Next: 1.1.1 An overview of
Up: 1 General introduction
Previous: 1 General introduction
It has been believed that a macroscopic spin system with an
antiferromagnetic interaction would freeze at a Néel temperature,
which is comparable to the magnitude of the interaction (J). But
recently, several theoretical situations have been proposed, in which
an antiferromagnetic spin system prefers a manybody singlet
ground state, rather than the Néel state. These situations include
low dimensionality and/or geometrical frustration of the spins, so
that the conventional Néel order is suppressed. Amazingly, several
materials have been discovered which may realize the theoretical
situations. In this thesis, I will report experimental results of
three such spin systems, namely, (1) the spinladder system Sr_{n1}Cu_{n+1}O_{2n},
(2) Haldane compound Y_{2}BaNiO_{5} and (3) the spinPeierls system CuGeO_{3}.
Although the detailed structures of the ground states differ
among these spin systems, they share one important concept for a
general understanding of the manybody singlet ground states; it is
the singlet pair formation of two spins.
Figure 1:
(a, b) The Néel state and (c) the singlet pair state for a two
S=1/2 spin system.

Suppose two S=1/2 spins interact with an antiferromagnetic coupling (J):
In classical mechanics, the ground state of this twospin system
is the Néel state, in which the two spins point in opposite
directions (Fig.1a, b). In quantum mechanics,
spinflips caused by the xy terms of the Hamiltonian (eq.1)
prevent the Néel state from serving as an eigenstate of the Hamiltonian.
After a simple calculation, one finds that the spin singlet pair
is the
quantum mechanical ground state of this system (Fig.1c).
The singlet pair state is a mixed state of the two Néel states and
does not have a classical counterpart. Still, this state is often
realized in localized two electron systems, such as valence bonds in
molecules. One characteristic feature of the singlet pair is that the
magnetic dipolar field from each spin is exactly canceled; in other
words, there is no magnetic field induced around a singlet pair. This
is the main reason why most molecules do not show magnetism. In
macroscopic localized spin systems, singlet pair formation becomes
difficult, because a spin on a lattice has at least two nearest
neighbors. Since the singlet pair is a state for just two S=1/2
spins, one spin on the lattice must select one specific partner from
the equivalent neighboring spins, which is difficult in
translationally symmetric systems. Consequently, most macroscopic
spin systems with an antiferromagnetic interaction exhibit Néel order.
Figure 2:
(a) An example of a trivial spingap system: local singlet pairs without
any correlations.
(b) The first excited state.

As shown in the next section, some macroscopic spin systems still
prefer a ground state based on the singlet pair formations of the
spins. Some of these unconventional spin systems are characterized by
an energy gap between the ground state and the magnetic excited
states. Since this energy gap originates from the spin degrees of
freedom, it is often called a `spin gap'. The existence/absence of the
spin gap is probably related to how well the singlet pairs are localized.
For example, a crystal made up of many uncorrelated singlet
pairs (Fig.2a) is a trivial example of a spingap
system; the energy excitation spectrum of this system will have a gap,
which corresponds to the singlettriplet excitation of a singlet pair
(Fig.2b).
Another example, the S=1/2 spinchain with an antiferromagnetic
Heisenberg interaction is a nontrivial gapless system. The ground
state of this system is a manybody singlet [11], which
is approximately expressed as the superposition of every
possible singlet pairing on the chain [12]. This ground
state, which is known as the Resonating Valence Bond (RVB) state, has
completely delocalized singlet pairs, and the excitation to the
triplet state becomes gapless [13].
In this thesis, materials with a spin gap, namely, the
spin systems with relatively well localized singlet pairs, are investigated.
Next: 1.1.1 An overview of
Up: 1 General introduction
Previous: 1 General introduction