15 Molecular Theory of Graphene
257
The obtained results highlight another noteworthy aspect of the graphene magnetism attributing the phenomenon to size-dependent ones. The latter means that the
graphene magnetization is observed for nanosize samples only, moreover, for the
samples whose linear dimensions fit a definite interval, while the phenomenon does
not take place at either smaller or bigger samples outside the critical region. An individual benzenoid unit (including benzene molecule) is non-magnetic (only slightly
diamagnetic [34]). When the units are joined to form a graphene-like benzenoid
cluster, the effectively unpaired electrons appear due to weakening the interaction
between the odd electrons followed by their correlation. The correlation accelerates
when the cluster size increases, which is followed with the magnetic constant |J |
decreasing until the latter achieves a critical level that provides a noticeable mixing
of the singlet ground state with high-spin states for the cluster magnetization to be
fixed. Until the enlargement of the cluster size does not violate the molecular behavior of the odd electrons, the sample magnetization will grow. However, as soon
as the electron behavior becomes spatially quantized, the molecular character of the
magnetization will be broken and will be substituted by that one determined by the
electron properties of the crystal unit cell [22]. The critical cluster size is determined
by the electron mean free path l el . Evidently, when the cluster size exceeds l el the
spatial quantization quenches the cluster magnetization. The accurate determination
of l el for the odd electrons in graphene is not known, but the analysis of a standard
data base for the electron mean free paths in solids [35] shows the quantity should
be ∼10 nm, which is supported by the experimental data of 3–7 nm electron free
path in thin films of Cu-phthalocyanine [36].
Another scenario of getting magnetic graphene is connected with introducing the
impurity and structural defects in the graphene body. The best illustration of such
scenario reality can be found in a recent publication of the Geim team [26] where
a paramagnetic behaviour of graphene laminates consisting of 10–50 nm sheets has
been recorded after either their fluorination or bombarding by electrons. The treatment provides the ‘spin-half paramagnetism in graphene induced by point defects’.
In both cases, the magnetization is weak and is characterized by one moment per
approximately 1,000 carbon atoms, which is explained by the authors by clustering of adatoms and, for the case of vacancies, by the loss of graphene’s structural
stability. Besides, the unit cell contains one additional spin thus lifting the spin multiplicity to doublet. The latter explains the paramagnetic behaviour of the sample
while the size of the cell provides small value of the magnetic constant |J | due to
large (∼40 nm) cell dimension. Therefore, introduced adatoms and point defects
cause a magnetic nanostructuring of the pristine crystal that favors the realization of
the size-dependent magnetism.
Explaining magnetic behavior of the graphene molecule, we attribute the phenomenon to the correlation of the molecule odd electrons. As was said in Introduction, Criterion 2 highlights the fact that the electron correlation is accompanied with
the appearance of the effectively unpaired electrons that provide the molecule radicalization [12, 13, 15]. A natural question arises which characteristic of graphene
does control its electrons correlation? Looking for answering the question we have
come to Answer 3.
257
The obtained results highlight another noteworthy aspect of the graphene magnetism attributing the phenomenon to size-dependent ones. The latter means that the
graphene magnetization is observed for nanosize samples only, moreover, for the
samples whose linear dimensions fit a definite interval, while the phenomenon does
not take place at either smaller or bigger samples outside the critical region. An individual benzenoid unit (including benzene molecule) is non-magnetic (only slightly
diamagnetic [34]). When the units are joined to form a graphene-like benzenoid
cluster, the effectively unpaired electrons appear due to weakening the interaction
between the odd electrons followed by their correlation. The correlation accelerates
when the cluster size increases, which is followed with the magnetic constant |J |
decreasing until the latter achieves a critical level that provides a noticeable mixing
of the singlet ground state with high-spin states for the cluster magnetization to be
fixed. Until the enlargement of the cluster size does not violate the molecular behavior of the odd electrons, the sample magnetization will grow. However, as soon
as the electron behavior becomes spatially quantized, the molecular character of the
magnetization will be broken and will be substituted by that one determined by the
electron properties of the crystal unit cell [22]. The critical cluster size is determined
by the electron mean free path l el . Evidently, when the cluster size exceeds l el the
spatial quantization quenches the cluster magnetization. The accurate determination
of l el for the odd electrons in graphene is not known, but the analysis of a standard
data base for the electron mean free paths in solids [35] shows the quantity should
be ∼10 nm, which is supported by the experimental data of 3–7 nm electron free
path in thin films of Cu-phthalocyanine [36].
Another scenario of getting magnetic graphene is connected with introducing the
impurity and structural defects in the graphene body. The best illustration of such
scenario reality can be found in a recent publication of the Geim team [26] where
a paramagnetic behaviour of graphene laminates consisting of 10–50 nm sheets has
been recorded after either their fluorination or bombarding by electrons. The treatment provides the ‘spin-half paramagnetism in graphene induced by point defects’.
In both cases, the magnetization is weak and is characterized by one moment per
approximately 1,000 carbon atoms, which is explained by the authors by clustering of adatoms and, for the case of vacancies, by the loss of graphene’s structural
stability. Besides, the unit cell contains one additional spin thus lifting the spin multiplicity to doublet. The latter explains the paramagnetic behaviour of the sample
while the size of the cell provides small value of the magnetic constant |J | due to
large (∼40 nm) cell dimension. Therefore, introduced adatoms and point defects
cause a magnetic nanostructuring of the pristine crystal that favors the realization of
the size-dependent magnetism.
Explaining magnetic behavior of the graphene molecule, we attribute the phenomenon to the correlation of the molecule odd electrons. As was said in Introduction, Criterion 2 highlights the fact that the electron correlation is accompanied with
the appearance of the effectively unpaired electrons that provide the molecule radicalization [12, 13, 15]. A natural question arises which characteristic of graphene
does control its electrons correlation? Looking for answering the question we have
come to Answer 3.