Pronounced 2/3 magnetization plateau in a frustrated $S$ = 1 isolated spin-triangle compound: Interplay between Heisenberg and biquadratic exchange interactions
S. Chattopadhyay, B. Lenz, S. Kanungo, Sushila, S. K. Panda, S. Biermann, W. Schnelle, K. Manna, R. Kataria, M. Uhlarz, Y. Skourski, S. A. Zvyagin, A. Ponomaryo… 展开作者
S. Chattopadhyay, B. Lenz, S. Kanungo, Sushila, S. K. Panda, S. Biermann, W. Schnelle, K. Manna, R. Kataria, M. Uhlarz, Y. Skourski, S. A. Zvyagin, A. Ponomaryov, T. Herrmannsdörfer, R. Patra, J. Wosnitza
We report the synthesis and characterization of a new quantum magnet [2-[Bis(2-hydroxybenzyl)aminomethyl]pyridine]Ni(II)-trimer (BHAP-Ni3) in single-crystalline form. Our combined experimental and theoretical investigations reveal an exotic spin state that stabilizes a robust 2/3 magnetization plateau between 7 and 20 T in an external magnetic field. AC-susceptibility measurements show the absence of any magnetic order/glassy state down to 60 mK. The magnetic ground state is disordered and specific-heat measurements reveal the gapped nature of the spin excitations. Most interestingly, our theoretical modeling suggests that the 2/3 magnetization plateau emerges due to the interplay between antiferromagnetic Heisenberg and biquadratic exchange interactions within nearly isolated spin $S$ = 1 triangles.
Quantum corrections of the biquadratic interaction in the 1D spin-1/2 frustrated ferromagnetic Heisenberg model are studied. The biquadratic interaction for spin-1/2 chains is eliminated and transformed to the quadratic interaction. Doing a numerical experiment, new insight as to how the classical phases get modified on the inclusion of quantum fluctuations is provided. Observed results suggest the existence of an intermediate region in the ground state phase diagram of the frustrated ferromagnetic spin-1/2 chains with combination of dimer and chiral orders. In addition, from the quantum entan…
The ground state phase diagram is determined for the frustrated classical Heisenberg chain with added nearest-neighbor biquadratic exchange interactions. There appear ferromagnetic, incommensurate-spiral, and up-up-down-down phases; a lock-in transition occurs at the spiral boundary. The model contains an isotropic version of the ANNNI model; it is also closely related to a model proposed for some manganites. The Luttinger-Tisza method is not obviously useful due to the non-linear weak-constraint problem; however the ground state is obtained analytically by the exact cluster method of Lyons an…
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.…
Elucidating the nature of spin excitations is important to understanding the mechanism of superconductivity in the iron pnictides. Motivated by recent inelastic neutron scattering measurements in the nearly 100% detwinned BaFe$_{2}$As$_{2}$, we study the spin dynamics of an $S=1$ frustrated bilinear-biquadratic Heisenberg model in the antiferromagnetic phase with wavevector $(π,0)$. The biquadratic interactions are treated in a dynamical way using a flavor-wave theory in an $SU(3)$ representation. Besides the magnon (dipolar) excitations, the biquadratic interactions give rise to quadrupolar e…
In this work, we study a biquadratic Heisenberg model with coupled orbital degree of freedom using Monte Carlo simulation in order to investigate the phase transitions in iron-based superconductors. The antiferro-quadrupolar state, which may be related to the magnetism of FeSe [Phys. Rev. Lett. 115, 116401 (2015)], is stabilized by the anisotropic biquadratic interaction induced by a ferro-orbital-ordered state. It is revealed that the orbital and nematic transitions occur at the same temperature for all the cases, supporting the mechanism of the orbital-driven nematicity as revealed in most r…
The classical bilinear-biquadratic nearest-neighbor Heisenberg antiferromagnet on the pyrochlore lattice does not exhibit conventional Neel-type magnetic order at any temperature or magnetic field. Instead spin correlations decay algebraically over length scales r ~ \sqrt{T}, behavior characteristic of a Coulomb phase arising from a strong local constraint. Despite this, its thermodynamic properties remain largely unchanged if Neel order is restored by the addition of a degeneracy-lifting perturbation, e.g., further neighbor interactions. Here we show how these apparent contradictions can be r…
Recent neutron scattering studies revealed the three dimensional character of the magnetism in the iron pnictides and a strong anisotropy between the exchange perpendicular and parallel to the spin stripes. We extend studies of the J1-J2-Jc Heisenberg model with S = 1 using self-consistent spin-wave theory. A discussion of two scenarios for the instability of the columnar phase is provided. The relevance of a biquadratic exchange term between in-plane nearest neighbors is discussed. We introduce mean-field decouplings for biquadratic terms using the Dyson-Maleev and the Schwinger boson represe…
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.
