436
Iu. Gudyma et al.
Additional important information about the evolution of magnetization can be
extracted from the analysis of the Monte Carlo trajectories. From entire range
of temperature for which the transition curves have been calculated, we have
checked the evolution of the system magnetization at three most relevant values
of temperatures: the magnetization dynamics at transition temperature and at
temperatures where the system magnetization becomes saturated which correspond
to HS and LS ordered states. In Fig. 27.5 are shown the trajectories that describe the
evolution of magnetization at indicated values of temperatures on cooling branch
of transition curve separately for bulk and surface sites. Notice that the surface
sites form the surface magnetization of spin-crossover nanocrystal. We analyzed
only the cooling branch of transition curve since due to the symmetry reason, the
dynamics for cooling and heating physically is similar with only difference that
it occurs in opposite direction so the opposite physical processes can be observed
(e.g., instead of relaxation, one can see the excitation and so on). As it is observed
from the comparison of Fig. 27.5a, b which are calculated for bulk and surface
sites only with J s = J b , the relaxation of HS fractions on the surface takes place
with lower rate than the one for the HS molecules inside the crystal. It can serve
additional argument about smaller degree of cooperativity of surface sites. As it is
shown in Fig. 27.3b, the decrease of coupling of surface molecules shifts the surface
magnetization into non-hysteretic region with the gradual transition between the
states. The MC trajectories that correspond to that cases do not show the relaxation
dynamics but evolves around the value of magnetization which corresponds to
certain temperature (see Fig. 27.5c, d). However the smaller values of coupling
of surface molecules decrease the saturated magnetization of the surface which is
clearly seen from Fig. 27.5d where additionally the mean values of magnetization
of HS and LS states obtained at the same temperature for J s = 0.5J b (green dashed
lines) and J s = 0.25J b (yellow dashed lines) are indicated, respectively.
In more rigorous approach, we should consider the contact of the system with
environment. Usually this is made by the accounting of the random disordering
of effective field on system’s surface [18, 20, 21] (see also Sect. 27.2). In order
to analyze the system’s behavior for fluctuating effective ligand field, we have
followed its description given by Eq. (27.2) with condition (27.4). We have confined
to the description with fluctuating ligand field only for molecules on the surface,
since these molecules directly interact with environment including the control field
which here is temperature. For the next molecules inside the lattice, we assumed
that fluctuations caused by the external environment are completely vanished.
The comparison of temperature transition curves for fluctuationless lattice and the
system with fluctuations with different strengths is given in Fig. 27.6.
Due to fluctuating behavior manifested only in the case of surface coupling,
we have analyzed separately the temperature transition curves of molecules on the
surface from Fig. 27.3b for several fixed values of fluctuation strength. The increase
of the random field on the surface enlarges the hysteresis of 3D spin-crossover
lattice, despite the fact that only surface molecules fluctuate. It is important to notice
that the thermal hysteresis loop progressively increases similar to the results of the
work of [12], but the equilibrium temperature does not undergo a shift. It shows
Iu. Gudyma et al.
Additional important information about the evolution of magnetization can be
extracted from the analysis of the Monte Carlo trajectories. From entire range
of temperature for which the transition curves have been calculated, we have
checked the evolution of the system magnetization at three most relevant values
of temperatures: the magnetization dynamics at transition temperature and at
temperatures where the system magnetization becomes saturated which correspond
to HS and LS ordered states. In Fig. 27.5 are shown the trajectories that describe the
evolution of magnetization at indicated values of temperatures on cooling branch
of transition curve separately for bulk and surface sites. Notice that the surface
sites form the surface magnetization of spin-crossover nanocrystal. We analyzed
only the cooling branch of transition curve since due to the symmetry reason, the
dynamics for cooling and heating physically is similar with only difference that
it occurs in opposite direction so the opposite physical processes can be observed
(e.g., instead of relaxation, one can see the excitation and so on). As it is observed
from the comparison of Fig. 27.5a, b which are calculated for bulk and surface
sites only with J s = J b , the relaxation of HS fractions on the surface takes place
with lower rate than the one for the HS molecules inside the crystal. It can serve
additional argument about smaller degree of cooperativity of surface sites. As it is
shown in Fig. 27.3b, the decrease of coupling of surface molecules shifts the surface
magnetization into non-hysteretic region with the gradual transition between the
states. The MC trajectories that correspond to that cases do not show the relaxation
dynamics but evolves around the value of magnetization which corresponds to
certain temperature (see Fig. 27.5c, d). However the smaller values of coupling
of surface molecules decrease the saturated magnetization of the surface which is
clearly seen from Fig. 27.5d where additionally the mean values of magnetization
of HS and LS states obtained at the same temperature for J s = 0.5J b (green dashed
lines) and J s = 0.25J b (yellow dashed lines) are indicated, respectively.
In more rigorous approach, we should consider the contact of the system with
environment. Usually this is made by the accounting of the random disordering
of effective field on system’s surface [18, 20, 21] (see also Sect. 27.2). In order
to analyze the system’s behavior for fluctuating effective ligand field, we have
followed its description given by Eq. (27.2) with condition (27.4). We have confined
to the description with fluctuating ligand field only for molecules on the surface,
since these molecules directly interact with environment including the control field
which here is temperature. For the next molecules inside the lattice, we assumed
that fluctuations caused by the external environment are completely vanished.
The comparison of temperature transition curves for fluctuationless lattice and the
system with fluctuations with different strengths is given in Fig. 27.6.
Due to fluctuating behavior manifested only in the case of surface coupling,
we have analyzed separately the temperature transition curves of molecules on the
surface from Fig. 27.3b for several fixed values of fluctuation strength. The increase
of the random field on the surface enlarges the hysteresis of 3D spin-crossover
lattice, despite the fact that only surface molecules fluctuate. It is important to notice
that the thermal hysteresis loop progressively increases similar to the results of the
work of [12], but the equilibrium temperature does not undergo a shift. It shows