Full text of DOI:10.1007/s100510050028

Eur. Phys. J. B 13, 235–243 (2000)
THE EUROPEAN
PHYSICAL JOURNAL B
EDP Sciences
Societa` Italiana di Fisica
Springer-Verlag 2000
c
ꢀ
Magnetic properties of mixed graphite containing both hexagonal
and rhombohedral forms
S. Chehab, K. Gu´erin, J. Amiell, and S. Flandroisa
Centre de Recherche Paul Pascal, CNRS, avenue A. Schweitzer, 33600 Pessac, France
Received 4 February 1999 and Received in final form 28 April 1999
Abstract. Magnetic properties of graphite materials containing variable fractional amounts (up to 40%) of
the Rhombohedral graphite form have been investigated by means of electron spin resonance. The variations
with temperature and rhombohedral content of the Land´e g-factor, ESR linewidth and paramagnetic spin-
susceptibility have been analyzed. A narrow parallelism in the behaviours of the g-factor, linewidth and
diamagnetic susceptibility (as the latter is known from an earlier work by Gasparoux) has been perceived,
conforming to a similar parallelism between these three physical quantities present in earlier works on
graphitic-type systems, but there, as a function of high-temperature-treatment and dopant concentration.
From the g-value results, the g-anisotropy of the rhombohedral structure is inferred. The paramagnetic
spin-susceptibility shows an increased tendency toward 2D character with increased rhombohedral content,
in agreement with the theoretical predictions of McClure concerning (hypothetical) rhombohedral graphite.
PACS. 81.05.Tp Fullerenes and related materials; diamond, graphite – 76.30.-v Electron paramagnetic
resonance and relaxation – 75.30.Gw Magnetic anisotropy
1 Introduction
synthetically, but never in isolation, is known as rhom-
bohedral graphite (Rh-Gr); the latter is characterized by
a stacking sequence of the type ABCABCABC..., and is
always obtained in association, mixed with the Bernal
type [19,21,26,27]. As a matter of fact, it has been theo-
retically found, from an ab initio study, that the total en-
ergy of Rh-Gr is slightly larger, by 0.11 meV/atom, than
that of B-H-Gr [21]; this can explain the reason why the
rhombohedral phase is only observed to exist in combi-
nation with the hexagonal phase and in relatively smaller
percentages. As a result, the physical properties and be-
haviour of rhombohedral graphite could not easily be ex-
plored and hence, at least experimentally, are still not well
known.
In this work, B-H-Gr samples containing increasing
volume-fractions, up to ∼ 40%, of the rhombohedral phase
are investigated. The magnetic behavior of these graphitic
mosaic combinations, and the effects brought about by
the presence of the rhombohedral modification are probed
with the aid of the electron spin resonance (ESR) tech-
nique. The results are analysed and correlated with past
experimental and theoretical works.
The physical properties of graphite as well as graphitic-
type systems have been for the last eighty years or so
the subject of a very large number of investigations and
studies [1–4].
The peculiar properties of graphite in general, and
its magnetic behaviour in particular – the topic of this
study –, which is characterized by a very large and
highly anisotropic diamagnetic susceptibility χd, are be-
lieved to ensue from an interplay between an aromatic
(benzene-like) configuration of the carbon atoms at the
molecular level, and a layered structure, with a strong
two-dimensional (2D) character, at the crystallographic
level [4–10]. The inter-graphene-layer interactions (i.e. the
3D character), although they are known to be very weak
relative to the intra-layer interaction, still play an impor-
tant role by perturbing the perfect two-dimensionality of
the system, in turn, creating a non-zero band-overlap and
a finite Fermi surface. It turns out that the shape, volume
and energy of the Fermi surface and, consequently, the
subtilties of the electronic behaviour are very sensitive to
the way the graphene layers are stacked [11–24].
