Valence-bond crystal in a pyrochlore antiferromagnet with orbital degeneracy

We discuss the ground state of a pyrochlore lattice of threefold orbitally degenerate S=1/2 magnetic ions. We derive an effective spin-orbital Hamiltonian and show that the orbital degrees of freedom can modulate the spin exchange, removing the infinite spin-degeneracy characteristic of pyrochlore structures. The resulting state is a collection of spin-singlet dimers, with a residual degeneracy due to their relative orientation. This latter is lifted by a magnetoelastic interaction, induced in the spin-singlet phase space, that forces a tetragonal distortion. Such a theory provides an explanation for the helical spin-singlet pattern observed in the B spinel MgTi2O4.     

Semiclassical ordering in the large-N pyrochlore antiferromagnet

We study the semiclassical limit of the Sp(N) generalization of the pyrochlore lattice Heisenberg antiferromagnet by expanding about the N --> infinity saddlepoint in powers of a generalized inverse spin. To leading order, we write down an effective Hamiltonian as a series in loops on the lattice. Using this as a formula for calculating the energy of any classical ground state, we perform Monte Carlo simulations and find a unique collinear ground state. This state is not a ground state of linear spin-wave theory, and can therefore not be a physical (N = 1) semiclassical ground state.     

Order by disorder and gaugelike degeneracy in a quantum pyrochlore antiferromagnet

The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length S is a highly frustrated model with a macroscopic degeneracy of classical ground states. The zero-point energy of (harmonic-order) spin-wave fluctuations distinguishes a subset of these states. I derive an approximate but illuminating effective Hamiltonian, acting within the subspace of Ising spin configurations representing the collinear ground states. It consists of products of Ising spins around loops, i.e., has the form of a Z2 lattice gauge theory. The remaining ground-state entropy is still infinite but not extensive, being O(L) for system size O(L3). All these ground states have unit cells bigger than those considered previously.     

Chiral Kosterlitz-Thouless transition in the frustrated Heisenberg antiferromagnet on a pyrochlore slab

Ordering of the geometrically frustrated two-dimensional Heisenberg antiferromagnet on a pyrochlore slab is studied by Monte Carlo simulations. In contrast to the kagomé Heisenberg antiferromagnet, the model exhibits locally noncoplanar spin structures at low temperatures, bearing nontrivial chiral degrees of freedom. Under certain conditions, the model exhibits a novel Kosterlitz-Thouless-type transition at a finite temperature associated with these chiral degrees of freedom.     

Quantum optomechanics of a Bose-Einstein antiferromagnet

We investigate the cavity optomechanical properties of an antiferromagnetic Bose-Einstein condensate, where the role of the mechanical element is played by spin-wave excitations. We show how this system can be described by a single rotor that can be prepared deep in the quantum regime under realizable experimental conditions. This system provides a bottom-up realization of dispersive rotational optomechanics, and opens the door to the direct observation of quantum spin fluctuations.     

Quantum versus geometric disorder in a two-dimensional Heisenberg antiferromagnet

We present a numerical study of the spin-1/2 bilayer Heisenberg antiferromagnet with random interlayer dimer dilution. From the temperature dependence of the uniform susceptibility and a scaling analysis of the spin correlation length we deduce the ground state phase diagram as a function of nonmagnetic impurity concentration p and bilayer coupling g. At the site percolation threshold, there exists a multicritical point at small but nonzero bilayer coupling g(m)=0.15(3). The magnetic properties of the single-layer material La(2)Cu(1-p)(Zn,Mg)(p)O4 near the percolation threshold appear to be controlled by the proximity to this new quantum critical point.     

Field-induced order and spin waves in the pyrochlore antiferromagnet Tb2Ti207

High resolution time-of-flight neutron scattering measurements on Tb(2)Ti(2)0(7) reveal a rich low temperature phase diagram in the presence of a magnetic field applied along [110]. In zero field at T = 0.4 K, Tb(2)Ti(2)0(7) is a highly correlated cooperative paramagnet with disordered spins residing on a pyrochlore lattice of corner-sharing tetrahedra. Application of a small field condenses much of the magnetic diffuse scattering, characteristic of the disordered spins, into a new Bragg peak characteristic of a polarized paramagnet. At higher fields, a magnetically ordered phase is induced, which supports spin wave excitations indicative of continuous, rather than Ising-like, spin degrees of freedom.     

Quantum critical point of an itinerant antiferromagnet in a heavy fermion

A quantum critical point of the heavy fermion Ce(Ru(1-x)Rh(x))2Si2, (x = 0,0.03) has been studied by single-crystalline neutron scattering. By accurately measuring the dynamical susceptibility at the antiferromagnetic wave vector k3 = 0.35c*, we have shown that the inverse energy width gamma(k3), i.e., the inverse correlation time, depends on temperature as gamma(k3) = c1 + c2T((3/2)+/-0.1), where c1 and c2 are x dependent constants, in a low temperature range. This critical exponent 3/2 +/- 0.1 proves that the quantum critical point is controlled by that of the itinerant antiferromagnet.     

