## Geometrical Frustration in Magnetic B-Site Spinels

Using inelastic neutron scattering,
we have studied the effects of geometrical frustration in insulating and metallic spinels,
AB_{2}O_{4}, where the B sites form a lattice of corner-sharing tetrahedra.
Geometrical frustration leads to macroscopic degeneracies and qualitatively new states of matter.
In the insulating spinels,
such as ZnCr_{2}O_{4},
CdFe_{2}O_{4} and ZnFe_{2}O_{4},
we have found that fluctuating spins self-organize
into weakly interacting nano-scale spin clusters rather
than fluctuating individually.
The emergence of composite local spin entities suggests
an organizing principle for frustrated systems such that
interacting degrees of freedom combine to form rigid clusters
if macroscopic condensation is not possible.
The metallic spinel,
LiV_{2}O_{4}, shows heavy fermion (HF) behavior at low temperatures.
This is surprising because LiV_{2}O_{4}
has only one kind of electron around the Fermi level
and therefore the ordinary Kondo screening involving two types of electrons,
localized and itinerant,
is not likely.
In order to understand the origin of the HF behavior in LiV_{2}O_{4},
we have investigated how the spin dynamics evolve as a function of Li doping
in Zn_{1-x}Li_{x}V_{2}O_{4}.
We have found that the characteristic wave vector associated
with dynamic spin correlations decreases gradually as x increases up to 1,
which indicates the important role of frustration.
However, the relaxation rate changes dramatically at around x = 1,
suggesting the possible existence of a quantum critical point near x = 1.