Session F23: Shastry-Sutherland Magnets

Deconfined Quantum Criticality in a Shastry-Sutherland Compound SrCu2(BO3)2

Landau theory predicts that there is no continuous quantum phase transition (QPT) between two states with different types of symmetry breaking. However, about 20 years ago, field theory and quantum many-body calculations based on some specifically designed models support a beyond Landau paradigm: a continuous deconfined quantum critical point (QDCP) may exist which hosts emergent symmetries and fractional excitations [1,2]. DQCP became a frontier research in strongly correlated electrons, which may also help to understand novel properties of high temperature superconductors. Unfortunately, experimental evidence of DQCP has never been found after original theoretical proposals. A frustrated antiferromagnet SrCu2(BO3)2 [3], which is called a Shastry-Sutherland material, provides the possibility of exploring DQCP, where pressure-induced QPTs from dimerized spin singlet (DS), to plaquette singlet state (PS), and then to antiferromagnetic state (AFM) were suggested by specific heat and neutron scattering studies [4,5,6].

In this talk, I will present our 11B nuclear magnetic resonance (NMR) studies on SrCu2(BO3)2 with combined high-pressure and high-field tuning, and cooled in a dilution refrigerator, to approach DQCP [7]. At pressures above 2 GPa, we discovered microscopic experimental evidence of a full-plaquette (FP) singlet state, where the FWHM of the spectra behaves as an order parameter below a transition temperature of 1.8 K. Furthermore, at pressures of 2.1 and 2.4 GPa, our NMR spectra reveal a field-induced weakly first-order QPT from the FP state to the AFM state at a field about 6 T, where the coexistence temperature of two phases is as low as 0.07 K and the order parameter of the AFM phase becomes very small at the QPT. Furthermore, both transition temperatures of the PS and the AFM phases scale with |H-HC| when approaching the transition field HC with the same power-law exponent; such duality supports the emergence of enhanced symmetries, consistent with an enhanced O(3) symmetry by numerical simulations. The spin-lattice relaxation rate data 1/T1 at 2.4 GPa also reveals a quantum critical scaling behavior in the low-energy spin dynamics, which does not follow a traditional QCP. Therefore, our study provides concrete experiment evidences for realization of a proximate DQCP and a new platform for exploring DQCP. Note that the system may go beyond the Shastry-Sutherland model; many properties, such as the nature of a plaquette-liquid phase and existence of fractional excitations, call for further experimental studies.

References:
[1] R. R. P. Singh et al., Science 303, 1490 (2004).
[2] A. W. Sandvik, Phys. Rev. Lett 98, 227202 (2007).
[3] H. Kageyama et al., Phys. Rev. Lett 82, 3168 (1999).
[4] M. E. Zayed et al., Nature Phys. 13, 962 (2017).
[5] J. Guo et al., Phys. Rev. Lett 124, 206602 (2020).
[6] J. Larrea Jimenez et al., Nature 592, 370 (2021).
[7] Y. Cui et al., Science 380, 1179 (2023).   

Magnetic Disorder in the Shastry-Sutherland Lattice BaCe2ZnS5

The Shastry-Sutherland lattice (SSL) comprises a two-dimensional orthogonal arrangement of spin dimers. By varying the ratio of intra-dimer and inter-dimer interactions, the rich phase diagram can emerge, including exotic quantum phases. Single-ion and exchange magnetic anisotropies can further diversify the phased diagram and lead to quantum states beyond the toy model of antiferromagnetic Heisenberg SSL. For example, a quantum critical point was reached by applying a magnetic field in BaNd₂ZnS₅ SSL [1]. At zero field, it presents a 2Q non-collinear magnetic order. When Nd³⁺ is replaced with Ce³⁺, no magnetic order is detected until 40 mK. To understand the magnetic disorder in BaCe₂ZnS₅ SSL, we have studied its local site magnetic anisotropy my polarized neutron diffraction, crystal electric field excitations, magnetic dimer excitations through inelastic neutron scattering. In this presentation, I will introduce our latest data modeling results and make a comparison between the field-induced disorder in  BaNd₂ZnS₅ and the magnetic disorder observed in BaCe₂ZnS₅.     

