Frustrated Quantum Magnets

Abstract

A description of different phases of two dimensional magnetic insulators is given.The first chapters are devoted to the understanding of the symmetry breaking mechanism in the semi-classical Néel phases. Order by disorder selection is illustrated. All these phases break SU (2) symmetry and are gapless phases with ∆S z = 1 magnon excitations.Different gapful quantum phases exist in two dimensions: the Valence Bond Crystal phases (VBC) which have long range order in local S=0 objects (either dimers in the usual Valence Bond acception or quadrumers..), but also Resonating Valence Bond Spin Liquids (RVBSL), which have no long range order in any local order parameter and an absence of susceptibility to any local probe. VBC have gapful ∆S = 0, or1 excitations, RVBSL on the contrary have deconfined spin-1/2 excitations. Examples of these two kinds of quantum phases are given in chapters 4 and 5. A special class of magnets (on the kagome or pyrochlore lattices) has an infinite local degeneracy in the classical limit: they give birth in the quantum limit to different behaviors which are illustrated and questionned in the last lecture.

Competing Spin Phases in Geometrically Frustrated Magnetic Molecules

“…The minimum in dM/dB is due to the fact that for low temperatures when B ≈ Bsat/3 there exist two competing families of spin configurations of which one behaves magnetically "stiff" leading to a reduction of the differential susceptibility. The magnetism of frustrated one-, two-, and threedimensional lattice spin systems is a fascinating subject due to the richness of phenomena that are observed [1,2,3]. In this Letter we report that one effect of geometrical frustration, which so far has been reported [4] only for the theoretical model of classical spins on a Kagomé lattice, already appears for a class of zero-dimensional materials, namely certain magnetic molecules hosting highly symmetric arrays of classical or quantum spins.…”

“…In the quantum formula the multiplicity factor corresponds to the classical geometrical function G(S). Each of these quantities has two distinct branches, depending on whether n is in the interval [0, s] or [s + 1, 3s] or whether S is in the interval [0, 1] or [1,3]. In fact, the existence of two distinct branches becomes manifest in various higher derivatives of Z(t, b) at nonzero temperatures for fields in the vicinity of B = B sat /3.…”

“…This is the mathematical orgin of the pronounced minimum in dM/dB at B = B sat /3. Plateau like structures in the magnetization versus B in various two-and three-dimensional lattices built of corner-sharing triangles lattices at one-third of the saturated moment have been under investigation for the past two decades as an expression of geometric frustration [1,2,3,14,15]. Moreover, theoretical studies of the classical Heisenberg antiferromagnet on the Kagomé lattice show that dM/dB has a pronounced minimum at one-third of B sat [4].…”

“…The magnetization was measured at 0.42 K in pulsed magnetic fields up to 23 Tesla (sweep rate 15000 Tesla/s) at the Okayama High Magnetic Field Laboratory by using a standard inductive method. The sample was immersed in liquid 3 He to maintain good contact with the thermal bath. The experimental results for dM/dB (in arbitrary units) are shown in Fig.…”

Magnetic Ground State of an ExperimentalS=1/2Kagome Antiferromagnet

“…The presence of unpaired but nevertheless strongly interacting spins gives rise to a macroscopically degenerate ground state manifold, with increasingly glassy dynamics as x is lowered. Physical realisations of the S = 1/2 kagomé Heisenberg antiferromagnet have been long sought after because it is expected that the ground state of this system can retain the full symmetry of the underlying effective magnetic Hamiltonian [1,2]; the geometry of the kagomé lattice frustrates the classical Néel antiferromagnetic ordering, and no symmetry-breaking transition is expected even at T = 0 [3,4,5,6,7]. It has been suggested that even in the thermodynamic limit the symmetric quantum-mechanical electronic ground state is protected from quantum-mechanical dissipation [8] by a gap between the non-magnetic ground state and the lowest magnetic (triplet) excitations [9,10].…”