Executive Summary : | In 1973, physicist Philip W. Anderson proposed the existence of a new state of matter, the quantum spin liquid (QSL), which has been a major focus for the condensed matter community. QSL has no long-range magnetic order down to the lowest temperature, but strong correlation among spins exists and no spontaneous symmetry breaking occurs. It also has long-range entanglement between spins and topologically protected fractional spin excitations, such as spinon. This new state of matter has promising applications in high-temperature superconductors and advanced quantum computer technologies. Geometrically frustrated magnets with triangular, Kagomé, and pyrochlore geometry provide a fertile ground to explore novel and unconventional classes of magnetism, such as QSL, spin-ice, and colossal magnetoresistance (CMR). As the dimensionality of spin-lattice decreases, fluctuation effects become more, and systems with a low-spin quantum number show extreme quantum effects. Emergent degrees of freedom, such as lattice geometry, spin degrees of freedom, strength, and nature of exchange interactions, pave the way for some novel magnetic properties. Spin-liquids (SL) remain disordered down to the lowest temperatures and are of prime interest, especially after Anderson's proposal about their connection to high-Tc superconductivity in cuprates. |