The most common form of graphite, known to ex-
ist naturally and synthetically, is called Bernal hexagonal
graphite (B-H-Gr) and is characterised by a stacking se-
quence of the type ABABAB... [25]. Another less common
form of graphite, that is also found to occur naturally and
2 Experimental procedures
Three powder samples of commercial graphite containing
approximately 5, 15 and 40% of the rhombohedral phase
have been selected. This fractional amount of the rhombo-
hedral content (Rh%) was estimated using X-ray diffrac-
tion by comparing the intensities of the (101) peaks of
a
e-mail: flandrois@crpp.u-bordeaux.fr

236
The European Physical Journal B
g(av)-value
g(av)-value
2.015
Rh % : 40
Rh % : 15
Rh % : 5
2.022
2.020
2.018
2.016
2.014
2.012
2.010
2.008
2.006
2.004
60 K
80 K
130 K
160 K
180 K
2.010
220 K
295 K
2.005
0
100
200
300
T (K)
0
10 20 30 40 50 60 70 80 90 100
Fig. 1. Variation of the g(average)-value with temperature for
the three samples having rhombohedral-phase content Rh% =
5, 15 and 40%.
Rhombohedral content (%)
(a)
g(av)-value
2.022
2.020
2.018
2.016
2.014
2.012
2.010
2.008
2.006
40 K
20 K
10 K
both crystalline forms [18,27,28]. The width of the diffrac-
tion peaks were similar for both phases and close to the in-
strumental broadening, whatever the percentage of rhom-
bohedral phase. The corresponding coherence lengths can
˚
be estimated to be several hundred A.
ESR measurements were performed at the X-band fre-
quency (∼ 9.3 GHz) using a field-modulated spectrom-
eter in the temperature range between 4.2 K and room
temperature (RT). Prior to the ESR measurements, the
samples were treated with concentrated hydrochloric acid
at reflux, in order to remove possibly present ferromag-
netic metallic impurities; the samples were, then, thor-
oughly washed with water until complete elimination of
2.004
0
10 20 30 40 50 60 70 80 90 100
Rhombohedral content (%)
(b)
Fig. 2. Variation of the g(av)-value with rhombohedral content
chloride ions, and finally dried. The as-cleaned powder for constant temperatures.
samples were placed into quartz tubes which were subse-
quently sealed under vacuum. For the ESR measurements,
3 Results and analysis
the sealed tubes (with samples) were held vertically, and
hence they were in a perpendicular position to the static
applied magnetic field (the latter being mainly in the hor-
izontal plane). Consequently, since the platelet-like parti-
cles of graphite tended to stack up in layers, as they would
naturally do following from their layered crystal structure,
the field direction thus tended to be parallel to the crys-
tallites graphene planes. All this led to a configuration in
which the crystallites (of our polycrystalline graphite sam-
ples) retained an average preferential orientation relative
to the magnetic field and for which, given the smallness
of the particle size, the skin effect was negligible [29,30].
3.1 g-factor
It is clear from Figure 1 that the g-factor, as measured
from the ESR spectral line, depends on both temperature
and Rh%. For a given Rh%, and as T is lowered from room
temperature (RT), the g-factor behaviour is characterised
by a continuous increase in its value, reaching a maximum
(at a temperature we call TM(g)) in the lower temperature
region; this is followed by a quick decrease in the g-value
with continuing falling T. Further, at a given constant
temperature (T larger than ∼ 20 K), the g-value rises
monotonically with increasing Rh%; this is well demon-
strated in Figure 2 where a linear relationship can easily
be inferred for the g-value versus Rh% dependence.
To have more of a quantitative insight into the g-value
dependence on temperature, the variation of Ln(g) against
The observed ESR spectra show a slightly asymmetric
single line characteristic of mobile charged-carrier spins in
anisotropic graphite particles [29,30]. From these lines, the
Land´e g-factor, ESR linewidth (∆H) and paramagnetic
spin-susceptibility (χp) were obtained.

S. Chebab et al.: Magnetic properties of hexagonal and rhombohedral mixed graphite
237
g(av)-value
of the g-value vs. Rh% (shown in Fig. 2) to Rh% = 0%,
one can estimate the gav values that the pure Bernal-
hexagonal phase would have for the various measurement
temperatures; and knowing its (B-H-Gr) anisotropy ∆g
2.014
Rh % : 40
Rh % : 15
2.012
2.010
2.008
2.006
2.004
2.002
versus T [31] as well as g = 2.0026, a mean-value for
⊥
Rh % :
5
Cav (considered T-independent [18,30,33–36]) can then
be calculated and is found to be ≈ 1/25. Assuming that
Cav = [cos θ]2 [30,33–36], we can hence estimate the av-
erage angle θ to be roughly around 78◦.
