27 Cooperative Phenomena in Spin-Crossover Molecular Crystals
435
whereas the LS configuration is not magnetic (S = 0). Therefore, such analysis
also sheds light on the system’s magnetization and its variation during transition.
For the temperature at which the molecules inside the lattice are almost completely
switched, the switching of molecules on the surface is incomplete which is related
to smaller surface coupling and is the main reason of residual magnetization. The
spin configurations for n H S = 0.99 and n H S = 0.98 in Fig. 27.4a, b, respectively,
are obtained at relatively high temperature T = 240 which ideally should provide
the ordered HS configuration over entire lattice. However, only 1713 molecules for
J s = J b and 1697 molecules for J s = 0.5J b from total number of 1728 sites are
in HS state. Since the HS molecules are characterized by a magnetic moment, these
numbers of HS sites contribute to the total fictitious magnetization of studied Isinglike model m, and therefore the mentioned values of HS fraction (n H S ≈ 0.99 and
n H S ≈ 0.98) are obtained according to the relations m = 2n H S − 1. For this certain
case, the number of HS molecules inside the lattice is 993 for J s = J b and 998
for J s = 0.5J b ; therefore one can conclude that the main difference between the
magnetization of analyzed configurations is provided by molecules from the surface.
The smaller surface coupling also provides different starting points for the
switching (here from HS to LS state). From displayed spin configurations, one
can see that for n H S ≈ 0.95 at which the switching for the spin-crossover lattice
with J s = 0.5J b is just starting (see Fig. 27.4b at n H S ≈ 0.95), the switching
for the lattice with J s = J b has already begun and is propagating inside (see
Fig. 27.4a at the same value of n H S ). The corresponding numbers of HS molecules
from the surface and inside the lattice which provide the value of HS fraction
n H S = 0.95 in Fig. 27.4 are 670 and 985 for Fig. 27.4a vs 650 and 997, respectively,
for Fig. 27.4b. For J s = 0.5J b the number of HS molecules inside the lattice for
two consequent spin configuration (at n H S ≈ 0.99 and n H S ≈ 0.95 in Fig. 27.4a)
is almost unchanged, whereas the bulk HS sites for J s = 0.5J b and the same
spin configuration (at n H S ≈ 0.98 and n H S ≈ 0.95 in Fig. 27.4b) are changed
more pronounced. The next spin configurations in Fig. 27.4a, b are obtained for
the same values of HS fractions; therefore in order to understand what molecules
contribute to the HS states, we just enumerate the pair of molecules on the surface
and inside the lattice in the form (number of surface sites; number of bulk sites)
for both surface coupling indicated in the caption of Fig. 27.4. For J s = J b the
numbers of HS molecules on the surface and inside the lattice are (615; 905),
(530; 762), (463; 613), and (365; 497) for spin configurations at n H S ≈ 0.875,
n H S ≈ 0.75, n H S ≈ 0.62, and n H S ≈ 0.5 in Fig. 27.4a, respectively. For
J s = 0.5J b the numbers of HS molecules on the surface and inside the lattice
are (532; 979), (464; 837), (404; 679), and (342; 523) for spin configurations at the
same values of HS fraction in Fig. 27.4b. For smaller intermolecular interaction, the
magnetization which corresponds to HS fractions n H S is determined mostly by the
molecules inside the lattice (the number of HS molecules in this case is greater for
all-spin configurations), whereas for the homogeneous intermolecular interaction
over entire lattice (like in Fig. 27.4a), there are no prevailed contributions into total
magnetization from molecules on the surface and inside the lattice.
435
whereas the LS configuration is not magnetic (S = 0). Therefore, such analysis
also sheds light on the system’s magnetization and its variation during transition.
For the temperature at which the molecules inside the lattice are almost completely
switched, the switching of molecules on the surface is incomplete which is related
to smaller surface coupling and is the main reason of residual magnetization. The
spin configurations for n H S = 0.99 and n H S = 0.98 in Fig. 27.4a, b, respectively,
are obtained at relatively high temperature T = 240 which ideally should provide
the ordered HS configuration over entire lattice. However, only 1713 molecules for
J s = J b and 1697 molecules for J s = 0.5J b from total number of 1728 sites are
in HS state. Since the HS molecules are characterized by a magnetic moment, these
numbers of HS sites contribute to the total fictitious magnetization of studied Isinglike model m, and therefore the mentioned values of HS fraction (n H S ≈ 0.99 and
n H S ≈ 0.98) are obtained according to the relations m = 2n H S − 1. For this certain
case, the number of HS molecules inside the lattice is 993 for J s = J b and 998
for J s = 0.5J b ; therefore one can conclude that the main difference between the
magnetization of analyzed configurations is provided by molecules from the surface.
The smaller surface coupling also provides different starting points for the
switching (here from HS to LS state). From displayed spin configurations, one
can see that for n H S ≈ 0.95 at which the switching for the spin-crossover lattice
with J s = 0.5J b is just starting (see Fig. 27.4b at n H S ≈ 0.95), the switching
for the lattice with J s = J b has already begun and is propagating inside (see
Fig. 27.4a at the same value of n H S ). The corresponding numbers of HS molecules
from the surface and inside the lattice which provide the value of HS fraction
n H S = 0.95 in Fig. 27.4 are 670 and 985 for Fig. 27.4a vs 650 and 997, respectively,
for Fig. 27.4b. For J s = 0.5J b the number of HS molecules inside the lattice for
two consequent spin configuration (at n H S ≈ 0.99 and n H S ≈ 0.95 in Fig. 27.4a)
is almost unchanged, whereas the bulk HS sites for J s = 0.5J b and the same
spin configuration (at n H S ≈ 0.98 and n H S ≈ 0.95 in Fig. 27.4b) are changed
more pronounced. The next spin configurations in Fig. 27.4a, b are obtained for
the same values of HS fractions; therefore in order to understand what molecules
contribute to the HS states, we just enumerate the pair of molecules on the surface
and inside the lattice in the form (number of surface sites; number of bulk sites)
for both surface coupling indicated in the caption of Fig. 27.4. For J s = J b the
numbers of HS molecules on the surface and inside the lattice are (615; 905),
(530; 762), (463; 613), and (365; 497) for spin configurations at n H S ≈ 0.875,
n H S ≈ 0.75, n H S ≈ 0.62, and n H S ≈ 0.5 in Fig. 27.4a, respectively. For
J s = 0.5J b the numbers of HS molecules on the surface and inside the lattice
are (532; 979), (464; 837), (404; 679), and (342; 523) for spin configurations at the
same values of HS fraction in Fig. 27.4b. For smaller intermolecular interaction, the
magnetization which corresponds to HS fractions n H S is determined mostly by the
molecules inside the lattice (the number of HS molecules in this case is greater for
all-spin configurations), whereas for the homogeneous intermolecular interaction
over entire lattice (like in Fig. 27.4a), there are no prevailed contributions into total
magnetization from molecules on the surface and inside the lattice.