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We study spin-wave interactions in quantum antiferromagnets by expressing the usual magnon annihilation and creation operators in terms of Hermitian field operators representing transverse staggered and ferromagnetic spin fluctuations. In this parameterization, which was anticipated by Anderson in 1952, the two-body interaction vertex between staggered spin fluctuations vanishes at long wavelengths. We derive a new effective action for the staggered fluctuations only by tracing out the ferromagnetic fluctuations. To one loop order, the renormalization group flow agrees with the nonlinear-$sigma$-model approach.
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Motivated by the recent synthesis of the spin-1 A-site spinel NiRh$_{text 2}$O$_{text 4}$, we investigate the classical to quantum crossover of a frustrated $J_1$-$J_2$ Heisenberg model on the diamond lattice upon varying the spin length $S$. Applying a recently developed pseudospin functional renormalization group (pf-FRG) approach for arbitrary spin-$S$ magnets, we find that systems with $S geq 3/2$ reside in the classical regime where the low-temperature physics is dominated by the formation of coplanar spirals and a thermal (order-by-disorder) transition. For smaller local moments $S$=1 or $S$=1/2 we find that the system evades a thermal ordering transition and forms a quantum spiral spin liquid where the fluctuations are restricted to characteristic momentum-space surfaces. For the tetragonal phase of NiRh$_{text 2}$O$_{text 4}$, a modified $J_1$-$J_2^-$-$J_2^perp$ exchange model is found to favor a conventionally ordered Neel state (for arbitrary spin $S$) even in the presence of a strong local single-ion spin anisotropy and it requires additional sources of frustration to explain the experimentally observed absence of a thermal ordering transition.
We study and solve the ground-state problem of a microscopic model for a family of orbitally degenerate quantum magnets. The orbital degrees of freedom are assumed to have directional character and are represented by static Potts-like variables. In the limit of vanishing Hunds coupling, the ground-state manifold of such a model is spanned by the hard-core dimer (spin singlet) coverings of the lattice. The extensive degeneracy of dimer coverings is lifted at a finite Hunds coupling through an order-out-of-disorder mechanism by virtual triplet excitations. The relevance of our results to several experimentally studied systems is discussed.
We predict that an external field can induce a spin order in highly frustrated classical Heisenberg magnets. We find analytically stabilization of collinear states by thermal fluctuations at a one-third of the saturation field for kagome and garnet lattices and at a half of the saturation field for pyrochlore and frustrated square lattices. This effect is studied numerically for the frustrated square-lattice antiferromagnet by Monte Carlo simulations for classical spins and by exact diagonalization for $S=1/2$. The field induced collinear states have a spin gap and produce magnetization plateaus.
The Casimir effect is a general phenomenon in physics, which arises when the vacuum fluctuation of an arbitrary field is modified by static or slowly varying boundary. However, its spin version is rarely addressed, mainly due to the fact that a macroscopic boundary in quantum spin systems is hard to define. In this article, we explore the spin Casimir effect induced by the zero-point fluctuation of spin waves in a general non-collinear ordered quantum antiferromagnet. This spin Casimir effect results in a spin torque between local spins and further causes various singular and divergent results in the framework of spin-wave theory, which invalidate the standard $1/S$ expansion procedure. To avoid this dilemma, we develop a self-consistent spin-wave expansion approach, which preserves the spin-wave expansion away from singularities and divergence. A detailed spin-wave analysis of the antiferromagnetic spin-1/2 Heisenberg model on a spatially anisotropic triangular lattice is undertaken within our approach. Our results indicate that the spiral order is only stable in the region $0.5<alpha<1.2$, where $alpha$ is the ratio of the coupling constants. In addition, the instability in the region $1.2<alpha<2$ is owing to the spin Casimir effect instead of the vanishing sublattice magnetization. And this extended spiral instable region may host some quantum disordered phases besides the quantum order by disorder induced Neel phase. Furthermore, our method provides an efficient and convenient tool that can estimate the correct exchange parameters and outline the quantum phase diagrams, which can be useful for experimental fitting processes in frustrated quantum magnets.
The spin ice materials, including Ho2Ti2O7 and Dy2Ti2O7, are rare earth pyrochlore magnets which, at low temperatures, enter a constrained paramagnetic state with an emergent gauge freedom. Remarkably, the spin ices provide one of very few experimentally realised examples of fractionalization because their elementary excitations can be regarded as magnetic monopoles and, over some temperature range, the spin ice materials are best described as liquids of these emergent charges. In the presence of quantum fluctuations, one can obtain, in principle, a quantum spin liquid descended from the classical spin ice state characterised by emergent photon-like excitations. Whereas in classical spin ices the excitations are akin to electrostatic charges, in the quantum spin liquid these charges interact through a dynamic and emergent electromagnetic field. In this review, we describe the latest developments in the study of such a quantum spin ice, focussing on the spin liquid phenomenology and the kinds of materials where such a phase might be found.
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