Frustrated Antiferromagnets Research Articles

Phase diagram of the helical structure of a two-subsystem frustrated antiferromagnet

The expansion of the thermodynamic potential for the two-subsystem antiferromagnet with frustrated intersubsystem isotropic exchange is obtained. It is demonstrated that this expansion contains the first derivatives with respect to the antiferromagnetic vectors of the subsystems, i.e., the Lifshitz invariant. The equation for the temperature-field boundary of the helical phase for the two-subsystem frustrated antiferromagnet is derived by linearizing the variational equations for the minimum free energy within the mean-field approximation. Relationships are obtained for the critical field at T = 0, the angle of canting of moments of the antiferromagnetic sublattices, and the temperature of spontaneous appearance of helical ordering in the absence of an external field. It is revealed that there is a second higher temperature of formation of the helical magnetic structure induced by the magnetic field with the wave vector of the helix nonmonotonically depending on the external field. The phase boundary of the helical phase and the temperature dependence of the orientation of moments of the magnetic subsystem with weak exchange interaction are determined using numerical minimization of the free energy. It is shown that the transition to the commensurate phase is a first-order transition with a small magnetization jump. A comparative analysis of models with different spatial displacements of ions in the subsystems along the direction of the vector of the helical structure is performed. A criterion is proposed for the choice of the direction of the vector of the incommensurate magnetic structure.

Resonance-Like Magnetic Excitations in Spinel Ferrimagnets FeCr2O4 and NiCr2O4 Observed by Neutron Scattering

We performed powder neutron scattering experiments on spinel ferrimagnets A Cr 2 O 4 with magnetic and Jahn–Teller A 2+ ions ( A = Fe, Ni, Cu). In both FeCr 2 O 4 and NiCr 2 O 4 , although geometric frustration had been expected to vanish so far, resonance-like magnetic excitation modes were discovered around Q ≃1.4 A -1 and E ≃5 and 8 to 9 meV in a low-temperature magnetic order phase, similar to the local spin resonance modes early reported in highly frustrated spinel antiferromagnets A Cr 2 O 4 with nonmagnetic and non-Jahn–Teller A 2+ ions ( A = Mg, Zn). In a high-temperature magnetic order phase the resonance-like inelastic scattering transformed into quasielastic scattering. In CuCr 2 O 4 no such diffusive scattering was observed. We interpret the resonance-like magnetic excitations as a dynamical spin-frustration effect, and discuss a necessary condition for the appearance of them.

Weak quasistatic magnetism in the frustrated Kondo lattice Pr2Ir2O7

Abstract Muon spin relaxation experiments have been performed in the pyrochlore iridate Pr2Ir2O7 for temperatures in the range 0.025–250 K. Kubo–Toyabe relaxation functions are observed up to ≳ 200 K , indicating static magnetism over this temperature range. The T → 0 static muon spin relaxation rate Δ ( 0 ) ≈ 8 μ s - 1 implies a weak quasistatic moment ( ∼ 0.1 μ B ) . The temperature dependence of Δ is highly nonmean-field-like, decreasing smoothly by orders of magnitude but remaining nonzero for T T f . The data rule out ordering of the full Pr 3 + CEF ground-state moment ( 3.0 μ B ) down to 0.025 K. The weak static magnetism is most likely due to hyperfine-enhanced 141Pr nuclear magnetism. The dynamic relaxation rate λ increases markedly below ∼ 20 K , probably due to slowing down of spin fluctuations in the spin-liquid state. At low temperatures λ is strong and temperature-independent, indicative of a high density of low-lying spin excitations as is common in frustrated antiferromagnets.

Frustration effects in antiferromagnetic molecules: The cuboctahedron

Frustration of magnetic systems which is caused by competing interactions is the driving force of several unusual phenomena such as plateaus and jumps of the magnetization curve as well as of unusual energy spectra with for instance many singlet levels below the first triplet state. The antiferromagnetic cuboctahedron can serve as a paradigmatic example of certain frustrated antiferromagnets. In addition it has the advantage that its complete energy spectrum can be obtained up to individual spin quantum numbers of s = 3/2 (16 777 216 states).

