Session M56: Quantum Spin Liquid Materials II: Geometric Frustration, Shastry-Sutherland, and Valence Bond Solids

Spinon Fermi Surface Spin Liquid in a Triangular Lattice Antiferromagnet NaYbSe2

Triangular lattice of rare-earth ions with interacting effective spin-1/2 local moments is an ideal platform to explore the physics of quantum spin liquids (QSLs) in the presence of strong spin-orbit coupling, crystal electric fields, and geometrical frustration. The Yb delafossites, NaYbCh2 (Ch=O, S, Se) with Yb ions forming a perfect triangular lattice, have been suggested to be candidates for QSLs. Previous thermodynamics, nuclear magnetic resonance, and powder-sample neutron scattering measurements on NaYbCh2 have supported the suggestion of the QSL ground states. The key signature of a QSL, the spin excitation continuum, arising from the spin quantum number fractionalization, has not been observed. Here we perform both elastic and inelastic neutron scattering measurements as well as detailed thermodynamic measurements on high-quality single-crystal NaYbSe2 samples to confirm the absence of long-range magnetic order down to 40 mK, and further reveal a clear signature of magnetic excitation continuum extending from 0.1 to 2.5 meV. The comparison between the structure of the magnetic excitation spectra and the theoretical expectation from the spinon continuum suggests that the ground state of NaYbSe2 is a QSL with a spinon Fermi surface.   

Quantum spin liquid with the Ising character in the triangular-lattice antiferromagnet neodymium heptatantalate

Quantum spin liquid (QSL) has in recent years become a key concept in the realm of quantum materials. This fascinating state of mater that is highly entangled, yet it preserves lattice symmetries, has been experimentally observed in a variety of geometrically frustrated materials, including a few realizations of the two-dimensional triangular spin lattice. However, in the majority of these materials the QSL state is intimately related to structural disorder.

We have recently discovered a QSL state in a novel triangular antiferromagnet neodymium heptatantalate, NdTa7O₁₉, in which no structural imperfections have been observed [1]. Our in-depth experimental study detected no magnetic ordering even at temperatures of only a few tens of millikelvins, much below the exchange-interaction scale of this compound. Furthermore, sizable Ising-like spin correlations between the nearest neighbors on the triangular lattice and persistent spin dynamics have been detected in the ground state. The QSL state in this rare-earth based material has been attributed to strong magnetic anisotropy. The investigated compound is a member of a broad rare-earth heptatantalate family, which is thus introduced as a novel generic framework for QSLs.

[1] T. Arh, B. Sana, M. Pregelj, P. Khuntia, Z. Jaglicic, M. D. Le, P. K. Biswas, P. Manuel, L. Mangin-Thro, A. Ozarowski, A. Zorko, The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate, Nat. Mater. 21, 416 (2022).   

Probing Spinon Excitations in Single Crystals of the Kagome Quantum Spin Liquid Candidate Zn-barlowite Using Inelastic Neutron Scattering.

The spin-½ Heisenberg antiferromagnet on the kagome lattice (KAF) is among the most promising models which could host a quantum spin liquid (QSL) in two-dimensions. Zn-Barlowite (Zn_xCu_4-x(OH)₆BrF) is a newly discovered KAF material that shows strong signatures of a QSL ground state, including no measured magnetic order down to 50mK. Excitingly, Zn-Barlowite has a different interlayer impurity environment and a simpler A-A kagome layer stacking as compared to the related KAF material Herbersmithite (Zn_xCu_4-x(OH)₆Cl₂). This makes it promising as a potentially more pristine KAF QSL host and allows us to investigate the universality of the underlying kagome spin physics. Recently we have successfully synthesized millimeter-size single domain crystals of deuterated Zn-Barlowite. This allowed us to perform inelastic neutron scattering measurements on a large co-aligned crystal assembly for the first time. At high energies above ~1meV the magnetic scattering in Zn-barlowite is qualitatively similar to Herbersmithite’s and is likely due to kagome layer spinon excitations. However, there are clear differences in the low energy magnetic excitations. In Herbersmithite, it is dominated by nearest neighbor impurity correlations, whereas in Zn-Barlowite this magnetic impurity contribution is considerably smaller and cannot account for all observed magnetic excitations. Our data sheds new light on the KAF magnetic excitations and helps to gain a more unambiguous understanding of kagome QSL physics.

