Geometrically Frustrated Magnets

In geometrically frustrated systems the energy of all pair – wise interactions can not be minimized simultaneously. The large degeneracy of states resulting from the frustration leads to novel types of ground states, excited states and also qualitatively new phenomena. Frustration seems to play a key role in processes occurring in various physical objects, for example, phase transitions in liquid crystals, stripe-like structures observed in cuprate high-temperature superconductors, magnetic domain structures in selected ferromagnets.  The phenomenon of frustration goes beyond the solid state physics as it significantly influences spreading signal in neural networks or protein folding.
The first identified frustrated system was ordinary water ice. The specific heat measurements performed by Giauque et al. in 1933 [1] revealed missing entropy down to the lowest temperatures.  In other words, water ice seemed not to obey the third law of thermodynamics. This conceptual difficulty was overcome by Pauling [2] who offered an explanation based on the disorder in displacement of hydrogen atoms in the crystal structure consisting of hydrogen bonded water molecules. Specifically, for each oxygen atom, two hydrogen atoms are located near and two far from it, according to so-called ice-rules originally formulated by Bernal and Fowler [3]. The macroscopic degeneracy of the ground state arising from the applicability of the ice-rules to water ice leads to non-zero, residual entropy, which persists in the water ice even at absolute zero.  Pauling’s estimate of the residual entropy S0=R/2ln(3/2) reasonably agrees with the experimental results. Subsequent neutron diffraction experiments confirmed that space arrangement of hydrogen atoms in water ice is governed by ice-rules [4].
The question how to release the residual entropy was addressed by Tajima et al. [5]. Their calorimetric experiment of KOH-doped water ice revealed that the presence of a first-order phase transition which removes most of the residual entropy of the water ice. It was assumed that KOH doping introduces various kinds of lattice defects and accelerates rearrangement of hydrogen atoms to the rate sufficient for the onset of long-range ordering.
Magnetic systems represent a promising class of materials in which collective behavior governed by frustration can be investigated by many experimental techniques. The diversity of magnetic materials offers an opportunity to find an appropriate representative for a theoretical model of a frustrated system. Indeed, up to now several materials have been identified as frustrated magnets and studied experimentally in detail.  However, more detailed and systematic studies ultimately require new types of frustrated magnets, consequently, current efforts are devoted also to synthesis of new materials in which frustration can be foreseen.
The interest of our group is focused on the following classes of frustrated magnetic systems:

Spin ice
Three dimensional frustrated systems

Magnets of lower dimensions containing non-covalent bonds


[1] W. F. Giauque and M. F. Ashley, Phys. Rev. 43, (1933) 81.
[2] L. Pauling, J. American Chem. Soc. 57, (1935) 2680.
[3] D. Bernal and R. H. Fowler, J. Chem. Phys. 1, (1933) 515.
[4] E. O. Wollan et al., Phys. Rev. B 75, (1949) 1348.
[5] Y. Tajima, T Matsuo and H. Suga, Nature 299, (1982) 810.