Nonlocal Landau theory of the magnetic phase diagram of highly frustrated magnetoelectricCuFeO2

A nonlocal Landau-type free-energy functional of the spin density is developed to model the large variety of magnetic states, which occur in the magnetic-field\char21{}temperature phase diagram of magnetoelectric ${\text{CuFeO}}_{2}$. Competition among long-range quadratic exchange, biquadratic antisymmetric exchange, and trigonal anisotropy terms, consistent with the high-temperature rhombohedral $R\overline{3}m$ crystal symmetry, are shown to all play important roles in stabilizing the unusual combination of commensurate and incommensurate spin structures in this highly frustrated triangular antiferromagnet. It is argued that strong magnetoelastic coupling is largely responsible for the nonlocal nature of the free energy. A key feature of the analysis is that an electric polarization is induced by a canting of the noncollinear incommensurate spin structure. Application of the model to ordered spin states in the triangular antiferromagnets ${\text{MnBr}}_{2}$ and ${\text{NaFeO}}_{2}$ is also discussed.

Topological Spin Liquid on the Hyperkagome Lattice ofNa4Ir3O8

Recent experiments on the "hyperkagome" lattice system Na4Ir3O8 have demonstrated that it is a rare example of a three-dimensional spin-1/2 frustrated antiferromagnet. We investigate the role of quantum fluctuations as the primary mechanism lifting the macroscopic degeneracy inherited by classical spins on this lattice. In the semiclassical limit we predict, based on large-N calculations, that an unusual q[over -->]=0 coplanar magnetically ordered ground state is stabilized with no local zero modes that correspond to local deformations of the spin configurations. This phase melts in the quantum limit and a gapped topological Z2 spin liquid phase emerges. In the vicinity of this quantum phase transition, we study the dynamic spin structure factor and comment on the relevance of our results for future neutron scattering experiments.

Magnetization behavior and magnetic entropy change of frustrated Ising antiferromagnetson two- and three-dimensional lattices

The magnetization behavior and the magnetic entropy change of frustrated Ising antiferromagnets withspin-1/2 on two-dimensional triangular and three-dimensional hexagonal closed-packedlattices are calculated by using Monte Carlo simulation. The results indicatethat the normalized magnetization as a function of external field shows a1/3 plateau on the two-dimensional system, while it shows0 and 1/2 plateaus on the three-dimensional system at low temperature. Consequently, it causes aninverse magnetocaloric effect, namely, the value of magnetic entropy change may bepositive in some ranges of magnetic fields. This phenomenon may be used to cool in a fieldby adiabatic demagnetization. Moreover, we analyze the spin configurations ofsystems on the magnetization plateaus, and discuss the impact of the frustration.We also find a mapping of the magnetization plateaus to the magnetic entropychanges at low temperature. The study of such systems showing field-inducedmetamagnetic transition in relation to frustrated antiferromagnets may open animportant field in searching for good candidates for room-temperature magneticrefrigeration.

Magnetic structure of theS=1Ni5(TeO3)4Br2layered system governed by magnetic anisotropy

Magnetization, neutron diffraction, and antiferromagnetic resonance measurements were employed to investigate the magnetic ground state of Ni-5(TeO3)(4)Br-2 single crystal. Despite the layered topology of the Ni2+ sites, typical for frustrated antiferromagnets, the system orders antiferromagnetically below T-N=29 K. Noncollinear arrangements of the Ni sublattices having a very complex temperature dependence were found from the neutron diffraction and magnetization measurements. Single-ion anisotropy, associated with the strongly distorted Ni-centered octahedra, has the same magnitude as the antiferromagnetic exchange interaction. The effect of these anisotropies prevails over the geometrical frustration leading to a long-range magnetic ordering below T-N.

Is Deconfined Quantum Criticality in Frustrated Antiferromagnets Ruled Out by Generic Fluctuation Induced First Order Behavior?

Recently, it was argued that quantum phase transitions in frustrated two dimensional antiferromagnets can be radically different from their classical counterparts with as a highlight, the “deconfined critical points” exhibiting fractionalization of quantum numbers due to Berry phase effects. However, field theoretical descriptions rest on a naïve coarse graining of the microscopic lattice model assuming order parameter fluctuations on small scales to be smooth. We have developed a novel renormalization approach for such systems which incorporates fluctuations on small scales in a natural way, and is fully respecting the underlying lattice structure and the frustration mechanism. According to our findings, another profound phenomenon is around the corner: a fluctuation induced first order transition.