    

Inelastic neutron scattering studies of the role of interlayer spins in the kagome quantum magnets barlowite and Zn-barlowite

Geometrically frustrated spins on kagome lattices may exhibit long-range entanglement in the form of a quantum spin liquid (QSL) ground state. Substituting inter-kagome-layer copper atoms in barlowite (Cu₄(OH)₆Cl₂) with zinc atoms yields Zn-barlowite (Zn_xCu_4-x(OH)₆Cl₂), which has emerged as a recent candidate QSL material. In real growths, this substitution is imperfect (x<1), and some magnetic atoms remain between kagome layers. Ground states of impurity-affected kagome lattices are still poorly understood and open questions remain on how impurities may modify QSL states in frustrated magnets. This talk highlights recent inelastic neutron scattering measurements on barlowite and on large single crystals of Zn-barlowite. Quantitative analyses and comparisons of these data uncover kagome-to-interlayer coupling behaviors and elucidate how interlayer spins may affect magnetic ordering in barlowite and QSL formation in Zn-barlowite.   

Magnetic excitations in the Kitaev quantum spin liquid candidate Na2Co2TeO6 – Part I: Experiment

Layered honeycomb magnets have received lots of attention as potential candidates to realize Kitaev physics [1,2]. Among them, Co-based honeycomb Na₂Co₂TeO₆ (NCTO) is recently proposed to be a potential Kitaev material. NCTO is antiferromagnetic ordered below T_N = 25K. A complex temperature-field (T-B) phase diagram with multiple ordered, disordered states is proposed [3]. Here in Part I, we report the low-energy infrared and electron spin resonance spectroscopy measurements on NCTO in a broad range of temperatures and magnetic fields. The measurement results reveal a rich structure of magnetic excitations across the AFM, disordered and polarized states. Such richness of excitations is at variance with presently available theoretical models and suggests that other factors need to be taken into account. The experimental results will be further discussed with theoretical calculations in Part II.

[1] Liu et. al., Phys. Rev. B 97, 014407 (2018)

[2] Liu et. al., Phys. Rev. Lett. 125, 047201 (2020)

[3] Lin  et al. Nat Commun 12, 5559 (2021).   

Magnetic field effects in an octupolar quantum spin liquid candidate

Quantum spin liquid (QSL) is a disordered state of quantum-mechanically entangled spins commonly arising from frustrated magnetic dipolar interactions. However, QSL in some pyrochlore magnets can also come from frustrated magnetic octupolar interactions. Although the key signature for both dipolar and octupolar interaction-driven QSL is the presence of a spin excitation continuum (spinons) arising from the spin quantum number fractionalization, an external magnetic field-induced ferromagnetic order will transform the spinons into conventional spin waves in a dipolar QSL. By contrast, in an octupole QSL, the spin waves carry octupole moments that do not couple, in the leading order, to the external magnetic field or to neutron moments but will contribute to the field dependence of the heat capacity. Here we use neutron scattering to show that the application of a large external magnetic field to Ce2Zr2O7, an octupolar QSL candidate, induces an Anderson-Higgs transition by condensing the spinons into a static ferromagnetic ordered state with octupolar spin waves invisible to neutrons but contributing to the heat capacity. Our theoretical calculations also provide a microscopic, qualitative understanding of the presence of octupole scattering at large wavevectors in Ce2Sn2O7 pyrochlore, and its absence in Ce2Zr2O7. Therefore, our results identify Ce2Zr2O7 as a strong candidate for an octupolar U (1) QSL, establishing that frustrated magnetic octupolar interactions are responsible for QSL properties in Ce-based pyrochlore magnets.   