Given the fact that g is always a constant indepen-
dent of physical variable⊥s such as temperature, doping,
HTT and others, and that Cav can be safely considered
to be the same for all our samples independent of T, the
variation of gav is thus due solely to the shifting of g or,
equivalently, of the anisotropy ∆g [18,31,33–36]. Itk fol-
lows that our experimental data for the g-factor are well
described by equations (1), where an increase in temper-
ature leads to a decrease of the anisotropy (∆g ∝ T−0.5),
which eventually goes to zero when T tends to infinity,
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11
1/
T
Fig. 3. Linear dependence of the g(av)-value plotted as a func-
tion of T−0.5 in the higher (than ∼100 K) temperature region.
leaving a g-value equal to g = 2.0026. It is worth noting
⊥
Ln(T) was plotted. This shows a linear dependence for
temperatures above 100 K, with a slope of ≈ −0.5. In-
deed, plotting the g-value as a function of 1/T0.5 exhibits
a linear behaviour as it is evident in Figure 3 for the three
samples with Rh% = 5, 15 and 40%. Furthermore, the
extrapolations of the three fitted straight lines converge
that Singer and Wagoner’s g-value data for polycrystalline
graphite [29] have a similar temperature dependence to
ours: their data replotted as a function of 1/T0.5, also,
exhibit a linear variation.
One can go further and determine g for Rh-graphite:
k
by extrapolating the straight line behaviour in Figure 2
to Rh% = 100%, one can obtain gav for the pure rhom-
bohedral phase; then, assuming the same average orienta-
tion for the rhombohedral crystallites (and hence the same
to the same intercept (at T = ∞) of g ≈ 2.0026. This
∞
is quite significant as it corresponds to the value of g
(obtained when the magnetic field is applied parallel t⊥o
the graphene layers and hence perpendicular to the c-
axis of single crystal graphite) [29–32]. Taking into ac-
count the crystallographic in-plane and axial symmetries
of graphite, the g-value can have the following general ex-
pression [33]:
Cav), and of course the same g value, gk(Rh−Gr) can be
estimated and is found to be ≈⊥2.24 at RT, compared to
2.05 for the hexagonal graphite. Repeating the same pro-
cedure for the different measurement temperatures allows
us to obtain the variation of gk(Rh−Gr) with T; the latter is
g = [g + C(θ)∆g]
(1a)
⊥
presented in Figure 4. This result and the g-value depen-
dence on Rh% will further be discussed later in connection
with the diamagnetic susceptibility.
where ∆g = g − g , known as the g-factor anisotropy,
⊥
k
(and g corresponds to the magnetic field applied parallel
to the kc-axis of single crystal graphite and hence perpen-
dicular to the graphene layers). C(θ) describes the an-
gular variation of the g-factor with θ, the angle between
the applied magnetic field direction and the c-axis of the
graphitic crystallite. For a single crystal C(θ) was found
to behave like a cos2θ function [31]. In the case of a poly-
crystalline graphite with its crystallites having a statis-
tical random-Gaussian orientation, the distribution rela-
tive to the applied magnetic field direction, C(θ), takes
an average value Cav−rand = 1/3, and hence the observed
g-value represents, in this case [29,30,33–36], an average
3.2 Linewidth
With regards to the ESR linewidth (∆H), it is interest-
ing to note that ∆H appears to exhibit an analogous be-
haviour to that of the g-factor in connection to its depen-
dence on T and Rh%. This is seen by comparing Figures 5
(∆H vs. T) and 6 (∆H vs. Rh%) to Figures 1 (g-value vs.
T) and 2 (g-value vs. Rh%). Moreover, a closer compara-
tive look at Figures 1 and 5 reveals that the temperatures,
TM(g) and TM(∆H ), at which the maxima occur are very
close, and both shift to higher values in the same man-
ner when Rh% is increased. Furthermore, the plotting of
∆H versus 1/T0.5, presented in Figure 7, also reveals a
linear behaviour for T >100 K. All this points to a di-
rect correlation between the gav-value and the linewidth.