Effective Hamiltonians forlarge-S pyrochlore antiferromagnets

The pyrochlore lattice Heisenberg antiferromagnet has a massive classical ground-statedegeneracy. We summarize three approximation schemes, valid for large spin lengthS, to capture the (partial) lifting of this degeneracy when zero-point quantum fluctuationsare taken into account; all three are related to analytic loop expansions. The first isharmonic-order spin waves; at this order, there remains an infinite manifold of degeneratecollinear ground states, related by a gauge-like symmetry. The second is anharmonic (quarticorder) spin waves, using a self-consistent approximation; the harmonic-order degeneracy issplit, but (within numerical precision) some degeneracy may remain, with entropy still of orderL in a systemof L3 sites. Thethird is a large-N approximation, a standard and convenient approach for frustrated antiferromagnets; however, thelarge-N result contradicts the harmonic order atO(S) and hence mustbe wrong (for large S).

Spin dynamics in classical and quantum Kagome lattice magnets studied by NMR

Jarosite, KFe3(OH)6(SO4)2, is a typical example of a classical frustrated antiferromagnet withs = 5/2 Fe3+ ions on the Kagome lattice, and a metallic complex,[Cu3(titmb)2(CH3CO2)6]·H2O,abbreviated as Cu-titmb, is considered to be a candidate material for a quantum frustrated magnetwith s = 1/2 on the Kagome lattice. Jarosite has a Weiss temperature of−530 K and shows magnetic ordering below 65 K due to weak anisotropy. The magnetic structurein the ordered phase has been determined, using neutron scattering and NMR, to be aq = 0 type120° spinstructure with + chirality. The nuclear spin–lattice relaxation rateT1−1 and the spontaneous magnetization indicate the existence of the spin wave in the orderedphase. A small number of substitutions or deficiencies induce successive phase transitions,which represent two-dimensional ordering on the Kagome planes and three-dimensionalordering between the planes. For the quantum spin magnet, Cu-titmb, the nuclear spinrelaxation at low temperatures shows the existence of anomalous low-lying excitedstates in the magnetic field. The relaxation rates at high temperatures give muchsmaller exchange interaction compared to the value estimated from the specificheat. Several interesting properties, such as double peaks of the specific heat, a1/3 magnetization plateau for the pulse field and a ferromagnetic transition at 56 mK have beenreported. We review the experimental results of Cu-titmb.

Modeling bond-order wave instabilities in doped frustrated antiferromagnets: Valence bond solids at fractional filling

We explore both analytically and numerically the properties of doped t-J models on a class of highly frustrated lattices, such as the kagome and the pyrochlore lattice. Focussing on a particular sign of the hopping integral and antiferromagnetic exchange, we find a generic symmetry breaking instability towards a twofold degenerate ground state at a fractional filling below half filling. These states show modulated bond strengths and only break lattice symmetries. They can be seen as a generalization of the well-known valence bond solid states to fractional filling.

Neutron-scattering studies of magnetism in multiferroic HoMnO3 (invited)

Hexagonal HoMnO3 is a frustrated antiferromagnet (TN=72K) ferroelectric (TC=875K) with a rich magnetic phase diagram consisting of multiple temperature- and field-dependent phases. Previously observed anomalies in the dielectric constant at magnetic phase transitions indicate strong coupling between the ferroelectricity and magnetism. Neutron-diffraction measurements in a magnetic field reveal new intermediate-field phases at low temperatures. Inelastic neutron-scattering measurements are used to establish the primary magnetic interactions and demonstrate that the spin dynamics in HoMnO3 are well described by a simple two-dimensional nearest-neighbor Heisenberg antiferromagnetic exchange J=2.44meV and a temperature-dependent anisotropy D.

Spinon deconfinement in doped frustrated quantum antiferromagnets

The confinement of a spinon liberated by doping two-dimensional frustrated quantum antiferromagnets with a non-magnetic impurity or a mobile hole is investigated. For a static vacancy, an intermediate behavior between complete deconfinement (kagome) and strong confinement (checkerboard) is identified in the J_1{-}J_2{-}J_3 model on the square lattice, with the emergence of two length scales, a spinon confinement length larger than the magnetic correlation length. For mobile holes, this translates into an extended spinon-holon boundstate allowing one to bridge momentum (ARPES spectral function) and real space (STM) experimental observations. These features provide clear evidence for a nearby "deconfined critical point" in a doped microscopic model.

