256
E.F. Sheka
first-order perturbation theory, it depends on the J value that determines the energy differences in denominators. Consequently, J should be small by the absolute
value to provide noticeable magnetization. Estimated for molecular magnets [24],
the phenomenon can be fixed at |J | of 10 −2 –10 −3 kcal/mole or less.
The joint unit cell of graphene crystal involves two atoms that form one C–C
bond of the benzenoid unit. Estimation of J value for the ethylene and benzene
molecule with stretched C–C bonds up to 1.42 Å in length gives −13 kcal/mole
and −16 kcal/mole, respectively. In spite of the molecules do not reproduce the unit
cell of graphene crystal exactly, a similar J value of the cell constant is undoubted.
Owing to this, the magnetization of the graphene crystal cannot be observed so
that the crystal should demonstrate the diamagnetic behaviour only. The latter is
supported both theoretically [25] and empirically (see [26] and references therein).
To provide a remarkable magnetization means to drastically decrease the magnetic
constant |J |, which, in its turn, determines a severe strengthening of the odd electron
correlation. Since it is impossible to the regular crystal, let us look what can be
expected at the molecular level.
Analyzing data published earlier [27, 28] and addressing the discussion presented
in the previous section, one may suggest the NGr molecule size as a regulating factor
of the electron correlation. As shown in Table 15.2, the magnetic constant |J | decreases when the molecule becomes larger. When speaking about mixing the ground
singlet state with those of high-spin ones, obviously, the singlet-triplet mixing is the
most influent. As follows from Table 15.2, the energy gap to the nearest triplet state,
equal 2|J |, for the studied molecules constitutes 2.8–0.6 kcal/mole. The value is
still large to provide a recordable magnetization of these molecular magnets, but the
trend is quite optimistic.
In view of this idea, let us estimate how large should be the graphene molecule to
provide a noticeable magnetization. As mentioned earlier, the molecular magnetism
can be fixed at |J | ∼ 10 −2 –10 −3 kcal/mole or less. Basing on the data presented in
Table 15.2 and supposing the quantity to be inversely proportional to the number
of odd electrons, we get N ∼ 10 5 . For rectangular NGrs with N odd electrons, the
number of carbon atoms constitutes N = N − 2(n a + n z + 1) that, according to [19],
is determined as
N = 2(n α n z + n α + n z ).
(15.6)
To fit the needed N value, the indices n α and n z should be of hundreds, which leads
to linear sizes of the NGrs from a few units to tens nm. The estimation is rather
approximate, but it, nevertheless, correlates well with the experimental observations
of the magnetization of activated carbon fibers consisting of nanographite domains
of ∼2 nm in size [29, 30]. Recently, has been reported a direct observation of the
size-dependent large-magnitude room-temperature ferromagnetism of graphene interpore regions [31, 32]. The maximum effect was observed at the region width of
20 nm after which the signal gradually decreased when the width increased. The
behaviour is similar to that obtained for fullerene oligomers [33] that led to the suggestion of a scaly mechanism of the nanostructured solid state magnetism of the
polymerized fullerene C 60 that was confirmed experimentally.
E.F. Sheka
first-order perturbation theory, it depends on the J value that determines the energy differences in denominators. Consequently, J should be small by the absolute
value to provide noticeable magnetization. Estimated for molecular magnets [24],
the phenomenon can be fixed at |J | of 10 −2 –10 −3 kcal/mole or less.
The joint unit cell of graphene crystal involves two atoms that form one C–C
bond of the benzenoid unit. Estimation of J value for the ethylene and benzene
molecule with stretched C–C bonds up to 1.42 Å in length gives −13 kcal/mole
and −16 kcal/mole, respectively. In spite of the molecules do not reproduce the unit
cell of graphene crystal exactly, a similar J value of the cell constant is undoubted.
Owing to this, the magnetization of the graphene crystal cannot be observed so
that the crystal should demonstrate the diamagnetic behaviour only. The latter is
supported both theoretically [25] and empirically (see [26] and references therein).
To provide a remarkable magnetization means to drastically decrease the magnetic
constant |J |, which, in its turn, determines a severe strengthening of the odd electron
correlation. Since it is impossible to the regular crystal, let us look what can be
expected at the molecular level.
Analyzing data published earlier [27, 28] and addressing the discussion presented
in the previous section, one may suggest the NGr molecule size as a regulating factor
of the electron correlation. As shown in Table 15.2, the magnetic constant |J | decreases when the molecule becomes larger. When speaking about mixing the ground
singlet state with those of high-spin ones, obviously, the singlet-triplet mixing is the
most influent. As follows from Table 15.2, the energy gap to the nearest triplet state,
equal 2|J |, for the studied molecules constitutes 2.8–0.6 kcal/mole. The value is
still large to provide a recordable magnetization of these molecular magnets, but the
trend is quite optimistic.
In view of this idea, let us estimate how large should be the graphene molecule to
provide a noticeable magnetization. As mentioned earlier, the molecular magnetism
can be fixed at |J | ∼ 10 −2 –10 −3 kcal/mole or less. Basing on the data presented in
Table 15.2 and supposing the quantity to be inversely proportional to the number
of odd electrons, we get N ∼ 10 5 . For rectangular NGrs with N odd electrons, the
number of carbon atoms constitutes N = N − 2(n a + n z + 1) that, according to [19],
is determined as
N = 2(n α n z + n α + n z ).
(15.6)
To fit the needed N value, the indices n α and n z should be of hundreds, which leads
to linear sizes of the NGrs from a few units to tens nm. The estimation is rather
approximate, but it, nevertheless, correlates well with the experimental observations
of the magnetization of activated carbon fibers consisting of nanographite domains
of ∼2 nm in size [29, 30]. Recently, has been reported a direct observation of the
size-dependent large-magnitude room-temperature ferromagnetism of graphene interpore regions [31, 32]. The maximum effect was observed at the region width of
20 nm after which the signal gradually decreased when the width increased. The
behaviour is similar to that obtained for fullerene oligomers [33] that led to the suggestion of a scaly mechanism of the nanostructured solid state magnetism of the
polymerized fullerene C 60 that was confirmed experimentally.