Dzyaloshinski-Moriya interaction in the 2D spin gap system SrCu(2)(BO(3))(2)

Higher-Magnesium-Doping Effects on the Singlet Ground State of the Shastry-Sutherland SrCu2(BO3)2

Doping of quantum antiferromagnets is an established approach to investigate the robustness of their ground state against the competing phases. Predictions of doping effects on the ground state of the Shastry-Sutherland dimer model are here verified experimentally on Mg-doped SrCu2(BO3)2. A partial incorporation of Mg2+ on the Cu2+ site in the SrCu2(BO3)2 structure leads to a subtle but systematic lattice expansion with the increasing Mg-doping concentration, which is accompanied by a slight decrease in the spin gap, the Curie-Weiss temperature, and the peak temperature of the susceptibility. These findings indicate a doping-induced breaking of Cu2+ spin-1/2 dimers that is also corroborated by X-band EPR spectroscopy that points to a systematic increase in the intensity of free Cu2+ sites with increasing Mg-doping concentration. Extending the Mg-doping up to nominal x = 0.10 yielding SrCu1.9Mg0.1(BO3)2, in the magnetization measurements taken up to 35 T, a suppression of the pseudo-1/8 plateau is found along with a clear presence of an anomaly at an onset critical field μ0H'C0 ≈ 9 T. The latter, absent in pure SrCu2(BO3)2, emerges due to the pairwise coupling of liberated Cu2+ spin-1/2 entities in the vicinity of Mg-doping induced impurities.

Quantum Criticality with Emergent Symmetry in the Extended Shastry-Sutherland Model

Motivated by the novel phenomena observed in the layered material SrCu_{2}(BO_{3})_{2}, the Shastry-Sutherland model (SSM) has been extensively studied as the minimal model for SrCu_{2}(BO_{3})_{2}. However, the nature of its quantum phase transition from the plaquette valence-bond solid to antiferromagnetic phase is under fierce debate, posing a challenge to understand the underlying quantum criticality. Via the state-of-the-art tensor network simulations, we study the ground state of the SSM on large-scale size up to 20×20 sites. We identify the continuous transition nature accompanied by an emergent O(4) symmetry between the plaquette valence-bond solid and antiferromagnetic phase, which strongly suggests a deconfined quantum critical point (DQCP). Furthermore, we map out the phase diagram of an extended SSM that can be continuously tuned to the SSM, which demonstrates the same DQCP phenomena along a whole critical line. Our results indicate a compelling scenario for understanding the origin of the proposed proximate DQCP in recent experiments of SrCu_{2}(BO_{3})_{2}.

Field-induced bound-state condensation and spin-nematic phase in SrCu2(BO3)2 revealed by neutron scattering up to 25.9 T

In quantum magnetic materials, ordered phases induced by an applied magnetic field can be described as the Bose-Einstein condensation (BEC) of magnon excitations. In the strongly frustrated system SrCu2(BO3)2, no clear magnon BEC could be observed, pointing to an alternative mechanism, but the high fields required to probe this physics have remained a barrier to detailed investigation. Here we exploit the first purpose-built high-field neutron scattering facility to measure the spin excitations of SrCu2(BO3)2 up to 25.9 T and use cylinder matrix-product-states (MPS) calculations to reproduce the experimental spectra with high accuracy. Multiple unconventional features point to a condensation of S = 2 bound states into a spin-nematic phase, including the gradients of the one-magnon branches and the persistence of a one-magnon spin gap. This gap reflects a direct analogy with superconductivity, suggesting that the spin-nematic phase in SrCu2(BO3)2 is best understood as a condensate of bosonic Cooper pairs.

Discovery of quantum phases in the Shastry-Sutherland compound SrCu2(BO3)2 under extreme conditions of field and pressure

The 2-dimensional layered oxide material SrCu2(BO3)2, long studied as a realization of the Shastry-Sutherland spin topology, exhibits a range of intriguing physics as a function of both hydrostatic pressure and magnetic field, with a still debated intermediate plaquette phase appearing at approximately 20 kbar and a possible deconfined critical point at higher pressure. Here, we employ a tunnel diode oscillator (TDO) technique to probe the behavior in the combined extreme conditions of high pressure, high magnetic field, and low temperature. We reveal an extensive phase space consisting of multiple magnetic analogs of the elusive supersolid phase and a magnetization plateau. In particular, a 10 × 2 supersolid and a 1/5 plateau, identified by infinite Projected Entangled Pair States (iPEPS) calculations, are found to rely on the presence of both magnetic and non-magnetic particles in the sea of dimer singlets. These states are best understood as descendants of the full-plaquette phase, the leading candidate for the intermediate phase of SrCu2(BO3)2.

