Chemistry Reference
In-Depth Information
A small interlayer hopping between neighboring layers
t
⊥
∼
0
.
2
eV
(
, the in plane hopping matrix element), has been always in-
voked in the band theory approaches to understand various magneto os-
cillation experiments and also c-axis transport in graphite.
<<
2
.
5
eV
However, a
strong renormalization of
t
⊥
is possible, as anomalously large anisotropic
resistivity ratio
ρ
c
10
4
have been reported in some early experiments
on graphite single crystals; a many body renormalization is also partly im-
plied by the existence of our spin-1 collective mode at low energies. As
the emergence of the small electron and hole pockets (cylinders) are due
to interlayer hopping, interlayer hopping affect the spin-1 collective modes
only in a small window of energy 0 and
ρ
ab
∼
∼
.
eV
. For the same reason the
collective modes do not have much dispersion along the c-axis.
Within our RPA analysis the collective mode frequency becomes nega-
tive at the Γ point for
U>U
c
∼
0
1
. Because there are two atoms per unit
cell, this could be either an antiferromagnetic or ferromagnetic instability.
Other studies [22; 25] have indicated an AFM instability for
2
t
.
Now we discuss the experimental observability of spin-1 collective mode
branch. The collective mode has a wide energy dispersion from 0 to
U>U
c
∼
2
t
∼
2
eV
.
The low energy 0 to 0
part of the collective modes determines the
nature of the spin susceptibility (Eq. (3)) of graphite and leaves its signa-
tures in NMR and ESR results. For higher energies we have to use other
probes.
Inelastic neutron scattering can be used to study the line shapes and
dispersion of our spin-1 collective modes. However, epithermal neutrons
in the energy range 0
.
05
eV
.
1
eV
to
∼
1
eV
, rather than the cold and thermal,
0
, neutrons is needed in our case, due to the large energy
dispersion. The dynamic structure factor
.
2to50
meV
) as measured by inelastic
neutron scattering is obtained by using our calculated RPA expression for
our magnetic response function using the relation:
S
(
q
,ω
1
π
− e
−βω
)
(1
S
(
q
,ω
)=
−
Im χ
(
q
,ω
)
(6)
Another probe for studying the spin-1 collective mode is the spin polar-
ized electron energy loss spectroscopy (SPEELS); exchange interaction of
the probing electron with the
-electrons of graphite can excite the spin-1
collective mode. As the electron current and spin depolarization essen-
tially measures the magnetic response function, our calculation of
π
χ
,ω
(
q
)
(Eq. (2)) can be profitably used to interpret the experimental results.
The square root divergence of density of states at the bottom edge
of the particle-hole continuum tells us that
the low energy spin physics is
