We study in this paper the resistivity encountered by Ising itinerant spins traveling in the so-called $J_1-J_2$ frustrated simple cubic Ising lattice. For the lattice, we take into account the interactions between nearest-neighbors and next-nearest-neighbors, $J_1$ and $J_2$ respectively. Itinerant spins interact with lattice spins via a distance-dependent interaction. We also take into account an interaction between itinerant spins. The lattice is frustrated in a range of $J_2$ in which we show that it undergoes a very strong first-order transition. Using Monte Carlo simulation, we calculate the resistivity $ρ$ of the itinerant spins and show that the first-order transition of the lattice causes a discontinuity of $ρ$.
In this review, we outline the important results on the resistivity encountered by an electron in magnetically ordered materials. The mechanism of the collision between the electron and the lattice spins is shown. Experiments on the spin resistivity in various magnetic materials as well as theoretical background are recalled. We focus on our works since 15 years using principally Monte Carlo simulations. In these works, we have studied the spin resistivity in various kinds of magnetic systems ranging from ferromagnets and antiferromagnets to frustrated spin systems. It is found that the spin r…
We study the scaling behavior and critical dynamics of the resistive transition in Josephson-junction arrays, at f=1/2 flux quantum per plaquette, by numerical simulation of an on-site dissipation model for the dynamics. The results are compared with recent simulations using the resistively-shunted-junction model. For both models, we find that the resistivity scaling and critical dynamics of the phases are well described by the same critical temperature as for the chiral (vortex-lattice) transition, with a power-law divergent correlation length. The behavior is consistent with the single trans…
We analyze the universal features of the critical behaviour of frustrated spin systems with noncollinear order. By means of the field theoretical renormalization group approach, we study the 3d model of a frustrated magnet and obtain pseudo-epsilon expansions for its universal order parameter marginal dimensions. These dimensions govern accessibility of the renormalization group transformation fixed points, and, hence, define the scenario of the phase transition.
Recent studies on the frustrated quantum spin chains with easy-plane anisotropy are reviewed. We are particularly interested in novel "chiral" phases characterized by the spontaneous breaking of the parity symmetry. The ground-state phase diagrams of the chains are discussed.
In an effort to understand the glass transition, the dynamics of a non-randomly frustrated spin model has been analyzed. The phenomenology of the spin model is similar to that of a supercooled liquid undergoing the glass transition. The slow dynamics can be associated with the presence of extended string-like structures which demarcate regions of fast spin flips. An entropy-vanishing transition, with the string density as the order parameter, is related to the observed glass transition in the spin model.
Using a {\it collective} Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large class of Heisenberg frustrated spin systems. They are constructed so that to differ only by their topological properties. The spin-stiffnesses for the two systems of tops are calculated for different temperatures and different sizes of the sample. This allows to investigate the role of topological defects in frustrated spin systems. Comparisons with Renormali…
We discuss three exactly solvable spin models of geometric frustration. First, we discuss a 1-parameter subfamily of the 16 vertex model, which can be mapped to a planar Ising model and solved via Fisher-Dubedát decorations. We then consider a 1-parameter family generalization of the Villain's fully frustrated model, which interpolates between Onsager's 2D Ising model and the Villain one. We then discuss spin ice models on a tree, which can be solved exactly using recursions \textit{a lá Bethe}.
We study frustrated quantum spin systems consisting of dimers of spin-1/2 spins. We derive several models that have the exact ground state of the form of the direct product of dimer states. The ground states realized include the product state of dimer singlets, that of dimer triplets with zero magnetization, those of dimer-spin-nematic states, and those of a mixture of the dimer states. Pseudo spin-1/2 operators emerging in each dimer are also introduced.
The spin-1/2 Ising-Heisenberg model on the triangulated Kagome (triangles-in-triangles) lattice is exactly solved by establishing a precise mapping correspondence to the simple spin-1/2 Ising model on Kagome lattice. It is shown that the disordered spin liquid state, which otherwise occurs in the ground state of this frustrated spin system on assumption that there is a sufficiently strong antiferromagnetic intra-trimer interaction, is eliminated from the ground state by arbitrary but non-zero Dzyaloshinskii-Moriya anisotropy.
Lieb and Schupp have obtained, using certain version of ``spin-reflection positivity'' method, a number of ground-state properties for frustrated Heisenberg models. One group of these results is related to singlet nature of ground state and it needs an assumption of reflection symmetry present in the system. In this paper, it is shown that the result holds also for other symmetries (inversion etc.). The second Lieb-Schupp result is relation between ground-state energies of certain systems. In the paper, this relation is applied to multidimensional models on various lattices.