Single crystal synthesis and physical properties of a Shastry-Sutherland compound, BaCe2ZnS5

In this talk, we present our recent work on a high-purity, single-crystalline BaCe₂ZnS₅ where Ce atoms form a two-dimensional Shastry-Sutherland (SS) lattice. The SS lattice is a classical geometrically frustrated lattice type featuring a competition between nearest neighbor and next nearest neighbor interactions. Crystal synthesis procedure and detailed physical property characterizations via x-ray diffraction, magnetization, heat capacity, and neutron diffraction measurements will be presented. BaCe₂ZnS₅ does not exhibit long range magnetic ordering down to 70 mK. Comparison to the magnetic properties of other rare earth members in this family of compounds such as BaNd₂ZnS₅ will also be discussed.   

Phase diagram and quantum criticality in Shastry-Sutherland lattice BaNd2ZnS5

The Shastry-Sutherland (SS) model originally focuses on the antiferromagnetic interactions between nearest-neighbors and alternating next-nearest-neighbors in a two-dimensional square lattice. The original SS model predicted the emergence of various magnetic phases, including spin liquid phases, magnetic superlattice structures, and canted spin phases that bear magnetic analogies to the supersolid phase. BaNd₂ZnS₅ has a topologically equivalent lattice structure with the SS model. The magnetically ordered state is destabilized by external magnetic field and the emergence of a liquid-like state has been proposed. Here, we studied the magnetic field-induced ground state of BaNd₂ZnS₅ using magnetization, resonant ultrasound spectroscopy, ac magnetic susceptibility, and specific heat measurement at low temperature; a series of phase transitions were identified for H along (110). Near 2 T, when q₂ = (-1/2, 1/2, 0) is completely suppressed showing signatures of quantum criticality in various measurements while q₁ = (1/2, 1/2, 0) remains intact up to 12 T.   

Constructing the magnetic phase diagram of BaNd2ZnS5 with elastic constants and ultrasonic attenuation measured by resonant ultrasound spectroscopy

Elastic constants are ideal to study phase transitions because they are the thermodynamic susceptibility of strain. Strain, being a second-rank tensor quantity, can couple to order parameters in ways that are inaccessible to thermal, electric, or magnetic fields alone. As such, ultrasound measurements have been used to great effect to study changes in elastic constants and attenuation at phase transitions under applied magnetic fields. Such approaches have often been based on pulse-echo techniques which require multiple sample-transducer combinations to obtain the complete elastic constant tensor. This can be prohibitive for low symmetry materials and introduce systematic errors.

Here, we share recent advances in resonant ultrasound spectroscopy (RUS) which enable the non-destructive determination of the entire elastic constant tensor with high accuracy and precision from a single sample in DC magnetic fields up to 14T and temperatures down to 1.7K. We apply these developments to study phase transitions in elemental Gd and the geometrically-frustrated Shastry-Sutherland-like compound BaNd₂ZnS₅. Clear thermodynamic signatures of phase transitions are identified in both elastic constants and ultrasonic attenuation as a function of temperature and magnetic field. These results clarify the rich phase diagram of BaNd₂ZnS₅ and demonstrate our ability to perform RUS in high magnetic fields.   

Thermodynamic and neutron scattering studies of the Shastry-Sutherland Compound Yb2Be2GeO7

In the study of frustrated magnetism, the Shastry-Sutherland lattice (SSL), an arrangement of orthogonal dimers with competing interactions J and J’ between and within the dimers, represents one of the few exactly solvable structures. The SSL ground state is known when the ratio J’/J is small and large, but the states of the intermediate values are still unclear. We have recently begun synthesizing the Yb-based SSL compound Yb₂Be₂GeO₇. We have produced pure powder samples and successfully grown large single crystals using the optical floating zone technique. Based on our initial magnetic and thermal characterization measurements, we observe no sign of magnetic ordering down to 60 mK. In this talk we present these results, as well as the results of our recent elastic and inelastic neutron scattering experiments on this compound.   

Neutron scattering and thermodynamics studies on Er-based Ising Shastry Sutherland Lattice compound.

In two-dimensional magnetic compounds, the Shastry-Sutherland lattice (SSL), an orthogonal arrangement of dimers with antiferromagnetic interdimer coupling J′ and the intradimer coupling J, have attracted attention due to their complex phase diagrams, displaying a variety of magnetic phases in magnetic fields and pressure; such as dimer state, plaquette state, fractional magnetization plateaus, and crystals of bound states. We have synthesized single crystals of Er-based SSL compound and characterized them using thermal, magnetic, and neutron scattering measurements. In this talk, we will present our results in understanding the multiple magnetization plateaus hosted by this system   

