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I. Gudyma and A. Maksymov
The transition curves in three-dimensional spin-crossover crystal were computed
by Monte Carlo simulations for various external fields: (i) without fluctuations; (ii)
with white fluctuations; and (iii) with colored time-correlated fluctuations. It was
shown that the strengthening of fluctuation of crystal field in 3D spin-crossover
acts qualitatively different whether the first- or gradual phase transition occurs. In
the case of first-order phase transition, the white and colored fluctuations tend to
narrow the loop width; however, the rate of narrowing is very dependent on the
statistical characteristics of fluctuations that we have probed in our study (the strength
of fluctuations and the autocorrelation time). The presence of time correlations in
fluctuations makes hysteresis to collapse at much higher fluctuation strength. For the
system located on the boundary between non-hysteretic and hysteretic phase regions,
characterized by threshold spin–spin coupling, the presence of fluctuations favors the
appearance of hysteresis and, therefore, reduces the threshold spin–spin interaction.
The impact of the size and surface effects on the hysteresis loops of twodimensional and three-dimensional spin-crossover system with temperature changes
and perturbed by fluctuations has been examined as well. The conditions of monoand bistable behavior of spin-crossover compounds were characterized, and respective regions of first-order and gradual phase transitions were found. Likewise, the
detailed discussion of the relations of hysteresis width on the size effects and the
strength of statistical fluctuations were given.
It has been found out that for spin-crossover system the increase of system
size leads to the increase in hysteresis width, whereas the high enough fluctuations (ε 15% of ligand field strength) are destructive and move the system toward
gradual transitions on phase space. It was shown the special role of fluctuations
at the border between gradual and first-order phase transition which corresponds
to the critical point of the system. In this regime, the presence of fluctuations of
small strength (ε ≈ 1.5 − 5% of ligand field strength) favors the manifestation of
hysteresis, which therefore means the shifting of the system from the region of gradual transition to the one with first-order phase transition. The reduction of intersite
interactions by increasing fluctuation strength emphasizes the role of fluctuations in
hysteretic behavior of spin-crossover systems and makes possible the obtaining of
spin-crossover solids with bistable properties with weaker coupling between their
sites.
We have analyzed the properties of spin-crossover 3D nanocrystals in terms of
cooperativity accounting for changing from the surface of nanocrystal to the bulk
of the lattice in the presence of Gaussian random white fluctuations. The implied
change of cooperativity represents better approach for the system with nanoscopic
size that is exposed to the environment. It demonstrates the effect of cooperativity
of surface molecules on the shifting of critical temperatures of spin transition under
fluctuations. We have determined also that the critical temperature of establishing
the targeted phase (whether LS or HS) depends on the effective cooperativity defined
by all system sites.
It was shown that the nature of cooperativity for sites on the surface has the drastic
impact on the completeness of phase transition. For a system with antiferromagnetic
coupling of the sites on the surface, the temperature transition curves demonstrate a
I. Gudyma and A. Maksymov
The transition curves in three-dimensional spin-crossover crystal were computed
by Monte Carlo simulations for various external fields: (i) without fluctuations; (ii)
with white fluctuations; and (iii) with colored time-correlated fluctuations. It was
shown that the strengthening of fluctuation of crystal field in 3D spin-crossover
acts qualitatively different whether the first- or gradual phase transition occurs. In
the case of first-order phase transition, the white and colored fluctuations tend to
narrow the loop width; however, the rate of narrowing is very dependent on the
statistical characteristics of fluctuations that we have probed in our study (the strength
of fluctuations and the autocorrelation time). The presence of time correlations in
fluctuations makes hysteresis to collapse at much higher fluctuation strength. For the
system located on the boundary between non-hysteretic and hysteretic phase regions,
characterized by threshold spin–spin coupling, the presence of fluctuations favors the
appearance of hysteresis and, therefore, reduces the threshold spin–spin interaction.
The impact of the size and surface effects on the hysteresis loops of twodimensional and three-dimensional spin-crossover system with temperature changes
and perturbed by fluctuations has been examined as well. The conditions of monoand bistable behavior of spin-crossover compounds were characterized, and respective regions of first-order and gradual phase transitions were found. Likewise, the
detailed discussion of the relations of hysteresis width on the size effects and the
strength of statistical fluctuations were given.
It has been found out that for spin-crossover system the increase of system
size leads to the increase in hysteresis width, whereas the high enough fluctuations (ε 15% of ligand field strength) are destructive and move the system toward
gradual transitions on phase space. It was shown the special role of fluctuations
at the border between gradual and first-order phase transition which corresponds
to the critical point of the system. In this regime, the presence of fluctuations of
small strength (ε ≈ 1.5 − 5% of ligand field strength) favors the manifestation of
hysteresis, which therefore means the shifting of the system from the region of gradual transition to the one with first-order phase transition. The reduction of intersite
interactions by increasing fluctuation strength emphasizes the role of fluctuations in
hysteretic behavior of spin-crossover systems and makes possible the obtaining of
spin-crossover solids with bistable properties with weaker coupling between their
sites.
We have analyzed the properties of spin-crossover 3D nanocrystals in terms of
cooperativity accounting for changing from the surface of nanocrystal to the bulk
of the lattice in the presence of Gaussian random white fluctuations. The implied
change of cooperativity represents better approach for the system with nanoscopic
size that is exposed to the environment. It demonstrates the effect of cooperativity
of surface molecules on the shifting of critical temperatures of spin transition under
fluctuations. We have determined also that the critical temperature of establishing
the targeted phase (whether LS or HS) depends on the effective cooperativity defined
by all system sites.
It was shown that the nature of cooperativity for sites on the surface has the drastic
impact on the completeness of phase transition. For a system with antiferromagnetic
coupling of the sites on the surface, the temperature transition curves demonstrate a