In an effort to understand the glass transition, the kinetics of a spin model with frustration but no quenched randomness has been analyzed. The phenomenology of the spin model is remarkably similiar to that of structural glasses. Analysis of the model suggests that defects play a major role in dictating the dynamics as the glass transition is approached.
We calculate the spin stiffness of the S=1/2 frustrated Heisenberg antiferromagnet directly from a general formula which is evaluated in the Schwinger boson mean-field approximation. Both Néel and collinear ordering are considered. For collinear ordering, we take the anisotropy of this phase into account, unlike previous approaches. For Néel ordering, a detailed study is made of the finite-size scaling behavior of the two terms that make up the spin stiffness. The exponents of the scaling with the system size of the two terms comprising the spin stiffness turn out to be identical to those of t…
We study the transport properties for a family of geometrically frustrated models on the triangular lattice with an interaction scale far exceeding the single-particle bandwidth. Starting from the interaction-only limit, which can be solved exactly, we analyze the transport and thermodynamic behavior as a function of filling and temperature at the leading non-trivial order in the single-particle hopping. Over a broad range of intermediate temperatures, we find evidence of a dc resistivity scaling linearly with temperature and with typical values far exceeding the quantum of resistance, $h/e^2$…
Low-temperature thermodynamics of the classical frustrated ferromagnetic spin chain is studied. Using transfer-matrix method we found the behavior of the correlation function and zero-field susceptibility at the ferromagnetic-helical transition point. It is shown that the critical exponent for the susceptibility is changed from 2 to 4/3 at the transition point.
A mixed Heisenberg spin chain with frustrated side chains is investigated by numerical and perturbational calculations. A frustration-induced quantum partially polarized ferrimagnetic phase and a nonmagnetic spin quadrupolar phase are found adjacent to the conventional Lieb-Mattis type ferrimagnetic phase or the nonmagnetic singlet cluster solid phases. The partially polarized ferrimagnetic phase has an incommensurate spin structure. Similar structures are commonly found in other frustration-induced partially polarized ferrimagnetic phases. Numerical results also suggest a series of almost cri…
In this publication I discuss the phase diagram of a frustrated spin-1/2 Heisenberg model suggested in A. A. Nersesyan and A. M. Tsvelik, Phys. Rev. B{\bf 67}, 024422 (2003). The phase diagram contains $(π,0)$ and $(π,π)$ antiferromagnetic phases separated by the Valence Bond Crystal (VBC) state. I argue that the point of the phase diagram with deconfined spinons, predicted in the aforementioned work, is situated in the middle of VBC state, at the point where the dimerization order parameter changes sign.
Sharp quantum phase transitions typically require a large system with many particles. Here we show that for a frustrated fully-connected Ising spin network represented by trapped atomic ions, the competition between different spin orders leads to rich phase transitions whose sharpness scales exponentially with the number of spins. This unusual finite-size scaling behavior opens up the possibility of observing sharp quantum phase transitions in a system of just a few trapped ion spins.
We show that one-dimensional topological objects (kinks) are natural degrees of freedom for an antiferromagnetic Ising model on a triangular lattice. Its ground states and the coexistence of spin ordering with an extensive zero-temperature entropy can be easily understood in terms of kinks forming a hard-sphere liquid. Using this picture we explain effects of quantum spin dynamics on that frustrated model, which we also study numerically.