Magnetic Anisotropy of a Triangular Spin-Chain System K2Co3(MoO4)3(OH)2

Low-dimensional magnetic materials have drawn continued attention in condensed matter physics, owing to their distinct electronic and magnetic properties. In particular, the oxyanion-based transition-metal (M) oxide sublattices that are magnetically isolated by closed-shell nonmagnetic oxyanions (MoO₄^2-, SiO₄⁴⁻, PO₄³⁻, AsO₄³⁻) show great potential for exploring and characterizing new emergent phenomena. Recently we have synthesized single crystals of K2Co3(MoO4)3(OH)2 and characterized the crystals structure and magnetic properties. K2Co3(MoO4)3(OH)2 belongs to a rare class of compounds, namely half sawtooth-chain type structure in which corner sharing isosceles triangles whose vertices consist of one Co(1) and two Co(2) atoms. The magnetic susceptibility reveals a long-range ordering around 7 K with a strong anisotropy. The isothermal magnetization data shown a stepwise magnetization when the magnetic field along the Co-O-Co (half sawtooth chain) direction. Two noticeable metamagnetic transitions were observed at Hc1 = 1 kOe and Hc2 = 2.1 kOe. The magnetic structure was determined using single crystals neutron diffraction. The magnetic structure consists of ferrimagnetic chains which are antiferromagnetically coupled with each other.   

Inelastic neutron scattering study of oxyanion-based compounds with sawtooth-chain lattice

The sawtooth spin chain with its compelling triangle-based spin structure offers a fascinating playground for competing antiferromagnetic interactions. Theoretical investigations showed that for special relations between exchange interactions such systems can host flat-band magnons that are of great interest for the development of magnonics devices. To date, experimental realization of a magnetic sawtooth lattice has been limited to a handful of compounds. In real materials, such sawtooth topologies imply the presence of magnetic ions in at least two nonequivalent structural positions that creates an interplay between different magnetic order parameters and, consequently, a rich magnetic phase diagram. We recently undertook a systematic investigation of the magnetic properties of several sawtooth systems where magnetic chains are linked by nonmagnetic oxyanion groups such as AsO4 and MoO4. In this presentation, we will discuss the static and dynamic magnetic properties of two transition-metal sawtooth chain systems: Rb2Fe2O(AsO4)2 [1] and CsCo2(MoO4)2(OH) [2]. These compounds exhibit long-range magnetic order that consists of antiferromagnetically coupled ferrimagnetic chains. Within each chain, the magnetic moments located at the tip of the sawtooth are aligned collinearly along the b-direction (the chain direction), while the moments on the spine sites are reversely canted to form a zigzag pattern inside the plane of the triangular chain. For both compounds, applied magnetic fields induce transitions to ferrimagnetic states where the coupling between adjacent sawtooth chains changed from antiferromagnetic to ferromagnetic. Hamiltonian models describing the main magnetic interactions are proposed based on the observed low-energy spin-wave excitations from inelastic neutron scattering data.   

Translational Symmetry Broken Magnetization Plateau of the One-Dimensional Quantum Spin Systems with Competing Anisotropies

The magnetization plateau is one of interesing phenomena in the field of the condensed matter physics. It was proposed as the spin gap induced by the external magnetic field[1]. According to the rigorous theorem derived from the Lieb-Schultz-Mattis one, the necessary condition of the magnetization plateau is the relation Q(S-m)=integer, where S and m are the total spin and the magnetization per unit cell, respectively, and Q is the periodicity of the wave function. The numerical diagonalization of finite-size clusters and the size scaling analysis[2] indicated that the spin-3/2 antiferromagnetic chain with the single-ion anisotropy exhibits the 1/3 magnetization plateau with Q=1. In the case of the spin-1/2 ferromagnetic-antiferromagnetic bond-alternating chain, because of S=1, the translational symmetry should be broken for the appearance of the magnetization plateau with m=1/2. Now the competing coupling anisotropies are introduced to the ferromagnetic and antiferromagnetic bonds.The numerical diagonalization of finite-size clusters and the level spectroscopy analysis indicate that the 1/2 magnetization plateau would appear, if the easy-plane anisotropy at the ferromagnetic bond and the easy-axis one at the antiferromagnetic bond are sufficielntly large. The several phase diagram with respect to the two anisotropies at m=1/2, depending on the ratio of the ferromagnetic and antiferromagnetic coupling constants. The translational symmetry broken plateau based on a similar mechanism is predicted for the S=1 and S=2[3,4] antiferromagnetic chains with the single-ion anisotropy and the couplind anisotropy competing with each other. 

[1]M. Oshikawa, M. Yamanaka and I. Affleck, Phys. Rev. Lett. 78, 1984 (1997). 