Quantum fluctuations in a two-dimensional antiferromagnet with four-spin interaction of cubic symmetry

The excitation spectrum of a non-Heisenberg 2D antiferromagnet with the four-spin interaction of cubic symmetry has been calculated in the first order of 1/2S. It has been shown that, for weak anisotropy, the Néel state is destroyed by quantum fluctuations. The phase diagrams showing the stability regions of the Néel phase in the space of spin-anisotropy parameters have been plotted.     

Quantum magnetostriction oscillations in a two-dimensional antiferromagnet with spin-phonon interaction in a magnetic field

The ground state of a two-dimensional antiferromagnet with S=1/2 interacting with acoustic phonons in a magnetic field was studied by the quantum Monte Carlo method in the nonadiabatic approximation. Oscillations of the amplitude of the root-mean-square displacement of ions and the average phonon occupation number in a magnetic field were found. Local maxima were revealed in the distribution functions of site magnetic moments and ion displacements. The saturation magnetization was calculated as a function of the spin-phonon coupling constant.     

Quantum spin liquid in an antiferromagnet with four-spin interactions

A quantum Monte Carlo study of the anisotropic antiferromagnet with four-spin interaction (K) and with spin S=1/2 on a square lattice is reported. Temperature dependences of the capacity, susceptibility, spin correlation functions, and correlation length, and field dependences of magnetization are calculated. Phase diagrams of the ground-state antiferromagnet and gap (K>0) and gapless (K<0) quantum spin liquids are determined in the exchange-anisotropy-four-spin-coupling-constant (K), magnetic-field (H)-temperature (T), and temperature-(T)-K planes for an exchange anisotropy of 0.1 J. Fiz. Tverd. Tela (St. Petersburg) 39, 1404–1409 (August 1997)     

Quantum dimer model for trimerized kagomé antiferromagnet

Low-energy singlet states of a spin-1/2 trimerized kagomé antiferromagnet are mapped to an effective quantum dimer model on a triangular lattice. The mapping is done in the first-order of perturbation theory in a weaker coupling constant of the trimerized model. The derived quantum dimer model is dominated by kinetic energy terms (dimer resonances) on a few shortest loops of the triangular lattice.     

Quantum to classical transition in the ground state of a spin-S quantum antiferromagnet

We study a frustrated spin-S staggered-dimer Heisenberg model on square lattice by using the bond-operator representation for quantum spins, and investigate the emergence of classical magnetic order from the quantum mechanical (staggered-dimer singlet) ground state for increasing S. Using triplon analysis, we find the critical couplings for this quantum phase transition to scale as 1 /S(S + 1). We extend the triplon analysis to include the effect of quintet dimer-states, which proves to be essential for establishing the classical order (Néel or collinear in the present study) for large S, both in the purely Heisenberg case and also in the model with single-ion anisotropy.     

Spin waves and quantum criticality in the frustrated XY pyrochlore antiferromagnet Er2Ti2O7

We report detailed measurements of the low temperature magnetic phase diagram of Er2Ti2O7. Heat capacity and time-of-flight neutron scattering studies of single crystals reveal unconventional low-energy states. Er3+ magnetic ions reside on a pyrochlore lattice in Er2Ti2O7, where local XY anisotropy and antiferromagnetic interactions give rise to a unique frustrated system. In zero field, the ground state exhibits coexisting short and long-range order, accompanied by soft collective spin excitations previously believed to be absent. The application of finite magnetic fields tunes the ground state continuously through a landscape of noncollinear phases, divided by a zero temperature phase transition at micro{0}H{c} approximately 1.5 T. The characteristic energy scale for spin fluctuations is seen to vanish at the critical point, as expected for a second order quantum phase transition driven by quantum fluctuations.     

External magnetic field effects on a distorted kagome antiferromagnet

We report bulk magnetization, and elastic and inelastic neutron scattering measurements under an external magnetic field H on the weakly coupled distorted kagome system, Cu2(OD)3Cl. Our results show that the ordered state below 6.7 K is a canted antiferromagnet and consists of large antiferromagnetic ac components and smaller ferromagnetic b components. By first-principles calculations and linear spin wave analysis, we present a simple spin Hamiltonian with nonuniform nearest neighbor exchange interactions resulting in a system of coupled spin trimers with a single-ion anisotropy that can qualitatively reproduce the spin dynamics of Cu2(OD)3Cl.     

Quantum phase transition of the randomly diluted heisenberg antiferromagnet on a square lattice

Ground-state magnetic properties of the diluted Heisenberg antiferromagnet on a square lattice are investigated by means of the quantum Monte Carlo method with the continuous-time loop algorithm. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the two-dimensional percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. Furthermore, we found that the transition is not universal, i.e., the critical exponents significantly depend on S.