We examine a possible spin Hall effect for localized spin systems with no charge degrees of freedom. In this scenario, a longitudinal magnetic field gradient induces a transverse spin current carried by spin wave excitations with an anomalous velocity which is associated with the Berry curvature raised by spin chirality, in analogy with anomalous Hall effects in itinerant electron systems. Our argument is based on a semiclassical equations of motion applicable to general spin systems. Also, a microscopic model of frustrated magnets which exhibits the anamalous spin Hall effect is presented.
In frustrated magnets the Dzyaloshinsky-Moriya interaction arising from spin-orbit coupling can induce a magnetic long-range order. Here, we report a theoretical prediction of thermal Hall effect in frustrated kagomé magnets such as KCr$_3$(OH)$_6$(SO4)$_2$ and KFe$_3$(OH)$_{6}$(SO$_{4}$)$_2$. The thermal Hall effects in these materials are induced by scalar spin chirality as opposed to DMI in previous studies. The scalar spin chirality originates from magnetic-field-induced chiral spin configuration due to non-coplanar spin textures, but in general it can be spontaneously developed as a macro…
We study TmB_4, a frustrated magnet on the Archimedean Shastry-Sutherland lattice, through magnetization and transport experiments. The lack of anisotropy in resistivity shows that TmB_4 is an electronically three-dimensional system. The magnetoresistance (MR) is hysteretic at low-temperature even though a corresponding hysteresis in magnetization is absent. The Hall resistivity shows unconventional anomalous Hall effect (AHE) and is linear above saturation despite a large MR. We propose that complex structures at magnetic domain walls may be responsible for the hysteretic MR and may also lead…
In a ferromagnet, the spin excitations are the well-studied magnons. In frustrated quantum magnets, long-range magnetic order fails to develop despite a large exchange coupling between the spins. In contrast to the magnons in conventional magnets, their spin excitations are poorly understood. Are they itinerant or localized? Here we show that the thermal Hall conductivity $κ_{xy}$ provides a powerful probe of spin excitations in the "quantum spin ice" pyrochlore Tb$_2$Ti$_2$O$_7$. The thermal Hall response is large even though the material is transparent. The Hall response arises from spin exc…
Geometrically frustrated magnets provide abundant opportunities for discovering complex spin textures, which sometimes yield unconventional electromagnetic responses in correlated electron systems. It is theoretically predicted that magnetic frustration may also promote a topologically nontrivial spin state, i.e., magnetic skyrmions, which are nanometric spin vortices. Empirically, however, skyrmions are essentially concomitant with noncentrosymmetric lattice structures or interfacial-symmetry-breaking heterostructures. Here, we report the emergence of a Bloch-type skyrmion state in the frustr…
We establish that the interplay of itinerant fermions with localized magnetic moments on a checkerboard lattice leads to magnetic flux-phases. For weak itineracy the flux-phase is coplanar and the electronic dispersion takes the shape of graphene-like Dirac fermions. Stronger itineracy drives the formation of a non-coplanar, chiral flux-phase, in which the Dirac fermions acquire a topological mass that is proportional to a ferromagnetic spin polarization. Consequently the system self-organizes into a ferromagnetic Quantum Anomalous Hall state in which the direction of its dissipationless edge-…
Recently, the observation of large thermal Hall conductivities in correlated insulators with no apparent broken symmetry have generated immense interest and debates on the underlying ground states. Here, considering frustrated magnets with bond-dependent interactions, which are realized in the so-called Kitaev materials, we theoretically demonstrate that a large thermal Hall conductivity can originate from a classical ground state without any magnetic order. We discover a novel liquid state of magnetic vortices, which are inhomogeneous spin textures embedded in the background of polarized spin…
A current of electrons traversing a landscape of localized spins possessing non-coplanar magnetic order gains a geometrical (Berry) phase which can lead to a Hall voltage independent of the spin-orbit coupling within the material--a geometrical Hall effect. We show that the highly-correlated metal UCu5 possesses an unusually large controllable geometrical Hall effect at T<1.2K due to its frustration-induced magnetic order. The magnitude of the Hall response exceeds 20% of the ν=1 quantum Hall effect per atomic layer, which translates into an effective magnetic field of several hundred Tesla ac…