A similar indication was given before by Pacault et al. and
value gav−rand = [g + ∆g/3]. As for this study, our mea-
⊥
sured g-value also represents an average value (gav) for
polycrystalline graphite, but here, as indicated above, the
crystallites have a preferential orientation distribution rel-
ative to the applied magnetic field, the direction of which
tended to be parallel to the graphene planes. We write:
gav = [g + Cav∆g]
(1b)
⊥
Cav, which is directly related to the collective angular by Delhaes [34,37], but their observations were made in
average (θ) of the crystallite orientations, can be deter- connection to high-treatment-temperature (HTT for pre-
mined as follows: By extrapolating the linear behaviour and graphitic carbons) as the major variable. In fact, ∆H

238
The European Physical Journal B
Linewidth (G)
g// (Rh-Gr)
100
2.5
80 K
130 K
150 K
2.4
2.3
2.2
2.1
80
60
40
20
0
200 K
295 K
2.0
0
100
200
300
T (K)
(a)
0
10
20
30
40
50
g// (Rh-Gr)
Rhombohedral content (%)
Fig. 6. Variation of the ESR linewidth ∆H with rhombohedral
content for constant temperatures.
2.5
2.4
2.3
2.2
2.1
Linewidth (G)
100
Rh % : 40
Rh % : 15
Rh % : 5
80
60
40
20
0
2.0
0.00
0.02
0.04
1/ T
(b)
0.06
0.08
0.10
Fig. 4. Temperature variation of calculated g -value for rhom-
k
bohedral graphite (a); the g -value data plotted as a function
of T−0.5 in the higher (than ∼ 100 K) temperature region (b).
k
Linewidth (G)
0.05
0.06
0.07
0.08
1/ T
0.09
0.10
0.11
120
Rh % : 40
Rh % : 15
Rh % : 5
100
Fig. 7. Linear dependence of the ESR linewidth ∆H plotted as
a function of T−0.5 in the higher (than ∼ 100 K) temperature
region.
80
60
40
20
0
is thought to be determined primarily by the anisotropy
∆g, and hence the observed ESR line represents the col-
lective envelope of the resonance lines resulting from the
individual differently-oriented crystallites [29,30,34].
3.3 Comparison with diamagnetic behaviour
0
100
200
300
It is relevant to compare our study with the ear-
lier and pertinent work of Gasparoux [18], who inves-
tigated the diamagnetic susceptibility (χdia) of poly-
crystalline graphite samples (also) containing variable
fractional amounts (0-22%) of the rhombohedral phase.
T (K)
Fig. 5. Variation of the ESR linewidth ∆H with tempera-
ture for the three samples having rhombohedral-phase content
Rh% = 5, 15 and 40%.

S. Chebab et al.: Magnetic properties of hexagonal and rhombohedral mixed graphite
239
-Xd (10 -6emu cgs/g)
g(av)-value
g(av)-value
2.015
2.010
2.005
2.000
2.015
12
11
10
9
g(av)-value
Xd
2.013
2.011
2.009
2.007
8
7
2.005
0
6
10 20 30 40 50 60 70 80 90 100
Rhombohedral content (%)
0
2
4
6
8
10
12
14
Fig. 8. Average diamagnetic susceptibility χdia (Gasparoux
[18]) and g(av)-value (data at room-temperature) shown to-
gether as a function of Rh%, illustrating a parallel in the be-
haviour of both physical parameters.
- Xd (10 -6emu cgs/g)
Fig. 9. g(av)-value versus χdia; a replot of the data of Figure 8
the linear extrapolation of which heads toward the graphite
constant parameters {g , χ } (represented by the full circle),
⊥
⊥
demonstrating a universality in the direct relationship between
the diamagnetic susceptibility and the g-factor in graphitic sys-
tems.
He perceived the existence of a linear proportionality be-
tween χdia−av(erage) and Rh%, similar to our observation
for gav versus Rh% (as seen in Fig. 2). One thus can in-
fer that there are parallels between the χdia−av and gav
behaviours. This is clearly illustrated in Figure 8, where
both Gasparoux’s data for χdia−av and our data for gav
are together shown as a function of Rh%; both are lin-
early increasing functions of Rh%. Note that, similarly,
Castle et al. [38] and Pacault et al. [33,37], in earlier works
in which they have studied the effects of HTT on vari-
ous properties of pre- and graphitic carbons, noted the
existence of a correlation between χdia and the g-factor;
this was reviewed and reiterated later by Marchand [39].