Two coupled chains are simpler than one: field-induced chirality in a frustrated spin ladder

Although the frustrated (zigzag) spin chain is the Drosophila of frustrated magnetism, our understanding of a pair of coupled zigzag chains (frustrated spin ladder) in a magnetic field is still lacking. We address this problem through nuclear magnetic resonance (NMR) experiments on BiCu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}2PO\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_6$$\end{document}6 in magnetic fields up to 45 T, revealing a field-induced spiral magnetic structure. Conjointly, we present advanced numerical calculations showing that even a moderate rung coupling dramatically simplifies the phase diagram below half-saturation magnetization by stabilizing a field-induced chiral phase. Surprisingly for a one-dimensional model, this phase and its response to Dzyaloshinskii-Moriya (DM) interactions adhere to classical expectations. While explaining the behavior at the highest accessible magnetic fields, our results imply a different origin for the solitonic phases occurring at lower fields in BiCu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}2PO\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_6$$\end{document}6. An exciting possibility is that the known, DM-mediated coupling between chirality and crystal lattice may give rise to a new kind of spin-Peierls instability.

Synthesis, structure, and electronic properties of the Li11RbGd4Te6O30 single crystal

Materials with spin dimers have attracted much attention in the last several decades because they could provide a playground to embody simple quantum spin models. For example, the Bose–Einstein condensation of magnons has been observed in TlCuCl₃ with anti-ferromagnetic Cu₂Cl₆ dimers. In this work, we have synthesized a new kind of single-crystal Li₁₁RbGd₄Te₆O₃₀ with Gd₂O₁₅ dimers. This material belongs to the rhombohedral system with the lattice parameters: a = b = c = 16.0948 Å and α = β = γ = 33.74°. First-principles calculations indicate that Li₁₁RbGd₄Te₆O₃₀ is a wide-bandgap (about 4.5 eV) semiconductor. But unlike many other well studied quantum dimer magnets with an anti-ferromagnetic ground state, the Gd₂O₁₄ dimers in Li₁₁RbGd₄Te₆O₃₀ show ferromagnetic intra-dimer exchange interactions according to our calculations. Our work provides a new material which could possibly extend the studies of the spin dimers.

The prime novelty of this research is the synthesis and theory analyses of a new kind of single crystal compound Li₁₁RbGd₄Te₆O₃₀ with Gd₂O₁₅ dimers.

Development and application of 2.5 GPa-25 T high-pressure high-field electron spin resonance system using a cryogen-free superconducting magnet

We have developed a high-pressure electron spin resonance probe and successfully installed into the world's highest-field cryogen-free superconducting magnet having a maximum central field of 24.6 T. The high pressure of 2.5 GPa is achieved by the specially designed piston-cylinder pressure cell using THz-wave-transparent components. In the first application of this high-pressure high-field ESR system, we observed that the orthogonal dimer spin system SrCu₂(BO₃)₂ undergoes a quantum phase transition from the dimer singlet ground to the plaquette singlet ground states.

Dynamics and Instabilities of the Shastry-Sutherland Model

We study the excitation spectrum in the dimer phase of the Shastry-Sutherland model by using an unbiased variational method that works in the thermodynamic limit. The method outputs dynamical correlation functions in all possible channels. This output is exploited to identify the order parameters with the highest susceptibility (single or multitriplon condensation in a specific channel) upon approaching a quantum phase transition in the magnetic field versus the J^{'}/J phase diagram. We find four different instabilities: antiferro spin nematic, plaquette spin nematic, stripe magnetic order, and plaquette order, two of which have been reported in previous studies.