In the conventional ferromagnetic systems, topological magnon bands and thermal Hall effect are due to the Dzyaloshinskii-Moriya interaction (DMI). In principle, however, the DMI is either negligible or it is not allowed by symmetry in some quantum magnets. Therefore, we expect that topological magnon features will not be present in those systems. In addition, quantum magnets on the triangular-lattice are not expected to possess topological features as the DMI or spin-chirality cancels out due to equal and opposite contributions from adjacent triangles. Here, however, we predict that the isomo…
We study the Hubbard model on the frustrated honeycomb lattice with nearest-neighbor $t_1$ and second nearest-neighbor hopping $t_2$, which is isomorphic to the bilayer triangle lattice, using the SU(2)-invariant slave boson theory. We show that the Coulomb interaction $U$ induces antiferromagnetic (AF) chiral spin-density wave ($χ$-SDW) order in a wide range of $κ=t_2/t_1$ where both the two-sublattice AF order at small $κ$ and the decoupled three-sublattice 120$^\circ$ order at large $κ$ are strongly frustrated, leading to three distinct phases with different anomalous Hall responses. We fin…
By revealing an underlying relation between the Dzyaloshinskii-Moriya interaction (DMI) and the scalar spin chirality, we develop the theory of magnon thermal Hall effects in antiferromagnetic systems. The dynamic fluctuation of the scalar chirality is shown to directly respond to the nontrivial topology of magnon bands. In materials such as the jarosites compounds KFe$_3$(OH)$_6$(SO$_4$)$_2$ and veseignite BaCu$_3$V$_2$O$_8$(OH)$_2$ in the presence of in-plane DMI, the time-reversal symmetry can be broken by the fluctuations of scalar chirality even in the case of coplanar $\mathbf{q}=0$ magn…
The anomalous Hall effect is investigated for ferromagnetic Fe3Sn2 single crystal with geometrically frustrated kagome bilayer of Fe. The scaling behavior between anomalous Hall resistivity rho_{xy}^{A} and longitudinal resistivity rho_{xx} is quadratic and further analysis implies that the AHE in Fe3Sn2 single crystal should be dominated by the intrinsic Karplus-Luttinger mechanism rather than extrinsic skew-scattering or side-jump mechanisms. Moreover, there is a sudden jump of anomalous Hall conductivity sigma_{xy}^{A} appearing at about 100 K where the spin-reorientation transition from th…
We study geometrical responses of magnons driven by a temperature gradient in frustrated spin systems. While Dzyaloshinskii-Moriya (DM) interactions are usually incorporated to obtain geometrically nontrivial magnon bands, here we investigate thermal Hall responses of magnons that do no rely on the DM interactions. Specifically, we focus on frustrated spin systems with sublattice degrees of freedom and show that a nonzero Berry curvature requires breaking of an effective $PT$ symmetry. According to this symmetry consideration, we study the $J_1$-$J_2$-$J_2^\prime$ Heisenberg models on a honeyc…
In this paper, we propose a method to understand the nature for the quantum disorder phase of the two-dimensional (2D) high spin frustrated model. The ground state and excitation properties of a fully frustrated 2D spin-1 model are studied based on a model whose groundstate can be found exactly. By analogy to the pseudo-potential approach in the fractional quantum Hall effect, we conclude that the ground states of the fully frustrated spin-1 model are doubly degenerate valance bond solid (VBS) states along the horizontal or vertical direction of the square lattice. We also find that the ground…
We report on the observation of a large topological Hall effect (THE) over a wide temperature region in a geometrically frustrated Fe3Sn2 magnet with a kagome-bilayer structure. We found that the magnitude of the THE resistivity increases with temperature and reaches -0.875 μΩ.cm at 380 K. Moreover, the critical magnetic fields with the change of THE are consistent with the magnetic structure transformation, which indicates that the real-space fictitious magnetic field is proportional to the formation of magnetic skyrmions in Fe3Sn2. The results strongly suggest that the large THE originates f…
In these lectures we sketch a rapid survey of recent theoretical advances in the study of frustrated quantum magnets with a special emphasis on two dimensional magnets.