Anomalous spin excitations in honeycomb Na2+dNi2XO6 (X=Te and Sb) systems with zig-zag magnetic ordering

The honeycomb lattice offers a fertile playground for exploring a wide range of exotic magnetic ground states. In addition to the competition between first, second and third neighbor magnetic exchange interactions, the anisotropic exchange interactions that arise from the spin-orbit coupling can lead to various exotic quantum-disordered states. Here we discuss the results of an elastic and inelastic neutron scattering study of the layered honeycomb systems Na_2+dNi₂XO₆ (X=Te and Sb) [1,2] that were proposed as potential candidates for the realization of S=1 Kitaev model [3]. These compounds are derived from the triangular layered compounds NaNiO₂ by substituting 1/3 of the magnetic sites by non-magnetic Te/Sb cations in an ordered fashion. The diffusive Na atoms effectively control the interlayer magnetic coupling and, therefore, provide a route for tuning the lattice dimensionality. The changes in the static magnetic order and spin-dynamics for samples with different Na content are discussed. We also show that the obtained spin-wave excitation spectra from powder samples cannot be described using a simple Heisenberg spin Hamiltonian. An alternative generalized Kitaev-Heisenberg Hamiltonian model that accounts for bond-dependent anisotropic-exchange interactions is evaluated.

[1] A. Samarakoon, Q. Chen, H. Zhou , V. O. Garlea, Phys Rev B 104, 184415 (2021)

[2] E. A. Zvereva et al, B 92, 144401 (2015)

[3] P. P. Stavropoulos, D. Pereira, and H.-Y. Kee, Phys. Rev. Lett. 123, 037203 (2019)   

Inelastic neutron scattering investigation of the geometrically frustrated honeycomb cobaltate BaCo2(AsO4)2 in a transverse field

BaCo₂(AsO₄)₂ is a honeycomb quantum magnet where an antiferromagnetic third nearest neighbor interaction frustrates nearest neighbor ferromagnetic easy plane interactions which may place the material close to a quantum spin-liquid phase. In particular, a field applied transverse to the honeycomb plane should enhance quantum fluctuations and might be able to induce a quantum spin-liquid.

To explore this possibility, we performed inelastic neutron scattering measurements in a large transverse field. By tilting the c-axis by five degrees relative to a large vertical field, a small in-plane field was applied along the nearest-neighbor bond direction. Even with 10.9 tesla along c and 1 tesla along a, commensurate antiferromagnetic order and coherent, gapped spin wave exciations were found at T=1.8 K. Analysis of the corresponding anisotropic dispersion relation was used to further constrain the spin Hamiltonian for BaCo₂(AsO₄)₂, and gauge opportunities for realizing spin liquid phases in the honeycomb cobaltate.   

NMR studies of the spin liquid candidate material, κ-(BEDT-TTF)2Cu2(CN)3, with varying magnetic field and pressure

An organic triangular-lattice Mott insulator, κ-(BEDT-TTF)₂Cu₂(CN)₃, is the first candidate for a quantum spin liquid material. Even 20 years after the first report of this phenomenon, the nature of spin liquid state has still been debated. One of key phenomena to this issue is the so-called 6K-anomaly, which refers to the anomalies that appear in magnetic, thermodynamic, dielectric and lattice properties around 6K. We performed the in-depth study of the 6K-anomaly, combining ¹H and ¹³C NMR measurements in two ways; one is to examine the magnetic-field dependence of the anomaly and the other is to trace the fate of the anomaly upon the Mott transition to a metallic phase by pressure.

At ambient pressure, ¹³C NMR spectra show a significant decrease in the spin shift and a simultaneous line broadening suggestive of an inhomogeneous state below 6K. Moreover, we found that the 6K-anomaly is robust against the magnetic field up to 15Tesla. The 1/T₁ at ¹H sites, where the hyperfine coupling with conduction electrons is smaller than that at ¹³C sites, obeys similar temperature dependence to that at ¹³C sites down to 6K; however, below that, 1/T₁ shows quite different temperature variations at the ¹H and ¹³C sites, indicative of different relaxation mechanisms at the ¹³C and ¹H sites at low temperatures. This can be a key to understanding the anomalous state below 6K.

  With ¹H NMR measurements under pressure variation, we found that the 6K-anomaly suddenly and completely disappear when the system enters into the metallic.

