Filed in: Site.FrustratedMagnets · Modified on : Wed, 03 Apr 19

It all got started with the discovery of the quantum Hall effect (QHE) in 1980, which led to a new way of classifying matter by topology -- a transition to a different state does not have to be accompanied by a spontaneous symmetry breaking, and the appearance of an order parameter. This broke the paradigm of the Ginzburg-Landau classification of matter by phase transitions which stood for 50 years. This shift in classifying matter by topology has fuelled a large number of discoveries ranging from topological insulators to quantum spin liquids (QSL) in frustrated magnets. Apart from having strong magnetic interactions without magnetic order, each new kind of QSL is a unique and fascinating state of matter, a universe unto itself with its own set of novel, emergent quasi-particles. The defining characteristic of a QSL is a long-range entangled ground-state wave function that can be classified by its topology. Magnetic frustration is used to prevent classical magnetic order from establishing itself in the hope that at low temperature strong quantum fluctuations establish a QSL instead.

The study of frustration in magnetic systems goes back to the geometric problem of placing three spins with antiferromagnetic interactions on a triangle. The interaction between nearest neighbours favours an anti-parallel alignment between any of two neighbouring spins, which is a condition that is impossible to fulfill simultaneously for all three spins. As a result, the spins remain in a fluctuating state down to the lowest temperatures. The best known example is the so-called spin-ice state for magnetic ions located on sharing tetrahedrons in pyrochlores.

In a model between 1 and 2 dimensions, one can use AFM interactions on a zig-zag chain to create frustration. When the interaction J1 between nearest and next nearest neighbours J2 are of the same size, the system becomes frustrated. In SrRE2O4 the crystalline electric field changes the effective dimensionality of the magnetic interactions. As a result, the rare earth atoms shown in blue end up interacting on model that is effectively a 1D zig-zag chain known as ANNNI.

The frustration in a 1D zig-zag chain leads to diffusive scattering. So instead of seeing sharp Bragg peaks as for a long-range ordered classical antiferromagnet, ones sees rather broad features. This plot is from a neutron scattering experiment by Nicolas Gauthier in collaboration with the group Prof. Kenzelmann at the PSI in Switzerland.

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