Additionally, a simultaneous and dramatic reduction, of
approximately the same order of magnitude, in the χdia
and g-factor anisotropy is found to occur upon doping
graphite (even slightly) with an acceptor, such as boron
or bromine, and hence changing (even slightly) its Fermi
level [31,32,36,40,41].
from the free-spin value of ge = 2.0023, (both of which)
observed in semimetallic systems, such as Bi, and in small-
band-gap semiconductors, such as InSb, [47–51], have the
same physical origin. The interplay between (i) the per-
turbing influence of the applied magnetic field (triggering
of interband effects), (ii) the smallness of the band-gap
(or the band-overlap) and (iii) the lightness of the elec-
tronic effective mass (ii and iii are a direct consequence
of the electronic band structure), coupled with the facts
that (iv) the Fermi level lies in or very close to the band-
gap (or the band-overlap) region and that (v) the spin-
orbit interaction is of comparable magnitude to or larger
than the energy gap, (all these combined) give rise to “en-
hanced” Landau orbitals. It is these extended electronic
orbitals which (a) produce a more effective opposition
to the applied magnetic field, leading to a higher than
usual χdia, and (b) admix to the electron-spin intrinsic
moment (via spin-orbit coupling), resulting in a larger ef-
fective magnetic moment and, hence, the g-factor depar-
ture from ge. There is no question that graphite fulfills
those conditions stated above, as it has been shown by
Sharma [40] et al. and later by Maaroufi et al. [41] that the
theoretical formulations of Fukuyama explain extremely
well the behaviour of graphite’s diamagnetic susceptibil-
ity. In addition, it should be noted that Levintovich and
Kotosonov [8] have, based on the above mentioned physi-
cal criteria, derived theoretical expressions for the orbital
susceptibility of a “two-dimensional” graphitic system (in
which the inter-graphene-layer interactions are consid-
In an attempt to give this correlative character (be-
tween χdia and the g-factor) a more quantitative pic-
ture, one can, based on the information gained from Fig-
ure 8, directly plot the variation of χdia−av versus that of
gav. This is done in Figure 9, where the two illustrative
end points corresponding to Rh% = 0 and Rh% = 100
are displayed along with the point of “fixed” coordinates
{g , χ }, which are known to be constant, independent of
⊥
⊥
the variation of various physical quantities [6–8,29–36,40–
43]. Within the experimental errors, a straight-line curve
can be drawn through these points, pointing to a direct
proportionality between the g-factor and the diamagnetic
susceptibility for graphitic systems.
4 Discussion
As a matter of fact, according to Fukuyama [44,45], and as ered to be null), which provided a satisfactory descrip-
reviewed by White [46], both the large diamagnetic sus- tion of experimental data obtained earlier for graphitic
ceptibility and the substantial deviation of the g-factor pyrocarbons.

240
The European Physical Journal B
- Xd (10 -6emu cgs/g)
-Xd (10 emu cgs/g)
12
Gasparoux' data
400
300
200
100
0
Levintovich et al. 's data
10
8
Rh%: 22
Rh%:
0
6
4
2
0.0
0.00
0.10
0.20
0.30
0.40
0.50
0
0.00
0. 0
0.02
0.04
0.06
0.08
1/
T
1/
T
Fig. 11. χdia theoretical data of Levintovich and Kotosonov
[8] for 2D graphite replotted here as a function of T−0.5 for
T = 4.2, 77 and 300 K.
Fig. 10. χdia experimental data of Gasparoux [18] replotted
here as a function of T−0.5 in the higher (than ∼ 150 K) tem-
perature region.
With these conceptions in mind, the following obser-
vations can be readily understood: (a) the fact that 1/T0.5
behaviour is effective in the higher temperature region
above 100 K, and (b) the fact that χdia and the g-factor
(which are shown to be closely linked) increase with higher
Rh%. As it turns out from experimental observations
and theoretical considerations, in graphitic systems, (for
a given temperature) enhancing the 2D character results
in an increase of the conduction-electron orbital diamag-
netism [8,18,20,21,40,43]. This is quite reasonable, since
an enhancement of the two-dimensionality corresponds to
a reduction in the inter-layer interactions (characterized
by the energy band parameters γ1, γ2, . . . γi . . . ); this in
turn leads to a smaller basal effective mass (as the latter
is directly proportional to γ1), hence giving rise to more
energetic Landau orbitals [9,15,33,40,53–56].
