Peierls-like transition induced by frustration in a two-dimensional antiferromagnet

Spin-Peierls instability of the U(1) Dirac spin liquid

Quantum fluctuations can inhibit long-range ordering in frustrated magnets and potentially lead to quantum spin liquid (QSL) phases. A prime example are gapless QSLs with emergent U(1) gauge fields, which have been understood to be described in terms of quantum electrodynamics in 2+1 dimension (QED3). Despite several promising candidate materials, however, a complicating factor for their realisation is the presence of other degrees of freedom. In particular lattice distortions can act to relieve magnetic frustration, precipitating conventionally ordered states. In this work, we use field-theoretic arguments as well as extensive numerical simulations to show that the U(1) Dirac QSL on the triangular and kagome lattices exhibits a weak-coupling instability due to the coupling of monopoles of the emergent gauge field to lattice distortions, leading to valence-bond solid ordering. This generalises the spin-Peierls instability of one-dimensional quantum critical spin chains to two-dimensional algebraic QSLs. We study static distortions as well as quantum-mechanical phonons. Even in regimes where the QSL is stable, the singular spin-lattice coupling leads to marked temperature-dependent corrections to the phonon spectrum, which provide salient experimental signatures of spin fractionalisation. We discuss the coupling of QSLs to the lattice as a general tool for their discovery and characterisation.

Magnetoelastic coupling and critical behavior of some strongly correlated magnetic systems

The strongly correlated magnetic systems are attracting continuous attention in current condensed matter research due to their very compelling physics and promising technological applications. Being a host to charge, spin, and lattice degrees of freedom, such materials exhibit a variety of phases, and investigation of their physical behavior near such a phase transition bears an immense possibility. This review summarizes the recent progress in elucidating the role of magnetoelastic coupling on the critical behavior of some technologically important class of strongly correlated magnetic systems such as perovskite magnetites, uranium ferromagnetic superconductors, and multiferroic hexagonal manganites. It begins with encapsulation of various experimental findings and then proceeds toward describing how such experiments motivate theories within the Ginzburg-Landau phenomenological picture in order to capture the physics near a magnetic phase transition of such systems. The theoretical results that are obtained by implementing Wilson's renormalization-group to nonlocal Ginzburg-Landau model Hamiltonians are also highlighted. A list of possible experimental realizations of the coupled model Hamiltonians elucidates the importance of spin-lattice coupling near a critical point of strongly correlated magnetic systems.

A series of magnon crystals appearing under ultrahigh magnetic fields in a kagomé antiferromagnet

Geometrical frustration and a high magnetic field are two key factors for realizing unconventional quantum states in magnetic materials. Specifically, conventional magnetic order can potentially be destroyed by competing interactions and may be replaced by an exotic state that is characterized in terms of quasiparticles called magnons, the density and chemical potential of which are controlled by the magnetic field. Here we show that a synthetic copper mineral, Cd-kapellasite, which comprises a kagomé lattice consisting of corner-sharing triangles of spin-1/2 Cu2+ ions, exhibits an unprecedented series of fractional magnetization plateaus in ultrahigh magnetic fields of up to 160 T. We propose that these quantum states can be interpreted as crystallizations of emergent magnons localized on the hexagon of the kagomé lattice.

Symmetry Reduction in the Quantum Kagome Antiferromagnet Herbertsmithite

Employing complementary torque magnetometry and electron spin resonance on single crystals of herbertsmithite, the closest realization to date of a quantum kagome antiferromagnet featuring a spin-liquid ground state, we provide novel insight into different contributions to its magnetism. At low temperatures, two distinct types of defects with different magnetic couplings to the kagome spins are found. Surprisingly, their magnetic response contradicts the threefold symmetry of the ideal kagome lattice, suggesting the presence of a global structural distortion that may be related to the establishment of the spin-liquid ground state.

Magnetoelastic quantum fluctuations and phase transitions in the iron superconductors

We examine the relevance of magnetoelastic coupling to describe the complex magnetic and structural behavior of the different classes of the iron superconductors. We model the system as a two-dimensional metal whose magnetic excitations interact with the distortions of the underlying square lattice. Going beyond the mean field, we find that quantum fluctuation effects can explain two unusual features of these materials that have attracted considerable attention: first, why iron telluride orders magnetically at a non-nesting wave vector (π/2,π/2) and not at the nesting wave vector (π,0) as in the iron arsenides, even though the nominal band structures of both these systems are similar, and second, why the (π,0) magnetic transition in the iron arsenides is often preceded by an orthorhombic structural transition. These are robust properties of the model, independent of microscopic details, and they emphasize the importance of the magnetoelastic interaction.

Spin-lattice coupling, frustration, and magnetic order in multiferroic RMnO3

We have performed high-resolution neutron diffraction and inelastic neutron scattering experiments in the frustrated multiferroic hexagonal compounds RMnO_{3} (R = Ho,Yb,Sc,Y), which provide evidence of a strong magnetoelastic coupling in the whole family. We can correlate the atomic positions, the type of magnetic structure, and the nature of the spin waves whatever the R ion and temperature. The key parameter is the position of the Mn ions in the unit cell with respect to a critical threshold of 1/3, which determines the sign of the coupling between Mn triangular planes.

