Anomalous spin excitation spectrum of the Heisenberg model in a magnetic field

Quantum dynamics and entanglement of spins on a square lattice

Bulk magnetism in solids is fundamentally quantum mechanical in nature. Yet in many situations, including our everyday encounters with magnetic materials, quantum effects are masked, and it often suffices to think of magnetism in terms of the interaction between classical dipole moments. Whereas this intuition generally holds for ferromagnets, even as the size of the magnetic moment is reduced to that of a single electron spin (the quantum limit), it breaks down spectacularly for antiferromagnets, particularly in low dimensions. Considerable theoretical and experimental progress has been made in understanding quantum effects in one-dimensional quantum antiferromagnets, but a complete experimental description of even simple two-dimensional antiferromagnets is lacking. Here we describe a comprehensive set of neutron scattering measurements that reveal a non-spin-wave continuum and strong quantum effects, suggesting entanglement of spins at short distances in the simplest of all two-dimensional quantum antiferromagnets, the square lattice Heisenberg system.

Two-Dimensional Heisenberg Antiferromagnets: Syntheses, X-ray Structures, and Magnetic Behavior of [Cu(pz)2](ClO4)2, [Cu(pz)2](BF4)2, and [Cu(pz)2(NO3)](PF6)

We report on the syntheses, crystal structures, and magnetic susceptibilities of a family of copper pyrazine (pz)-based antiferromagnets with moderate in-plane magnetic exchange. These materials fall into two classes: monoclinic complexes [Cu(pz)2]A2 for A = ClO4 (1) or BF4 (2) and the tetragonal complex [Cu(pz)2(NO3)]PF6 (3). Compound 1 and its deuterated version [Cu(pz-d4)2](ClO4)2 (1a) crystallize in the space group C2/m at room temperature with disordered perchlorate anions. For both 1 and 2, the C centering of the Cu(II), S = 1/2, site yields four equivalent nearest neighbors, producing layers of Cu(II) ions bridged by the pz molecules, which map onto a square magnetic lattice. The layers are offset such that Cu(II) ions lie above and below the holes of adjacent layers. Compound 3 crystallizes in the space group I4/mcm with a layer structure similar to those of 1 and 2 but with Cu(II) ions of adjacent layers stacked above each other and bridged by semicoordinate NO3- ions. The variable-temperature susceptibilities in these compounds approximate a two-dimensional Heisenberg antiferromagnet with J values within the layers of 17.5(3) K (1), 15.3(3) K (2), and 10.8(3) K (3). Ordering transitions are observed in the magnetic data at 4.2(3) and 4.3(5) K for 1 and 2, respectively.

Low-energy spectra in t-J-type models at low doping levels

Based on a variational approach, we propose that there are two kinds of low-energy states in the t-J-type models at low doping. In a quasiparticle state an unpaired spin bound to a hole with a well-defined momentum can be excited with spin waves. The resulting state shows a suppression of antiferromagnetic order around the hole with the profile of a spin bag. These spin-bag states with spin and charge or hole separated form a continuum of low-energy excitations. Very different properties predicted by these two kinds of states explain a number of anomalous results observed in the exact diagonalization studies on small clusters up to 32 sites.