The remaining point to discuss on this subject con-
cerns the maximum (at T = TM), and hence the sub-
sequent decrease (for T lower than TM) observed in the
gav versus T (and concomitantly in the ∆H versus T)
variation. Two disparate effects/factors are invoked as
causing, or contributing to, this behaviour: (a) the nar-
row parallelism that exists between the g-factor and χdia
behaviours, and which we have discussed above at some
length; (b) the increasing influence, as T gets lower and
lower, of localized electronic spins, the latter believed to
result from defects/imperfections present in our graphitic
systems.
4.1 Parallelism between diamagnetism and g-factor
We can, based on empirical considerations, elaborate fur-
ther on the question of the analogous behaviour between
χdia−av and gav as a function of temperature. We show
in Figure 10 that Gasparoux’s data [18] of χdia−av ver-
sus T have, for T > 150 K or so, the same tempera-
ture variation as our gav data, i.e. a 1/T0.5 dependence.
As can be seen also, the linear curves in Figure 10, for
the different Rh%, extrapolate toward the constant χ
⊥
value of ≈ −0.5 × 10−6 emu/g, when T goes to infinity.
This is in complete concordance with the behaviour of
gav in Figure 3, which extrapolates to g , as discussed
⊥
earlier. Furthermore, Levintovich and Kotosonov [8], in
the work mentioned above, have theoretically calculated
values for χ , at T = 4.2 K, 77 K and 300 K, for per-
fect/ideal “tkwo-dimensional” graphite. The plot of these
χ
values versus 1/T0.5, presented in Figure 11, shows
akstraight-line behaviour which extrapolates through the
origin; i.e. χ vanishes when T goes to infinity, which is
k
plausible. The outcome of this analysis (Fig. 11) seems
to carry quite an interesting physical significance. It ap-
pears that the 1/T0.5 dependence is a characteristic of
two-dimensional (2D) behaviour in graphite. The 2D char-
acter is enhanced: (i) by raising the temperature, because
then the 3D inter-layer interactions are weakened and
the graphene planes become more and more independent,
and/or (ii) by increasing the degree of stacking disorder
of the graphitic layers, because then the correlation be-
Concerning point (a), McClure et al. [7,40] have pre-
tween the interaction between successive atomic plane- dicted theoretically, for B-H-Gr the existence of a maxi-
layers is diminished. The latter situation is believed to mum in the χdia versus T behaviour at a low temperature
take place when going from the highly ordered and hypo- of ∼ 20-30 K; later, this has been confirmed experimen-
thetical simple-hexagonal graphite with stacking sequence tally by Maaroufi et al. [41]. According to Levintovich
AAAA..., to the B-H-Gr (stacking sequence ABAB...), and Kotosonov [8], from a physical stand-point, the po-
to the Rh-Gr (stacking sequence ABCABC...), and, fi- sition of the diamagnetism maximum in a graphitic sys-
nally, to the most disordered graphite form, known as tur- tem corresponds to the temperature (TM) at which “the
bostratic graphite, having random stacking of its graphene relative fraction of the states with the maximum value
layers [17,19–22,52].
of the susceptibility is maximal”. Furthermore, McClure,

S. Chebab et al.: Magnetic properties of hexagonal and rhombohedral mixed graphite
241
stant conduction charge-carriers susceptibility (χP−cond),
so that the total χP is given by χP = χP−cond + χP−loc
Xp (normalized)
.
Further, a close comparative look at Figure 12 and Fig-
ure(s) 1 (and 5) reveals a close correspondence between
the onset temperature of the observed Curie-like in-
crease and the temperature of the maximum g-value (and
∆H) TM. According to Mrozowski [57], a strong exchange
interaction takes place, in such situations, between the free
and the localized spin centers, leading to a single ESR line
produced with a g-value intermediate between that for the
localized spin centres (gloc ∼ gfree = 2.0023) and for the
conduction charge-carriers (gcond = gdefect−free graphite). In
other words, there will be a simple mixing of the g-values
for the two kinds of spin centers; the observed (resultant-
average) g-value is weighed by the relative strength of
these two types of spins paramagnetic contributions and
hence it can be given by the simple mixture formula:
3
2
1
0
Rh % : 40
Rh % : 15
Rh % : 5
(a)
3
2
1
0
gavχP = gcondχP−cond + gfreeχP−loc
.
