We consider magnon excitations in the spin-glass phase of geometrically frustrated antiferromagnets with weak exchange disorder, focussing on the nearest-neighbour pyrochlore-lattice Heisenberg model at large spin. The low-energy degrees of freedom in this system are represented by three copies of a U(1) emergent gauge field, related by global spin-rotation symmetry. We show that the Goldstone modes associated with spin-glass order are excitations of these gauge fields, and that the standard theory of Goldstone modes in Heisenberg spin glasses (due to Halperin and Saslow) must be modified in this setting.
In systems with competing interactions, continuous degeneracies can appear which are accidental, in that they are not related to any symmetry of the Hamiltonian. Accordingly, the pseudo-Goldstone modes associated with these degeneracies are also unprotected. Indeed, through a process known as "order-by-quantum-disorder", quantum zero-point fluctuations can lift the degeneracy and induce a gap for these modes. We show that this gap can be exactly computed at leading order in $1/S$ in spin-wave theory from the mean curvature of the classical and quantum zero-point energies - without the need to …
Low-energy spin excitations in any long-range ordered magnetic system in the absence of magnetocrystalline anisotropy are gapless Goldstone modes emanating from the ordering wave vectors. In helimagnets, these modes hybridize into the so-called helimagnon excitations. Here we employ neutron spectroscopy supported by theoretical calculations to investigate the magnetic excitation spectrum of the isotropic Heisenberg helimagnet ZnCr2Se4 with a cubic spinel structure, in which spin-3/2 magnetic Cr3+ ions are arranged in a geometrically frustrated pyrochlore sublattice. Apart from the conventional…
The magnetothermodynamics of strongly frustrated classical Heisenberg antiferromagnets on kagome, garnet, and pyrochlore lattices is examined. The field induced adiabatic temperature change (dT/dH)_S is significantly larger for such systems compared to ordinary non-frustrated magnets and also exceeds the cooling rate of an ideal paramagnet in a wide range of fields. An enhancement of the magnetocaloric effect is related to presence of a macroscopic number of soft modes in frustrated magnets below the saturation field. Theoretical predictions are confirmed with extensive Monte Carlo simulations…
We study excitations in weakly interacting pairs of quantum spin ladders coupled through geometrically frustrated bonds. The ground state is a disordered spin liquid, that at high fields is replaced by an ordered chiral helimagnetic phase. The spectra observed by high-field inelastic neutron scattering experiments on the prototype compound Sul-Cu2Cl4 are qualitatively different from those in the previously studied frustration-free spin liquids. Beyond the critical field Hc=3.7 T, the soft mode that drives the quantum phase transition spawns two separate excitations: a gapless Goldstone mode an…
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…
Starting from the archetypical geometrically frustrated magnetic objects -- equilateral triangle and tetrahedron -- we consider an imaginary object: a multidimensional tetrahedron with spins $1/2$ in the each vertex and equal Heisenberg magnetic exchange along each edge. Many-particle case is obtained by setting dimensionality $d$ to high numbers, hence providing likely the most geometrically frustrated magnetic system ever possible. This problem has an exact solution for each $d$, obtained by simple student-level approach. As a result, this imaginary object clearly demonstrates at $d\to{}\inf…
Motivated by the properties of the iron chalcogenides, we study the phase diagram of a generalized Heisenberg model with frustrated bilinear-biquadratic interactions on a square lattice. We identify zero-temperature phases with antiferroquadrupolar and Ising-nematic orders. The effects of quantum fluctuations and interlayer couplings are analyzed. We propose the Ising-nematic order as underlying the structural phase transition observed in the normal state of FeSe, and discuss the role of the Goldstone modes of the antiferroquadrupolar order for the dipolar magnetic fluctuations in this system.…
Kane-Lubensky phonons in Maxwell lattice frustrated Mott insulators
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料科学中心）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；Beijing Key Laboratory of Quantum Devices（北京量子器件重点实验室）
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 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 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.