As discussed in several chapters of this volume, frustration leads to unconventional (insulating) ground states. On the other hand, doped holes are known to have profound effects in Mott insulators. Therefore doped frustrated systems offer the prospect of novel phases with some of the most fascinating, challenging and exotic behavior. In addition, at commensurate electron fillings and in the presence of strong (screened) Coulomb repulsion, geometrical frustration can also manifests itself as an extensive degeneracy of the classical ground-state manifold providing profound similarities with the…
We present a unified approach to the problem of degeneracy lifting in geometrically frustrated magnets with and without an external field. The method treats fluctuations around a classical spin configuration in terms of a real-space perturbation expansion. We calculate two lowest-order contributions for the Heisenberg spin Hamiltonian and use them to study the magnetization processes of spin-$S$ triangular and kagomé antiferromagnets.
Thermal transport in topologically-ordered phases of matter provides valuable insights as it can detect the charge-neutral quasiparticles that would not directly couple to electromagnetic probes. An important example is edge heat transport of Majorana fermions in a chiral spin liquid, which leads to a half-quantized thermal Hall conductivity. This signature is precisely what has recently been measured in $α$-RuCl$_3$ under external magnetic fields. The plateau-like behavior of the half-quantized thermal Hall conductivity as a function of external magnetic field, and the peculiar sign change de…
Giant anomalous Hall conductivity in frustrated magnet EuCo2Al9
Zhejiang University of Technology（浙江工业大学）；Zhejiang University（浙江大学）；Center for High Pressure Science & Technology Advanced Research（高压科学先进研究中心）；Renmin University of China（中国人民大学）；China Institute of Atomic Energy（中国原子能科学研究院）；Peking University（北京大学）；Huazhong University of Science and Technology（华中科技大学）；Songshan Lake Materials Laboratory（松山湖材料实验室）；Hefei National Laboratory（合肥国家实验室）；Nanjing University（南京大学）
Frustrated bilayer quantum magnets have attracted attention as flat-band spin systems with unconventional thermodynamic properties. We study the low-temperature properties of a frustrated honeycomb-lattice bilayer spin-$\frac{1}{2}$ isotropic ($XXX$) Heisenberg antiferromagnet in a magnetic field by means of an effective low-energy theory using exact diagonalizations and quantum Monte Carlo simulations. Our main focus is on the magnetization curve and the temperature dependence of the specific heat indicating a finite-temperature phase transition in high magnetic fields.
Frustrated systems exhibit remarkable properties due to the high degeneracy of their ground states. Stabilised by competing interactions, a rich diversity of typically nanometre-sized phase structures appear in polymer and colloidal systems, while the surface of ice pre-melts due to geometrically frustrated interactions. Atomic spin systems where magnetic interactions are frustrated by lattice geometry provide a fruitful source of emergent phenomena, such as fractionalised excitations analogous to magnetic monopoles. The degeneracy inherent in frustrated systems may prevail all the way down to…
We present a brief overview on some of the most significant achievements obtained by means of NMR and muSR techniques in highly frustrated magnets. First the basic quantities measured by the two techniques will be presented and their connection to the microscopic static and dynamical spin susceptibility recalled. Then the main findings will be outlined, starting from the most simple frustrated units, the molecular nanomagnets, to artificially built frustrated systems as $^{3}$He on graphite, to magnets with a macroscopically degenerate ground-state as the ones on a pyrochlore or kagomé lattice…
We argue that collinearly ordered states which exist in strongly frustrated spin systems for special rational values of the magnetization are stabilized by thermal as well as quantum fluctuations. These general predictions are tested by Monte Carlo simulations for the classical and Lanczos diagonalization for the S=1/2 frustrated square-lattice antiferromagnet.