Giant suppression of phononic heat transport in a quantum magnet BiCu2PO6

Thermal transport of quantum magnets has elucidated the nature of low energy elementary excitations and complex interplay between those excited states via strong scattering of thermal carriers. BiCu₂PO₆ is a unique frustrated spin-ladder compound exhibiting highly anisotropic spin excitations that contain both itinerant and localized dispersion characters along the b- and a-axes respectively. Here, we investigate thermal conductivity κ of BiCu₂PO₆ under high magnetic fields (H) of up to 30 tesla. A dip-feature in κ, located at ~15 K at zero-H along all crystallographic directions, moves gradually toward lower temperature (T) with increasing H, thus resulting in giant suppression by a factor of ~30 near the critical magnetic field of H_c ≅ 23.5 tesla. The giant H- and T-dependent suppression of κ can be explained by the combined result of resonant scattering of phononic heat carriers with magnetic energy levels and increased phonon scattering due to enhanced spin fluctuation at H_c, unequivocally revealing the existence of strong spin-phonon coupling. Moreover, we find an experimental indication that the remaining magnetic heat transport along the b-axis becomes almost gapless at the magnetic quantum critical point realized at H_c.

Field-Induced Magnonic Liquid in the 3D Spin-Dimerized Antiferromagnet Sr_{3}Cr_{2}O_{8}

We report on ultrasound and magnetization studies in three-dimensional, spin-dimerized Sr_{3}Cr_{2}O_{8} as a function of temperature and external magnetic field up to 61 T. It is well established [A. A. Aczel et al., Phys. Rev. Lett. 103, 207203 (2009)] that this system exhibits a magnonic-superfluid phase between 30 and 60 T and below 8 K. By mapping ultrasound and magnetization anomalies as a function of magnetic field and temperature we establish that this superfluid phase is embedded in a domelike phase regime of a high-temperature magnonic liquid extending up to 18 K. Compared to thermodynamic results, our study indicates that the magnonic liquid could be characterized by an Ising-like order but has lost the coherence of the transverse components.

Frequency Extension to the THz Range in the High Pressure ESR System and Its Application to the Shastry-Sutherland Model Compound SrCu2(BO3)2

We have made a survey of ceramics for the inner parts of the transmission-type pressure cell to achieve the high pressure and the high transmission in the THz range. By using the optimal combination of ZrO2-based ceramic and Al2O3 ceramic, we have succeeded in obtaining a pressure up to 1.5 GPa and a frequency region up to 700 GHz simultaneously. We show the high-pressure ESR results of the Shastry-Sutherland compound SrCu2(BO3)2 as an application. We observed the direct ESR transition modes between the singlet ground state and the triplet excited states up to a pressure of 1.51 GPa successfully, and obtained the precise pressure dependence of the gap energy. The gap energy is directly proved to be suppressed by the pressure. Moreover, we found that the system approaches the quantum critical point with pressure by comparing the obtained data with the theory. This result also shows the usefulness of high-pressure ESR measurement in the THz region to study quantum spin systems.

Hall effect of triplons in a dimerized quantum magnet

SrCu2(BO3)2 is the archetypal quantum magnet with a gapped dimer-singlet ground state and triplon excitations. It serves as an excellent realization of the Shastry-Sutherland model, up to small anisotropies arising from Dzyaloshinskii-Moriya interactions. Here we demonstrate that these anisotropies, in fact, give rise to topological character in the triplon band structure. The triplons form a new kind of Dirac cone with three bands touching at a single point, a spin-1 generalization of graphene. An applied magnetic field opens band gaps resulting in topological bands with Chern numbers ±2. SrCu2(BO3)2 thus provides a magnetic analogue of the integer quantum Hall effect and supports topologically protected edge modes. At a threshold value of the magnetic field set by the Dzyaloshinskii-Moriya interactions, the three triplon bands touch once again in a spin-1 Dirac cone, and lose their topological character. We predict a strong thermal Hall signature in the topological regime.

Emergence of long-range order in sheets of magnetic dimers

Quantum spins placed on the corners of a square lattice can dimerize and form singlets, which then can be transformed into a magnetic state as the interactions between dimers increase beyond threshold. This is a strictly 2D transition in theory, but real-world materials often need the third dimension to stabilize long-range order. We use high pressures to convert sheets of Cu(2+) spin 1/2 dimers from local singlets to global antiferromagnet in the model system SrCu2(BO3)2. Single-crystal neutron diffraction measurements at pressures above 5 GPa provide a direct signature of the antiferromagnetic ordered state, whereas high-resolution neutron powder and X-ray diffraction at commensurate pressures reveal a tilting of the Cu spins out of the plane with a critical exponent characteristic of 3D transitions. The addition of anisotropic, interplane, spin-orbit terms in the venerable Shastry-Sutherland Hamiltonian accounts for the influence of the third dimension.