We investigate the magnetic properties of Ru$_{2}$Mn$Z$ ($Z$ = Sn, Sb, Ge, Si) chemically ordered full Heusler compounds for zero as well as finite temperatures. Based on first principles calculations we derive the interatomic isotropic bilinear and biquadratic couplings between Mn atoms from the paramagnetic state. We find frustrated isotropic couplings for all compounds and in case of $Z$ = Si and Sb a nearest-neighbor biquadratic coupling that favors perpendicular alignment between the Mn spins. By using an extended classical Heisenberg model in combination with spin dynamics simulations we…
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 dimer-plaquette chain undergoes a first order transition driven by frustration to an orthogonal dimer ground state. We analyze the magnetization curve in this orthogonal dimer regime. Besides of the recently found magnetization plateaus at m=1/4 and the m=1/2 we find an infinite sequence of plateaus between m=1/4 and m=1/2. These additional plateaus belong to magnetizations m(n)=n/(2n+2), where n is a positive integer number.
We report on negative thermal expansion (NTE) in the high-field, half-magnetization plateau phase of the frustrated magnetic insulator CdCr2O4. Using dilatometry, we precisely map the phase diagram at fields of up to 30T, and identify a strong NTE associated with the collinear half-magnetization plateau for B > 27T. The resulting phase diagram is compared with a microscopic theory for spin-lattice coupling, and the origin of the NTE is identified as a large negative change in magnetization with temperature, coming from a nearly-localised band of spin excitations in the plateau phase. These res…
The $S=2$ quantum spin chain with the single-ion anisotropy $D$ and the biquadratic exchange interaction $J_{\rm BQ}$ is investigated using the numerical diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that the intermediate-$D$ phase corresponding to the symmetry protected topological (SPT) phase appears in a wide region of the ground state phase diagram. We also obtain the phase diagram at the half of the saturation magnetization which includes the SPT plateau phase.
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…
The ground state phase diagram is determined exactly for the frustrated classical Heisenberg model plus nearest-neighbor biquadratic exchange interactions on a 2-dimensional lattice. A square- and a rhombic-symmetry version are considered. There appear ferromagnetic, incommensurate-spiral, "up-up-down-down" (uudd) and canted ferromagnetic states, a non-spiral coplanar state that is an ordered vortex lattice, plus a non-coplanar ordered state (a "conical vortex lattice"). In the rhombic case, which adds biquadratic terms to the Heisenberg model used widely for insulating manganites, the uudd st…
We analyze the zero temperature phase diagrams of the spin S quantum antiferromagnet on square and triangular lattices with competing nearest and next-nearest exchange interactions as well as biquadratic couplings. We approach the problem from the large S limit. Our primary focus is on determining the extent to which the existence and character of any quantum disordered phases can be inferred from this approach.
We present a numerical study of the magnetization process of frustrated quantum spin-S chains with S=1, 3/2, 2 as well as the classical limit. Using the exact diagonalization and density-matrix renormalization techniques, we provide evidence that a plateau at one third of the saturation magnetization exists in the magnetization curve of frustrated spin-S chains with S>1/2. Similar to the case of S=1/2, this plateau state breaks the translational symmetry of the Hamiltonian and realizes an up-up-down pattern in the spin component parallel to the external field. Our study further shows that this…
The magnetization process of the S=1/2 antiferromagnetic spin ladder at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value (m=1/2) in the presence of a sufficiently large next-nearest-neighbor exchange interaction to yield the frustration, when the rung coupling is larger than the leg one. The phase diagram at m=1/2 is given by the analysis based on the conformal invariance. The magnetization curves are also presented in several cases.