The Faraday rotation and magneto-optical absorption spectral measurements were conducted to reveal the full-magnetization process and map out a magnetic phase diagram of a typical geometrical frustrated magnet, ZnCr2O4, by using the electromagnetic flux compression method in ultra-magnetic fields up to 600 T. A fully polarized ferromagnetic phase is observed in which the absorption spectra associated with an exciton-magnon-phonon transition disappears. Furthermore, prior to the fully polarized ferromagnetic phase above 410 T, we found a novel magnetic phase above 350 T followed by a canted 3:1…
Condensed matter exhibits a wide variety of exotic emergent phenomena such as the fractional quantum Hall effect and the low temperature cooperative behavior of highly frustrated magnets. I consider the classical Hamiltonian dynamics of spins of the latter phenomena using a method introduced by Dirac in the 1950s by assuming they are constrained to their lowest energy configurations as a simplifying measure. Focusing on the kagome antiferromagnet as an example, I find it is a gauge system with topological dynamics and non-locally connected edge states for certain open boundary conditions simil…
We propose to use the Contractor Renormalization (CORE) technique in order to derive effective models for quantum magnets in a magnetic field. CORE is a powerful non-perturbative technique that can reduce the complexity of a given microscopic model by focusing on the low-energy part. We provide a detailed analysis of frustrated spin ladders which have been widely studied in the past: in particular, we discuss how to choose the building block and emphasize the use of their reduced density matrix. With a good choice of basis, CORE is able to reproduce the existence or not of magnetization platea…
Frustrated magnets in high magnetic field have a long history of offering beautiful surprises to the patient investigator. Here we present the results of extensive classical Monte Carlo simulations of a variety of models of two dimensional magnets in magnetic field, together with complementary spin wave analysis. Striking results include (i) a massively enhanced magnetocaloric effect in antiferromagnets bordering on ferromagnetic order, (ii) a route to an $m=1/3$ magnetization plateau on a square lattice, and (iii) a cascade of phase transitions in a simple model of AgNiO$_2$.
The effect of site dilution by non magnetic impurities on the susceptibility of geometrically frustrated antiferromagnets (kagome and pyrochlore lattices) is discussed in the framework of the Generalized Constant Coupling model, for both classical and quantum Heisenberg spins. For the classical diluted pyrochlore lattice, excellent agreement is found when compared with Monte Carlo data. Results for the quantum case are also presented and discussed.
Ultrasound and magnetization studies of bond-frustrated ZnCr2S4 spinel are performed in static magnetic fields up to 18 T and in pulsed fields up to 62 T. At temperatures below the antiferromagnetic transition at T_N1 14 K the sound velocity as function of magnetic field reveals a sequence of steps followed by plateaus indicating a succession of crystallographic structures with constant stiffness. At the same time, the magnetization evolves continuously with field up to full magnetic polarization without any plateaus in contrast to geometrically frustrated chromium oxide spinels. The observed …
The applied magnetic field and temperature phase diagram of the archetypal frustrated magnet, Gd3Ga5O12, has been reinvestigated using single crystal magnetometry and polarised neutron diffraction. The updated phase diagram is substantially more complicated than previously reported and can be understood in terms of competing interactions with loops of spins, trimers and decagons, in addition to competition and interplay between antiferromagnetic, incommensurate and ferromagnetic order. Several additional distinct phase boundaries are presented. The phase diagram centers around a multiphase con…
Time-domain magneto-THz spectroscopy is utilized to study the frustrated magnet averievite Cu$_{5-x}$Zn$_x$V$_2$O$_{10}$(CsCl). Pronounced THz resonances are observed in unsubstituted samples ($x=0$) when cooling below the onset of short-range magnetic correlations. The influence of external magnetic effects confirms the magnetic origin of these resonances. Increasing Zn substitution suppresses the resonances, as frustration effects dominate, reflecting the non-magnetic phases for $x> 0.25$ compounds. The temperature evolution of the THz spectra is complemented with electron spin resonance spe…
Two geometrically frustrated pyrochlore stannates, undergoing long range magnetic order below 1K, were investigated at very low temperature. Anomalies in the behaviour of hyperfine quantities are found, by 155Gd Mossbauer spectroscopy in Gd2Sn2O7 and by low temperature specific heat measurements in Tb2Sn2O7. They are interpreted in terms of fluctuations of the correlated Gd or Tb spins, using a model two-level system (the nuclear spins) submitted to a randomly fluctuating (hyperfine) field.