We investigate the consequences for geometrically frustrated antiferromagnets of weak disorder in the strength of exchange interactions. Taking as a model the classical Heisenberg antiferromagnet with nearest neighbour exchange on the pyrochlore lattice, we examine low-temperature behaviour. We show that random exchange generates long-range effective interactions within the extensively degenerate ground states of the clean system. Using Monte Carlo simulations, we find a spin glass transition at a temperature set by the disorder strength. Disorder of this type, which is generated by random str…
We develop a microscopic theory of finite-temperature spin-nematic orderings in three-dimensional spatially anisotropic magnets consisting of weakly-coupled frustrated spin-1/2 chains with nearest-neighbor and next-nearest-neighbor couplings in a magnetic field. Combining a field theoretical technique with density-matrix renormalization group results, we complete finite-temperature phase diagrams in a wide magnetic-field range that possess spin-bond-nematic and incommensurate spin-density-wave ordered phases. The effects of a four-spin interaction are also studied. The relevance of our results…
We study the critical behavior of frustrated spin models with noncollinear order in two dimensions, including antiferromagnets on a triangular lattice and fully frustrated antiferromagnets. For this purpose we consider the corresponding $O(N) \times O(2)$ Landau-Ginzburg-Wilson (LGW) Hamiltonian and compute the field-theoretic expansion to four loops and determine its large-order behavior. We show the existence of a stable fixed point for the physically relevant cases of two- and three-component spin models. We also give a prediction for the critical exponent $η$ which is $η=0.24(6)$ and $η=0.…
Low temperature properties of the spin-1/2 frustrated ladder with ferromagnetic rungs and legs, and two different antiferromagnetic next nearest neighbor interaction are investigated using the modified spin wave approximation in the region with ferromagnetic ground state. The temperature dependence of the magnetic susceptibility and magnetic structure factors is calculated. The results are consistent with the numerical exact diagonalization results in the intermediate temperature range. Below this temperature range, the finite size effect is significant in the numerical diagonalization results…
Spin-spin correlations are calculated in frustrated hierarchical Ising models that exhibit chaotic renormalization-group behavior. The spin-spin correlations, as a function of distance, behave chaotically. The far correlations, but not the near correlations, are sensitive to small changes in temperature or frustration, with temperature changes having a larger effect. On the other hand, the calculated free energy, internal energy, and entropy are smooth functions of temperature. The recursion-matrix calculation of thermodynamic densities in a chaotic band is demonstrated. The leading Lyapunov e…
In a recent letter [Phys. Rev. Lett. 89, 156603 (2002); cond-mat/0201300], Alvarez and Gros have numerically analyzed the Drude weight for thermal transport in spin ladders and frustrated chains of up to 14 sites and have proposed that it remains finite in the thermodynamic limit. In this comment, we argue that this conclusion cannot be sustained if the finite-size analysis is taken to larger system sizes.
We study the magnetization plateau at 1/4 of the saturation magnetization of the S=1 antiferromagnetic spin ladder both analytically and numerically, with the aim of explaining recent experimental results on BIP-TENO by Goto et al. We propose two mechanisms for the plateau formation and clarify the plateau phase diagram on the plane of the coupling constants between spins.
We study a frustrated mixed spin chain with side chains, where the spin species and the exchange interactions are spatially varied. A nonlinear sigma model method is formulated for this model, and a phase diagram with two disordered spin-gap phases is obtained for typical cases. Among them we examine the case with a main chain consisting of an alternating array of spin-1 and spin-1/2 sites and side chains each of a single spin-1/2 site in great detail. Based on numerical, perturbational, and variational approaches, we propose a singlet cluster solid picture for each phase, where the ground sta…
The search for elementary excitations with fractional quantum numbers is a central challenge in modern condensed matter physics. We explore the possibility in a realistic model for several materials, the spin-1/2 spatially anisotropic frustrated Heisenberg antiferromagnet in two dimensions. By restricting the Hilbert space to that expressed by exact eigenstates of the Heisenberg chain, we derive an effective Schrödinger equation valid in the weak interchain-coupling regime. The dynamical spin correlations from this approach agree quantitatively with inelastic neutron measurements on the triang…
We analyze the Drude weight for both spin and thermal transport of one-dimensional spin-1/2 systems by means of exact diagonalization at finite temperatures. While the Drude weights are non-zero for finite systems, we find indications of a vanishing of the Drude weights in the thermodynamic limit for non-integrable models implying normal transport behavior.
Thermal entanglement of a geometrically frustrated spin-1 Heisenberg diamond cluster is examined within the framework of the exact diagonalization method by computing the measure of entanglement negativity. The calculated exact analytical results are applied in order to obtain theoretical prediction of the robustness of bipartite thermal entanglement of the tetranuclear nickel complex [Ni4(CO3)2(aetpy)8](ClO4)4 (aetpy = 2-aminoethyl-pyridine) against rising temperature and magnetic field.