Crystals of bound states in the magnetization plateaus of the Shastry-Sutherland model

Using infinite projected entangled-pair states, we show that the Shastry-Sutherland model in an external magnetic field has low-magnetization plateaus which, in contrast to previous predictions, correspond to crystals of bound states of triplets, and not to crystals of triplets. The first sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with experiments on the orthogonal-dimer antiferromagnet SrCu2(BO3)2, and they can be naturally understood as regular patterns of bound states, including the intriguing 2/15 one. We also show that, even in a confined geometry, two triplets bind into a localized bound state with Sz=2. Finally, we discuss the role of competing domain-wall and supersolid phases, as well as that of additional anisotropic interactions.

Spin interactions in mineral libethenite series: evolution of low-dimensional magnetism

Interesting magnetic properties and spin-exchange interactions along various possible pathways in the half-integral spin quantum magnetic tetramer system: A(2)PO(4)OH (A=Co, Cu) are investigated. Interplay of structural distortion and the magnetic properties with the evolution of localized band structure explain the gradual transition from a three-dimensional antiferromagnet to a low-dimensional frustrated magnetic system along the series. A detailed study of the exchange mechanism in this system explores various possibilities of complex magnetic interaction. The electronic structure of this series, studied with the help of different appropriate density functional approaches such as Nth order muffin-tin orbital (NMTO) and plane-wave pseudopotential calculations incorporating onsite Coulomb repulsion (U), identifies the underlying magnetic exchange mechanism of this series. Thereafter a generalized minimal model spin-Hamiltonian is constructed for the low-dimensional system. Solution of this model Hamiltonian within first-order perturbation theory results in the evaluation of spin-gap in the spin-tetramer system. In addition, the effects of size confinement and volume reduction on the relevant exchange integrals and spin-gap of the low-dimensional system are also discussed.

Continuous and discontinuous quantum phase transitions in a model two-dimensional magnet

The Shasty-Sutherland model, which consists of a set of spin 1/2 dimers on a 2D square lattice, is simple and soluble but captures a central theme of condensed matter physics by sitting precariously on the quantum edge between isolated, gapped excitations and collective, ordered ground states. We compress the model Shastry-Sutherland material, SrCu(2)(BO(3))(2), in a diamond anvil cell at cryogenic temperatures to continuously tune the coupling energies and induce changes in state. High-resolution X-ray measurements exploit what emerges as a remarkably strong spin-lattice coupling to both monitor the magnetic behavior and the absence or presence of structural discontinuities. In the low-pressure spin-singlet regime, the onset of magnetism results in an expansion of the lattice with decreasing temperature, which permits a determination of the pressure-dependent energy gap and the almost isotropic spin-lattice coupling energies. The singlet-triplet gap energy is suppressed continuously with increasing pressure, vanishing completely by 2 GPa. This continuous quantum phase transition is followed by a structural distortion at higher pressure.

Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice

We present measurements of the basic properties of Ce(2)Ge(2)Mg, Yb(2)Pt(2)Pb and Ce(2)Pt(2)Pb, which are members of a new class of geometrically frustrated magnets R(2)T(2)X (R = rare earth, T = transition metal, X = main group). Here, the moment-bearing R atoms are confined to layers where they are arranged in the Shastry-Sutherland lattice. Magnetic susceptibility and specific heat measurements indicate that Ce(2)Ge(2)Mg orders antiferromagnetically at 9.4 K and Yb(2)Pt(2)Pb at 2.07 K. No long ranged order is observed in Ce(2)Pt(2)Pb above 0.05 K. Analysis of Schottky peaks in the specific heat indicates that all three compounds have doublet ground states that are well separated in energy from the excited states of the crystal-field-split manifold. Electrical resistivity measurements show that Ce(2)Ge(2)Mg and Yb(2)Pt(2)Pb are excellent metals with small residual resistivities. However, the measured resistivity of Ce(2)Pt(2)Pb is large and almost temperature-independent, suggesting that strong disorder or perhaps strong quantum critical fluctuations saturate the quasiparticle scattering in this compound. The magnetic entropy develops very slowly above the onset of antiferromagnetic order and we discuss the possibility that a nonordered fluid of dimerized moments exists above T(N) in Ce(2)Ge(2)Mg and Yb(2)Pt(2)Pb, and for a wide range of temperatures in Ce(2)Pt(2)Pb, which appears to be close to a frustration-driven quantum critical point.