 

    

Low-Temperature Magnetic Characterization of the Rare-Earth Melitite-Like RE2Be2GeO7 (RE = Dy, Gd, Ho, Yb, and Er)

A 2-D Heisenberg Hamiltonian with nearest-neighbour(J) and next-nearest-neighbour(J') interactions has an exactly solvable groundstate, which corresponds to a Heisenberg antiferromagnet when J'>>J, and a dimer singlet state when J>>J'. This theoretical model is attributed to Shastry and Sutherland and is referred to as the Shastry-Sutherland lattice (SSL). Materials which exhibit the SSL are of interest due to their potential to host spin-liquid states- and their associated spin-gaps- in the singlet state, as exemplified by SrCu2(BO3)2. The rare-earth Melitites, RE2Be2GeO7, are recently proposed spin-liquid candidates, hence they exhibit the Shastry-Sutherland lattice motif. However, true low-temperature data is not currently embodied by the available literature. Here, we present macroscopic and microscopic magnetic characterisation of some members (Dy, Gd, Ho, Yb, and Er) of the rare-earth melitite family, down to hundreds-to-tens of millikelvin scale.   

Proximate Deconfined Quantum Critical Point in a Shastry-Sutherland Compound SrCu2(BO3)2

    The deconfined quantum critical point (DQCP) describes a continuous quantum phase transition (QPT) beyond Landau paradigm, which takes place between two spontaneous symmetry-breaking states. The DQCP hosts novel phenomena such as emergent symmetries and fractionized excitations. Experimentally, however, DQCP has not been realized. Recently, a frustrated, quasi-2D compound SrCu₂(BO₃)₂ is found to be described proximately by the Shastry-Sutherland model¹. When tuned by pressure and field, its ground states transition from dimer singlet (DS) to plaquette singlet (PS) and long-range-ordered antiferromagnetism (AFM) ^2,3,4 , and therefore SrCu₂(BO₃)₂ may be a candidate material to search for a DQCP³.

    Here I report our high-pressure and ultra-low temperature NMR studies on SrCu₂(BO₃)₂⁵. We first established microscopic evidences for a pressure-induced DS-PS phase transition at pressures above 1.8 GPa and zero field. At 2.1 and 2.4 GPa, a field-induced weakly first-order PS-AFM QPT is firmly identified with several key observations: the coexistence temperature for two phases is as low as 0.07 K at the transition; the (H, T ) phase boundaries of both PS and AFM phases follow the power-law scaling with a single power-law exponent at each pressure; with increasing pressure, the QPT goes toward a continuous type with further suppressed AFM order parameters at the transition; the spin dynamics at 2.4 GPa revealed by the spin-lattice relaxation rates exhibits a quantum critical scaling. These facts can be understood by an approximate DQCP, with a crossover from an emergent O(3) symmetry to an O(4) type with increasing pressure, and offer a concrete platform for studying the long-sought-for DQCP in a real material.

     References:

1. H. Kageyama, et al., Phys. Rev. Lett. 82, 3168 (1999).

2. M. E. Zayed, et al., Nat. Phys. 13, 962 (2017).

3. J. Guo, et al., Phys. Rev. Lett. 124, 206602 (2020).

4. J. Larrea Jimenez, et al., Nature 592, 370 (2021).

5. Y. Cui et al., arXiv: 2204.08133.   

Magnetic excitations in the Kitaev quantum spin liquid candidate Na2Co2TeO6 – Part II: Theory

The honeycomb cobaltates are pseudospin-1/2 materials known for their highly anisotropic and bond-dependent magnetic couplings, which have been recently highlighted as potential Kitaev materials. In this contribution, we discuss the stacked honeycomb material Na₂Co₂TeO₆, for which a variety of magnetic models have been proposed on the basis of neutron scattering[1,2] and electron spin resonance measurements[3]. Combining ab-initio calculations with modeling of the neutron scattering and infrared / ESR (part I) experiments, we present a complete picture of the magnetic Hamiltonian and excitations. The effect of disorder of inter-layer Na ions on Co-Co magnetic coupling will also be discussed.

[1] W. Yao, et al., Phys. Rev. Lett. 129, 147202 (2022)

[2] W. Chen, et al., Phys. Rev. B 103, L180404 (2021)

[3] G. Lin, et al., Nat. Commun.12, 1-8 (2021)