Using mean-field theory, exact diagonalizations and SU(3) flavour theory, we have precisely mapped out the phase diagram of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice in a magnetic field, with emphasis on the quadrupolar phases and their excitations. In particular, we show that ferroquadrupolar order can coexist with short-range helical magnetic order, and that the antiferroquadrupolar phase is characterized by a remarkable 2/3 magnetization plateau, in which one site per triangle retains quadrupolar order while the other two are polarized along the field. Implicat…
The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaux in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaux are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasi-spinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasi-spino…
Biquadratic {\it antisymmetric} exchange terms of the form $ - [C_{ij} e^α_{ij}({\bf s}_i\times{\bf s}_j)_z]^2$, where ${\bf e}_{ij}$ is the unit vector connecting sites $i$ and $j$ and $α= x,y$, due partially to magnetoelectric coupling effects, are shown to be responsible for the spin-flop helical phase in CuFeO$_2$ at low magnetic field and temperature. Usual biquadratic {\it symmetric} exchange, likely due to magnetoelastic coupling, is found to support the stability of axial magnetic states at higher fields in this nearly-Heisenberg like stacked triangular antiferromagnet. A model Hamilto…
We use a semiclassical large-$S$ expansion to study a plateau at $1/3$ saturation in the magnetization curve of a frustrated ferrimagnet on a spatially anisotropic kagomé lattice. The spins have both ferromagnetic and antiferromagnetic nearest-neighbor Heisenberg couplings, and a frustrating next-nearest-neighbor coupling in one lattice direction. The magnetization plateau appears at the classical level for a certain range of couplings, and quantum fluctuations significantly broaden it at both ends. Near the region of the phase diagram where the classical plateau destabilizes, we find an exoti…
We investigate a highly frustrated spin-1 model on the triangular lattice, with nearest- and next-nearest-neighbor antiferromagnetic $S\cdot S$ interactions and nearest-neighbor $(S\cdot S)^2$ interactions. Using the density matrix renormalization group (DMRG) technique, we find three magnetically ordered phases, namely 120$^\circ$ spiral order, stripe order, and tetrahedral order, as well as two spin nematic phases: ferroquadrupolar and antiferroquadrupolar. While our data could be consistent with a spin liquid phase between the 120$^\circ$ spiral and antiferroquadrupolar orders, the more lik…
Thermodynamic theory of square skyrmion lattice in tetragonal frustrated antiferromagnets
Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS)（复杂系统理论物理中心，基础科学研究院）；National Research University “Higher School of Economics”（国立高等经济大学）；The Faculty of Physics of St. Petersburg State University（圣彼得堡国立大学物理系）
The icosahedron has a ground state magnetization discontinuity in an external magnetic field when classical spins mounted on its vertices are coupled according to the antiferromagnetic Heisenberg model. This is so even if there is no magnetic anisotropy in the Hamiltonian. The discontinuity is a consequence of the frustrated nature of the interactions, which originates in the topology of the cluster. Here it is found that the addition of the next order isotropic spin exchange interaction term in the Hamiltonian, the biquadratic exchange interaction, significantly enriches the classical ground …
We study the ground state phase diagram of a frustrated spin-1/2 four-leg spin tube in an external magnetic field. We explore the parameter space of this model in the regime of all-antiferromagnetic exchange couplings by means of three different approaches: analysis of low-energy effective Hamiltonian (LEH), a Hartree variational approach (HVA) and density matrix renormalization group (DMRG) for finite clusters. We find that in the limit of weakly interacting plaquettes, low-energy singlet, triplet and quintuplet states play an important role in the formation of fractional magnetization platea…
We have found an unusual competition of two frustration mechanisms in the 2D quantum antiferromagnet Cs$_2$CoBr$_4$. The key actors are the alternation of single-ion planar anisotropy direction of the individual magnetic Co$^{2+}$ ions, and their arrangement in a distorted triangular lattice structure. In particular, the uniquely oriented Ising-type anisotropy emerges from the competition of easy-plane ones, and for a magnetic field applied along this axis one finds a cascade of five ordered phases at low temperatures. Two of these phases feature magnetization plateaux. The low-field one is su…
The magnetic phase diagram of a plaquette dimerized antiferromagnetic system is studied by using a combination of numerical and analytical techniques. For the strongly frustrated regime, series expansions and bond operators techniques are employed to analyze zero magnetization plateau, whereas low energy effective models are used to study the complete magnetization process. The interplay between frustration and dimerization gives rise to a rich plateaus structure that is captured by effective models and corroborated by numerical density matrix renormalization group simulations, in particular t…
A class of the symmetrically frustrated SU(N) models is constructed for quantum magnets based on the generators of SU(N) group. The total Hamiltonian lacks SU(N) symmtry. A mean field theory in the quasi-particle representation is developed for spin liquid states. Numerical solutions in two dimension indicate that the ground states are gapless and the quasi-particles are Dirac particles. The mechanism may be helpful in exploring the spin liquid phases in the spin-1 bilinear-biquadratic model and the spin-orbital model in higher dimensions.