The dynamics of a mobile hole in two-dimensional frustrated quantum magnets is investigated by exact diagonalization techniques. Our results provide evidence for spin-charge separation upon doping the kagome lattice, a prototype of a spin liquid. In contrast, in the checkerboard lattice, a symmetry broken Valence Bond Crystal, a small quasi-particle peak is seen for some crystal momenta, a finding interpreted as a restoration of weak holon-spinon confinement.
At low temperatures, weakly coupled spin chains develop a magnetic order that reflects the character of gapless spin fluctuations along the chains. Using nuclear magnetic resonance, we identify and characterize two ordered states in the gapless region of the antiferromagnetic, Ising-like spin-chain system BaCo2V2O8, both arising from the incommensurate fluctuations along the chains. They correspond to the columnar and ferromagnetic ordered states of the frustrated J1-J2 spin model on a square lattice, where the spins are encoded in original spin chains. As a result of field-dependent incommens…
Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung by the infamous "sign problem." Here we exploit the fact that the sign problem is basis-dependent. Recent studies have shown that passing to a dimer (two-site) basis eliminates the sign problem completely for a fully frustrated spin model on the two-leg ladder. We generalize this result to all partially frustrated two-leg spin-1/2 ladders, meaning those whe…
The spin-lattice coupling plays an important role in strongly frustrated magnets. In ZnCr$_2$O$_4$, an excellent realization of the Heisenberg antiferromagnet on the ``pyrochlore'' network, a lattice distortion relieves the geometrical frustration through a spin-Peierls-like phase transition at $T_c = 12.5$ K. Conversely, spin correlations strongly influence the elastic properties of a frustrated magnet. By using infrared spectroscopy and published data on magnetic specific heat, we demonstrate that the frequency of an optical phonon triplet in ZnCr$_2$O$_4$ tracks the nearest-neighbor spin co…
We show that correlated hopping of triplets, which is often the dominant source of kinetic energy in dimer-based frustrated quantum magnets, produces a remarkably strong tendency to form supersolid phases in a magnetic field. These phases are characterized by simultaneous modulation and ordering of the longitudinal and transverse magnetization respectively. Using Quantum Monte Carlo and a semiclassical approach for an effective hard-core boson model with nearest-neighbor repulsion on a square lattice, we prove in particular that a supersolid phase can exist even if the repulsion is not strong …
The very interesting magnetic properties of frustrated magnetic molecules are often hardly accessible due to the prohibitive size of the related Hilbert spaces. The finite-temperature Lanczos method is able to treat spin systems for Hilbert space sizes up to 10^9. Here we first demonstrate for exactly solvable systems that the method is indeed accurate. Then we discuss the thermal properties of one of the biggest magnetic molecules synthesized to date, the icosidodecahedron with antiferromagnetically coupled spins of s=1/2. We show how genuine quantum features such as the magnetization plateau…
We develop a general framework, which combines exact diagonalization in small clusters with a density matrix variational principle, to study frustrated magnets at finite temperature. This thermodynamic hierarchical mean-field technique is used to determine the phase diagram and magnetization process of the three-dimensional spin-1/2 $J_1$-$J_2$ antiferromagnet on a stacked square lattice. Its non-magnetic phase exhibits a thermal crossover from a quantum to a classical paramagnet at a temperature $T=T_0$ which can be extracted from thermodynamic measurements. At low temperature an applied magn…
Above 40K, the magnetic susceptibility of the heavy Fermion spinel LiV2O4 has many features in common with those of geometrically frustrated magnetic insulators, while its room temperature resistivity comfortably exceeds the Mott-Regel limit. This suggests that local magnetic moments, and the underlying geometry of the pyrochlore lattice, play an important role in determining its magnetic properties. We extend a recently introduced tetragonal mean field theory for insulating pyrochlore antiferromagnets to the case where individual tetrahedra contain spins of different lengths, and use this as …
We discuss theoretically frustrated Heisenberg spiral magnets in magnetic field $\bf H$. We demonstrate that small anisotropic spin interactions (single-ion biaxial anisotropy or dipolar forces) select the plane in which spins rotate (spiral plane) and can lead to the spiral plane flop upon in-plane field increasing. Expressions for the critical fields $H_{flop}$ are derived. It is shown that measuring of $H_{flop}$ is an efficient and simple method of quantifying the anisotropy in the system (as the measurement of spin-flop fields in collinear magnets with axial anisotropy). Corresponding rec…
