonzero fluctuation case
as is given in (6). In the present studies, the initial system has been prepared in firstorder phase transition mode that was reached by picking up the positive coupling
value of molecules inside the lattice at J
b
= 85.