We study a two-leg spin-1/2 ladder with isotropic exchanges and biquadratic interactions in the basic plaquettes. It is shown that for the extremely frustrated case, the system exhibits a self-organized phase separation. In some parameter regions, the singlet rungs form a Wigner-like lattice in the triplet-rung host. There are three types of elementary excitations in this modulation phase, i.e., the spinons in a triplet domain, the broken singlet rungs and the deformation of the Wigner-like lattice. The flux phase induced by an external magnetic field in the rung-dimerized phase is also discus…
Motivated by the ever-increasing experimental effort devoted to the properties of frustrated quantum magnets in a magnetic field, we present a careful and detailed theoretical analysis of a one-dimensional version of this problem, a frustrated ladder with a magnetization plateau at m=1/2. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly t…
The field induced magnetic phase transitions of Cs$_2$CuBr$_4$ were investigated by means of magnetization process and neutron scattering experiments. This system undergoes magnetic phase transition at Neél temperature $T_\mathrm{N}=1.4$ K at zero field, and exhibits the magnetization plateau at approximately one third of the saturation magnetization for the field directions $H\parallel b$ and $H\parallel c$. In the present study, additional symptom of the two-third magnetization plateau was found in the field derivative of the magnetization process. The magnetic structure was found to be inco…
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 reveal the significance of kinetic-driven multiple-spin interactions hidden in geometrically-frustrated Kondo lattice models. Carefully examining the perturbation in terms of the spin-charge coupling up to the fourth order, we find that a positive biquadratic interaction is critically enhanced and plays a crucial role on stabilizing a spin scalar chiral order near 1/4 filling in a triangular lattice case. This is a generalized Kohn anomaly, appearing only when the second-order perturbation is inefficient because of the degeneracy under frustration. The mechanism is potentially common to fru…
A large part of the interest in magnets with frustrated antiferromagnetic interactions comes from the many new phases found in applied magnetic field. In this Article, we explore some of the new phases which arise in a model with frustrated ferromagnetic interactions, the $J_1-J_2-J_3$ Heisenberg model on a square lattice. Using a combination of classical Monte-Carlo simulation and spin-wave theory, we uncover behaviour reminiscent of some widely-studied frustrated antiferromagnets, but with a number of new twists. We first demonstrate that, for a suitable choice of parameters, the phase diagr…
The antiferromagnetic Heisenberg model on a pyrochlore lattice under external magnetic field is studied by classical Monte Carlo simulation. The model includes bilinear and biquadratic interactions; the latter effectively describes the coupling to lattice distortions. The magnetization process shows a half-magnetization plateau at low temperatures, accompanied with strong suppression of the magnetic susceptibility. Temperature dependence of the plateau behavior is clarified. Finite-temperature phase diagram under the magnetic field is determined. The results are compared with recent experiment…
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.