The formation of coplanar spin spirals is a common motif in the magnetic ordering of many frustrated magnets. For classical antiferromagnets, geometric frustration can lead to a massively degenerate ground state manifold of spirals whose propagation vectors can be described, depending on the lattice geometry, by points (triangular), lines (fcc), surfaces (frustrated diamond) or completely flat bands (pyrochlore). Here we demonstrate an exact mathematical correspondence of these spiral manifolds of classical antiferromagnets with the Fermi surfaces of free-fermion band structures. We provide an…
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 lat…
We consider the archetypal frustrated antiferromagnet SrCr$_{9p}$Ga$_{12-9p}$O$_{19}$ in its well-known spin-liquid state, and demonstrate that a Cr$^{3+}$ spin $S=3/2$ ion in direct proximity to a pair of vacancies (in disordered $p<1$ samples) is cloaked by a spatially extended spin texture that encodes the correlations of the parent spin-liquid. In this spin-liquid regime, the combined object has a magnetic response identical to a classical spin of length $S/2 = 3/4$, which dominates over the small intrinsic susceptibility of the pure system. This fractional-spin texture leaves an unmistaka…
We determine the magnetic phase diagram of the antiferromagnetic(AF) zigzag spin chain in the strongly frustrated region, using the density matrix renormalization group method. We find the magnetization plateau at 1/3 of the full moment accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve. We also discuss the formation mechanisms of the plateau and cusps briefly.
We perform large scale simulations of the frustrated Ising lattice gas, a three-dimensional lattice model of a structural glass, using the parallel tempering technique. We evaluate the spin and density overlap distributions, and the corresponding non-linear susceptibilities, as a function of the chemical potential. We then evaluate the relaxation functions of the spin and density self-overlap, and study the behavior of the relaxation times. The results suggest that the spin variables undergo a transition very similar to the one of the Ising spin glass, while the density variables do not show a…
We consider discrete spin models on arbitrary planar graphs and lattices with frustrated interactions. We first analyze the Ising model with frustrated plaquettes. We use an algebraic approach to derive the result that an Ising model with some of its plaquettes frustrated has a dual which is an Ising model with an external field $iπ/2$ applied to the dual sites centered at frustrated plaquettes. In the case that all plaquettes are frustrated, this leads to the known result that the dual model has a uniform field $iπ/2$ whose partition function can be evaluated in the thermodynamic limit for re…
We study ordering mechanisms which are induced by the quantum fluctuation in fully frustrated Ising spin systems. Since there are many degenerated states in frustrated systems, "order by thermal disorder" often takes place due to a kind of entropy effect. To consider "order by quantum disorder" in fully frustrated Ising spin systems, we apply transverse field as quantum fluctuation. There exists a ferromagnetic correlation in each sublattice. The sublattice correlation at zero temperature is enlarged due to transverse field. The quantum fluctuation enhances the solid order at zero temperatures…
Effects of interlayer coupling and spatial anisotropy on spin-wave excitation spectra of a three-dimensional spatially anisotropic, frustrated spin-$\half$ Heisenberg antiferromagnet (HAFM) is investigated for the two ordered phases using second-order spin-wave expansion. We show that the second-order corrections to the spin-wave energies are significant and find that the energy spectra of the three-dimensional HAFM shares similar qualitative features with the energy spectra of the two-dimensional HAFM on a square lattice. We also discuss the features that can provide experimental measures for…
Spin crossover materials contain metal ions that can access two spin-states: one low-spin (LS), the other high-spin (HS). We propose that frustrated elastic interactions can give rise to spin-state ices -- phases of matter without long-range order, characterized by a local constraint or `ice rule'. The low-energy physics of spin-state ices is described by an emergent divergence-less gauge field with a gap to topological excitations that are deconfined quasi-particles with spin fractionalized midway between the spins of the LS and HS states.
We study the critical behavior of frustrated spin models with noncollinear order, including stacked triangular antiferromagnets and helimagnets. For this purpose we compute the field-theoretic expansions at fixed dimension to six loops and determine their large-order behavior. For the physically relevant cases of two and three components, we show the existence of a new stable fixed point that corresponds to the conjectured chiral universality class. This contradicts previous three-loop field-theoretical results but is in agreement with experiments.
We find that ground states of the quantum Heisenberg antiferromagnet on the geometrically frustrated pyrochlore checkerboard lattice are singlets and can be expressed in terms of positive matrices. The magnetization at zero external field vanishes for each frustrated tetrahedral unit separately and there is an upper bound of 1/8 in natural units on the susceptibility both for the ground state and at finite temperature. These results are the first exact ones in this field and generalize to some other lattices; the approach is also of interest for other spin systems.
We compute the chiral critical exponents for the chiral transition in frustrated two- and three-component spin systems with noncollinear order, such as stacked triangular antiferromagnets (STA). For this purpose, we calculate and analyze the six-loop field-theoretical expansion of the renormalization-group function associated with the chiral operator. The results are in satisfactory agreement with those obtained in the recent experiment on the XY STA CsMnBr_3 reported by V. P. Plakhty et al., Phys. Rev. Lett. 85, 3942 (2000), providing further support for the continuous nature of the chiral tr…
