Frustration and Exotic Magnetism
Spin Protectorates in Frustrated Magnets
Geometric frustration. Ten-membered spin “protectorate” in geometrically frustrated garnet GGG (blue and red spins) protected by the local field anisotropy created by the backbone of black spins. This perfect picture is strongly affected by the presence of imperfections in the form of off-stoichiometric concentration or intentional doping.
A major focus of condensed matter physics is the study of collective, many-body behavior in strongly-correlated systems of fermions, bosons or magnetic moments. In these systems, the interplay of thermal and quantum fluctuations in both charge and spin degrees of freedom give rise to many competing and co-existing novel phases. We aim to study a variety of compounds belonging to a class of correlated magnetic systems, called frustrated magnets, using ultra-fast optical techniques to access high-resolution spatial and temporal regimes inaccessible by any existing methods.
What is frustration? Magnetic moments are expected to order when cooled below a certain temperature. The value of this temperature is set by the strength of coupling between the individual moments (spins). In most magnetic solids these magnetic moments form a long-range ordered ferromagnetic (parallel moments) or antiferromagnetic (alternating moments) structure, depending on the nature and strength of the interactions of the spins. However, in some “frustrated” magnetic solids, the low temperature phase has no long-range order. Instead, they develop some exotic states with short-range spin correlations.
One of the causes for frustration in magnetic materials is geometric, arising purely from crystal symmetries which result in triangular or tetrahedral arrangements of anti-ferromagnetically (AFM) coupled spins. Typical examples of geometrically frustrated structures are pyrochlore or kagome lattices, where the lattice consists of linked corner-sharing triangles or tetrahedra. This kind of lattice geometry creates a high degeneracy of ground states between which the system can fluctuate with almost no energy expenditure, even down to a few milliKelvin temperatures. Geometric frustration in magnetic solids leads to a variety of cooperative spin states, some of which are spin liquids, some spin glasses, and spin ice systems.
Why study these systems? There has been considerable interest in the study of geometrically frustrated systems for over a decade in the scientific community as they exhibit many interesting properties. These consist of pressure magnetic field-induced anti-ferromagnetic phase transitions, Bose-Einstein condensation and possible applications in topological quantum computation, to name a few. From the perspective of condensed matter physicists frustrated magnets provide a perfect platform for studying strongly correlated systems. They are “simple” systems where the spin and charge degrees of freedom are separated, making it possible to focus on spin correlations without too many complications. They exhibit many distinct magnetic phases, often in the same material, with phase transitions being simply controllable by varying temperature or applied magnetic field. They show both classical phases as well as quantum phases with interesting cross-over regimes. The unique properties of these systems also make them a natural candidate for quantum information processing applications.
Interestingly, frustration also plays a role in diverse non-magnetic phenomena such as high temperature superconductors, protein folding and shape formation of nanoclusters.
Frustrated magnetic systems often lead to the realization of clusters of spins which are protected from the rest of the lattice. Our measurements of bulk ac susceptibility in the geometrically frustrated magnetic Gadolinium Gallium garnet (popularly known as GGG) reveal the presence of such spin clusters at temperatures below 200 milliKelvin. We have demonstrated that these clusters can be accessed by the process of magnetic analogue of optical “hole-burning”. The total number of spins responding in such non-linear effects is a macroscopic quantity (~ 1015 cm-3).
Visualizing frustration – ultra-fast optics and magnetism
The most common techniques of experimentally probing these low temperature phases of frustrated spin systems have been restricted to bulk measurements, such as elastic and inelastic neutron scattering, muon spin relaxation and magnetic susceptibility measurements (ac susceptibility, linear and non-linear magnetization). These measurements have provided a lot of information, including the effective transition temperatures and interaction strength of the spin correlations. However, all these investigations have two disadvantages (a) they are bulk techniques with no capabilities of looking at the microscopic details of the materials, and (b) they capture the slower dynamics of the spins, ranging from milliseconds down to hundreds of nanoseconds.