Frustrated Magnets

Physics: Geometric frustration: antiferromagnetic bonds on a triangle cannot all be satisfied simultaneously — any configuration leaves at least one bond frustrated. This leads to a macroscopic degeneracy of ground states and residual entropy. Spin ice (Dy₂Ti₂O₇, Ho₂Ti₂O₇): spins on pyrochlore lattice obey "2-in/2-out" ice rule — Pauling residual entropy S ≈ R·ln(3/2)/2 per spin. Magnetic monopole excitations emerge when ice rule is violated (Castelnovo 2008). Kagome lattice: 1/9 of spins remain paramagnetic, extensive ground state degeneracy. Quantum spin liquids have no order down to T=0, with long-range entanglement.