Spin phonon induced collinear order and magnetization plateaus in triangular and kagome antiferromagnets: applications to CuFeO2

We study the effect of spin-lattice coupling on triangular and kagome antiferromagnets and find that even moderate couplings can induce complex collinear orders. On coupling classical Heisenberg spins on the triangular lattice to Einstein phonons, a rich variety of phases emerge including the experimentally observed four sublattice state and the five sublattice 1/5th plateau state seen in the magnetoelectric material CuFeO(2). Also, we predict magnetization plateaus at 1/3, 3/7, 1/2, 3/5, and 5/7 at these couplings. Strong spin-lattice couplings induce a striped collinear state, seen in alpha-NaFeO(2) and MnBr(2). On the kagome lattice, moderate spin-lattice couplings induce collinear order, but an extensive degeneracy remains.

Mott transition in a valence-bond solid insulator with a triangular lattice

We have investigated the Mott transition in a quasi-two-dimensional Mott insulator EtMe{3}P[Pd(dmit){2}]{2} with a spin-frustrated triangular-lattice in hydrostatic pressure and magnetic-field [Et and Me denote C2H5 and CH3, respectively, and Pd(dmit){2} (dmit=1,3-dithiole-2-thione-4,5-dithiolate,dithiolate) is an electron-acceptor molecule]. In the pressure-temperature (P-T) phase diagram, a valence-bond solid phase is found to neighbor the superconductor and metal phases at low temperatures. The profile of the phase diagram is common to those of Mott insulators with antiferromagnetic order. In contrast to the antiferromagnetic Mott insulators, the resistivity in the metallic phase exhibits anomalous temperature dependence, rho=rho{0}+AT(2.5).

Half-magnetization plateau stabilized by structural distortion in the antiferromagnetic heisenberg model on a pyrochlore lattice

Magnetization plateaus, visible as anomalies in magnetic susceptibility at low temperatures, are one of the hallmarks of frustrated magnetism. We show how an extremely robust half-magnetization plateau can arise from coupling between spin and lattice degrees of freedom in a pyrochlore antiferromagnet and develop a detailed symmetry of analysis of the simplest possible scenario for such a plateau state. The application of this theory to the spinel oxides CdCr2O4 and HgCr2O4, where a robust half-magnetization plateau has been observed, is discussed.

Pressure and field induced magnetic order in the spin liquid Tb2Ti2O7 as studied by single crystal neutron diffraction

We have studied the spin liquid Tb2Ti2O7 by single crystal neutron diffraction under high pressure up to 2.8 GPa, together with uniaxial stress, down to 0.1 K, in zero and high magnetic fields up to 7 T. In zero magnetic field, a long-range ordered antiferromagnetic structure is induced by pressure. The Néel temperature and ordered magnetic moment can be tuned by the anisotropic pressure component. Under magnetic field, the antiferromagnetic structure transforms into a canted ferromagnetic one at 0.6 T. Spin canting persists even at 7 T. The magnetic phase diagram under pressure shows a strong increase of the Néel temperature with the field.

Magnetic-field induced spin-Peierls instability in strongly frustrated quantum spin lattices

For a class of frustrated antiferromagnetic spin lattices (in particular, the square-kagomé and kagomé lattices) we discuss the impact of recently discovered exact eigenstates on the stability of the lattice against distortions. These eigenstates consist of independent localized magnons embedded in a ferromagnetic environment and become ground states in high magnetic fields. For appropriate lattice distortions fitting to the structure of the localized magnons the lowering of magnetic energy can be calculated exactly and is proportional to the displacement of atoms leading to a spin-Peierls lattice instability. Since these localized states are present only for high magnetic fields, this instability might be driven by magnetic-field. The hysteresis of the spin-Peierls transition is also discussed.

Direct determination of the magnetic ground state in the square lattice S = 1/2 antiferromagnet Li2VOSiO4

Powder neutron diffraction and resonant x-ray scattering measurements from a single crystal have been performed to study the low-temperature state of the 2D frustrated, quantum-Heisenberg system Li2VOSiO4. Both techniques indicate a collinear antiferromagnetic ground state, with propagation vector k=(1 / 2 1 / 2 0), and magnetic moments in the a-b plane. Contrary to previous reports, the ordered moment at 1.44 K, m=0.63(3)micro(B), is very close to the value expected for the square lattice Heisenberg model ( approximately 0.6micro(B)). The magnetic order is three dimensional, with antiferromagnetic a-b layers stacked ferromagnetically along the c axis. Neither x-ray nor neutron diffraction shows evidence for a structural distortion between 1.6 and 10 K.

Ising transition driven by frustration in a 2D classical model with continuous symmetry

We study the thermal properties of the classical antiferromagnetic Heisenberg model with both nearest (J1) and next-nearest (J2) exchange couplings on the square lattice by extensive Monte Carlo simulations. We show that, for J2/J1>1/2, thermal fluctuations give rise to an effective Z2 symmetry leading to a finite-temperature phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that T(c)-->0 with an infinite slope when J2/J1-->1/2.