Low-temperature magnetization curves and thermodynamics of a frustrated spin-1/2 Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are investigated in a highly frustrated parameter region, where localized many-magnon eigenstates provide the most dominant contribution to magnetothermodynamics. Low-energy states of the highly frustrated spin-1/2 Heisenberg triangular bilayer can be accordingly found from a mapping correspondence with an effective triangular-lattice spin-1/2 Ising model in a field. …
We use density matrix renormalization group to study the first-order quantum phase transition induced by a magnetic field $h$ in a frustrated ferrimagnetic chain. The magnetization ($m$) curve as a function of $h$ presents a macroscopic jump and the energy curve as a function of $m$ has two global minima. We characterize the two competing phases and study the phase-separated states in the coexistence region. Also, we observe that the transition is accompanied by an increase in the number of itinerant singlet pairs between sites in the unit cells of the chain. Finally, we identify the critical …
Magnetization, entropy and magnetocaloric properties of various geometrically frustrated tetrahedra-based Ising antiferromagnetic nanoclusters with corner-, edge-, and face-sharing topologies are studied by exact enumeration. It is found that the studied properties strongly depend on the nanocluster topology and can be very different from those of a single tetrahedron as well as the pyrochlore lattice formed by an infinite number of corner-sharing tetrahedra. From the magnetocaloric point of view an important difference from the latter two systems is the absence of the ground-state zero-magnet…
Many-body systems subject to a high-frequency drive can show intriguing thermalization behavior. Prior to heating to a featureless infinite-temperature state, these systems can spend an exponentially long time in prethermal phases characterized by various kinds of order. Here, we uncover the rich non-equilibrium phase diagram of a driven frustrated two-dimensional Ising magnet with competing short-range ferromagnetic and long-range dipolar interactions. We show that the ordered stripe and nematic phases, which appear in equilibrium as a function of temperature, underpin subsequent prethermal p…
We study, at T=0, the anomalies in the magnetization curve of the S=1 two-leg ladder with frustrated interactions. We focus mainly on the existence of the $M=\Ms/2$ plateau, where $\Ms$ is the saturation magnetization. We use analytical methods (degenerate perturbation theory and non-Abelian bosonization) as well as numerical methods (level spectroscopy and density matrix renormalization group), which lead to the consistent conclusion with each other. We also touch on the $M=\Ms/4$ and $M=(3/4)\Ms$ plateaux and cusps.
The low-energy physics of three-leg frustrated antiferromagnetic spin-S tubes in the vicinity of the upper critical field are studied. Utilizing the effective field theory based on the spin-wave approximation, we argue that in the intermediate-interchain-coupling regime, the ground state exhibits a vector chiral order or an inhomogeneous magnetization for the interchain (rung) direction and the low-energy excitations are described by a one-component Tomonaga-Luttinger liquid (TLL). In both chiral and inhomogeneous phases, the Z_2 parity symmetry along the rung direction is spontaneously broken…
We present the phase diagram of the frustrated ferromagnetic S=1/2 Heisenberg J_1-J_2 chain in a magnetic field, obtained by large scale exact diagonalizations and density matrix renormalization group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin-multipolar Luttinger liquid phases up to hexadecupolar kind are found. We provide numerical evidence for a locking mechanism, which can drive spiral states towards spin-multipolar phases, such as quadrupolar or octupolar phases. Our results also shed light on previously discovered spin-multipolar phases in …
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…
The magnetic properties of the antiferromagnetic spin ladder with the next-nearest neighbor interaction, particularly under external field, are investigated by the exact diagonalization of the finite clusters and size scaling techniques. It is found that there exist two phases, the rung-dimer and rung-triplet phases, not only in the nonmagnetic ground state but also magnetized one, where the phase boundary has a small magnetization dependence. Only in the former phase, the magnetization curve is revealed to have a possible plateau at half the saturation moment, with a sufficient frustration.
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…
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.