The quasi-spin correlations in a frustrated quantum spin ladder with one-half magnetization are theoretically studied by using the density-matrix renormalization-group method and the quasi-spin transformation. In this model, the frustration induces a gapless-to-gapful phase transition with a strong rung coupling. The gapful state is observed as the one-half magnetization plateau in the magnetization curve. In the magnetization-plateau state, we find that the quasi-spin dimer has a large expectation value with long-ranged correlations. This result does not only comes in useful to clarify the ma…
Strong geometrical frustration in magnets leads to exotic states, such as spin liquids, spin supersolids and complex magnetic textures. SrCu2(BO3)2, a spin-1/2 Heisenberg antiferromagnet in the archetypical Shastry-Sutherland lattice, exhibits a rich spectrum of magnetization plateaus and stripe-like magnetic textures in applied fields. The structure of these plateaus is still highly controversial due to the intrinsic complexity associated with frustration and competing length scales. We reveal new magnetic textures in SrCu2(BO3)2 via magnetostriction and magnetocaloric measurements in fields …
Motivated by the recent inelastic neutron scattering (INS) measurements in the iron pnictides which show a strong anisotropy of spin excitations in directions perpendicular and parallel to the ordering wave-vector even above the magnetic transition temperature $T_N$, we study the frustrated Heisenberg model with a biquadratic spin-spin exchange interaction. Using the Dyson-Maleev (DM) representation, which proves appropriate for all temperature regimes, we find that the spin-spin dynamical structure factors are in excellent agreement with experiment, exhibiting breaking of the $C_4$ symmetry e…
We study the magnetic excitations on top of the plateaux states recently discovered in spin-Peierls systems in a magnetic field. We show by means of extensive density matrix renormalization group (DMRG) computations and an analytic approach that one single spin-flip on top of $M=1-\frac2N$ ($N=3,4,...$) plateau decays into $N$ elementary excitations each carrying a fraction $\frac1N$ of the spin. This fractionalization goes beyond the well-known decay of one magnon into two spinons taking place on top of the M=0 plateau. Concentrating on the $\frac13$ plateau (N=3) we unravel the microscopic s…
We investigate a simple model of a frustrated spin-1/2 Heisenberg chain coupled to adiabatic phonons under an external magnetic field. Using field theoretic methods complemented by extensive Density Matrix Renormalisation Group techniques generalized to include self-consistent lattice distortions, we show that magnetization plateaux at non-trivial rational values of the magnetization can be stabilized by the lattice coupling. We suggest that such a scenario could be relevant for some low dimensional frustrated spin-Peierls compounds.
We investigate properties of a spin-1 Heisenberg model with extended and biquadratic interactions, which captures crucial aspects of the low energy physics in FeSe. While we show that the model exhibits a rich phase diagram with four different magnetic ordering tendencies, we identify a parameter regime with strong competition between Nèel, staggered dimer, and stripe-like magnetic fluctuations, accounting for the physical properties of FeSe. Through the comparison of numerically evaluated spin and Raman response with experiments, we find evidence for enhanced magnetic frustration between Nèel…
By utilizing tensor-network-based methods, we investigate the zero- and finite-temperature properties of the spin-1/2 Heisenberg antiferromagnetic (HAF) model on an infinite Husimi lattice that contains 3/2 sites per triangle. The ground state of this model is found to possess vanishing local magnetization and is featureless; the spin-spin and dimer-dimer correlation functions are verified to decay exponentially; and its ground-state energy per site is determined to be $e_0=-0.4343(1)$, which is very close to that [$e_0=-0.4386(5)$] of the intriguing kagome HAF model. The magnetization curve s…
The competition between quantum and classical magnetization plateaus of S=1/2 frustrated Heisenberg chains with modified exchange couplings is investigated. The conventional S=1/2 frustrated Heisenberg chains is known to exhibit a 3-fold degenerate udu-type classical plateau at 1/3 of the saturation magnetization accompanied by the spontaneous Z_3 translational symmetry breakdown. The stability of this plateau phase against period 3 exchange modulation which favors the 00u-type quantum plateau state (00= singlet dimer) is studied by bosonization, renormalization group and numerical diagonaliza…
We have formulated a twist operator argument for the geometrically frustrated quantum spin systems on the kagome and triangular lattices, thereby extending the application of the Lieb-Schultz-Mattis (LSM) and Oshikawa-Yamanaka-Affleck (OYA) theorems to these systems. The equivalent large gauge transformation for the geometrically frustrated lattice differs from that for non-frustrated systems due to the existence of multiple sublattices in the unit cell and non-orthogonal basis vectors. Our study for the $S=1/2$ kagome Heisenberg antiferromagnet at zero external magnetic field gives a criterio…
The $S=1/2$ frustrated Heisenberg chains with bond alternation is known to exhibit a magnetization plateau at half of the saturation magnetization $\Ms$ accompanied by the spontanuous translational symmetry breakdown. The effect of randomness on the magnetization process of this model is investigated. First we consider the mixture of the two kinds of chains both of which possess the $\Ms/2$-plateau in the common interval of the magnetization field. The plateau at $\Ms/2$ is found to vanish immediately if the randomness is switched on in agreement with Totsuka's prediction. The small plateau al…
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.