[2]T. Sakai and M. Takahashi, Phys. Rev. B 57, R3201 (1998).

[3]T. Sakai, T. Yamada, R. Nakanishi, R. Furuchi, H. Nakano, H. Kaneyasu, K. Okamoto and T. Tonegawa, J. Phys. Soc. Jpn. 91, 074702 (2022).

[4]T. Yamada, R. Nakanishi, R. Furuchi, H. Nakano, H. Kaneyasu, K. Okamoto and T. Tonegawa, JPS Conf. Proc. 38, 011163 (2022).   

Ferromagnetic Haldane state in an S=2 bilinear-biquadratic spin system on an orthogonal-dimer chain

  We present a theory of the realization of a ferromagnetic Haldane state in an S=2 bilinear-biquadratic (BLBQ) model on an orthogonal-dimer chain. The coexistence of a ferromagnetic state and a Haldane state is due to the "eigensystem embedding," i.e., the rigorous correspondence between a subset of the eigenstates in the S=2 BLBQ model and the entire set of the eigenstates in the S=1/2 Heisenberg model [1]. Exact-diagonalization calculations indicate that the ground state in the BLBQ model is a fractionally magnetized M = 3/4 Haldane state and the excitations of the ferromagnetic Haldane state consist from Haldane gap excitation and magnon like gapless mode [2]. Moreover, a ferromagnetic-dimer multiplet state is an exact ground state on the BLBQ model on an orthogonal dimer chain. The eigensystem embedding demonstrates that a quantum ferromagnet can be obtained for an arbitrary spin S >= 2 in any dimension and for any lattice.   

Evidence for an unconventional Néel-ordered phase in the frustrated S=1/2 two-leg ladder antiferromagnet C9H18N2CuBr4

In this talk, we report an unconventional Néel-ordered phase in the frustrated S=1/2 two-leg ladder antiferromagnet C₉H₁₈N₂CuBr₄ (DLCB for short). The temperature dependence of the gapped transverse excitations in the ordered phase at ambient pressure cannot be described by the conventional S=1 magnons, associated with explicit symmetry breaking. Contrary to conventional understanding, the ground state is best described as a disordered singlet with a spin gap. Accordingly, the origin of the spin gap in DLCB is not owing to the spin anisotropy and the three-dimensional magnetic order ought to emerge in an unconventional way. Haldane’s conjecture on spin-1 chains [1] is proposed to explain the opening of the spin gap in DLCB and the analysis of the free energy of the S=1/2 two-leg ladder sublattices supports that the magnetic order of DLCB can arise exclusively from thermal fluctuations by the mechanism of order-by-disorder [2, 3]. Our work indicates the presence of a symmetry-protected topological phase at ambient pressure in DLCB [4], which cannot be described by Landau’s symmetry-breaking theory.

References:

[1] F. D. M. Haldane, Phys. Lett. 93A, 464 (1983); Phys. Rev. Lett. 50, 1153 (1983).

[2] J. Villain et al., J. Physique 41, 1263-1272 (1980).

[3] C. L. Henley, Phys. Rev. Lett. 62, 2056 (1989).

[4] T. Hong et al., arXiv: 2306.06021.   

Investigation of magnetic order in novel pseudo-hexagonal Co-dimer material K7Co6Te11O46Hx

In the past decade, significant effort has been devoted to the study of effective S = ½ triangular dimer and honeycomb lattice antiferromagnets containing the Co²⁺ cation. The restricted geometry of the triangular lattice, as well as proposed Kitaev-type interactions in honeycomb systems have both been shown to give rise to exotic spin dynamics, even below the bulk magnetic ordering transition. We present a new Co-based antiferromagnet, K₇Co₆Te₁₁O₄₆H_x, possessing a pseudo-hexagonal arrangement of cobalt cations in the ac-plane which dimerize along b, with chiral chains of K atoms filling the hexagonal channels. The material orders antiferromagnetically below T_N­ = 9 K, with ferrimagnetic correlations persisting up to T = 50 K. While the overall structure is more three-dimensional than other Co-based QSL candidates, it contains both the triangular dimer geometry of the Heisenberg-type systems and the overall pseudo-hexagonal pattern of the Ising-like phases. As such, it presents a unique opportunity to explore the interplay between the geometric and non-geometric frustration intrinsic to each model in a hybrid structure. Further development of this structure type to magnetically isolate two-dimensional layers would also offer a novel avenue for stabilizing spin liquid-like behavior.