Geometrically frustrated magnetic molecules have attracted a lot of interest in the field of molecular magnetism as well as frustrated Heisenberg antiferromagnets. In this article we demonstrate how an approximate diagonalization scheme can be used in order to obtain thermodynamic and spectroscopic information about frustrated magnetic molecules. To this end we theoretically investigate an antiferromagnetically coupled spin system with cuboctahedral structure modeled by an isotropic Heisenberg Hamiltonian.
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.
The inability of systems of interacting objects to satisfy all constraints simultaneously leads to frustration. A particularly important consequence of frustration is the ability to access certain protected parts of a system without disturbing the others. For magnets such "protectorates" have been inferred from theory and from neutron scattering, but their practical consequences have been unclear. We show that a magnetic analogue of optical hole-burning can address these protected spin clusters in a well-known, geometrically frustrated Heisenberg system, gadolinium gallium garnet. Our measurem…
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…
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$_2$.
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…
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 …
We study the electron dynamics in magnetic conductors with frustrated interactions dominated by isotropic exchange. We present a transport theory for itinerant carriers built upon the (single-band) doped Hubbard model and the slave-boson formalism, which incorporates the spin-exchange with the magnetically frustrated background into the representation of electron operators in a clear and controllable way. We also formulate hydrodynamic equations for the itinerant charge and spin degrees of freedom, whose currents contain new contributions that depend on the spatiotemporal variations of the ord…
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…
Frustrated magnetism plays a central role in the phenomenology of exotic quantum states. However, because the magnetic structures of frustrated systems are aperiodic, there has always been the problem that they cannot be determined using traditional crystallographic techniques. Here we show that the magnetic component of powder neutron scattering data is actually sufficiently information-rich to drive magnetic structure solution for frustrated systems, including spin ices, spin liquids, and molecular magnets. Consequently, single-crystal samples are not prerequisite for detailed characterisati…
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…
Quantum fluctuations become particularly relevant in highly frustrated quantum magnets and can lead to new states of matter. We provide a simple and robust scenario for inducing magnetic vortex crystals in frustrated Mott insulators. By considering a quantum paramagnet that has a gapped spectrum with six-fold degenerate low energy modes, we study the magnetic field induced condensation of these modes. We use a dilute gas approximation to demonstrate that a plethora of multi-$\mathbf{Q}$ condensates are stabilized for different combinations of exchange interactions. This rich quantum phase diag…
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…
We discuss theoretically a frustrated Heisenberg antiferromagnet in magnetic field close to the saturation one. It is demonstrated that a small biaxial anisotropy and/or the magnetic dipolar interaction produce a delicate balance between phases with a commensurate canted, incommensurate helical (conical), and fan spin orderings. As a result, different sequences of phase transitions are realized depending on values of these small anisotropic interactions. We derive analytical expressions for critical fields and ground-state energies of the phases which are in a quantitative agreement with our a…
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 consider the spin-1/2 antiferromagnetic Heisenberg model on two one-dimensional frustrated lattices, double-tetrahedral chain and octahedral chain, with almost dispersionless (flat) lowest magnon band in a strong magnetic field. Using the localized magnons picture, we construct an effective description of the one-dimensional chains with triangle and square traps within the strong coupling approximation. We perform extensive exact diagonalization and density matrix renormalization group calculations to check the validity of the obtained effective Hamiltonians by comparison with the initial m…
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 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.
We clarify the conditions for the emergence of multiple-${\bf Q}$ structures out of lattice and easy-axis spin anisotropy in frustrated magnets. By considering magnets whose exchange interaction has multiple global minima in momentum space, we find that both types of anisotropy stabilize triple-${\bf Q}$ orderings. Moderate anisotropy leads to a magnetic field-induced skyrmion crystal, which evolves into a bubble crystal for increasing spatial or spin anisotropy. The bubble crystal exhibits a quasi-continuous (devil's staircase) temperature dependent ordering wave-vector, characteristic of the…
