Theory of MX Chain Compounds - Material Designs and New Physical Properties in MX-and MMX-Chain Compounds - page 127

Table 8.1 Charge and spin of
the three types of solitons

Type Charge Spin

S

∓ e

0

S 0 0 1/2

e is the charge of the electron

equal to the same value counted by the electrons, that is, 2 ae , where e is the charge
of the electron. Just equating these two values, we evaluate Q S ¼ e . Repeating the
same procedure for the other solitons, we also find Q S þ ¼e and Q S 0 ¼ 0

(Fig. 8.16b ). Although the above counting is done in the localized limit, we can
perform the same type of counting in the itinerant case using real densities, and
confirm the same conclusion (see the summary in Table 8.1 ).

8.3 Mott-Insulator (M ¼ Ni) Systems

8.3.1 Ground State

The theory of the Ni system has a large overlap with that of the one-dimensional
Hubbard or extended-Hubbard model. This means that we can borrow so much
knowledge that was stored so far. The most important factor governing the ground
state is the existence of large U . This excludes most of double or empty occupancy,
leading to a single occupancy state like that in Fig. 8.1 (the Mott-insulator state).
This state is really an insulator, which is confirmed by the existence of an optical
gap, the absence of Drude weight in other words, which will be mentioned in the
next subsection. Regarding the charge gap, it is also opened. This corresponds to the
gap observed by photoemission, although we do not discuss it in this article.
Magnetic properties are more important in their ground state. As is well known,
the antiferromagnetic correlation as shown in Fig. 8.1 is not of a long-range order
but with a power decay, and there is no spin gap in this type of systems. Moreover,
since they are one-dimensional, the magnetic excitations are described as a pair
creation of spinons, instead of one magnon [ 26 ]. As a spin system, this can be
described by a Heisenberg model with an appropriate value of the exchange
coupling, J . We point out that we need no other term that destroys the isotropy of
spin directions. The coupling J is approximated by the relationship with
the parameters of the Hubbard or the extended Hubbard model, as J ¼ 4 t 0 =U and

4 t 0 =ðU VÞ J ¼ , respectively, using the second-order perturbational theory, while

it is much more complicated in the case of the dp model. The evaluation of the J
value is most easily done by the comparison of the temperature dependence of
susceptibility. In the theory, the same quantity is known to obey a Bonner-Fischer
curve that has a broad maximum around a temperature corresponding to the J value
[ 27 ]. However, it will be more accurate to estimate it from the dispersions of
magnetic excitations based on a neutron scattering experiment. Such an experiment