Frustration is the inabiblity of a system to find a unique ground state because of the geometry of the system. A large degeneracy of the ground state is expected. See for instance S.T. Bramwell and M.J.P. Gingras, Science 294 (2001) 1495 or A.P. Ramirez in Handbook of Magnetic Materials (K.H.J. Buschow ed.) Volume 13, Chapter 4 (2001).

We first present the crystal structure for which measurements have been performed. This is followed by a discussion of one system, Gd₂Ti₂O₇, which is characterized by a weak local anisotropy. Then, we present the theoretical activity of our team. 

Most of the experimental work has been performed with compounds of pyrochlore structure: the magnetic moments are located on a lattice of corner-sharing tetrahedra.

 

The crystal has been characterized by different experimental techniques. The specific heat data confirm the presence of two magnetic transitions near 1 K and 0.75 K.

 

Below ~ 1 K, the muon spin relaxation spectra exhibit a spontaneous muon spin precession pointing out to the existence of a long-range magnetic order. In addition, a persistent spin dynamics for T approaching 0 K is revealed since the spectra display a noticeable relaxation even far below the Néel point.

 

A density of states characterized by an accumulation of states at low energy and a gap proportional to the temperature explains the temperature dependences of the specific heat and the μSR relaxation rate. More details can be found in A. Yaouanc et al, Phys. Rev. Lett. 95, 047203 (2005).

Other examples of persisting spin dynamics in geometrically frustrated systems can be found in
P. Dalmas de Réotier et al.,
Phys. Rev. Lett. 91, 167201 (2003) and in J.A. Hodges et al.,
Phys. Rev. Lett. 88, 077204 (2002).

 

Theoretical research on frustrated spin models is focused on
two main directions: analytic theories of quantum
antiferromagnets and numerical Monte Carlo investigations
of classical models. An example of the first type of studies
is given by an investigation of a spin-1/2 kagome
antiferromagnet in the vicinity of the saturation field:

M. E. Zhitomirsky and H. Tsunetsugu, Phys. Rev. B 70 (2004) 100403.
In the saturated phase at high magnetc fields, kagome
antiferromagnet has localized magnon excitations. Once
localized magnons occupy isolated clusters they do not
interact with each, while putting them on adjacent
hexagons costs a finite energy. At low temperatures one
needs to consider only the lowest energy configurations of
noninteracting localized magnons. This maps a quantum spin
system onto exactly solvable model of hard-core particles on
a triangular lattice with nearest-neighbor exclusion. This is
the famous exactly solvable model in Statistical Physics.
Thus a great deal of exact information is also
available for a kagome antiferromagnet at high magnetic field. 

In Monte Carlo simulations every spin is represented
as a classical vector, which interact with other
spins via a suitably selected spin Hamiltonian. Using
the Metropolis algorithm one can model an approach to
thermodynamic equilibrium on a computer and `measure'
various equlibrium properties of a spin model.
In particular one can simulate the whole magnetization
process. A complicated phase diagram of a kagome
antiferomagnet has been found in
M. E. Zhitomirsky, Phys. Rev. Lett 88 (2002) 057204.
Relevance to real magnetic
materials depends on a complexity of magnetic
Hamiltonian utilized in Monte Carlo studies. Such
theoretical investigation have led to a prediction
of a very strong magnetocaloric effect
in frustrated magnetic materials

M. E. Zhitomirsky, Phys. Rev. B 67 (2003) 104421.
This prediction has been later confirmed by experiment

S. S. Sosin et al, Phys. Rev. B 71 (2005) 094413.