Consequently, in the low temperature region, since χP−loc
increases as 1/T, and since χP−cond is relatively T-
independent, gav will be weighed down toward the gfree
value. One should add that relatively poor precision at
low T made it difficult to obtain an accurate quantitative
(b)
4
3
2
1
evaluation of gcond
.
4.2 Pauli paramagnetism
Moving to the details of the paramagnetic spin-
susceptibility (χP) results presented in Figure 12, these
were obtained from the areas circumscribed by the ESR
absorption curves. Due to uncertainty about the mass of
the samples and to the usual error associated with the
spectral-curve integration process, the absolute magnitude
of χP is not very accurate; however in our analysis, we can
safely rely on the relative magnitude of χP and its varia-
tion with T which are certain. The variation of χP with
0
0
100
200
300
T (K)
(c)
Fig. 12. Temperature dependence of the spin susceptibility
(normalized) of the three samples with Rh% = 5, 15 and 40%.
in his theoretical analysis of the electronic properties of temperature appears to depend on the rhombohedral-
Rh-Gr [20], also predicted the existence of a maximum phase content. The sample with highest Rh%, ∼ 40%,
in the diamagnetism of the latter system, at a temper- displays the most variability in its χP vs. T behaviour
ature of ∼ 40-50 K (which is clearly higher than that of features; as T is raised from the lowest measurement tem-
B-H-Gr). However, to the best of our knowledge, no direct perature of 4.2 K, χP decreases rapidly to go through a
experimental confirmation of this is yet available. Never- relatively broad minimum, then slowly increases toward
theless, given the direct relationship that exists between a very broad maximum, which looks like a leveling-off re-
χdia and the g-factor, the maximum observed in each of gion, before showing a tendency to decrease around 250 K.
our gav versus T sets of data, as well as in the deduced The sample with Rh% ≈ 15% shows a similar χP vs. T
g (Rh-Gr) versus T behaviour, and the shift of the po- behaviour, as described before, except that now T around
k
sition (TM) of this maximum toward higher temperatures 250 K concurs with a leveling-off region, and the decreas-
with increasing Rh%, may represent indirect experimental ing tendency of χP is believed to take place somewhere
evidence for McClure’s theoretical predictions concerning above but close to RT, which is beyond the present range
the maximum diamagnetism in Rh-Gr.
of our measurements. As for the sample with the lowest
As for factor (b), the presence and effect of localized Rh% of ∼ 5%, the broad minimum which directly follows
spin centers can be inferred from the low-temperature the steep decrease of χP above 4.2 K appears rather as
Pauli paramagnetic susceptibility (χP) behaviour (see a wide low plateau spanning over ∼ 100 K, in this case,
Fig. 12, the full details of χP variation will be discussed be- beyond which all we can see is the rise in χP up to RT. A
low) which clearly exhibits a 1/T Curie-like dependence. careful examination of Wagoner’s χP data [29] obtained in
This 1/T Curie-like increase (χP−loc) in χP with falling the temperature range between 100 K and 500 K for B-H-
T is additively superimposed above the relatively con- Gr, shows a slow but net increase in χP, as T is raised from

242
The European Physical Journal B
100 K to around 400 K; beyond the latter temperature χP 5 Conclusion
displays a slight but clear decrease, resulting, overall, in a
very wide and low maximum centered around 400 K.