Spin–lattice interaction effect in frustrated antiferromagnets

Lattice-coupled antiferromagnetic spin model is analyzed for a number of frustrated lattices. In the pyrochlore lattice, a uniform hexagon contraction can take place and reduce the exchange energy within the hexagonal cluster. In the triangular and kagomé lattice, the mean-field theory predicts lack of lattice displacement. However, after considering the possibility of valence-bond formation, we argue that a type of valence-bond-solid order can be stabilized through spin–lattice interaction and leads to lattice deformation in the triangular structure. Excitation spectrum for the lattice-deformed ground state is worked out, which differs from the conventional spin waves and is in principle observable in neutron scattering.

Dynamics in pure and substituted volborthite kagome-like compounds

Volborthite Cu 3 V 2 O 7 ( OH ) 2 · 2 H 2 O is a natural frustrated antiferromagnet with a kagomé-like magnetic lattice decorated by S = 1 2 spins. Our μ SR results confirm the existence of a dynamical plateau below 2 K, as initially demonstrated in [Phys. Rev. Lett. 91 (2003) 207603] despite sensible quantitative differences in the relaxation rate values. Thanks to additional low temperature SQUID and NMR data we show that this plateau occurs concurrently with a freezing transition. Moreover, we revisited the effect of diluting the magnetic lattice for small dilution rates between 1% and 15%. Comparison is made with the well studied kagomé bilayer compounds. The ground state of volborthite appears to be far less stable with respect to dilution.

Order-parameter symmetries for magnetic and superconducting instabilities: Bethe-Salpeter analysis of functional renormalization-group solutions

The Bethe-Salpeter equation is combined with the temperature-cutoff functional renormalization group approach to analyze the order parameter structure for the leading instabilities of the 2D $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model. We find significant deviations from the conventional $s$-, $p$-, or $d$-wave forms, which is due to the frustration of antiferromagnetism at small and intermediate ${t}^{\ensuremath{'}}$. With adding a direct antiferromagnetic spin-exchange coupling the eigenfunctions in the particle-hole channel have extended $s$-wave form, while in the particle-particle singlet pairing channel a higher angular momentum component arises besides the standard ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ wave component, which flattens the angular dependence of the gap. For ${t}^{\ensuremath{'}}$ closer to $t∕2$ we find a delicate competition of ferromagnetism and triplet pairing with a nontrivial pair-wavefunction.

Quantum disordered ground states in frustrated antiferromagnets with multiple ring exchange interactions

We present a certain class of two-dimensional frustrated quantum Heisenberg spin systems with multiple ring exchange interactions which are rigorously demonstrated to have quantum disordered ground states without magnetic long-range order. The systems considered in this paper are s=1/2 antiferromagnets on a honeycomb and square lattices, and an s=1 antiferromagnet on a triangular lattice. We find that for a particular set of parameter values, the ground state is a short-range resonating valence bond state or a valence bond crystal state. It is shown that these systems are closely related to the quantum dimer model introduced by Rokhsar and Kivelson as an effective low-energy theory for valence bond states.

CORE: Frustrated Magnets, Charge Fractionalization, and QCD

I explain how to use a simple method to extract the physics of lattice Hamiltonian systems which are not easily analyzed by exact or other numerical methods. I will then use this method to establish the relationship between QCD and a special class of generalized, highly frustrated anti-ferromagnets.

Magnetic Order and Spin Dynamics in FerroelectricHoMnO3

Hexagonal HoMnO3 is a frustrated antiferromagnet (T(N)=72 K) ferroelectric (T(C)=875 K) in which these two order parameters are coupled. Our neutron measurements of the spin-wave dispersion for the S=2 Mn3+ on the layered triangular lattice are well described by a two-dimensional nearest-neighbor Heisenberg exchange J=2.44 meV, and an anisotropy D that is 0.28 meV above the spin-reorientation transition at 40 K and 0.38 meV below. For H parallel c the magnetic structures and phase diagram have been determined, and reveal additional transitions below 8 K where the ferroelectrically displaced Ho3+ ions are ordered magnetically.