We measure a sequence of quantum Hall-like plateaux at 1/q: 9 >= q >= 2 and p/q = 2/9 fractions in the magnetisation with increasing magnetic field in the geometrically frustrated spin system SrCu2(BO3)2. We find that the entire observed sequence of plateaux is reproduced by solving the Hofstadter problem on the system lattice when short-range repulsive interactions are included, thus providing a sterling demonstration of bosons confined by a magnetic and lattice potential mimicking fermions in the extreme quantum limit.
We present the results of the magnetization and dielectric constant measurements on untwinned single crystal samples of the frustrated S=1/2 chain cuprate LiCu_2O_2. Novel magnetic phase transitions were observed. A spin flop transition of the spiral spin plane was observed for the field orientations H||a,b. The second magnetic transition was observed at H~15 T for all three principal field directions. This high field magnetic phase is discussed as a collinear spin-modulated phase which is expected for an S=1/2 nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic chain sy…
Frustrated spin ladders show magnetization plateaux depending on the rung-exchange interaction and frustration defined by the ratio of first and second neighbor exchange interactions in each chain. This paper is the first report on its magnetic phase diagram. Using the variational matrix-product state method, we accurately determine phase boundaries. Several kinds of magnetization plateaux are induced by the frustration and the strong correlation among quasi-particles on a lattice. The appropriate description of quasi-particles and their relevant interactions are changed by a magnetic field. W…
We report a study of the geometrically frustrated magnetic material Tb2Sn2O7 by the positive muon spin relaxation technique. No signature of a static magnetically ordered state is detected while neutron magnetic reflections are observed in agreement with a published report. This is explained by the dynamical nature of the ground state of Tb2Sn2O7: the Tb3+ magnetic moment characteristic fluctuation time is ~ 10^{-10} s. The strong effect of the magnetic field on the muon spin-lattice relaxation rate at low fields indicates a large field-induced increase of the magnetic density of states of the…
We explore the magnetic phases in a Kondo lattice model on the geometrically frustrated Shastry-Sutherland lattice at metallic electron densities, searching for noncollinear and noncoplanar spin textures. Motivated by experimental observations in many rare-earth-based frustrated metallic magnets, we treat the local moments as classical spins and set the coupling between the itinerant electrons and local moments as the largest energy scale in the problem. Our results show that a noncollinear flux state is stabilized over an extended range of Hamiltonian parameters. These spin states can be quen…
Magnetization plateaux emerging in quantum spin systems due to spontaneously breaking of translational symmetry have been reported both theoretically and experimentally. The broken symmetry can induce reconstruction of elementary excitations such as Goldstone and Higgs modes, whereas its microscopic mechanism and reconstructed quasi-particle in magnetization-plateau phases have remained unclear so far. Here we theoretically study magnetic excitations in the magnetization-plateau phases of a frustrated spin ladder by using dynamical density-matrix renormalization-group method. Additionally, ana…
We report the $\mathbf{H}-T$ phase diagram of $S=1/2$ strongly frustrated anisotropic spin chain material linarite PbCuSO$_4$(OH)$_2$ in tilted magnetic fields up to 10 T and temperatures down to 0.2 K. By means of torque magnetometry we investigate the phase diagram evolution as the magnetic field undergoes rotation in $\mathbf{ba}^{\ast}$ and $\mathbf{bc}$ planes. The key finding is the robustness of the high field spin density wave-like phase, which may persist even as the external field goes orthogonal to the chain direction $\mathbf{b}$. In contrast, the intermediate collinear antiferroma…
We introduce a Quantum Monte Carlo (QMC) method which efficiently simulates in a sign-problem-free way a broad class of frustrated $S=1/2$ models with competing antiferromagnetic interactions. Our scheme uses the basis of total spin eigenstates of clusters of spins to avoid the severe sign problem faced by other QMC methods. We also flag important limitations of the new method, and comment on possibilities for further progress.