The magnetic behaviour of mixed graphitic systems,
consisting of different combinational proportions of the
Bernal-Hexagonal and Rhombohedral forms of graphite,
has been the focus of this work. Present electron spin
The variety of features observed in the χP vs. T depen- resonance (ESR) measurement results, when considered
dence is believed to result from the competing effects of in conjunction with previously published data, have al-
three disparate factors, each one of which would dominate lowed us to perceive a narrow parallelism in the behaviours
the behaviour of χP within a different range of tempera- of the Land´e g-factor, ESR linewidth (∆H) and dia-
tures. These factors are believed to be: (a) the concen- magnetic susceptibility (χdia) with varying temperature
tration of localized spin-moments resulting from impuri- (T) and rhombohedral content (Rh%). Concerning the T-
ties/defects within the graphite system; (b) the magnitude dependence, all three parameters (g-factor, ∆H and χdia
)
of the degeneracy Fermi temperature, TF; and (c) the rel- dependence in the higher temperature region. It is impor-
ative strength of the two-dimensional character. Starting tant to note that a theoretical basis for this empirically
from the lowest T (4.2 K) and up to a certain temper- observed T-dependence can be found from McClure’s the-
ature, the value of which depends on Rh%, the effect of oretical analysis of the rhombohedral graphite electronic
the localized spin-moments dominates, as is evident from properties [20]; there, the calculated χdia vs. T curve,
the 1/T-Curie-like dependence (the steep decrease) of χP. which shows a reasonable agreement with Gasparoux’s ex-
This Curie paramagnetism is then superseded by Pauli perimental results [18], indeed varies as 1/T0.5. As for the
paramagnetism, with χP exhibiting a levelling-off and/or variation with Rh%, both the g-value and ∆H increase
a relatively slow increase in its magnitude [58]. This be- linearly with increasing Rh%, in analogy to the χdia vs.
haviour is assumed to be directly related to the relative Rh% linear variation observed by Gasparoux. A direct lin-
value of TF, or more specifically to a factor of the general ear relationship between the g-factor and χdia has been
form {1 ꢀ [T/TF]2} [9,59]. As long as T is much smaller deduced and presented, and which seemingly extrapolates
than TF, the squared ratio [T/TF]2 can be ignored (relative toward the point of coordinates {g , χ }, the graphite
⊥
to one) and hence the Pauli susceptibility will exhibit a invariable parameters. The extrapo⊥lation of the [g-value
vs. Rh%]T linear curves allowed us to estimate gk(Rh−Gr)
,
temperature-independent behaviour; however, when T be-
comes of the same order of magnitude as TF, and higher,
χP is expected then to display a T2-like variation with
temperature. According to Kriessman and Callen [60], the
sign of the coefficient of the T2 term will be positive, i.e.
the Pauli susceptibility will increase with increasing tem-
perature, if/when the Fermi energy is in the vicinity of a
density-of-states minimum. This is, indeed, the case for
all allotropic forms of graphite [15,21,52]. Nonetheless,
the TF-value depends on the graphite form considered;
in the B-H-Gr case TF is of the order of 200 K, whereas
in Rh-Gr case TF is lower and of the order of 100 K [18].
Following the reasoning presented above, this difference
in the TF-value may well, therefore, account for the ob-
servation that the temperature at which χP begins its rise
gets smaller with higher Rh%. As the temperature contin-
ues to increase, the 2D character becomes more and more
influential and the conduction electrons are expected to
behave more and more like a two-dimensional Fermi gas,
which can lead to the observed decrease in χP, as gen-
erally expected of the Pauli susceptibility of a 2D Fermi
gas with rising temperature [10,34,58]. In the case of pure
B-H-Gr [29], χP starts its descent above ∼400 K, whereas
χP for the sample with Rh% = 40% starts going down
at ∼250 K. As it appears, increasing the rhombohedral-
phase content results in lowering the temperature at which
χP starts to go down. This is very much in line with our
earlier discussions referring to the enhancement of the
2D character in graphitic systems when going from the
hexagonal to the rhombohedral structure. In this context,
McClure has pointed out that [20], above approximately
150 K, rhombohedral graphite would behave almost like
two-dimensional graphite.
and hence the g-factor anisotropy for the Rh-Gr phase,
and its variation with temperature.
The T- and Rh%-dependence of the paramagnetic sus-
ceptibility (χp) behaviour indicates, aside from the usual
Pauli free-electron spins, also the existence of defect-
originating localized spin centers, characterized by a 1/T
Curie-like behaviour, becoming more and more effective
at lower T and for higher Rh%. χp shows, as well, in the
higher T region, an increased tendency toward 2D char-
acter with increased Rh%, in agreement with the theo-
retical predictions of McClure concerning Rhombohedral
graphite [20].
Finally, in order to have further insight into the mag-
netic properties of these mixed graphitic systems, and by
extrapolating into those of the Rh-Gr structure, magnetic
susceptometry experiments over the whole temperature
range between 4.2 K and RT and for variable magnetic
field strengths are being undertaken; the results of these
measurements will be presented in a forthcoming paper.
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