Ising-Like Model of Nanosize Spin-Crossover Molecular Crystals
155
We considered three main types of setups that are shown in Fig. 4a: (i) the coupling
of surface’s molecules is one half from coupling of bulk sites J
s
= 0.5J
b , whereas
the coupling of interface layer is the same as bulk one J
bs
= J
b (squared curve); (ii)
the coupling of surface’s molecules and the coupling of interface layer is one half
from the bulk coupling J
s
= J
bs
= 0.5J
b (red circled curve); (iii) the coupling of
surface molecules is one half from bulk coupling, but is of antiferromagnetic nature,
and the coupling of interface layer J
bs is the same as in (ii) (blue diamonded curve).
As one can observe the role of coupling with interface layer is rather small, it slightly
influences the reaching of saturated HS and LS states. The changing of the nature of
surface coupling from ferromagnetic to antiferromagnetic one changes the nonlinear
slopes of transition curves to linear. In the system with antiferromagnetic surface,
the transition is incomplete in comparison to ferromagnetic coupling of surface’s
molecules; however, the degree of incompleteness for the same parameters of the
system is bigger than in work [23] due to the presence of fluctuations.
The changing of transition temperatures for cooling and heating branches of hysteresis as a function of fluctuation strength is plotted in Fig. 4b for all three configurations of couplings considered in Fig. 4a. Here, the curves with filled markers are for
temperatures of cooling branch, and the ones with empty markers are the transition
temperatures during heating. The general tendency for all three configurations is the
collapsing of hysteresis width with increase in fluctuation strength. However, the
narrowing of hysteresis is non-uniform as a function of fluctuation strength which
is shown by ranges of constant values on temperature curves. The impact of chosen
configuration of couplings on hysteresis width is much more visible for small fluctuations. In this case, the coupling configurations (iii) described above give the larger
hysteresis width, but it is much sensitive to increase of fluctuation strength. The hysteresis width is the smallest one among analyzed cases for coupling configuration
(ii); however, this configuration as well as the configuration (i) shows almost stable
hysteresis width in large interval of fluctuation strength (0 < ε 150).
The presence of fluctuations in the model with ferromagnetic and antiferromagnetic coupling for surface’s molecules emphasizes the role of size effects by shifting
the collapse of hysteresis toward larger values of lattice side and reduce the role of
nature of coupling on the surface in reaching the saturated values of HS fractions
n H S for temperature transition curves.
6 Summary and Conclusion
In the present study, the conception of breathing crystal field was applied to spincrossover materials in the context of Ising-like Hamiltonian. The existence of an
external (relative to magnetic ion) crystal field of random statistical nature is the
crucial feature of the model. We have provided the study of spin-crossover magnetic
nanoparticles that are depicted by Ising-like model with the accounting of correlated
fluctuations.
155
We considered three main types of setups that are shown in Fig. 4a: (i) the coupling
of surface’s molecules is one half from coupling of bulk sites J
s
= 0.5J
b , whereas
the coupling of interface layer is the same as bulk one J
bs
= J
b (squared curve); (ii)
the coupling of surface’s molecules and the coupling of interface layer is one half
from the bulk coupling J
s
= J
bs
= 0.5J
b (red circled curve); (iii) the coupling of
surface molecules is one half from bulk coupling, but is of antiferromagnetic nature,
and the coupling of interface layer J
bs is the same as in (ii) (blue diamonded curve).
As one can observe the role of coupling with interface layer is rather small, it slightly
influences the reaching of saturated HS and LS states. The changing of the nature of
surface coupling from ferromagnetic to antiferromagnetic one changes the nonlinear
slopes of transition curves to linear. In the system with antiferromagnetic surface,
the transition is incomplete in comparison to ferromagnetic coupling of surface’s
molecules; however, the degree of incompleteness for the same parameters of the
system is bigger than in work [23] due to the presence of fluctuations.
The changing of transition temperatures for cooling and heating branches of hysteresis as a function of fluctuation strength is plotted in Fig. 4b for all three configurations of couplings considered in Fig. 4a. Here, the curves with filled markers are for
temperatures of cooling branch, and the ones with empty markers are the transition
temperatures during heating. The general tendency for all three configurations is the
collapsing of hysteresis width with increase in fluctuation strength. However, the
narrowing of hysteresis is non-uniform as a function of fluctuation strength which
is shown by ranges of constant values on temperature curves. The impact of chosen
configuration of couplings on hysteresis width is much more visible for small fluctuations. In this case, the coupling configurations (iii) described above give the larger
hysteresis width, but it is much sensitive to increase of fluctuation strength. The hysteresis width is the smallest one among analyzed cases for coupling configuration
(ii); however, this configuration as well as the configuration (i) shows almost stable
hysteresis width in large interval of fluctuation strength (0 < ε 150).
The presence of fluctuations in the model with ferromagnetic and antiferromagnetic coupling for surface’s molecules emphasizes the role of size effects by shifting
the collapse of hysteresis toward larger values of lattice side and reduce the role of
nature of coupling on the surface in reaching the saturated values of HS fractions
n H S for temperature transition curves.
6 Summary and Conclusion
In the present study, the conception of breathing crystal field was applied to spincrossover materials in the context of Ising-like Hamiltonian. The existence of an
external (relative to magnetic ion) crystal field of random statistical nature is the
crucial feature of the model. We have provided the study of spin-crossover magnetic
nanoparticles that are depicted by Ising-like model with the accounting of correlated
fluctuations.