Magnetic field effects on the one-dimensional frustrated ferromagnetic chain are studied by means of effective field theory approaches in combination with numerical calculations utilizing Lanczos diagonalization and the density matrix renormalization group method. The nature of the ground state is shown to change from a spin-density-wave region to a nematic-like one upon approaching the saturation magnetization. The excitation spectrum is analyzed and the behavior of the single spin-flip excitation gap is studied in detail, including the emergent finite-size corrections.
The magnetization curve in a frustrated two-leg spin-ladder system is theoretically studied using both analytical and numerical methods. This spin system is mapped onto a hard-core boson system, which is composed of bond-operators describing the triplon excitation. By the analytical method using the mean-field theory on the bond-operators, we show that cusp singularities emerge in the magnetization curve as a function of a magnetic field due to the strong frustration. This originates from a change of number of Fermi points in the bosonic dispersion relation with the applied field. It is analog…
We calculate the low-temperature thermodynamic quantities (magnetization, correlation functions, transverse and longitudinal correlation lengths, spin susceptibility, and specific heat) of the frustrated one-dimensional spin-half J1-J2 Heisenberg ferromagnet, i.e. for J2< 0.25|J1|, in an external magnetic field using a second-order Green-function formalism and full diagonalization of finite systems. We determine power-law relations for the field dependence of the position and the height of the maximum of the uniform susceptibility. Considering the specific heat at low magnetic fields, two maxi…
Using muon-spin-relaxation measurements we show that the pyrochlore compound Gd2Ti2O7, in its magnetically orderered phase below ~ 1 K, displays persistent spin dynamics down to temperatures as low as 20 mK. The characteristics of the induced muon relaxation can be accounted for by a scattering process involving two magnetic excitations, with a density of states characterized by an upturn at low energy and a small gap depending linearly on the temperature. We propose that such a density of states is a generic feature of geometrically frustrated magnetic materials.
We study the stability of some strongly frustrated antiferromagnetic spin lattices in high magnetic fields against lattice distortions. In particular, we consider a spin-s anisotropic Heisenberg antiferromagnet on the square-kagomé and kagomé lattices. The independent localized magnons embedded in a ferromagnetic environment, which are the ground state at the saturation field, imply lattice instabilities for appropriate lattice distortions fitting to the structure of the localized magnons. We discuss in detail the scenario of this spin-Peierls instability in high magnetic fields which essentia…
We study the dynamical response of frustrated, quasi-one-dimensional spin-1/2 Heisenberg antiferromagnets at finite temperatures. We allow for the presence of a Dzyaloshinskii-Moriya interaction. We concentrate on a model of weakly coupled planes of anisotropic triangular lattices. Combining exact results for the dynamical response of one dimensional Heisenberg chains with a Random Phase Approximation (RPA) in the frustrated interchain couplings, we calculate the dynamical susceptibility in the disordered phase. We investigate the instability of the disordered phase to the formation of collect…
Transverse field Ising model is a common model in quantum magnetism and is often illustrated as an example for quantum phase transition. Its physical origin in quantum magnets, however, is actually not quite well-understood. The quantum mechanical properties of this model on frustrated systems are not well-understood either. We here clarify the physical origin, both extrinsic one and intrinsic one, for the transverse field of the quantum Ising model, and then explain the quantum effects in the Kagome system. We discuss the quantum plaquette order and the quantum phase transition out of this or…