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…
It is well known that spin nematic phases can appear in either frustrated magnets or in those described by Hamiltonians with large exotic non-Heisenberg terms like biquadratic exchange. We show in the present study that non-frustrated spin-1 1D, 2D and 3D antiferromagnets with single-ion easy-axis anisotropy can show nematic phases in strong magnetic field. For 1D case we support our analytical results by numerical ones.
We investigate the non-trivial magnetization plateau at 1/4 of the saturation magnetization of S=1 spin ladder, especially with reference to recent experimental results on a new organic tetraradical 3,3',5,5'-tetrakis(N-tert-butylaminoxyl)biphenyl, abbreviated as BIP-TENO. We propose three mechanisms for the formation of the plateau; the Neel mechanism, the dimer mechanism and the spin-Peierls mechanism. We also discuss the effect of four-spin exchange interactions.
We study the magnetization process of the $S=1/2$ antiferromagnetic spin ladder in the presence of the second and the third-neighbor couplings which lead to frustration with the typical nearest-neighbor coupling. We use degenerate perturbation theory and level spectroscopy analysis of the numerical diagonalization data of the Hamiltonian for finite systems. We find two kinds of plateaux at half the saturation moment in the magnetization curve. One is mainly due to the second-neighbor couplings and the other to the third-neighbor couplings. The mechanisms of these two plateaux are quite differe…
Motivated by the intriguing report, in some frustrated quantum antiferromagnets, of magnetization plateaus whose simple collinear structure is {\it not} stabilized by an external magnetic field in the classical limit, we develop a semiclassical method to estimate the zero-point energy of collinear configurations even when they do not correspond to a local minimum of the classical energy. For the spin-1/2 frustrated square-lattice antiferromagnet, this approach leads to the stabilization of a large 1/2 plateau with "up-up-up-down" structure for J_2/J_1>1/2, in agreement with exact diagonalizati…
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…
Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state. In two dimensions, we discuss the square, triangular and Ka…
The magnetization curve of the two-dimensional spin-1/2 $J_1$-$J_2$ Heisenberg model is investigated by using the Chern-Simons theory under a uniform mean-field approximation. We find that the magnetization curve is monotonically increasing for $J_2/J_1 < 0.267949$, where the system under zero external field is in the antiferromagnetic Néel phase. For larger ratios of $J_2/J_1$, various plateaus will appear in the magnetization curve. In particular, in the disordered phase, our result supports the existence of the $M/M_{\rm sat}=1/2$ plateau and predicts a new plateau at $M/M_{\rm sat}=1/3$. B…
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 report an excellent realization of the highly non-classical incommensurate spin-density wave (SDW) state in the quantum frustrated antiferromagnetic insulator Cs$_2$CoBr$_4$. In contrast to the well-known Ising spin chain case, here the SDW is stabilized by virtue of competing planar in-chain anisotropies and frustrated interchain exchange. Adjacent to the SDW phase is a broad $m = 1/3$ magnetization plateau that can be seen as a commensurate locking of the SDW state into the up-up-down (UUD) spin structure. This represents the first example of long-sought SDW-UUD transition in triangular-t…