Fractalization drives crystalline states in a frustrated spin system

The fractalized Hofstadter butterfly energy spectrum predicted for magnetically confined fermions diffracted by a crystal lattice has remained beyond the reach of laboratory-accessible magnetic fields. We find the geometrically frustrated spin system SrCu(2)(BO(3))(2) to provide a sterling demonstration of a system in which bosons confined by a magnetic and lattice potential mimic the behavior of fermions in the extreme quantum limit, giving rise to a sequence of plateaus at all magnetization m(z)/m(sat) = 1/q ratios 9 > or = q > or = 2 and p/q = 2/9 (m(sat) is the saturation magnetization) in magnetic fields up to 85 T and temperatures down to 29 mK, within the sequence of previously identified plateaus at 1/8, 1/4, and 1/3 of the saturated magnetization. We identify this hierarchy of plateaus as a consequence of confined bosons in SrCu(2)(BO(3))(2) mimicking the high magnetic field fractalization predicted by the Hofstadter butterfly for fermionic systems. Such an experimental realization of the Hofstadter problem for interacting fermions has not been previously achieved in real materials, given the unachievably high magnetic flux densities or large lattice periods required. By a theoretical treatment that includes short-range repulsion in the Hofstadter treatment, stripe-like spin density-modulated phases are revealed in SrCu(2)(BO(3))(2) as emergent from a fluidic fractal spectrum.

Observation of higher-harmonic helical spin-resonance modes in the chromium spinel CdCr2O4

High frequency ESR measurements on the chromium spinel compound CdCr2O4 have been performed. The observed ESR modes below Hc' approximately 5.7 T can be explained well by the calculated resonance modes based on a molecular field theory assuming a helical spin structure. Other than the fundamental ones, we have succeeded in observing the higher-harmonic modes for the first time. A large change of the ESR modes above Hc' indicate that a variation of the spin structure from the helical to the four-sublattice canted one takes place around Hc'.

In-gap spin excitations and finite triplet lifetimes in the dilute singlet ground state system SrCu(2-x)Mgx(BO3)2

High resolution neutron scattering measurements on a single crystal of SrCu(2-x)Mgx(BO3)2 with x approximately 0.05 reveal the presence of new spin excitations within the gap of this quasi-two-dimensional, singlet ground state system. The application of a magnetic field induces Zeeman-split states associated with S=1/2 unpaired spins which are antiferromagnetically correlated with the bulk singlet. Substantial broadening of both the one- and two-triplet excitations in the doped single crystal is observed, as compared with pure SrCu2(BO3)2. Theoretical calculations using a variational algorithm and a single quenched magnetic vacancy on an infinite lattice are shown to qualitatively account for these effects.

High-resolution study of spin excitations in the singlet ground state of SrCu2(BO3)2

High-resolution, inelastic neutron scattering measurements on SrCu2(BO3)2, a realization of the Shastry-Sutherland model for two-dimensional Heisenberg antiferromagnets, reveal the dispersion of the three single triplet excitations continuously across the (H,0) direction within its tetragonal basal plane. These measurements also show distinct Q dependencies for the single and multiple triplet excitations, and that these excitations are largely dispersionless perpendicular to this plane. The temperature dependence of the intensities of these excitations is well described as the complement of the dc susceptibility of SrCu2(BO3)2.

Magnetic superstructure in the two-dimensional quantum antiferromagnet SrCu2(BO3)2

We report the observation of magnetic superstructure in a magnetization plateau state of SrCu2(BO3)2, a frustrated quasi-two-dimensional quantum spin system. The Cu and B nuclear magnetic resonance (NMR) spectra at 35 millikelvin indicate an apparently discontinuous phase transition from uniform magnetization to a modulated superstructure near 27 tesla, above which a magnetization plateau at 1/8 of the full saturation has been observed. Comparison of the Cu NMR spectrum and the theoretical analysis of a Heisenberg spin model demonstrates the crystallization of itinerant triplets in the plateau phase within a large rhomboid unit cell (16 spins per layer) showing oscillations of the spin polarization. Thus, we are now in possession of an interesting model system to study a localization transition of strongly interacting quantum particles.