Session G46: Pyrochlores II: Spin Liquids

Dynamics of a pyrochlore quantum spin liquid NaCaNi2F7

The Heinsenberg antiferromagnet on a pyrochlore lattice is a well-known model realizing a classical spin-liquid state at low temperatures [1]. Much less is known about the quantum version of this model. The spin-1 pyrochlore material NaCaNi₂F₇ is well described by a weakly perturbed Heisenberg Hamiltonian [2]. It shows no magnetic order down to extremely low temperatures, making it a prime candidate for a three-dimensional quantum spin liquid. Inelastic neutron scattering has revealed a lack of magnetic Bragg peaks and a broad continuum of excitations incompatible with a conventional magnetically ordered state. We combine analytical theory and numerical approaches to elucidate the nature of this enigmatic spin-liquid state [3]. The three approaches---molecular dynamics simulations, stochastic dynamical theory and linear spin wave theory---reproduce remarkably well the energy and momentum dependence of the experimental inelastic neutron scattering intensity with the exception of the lowest energies. Our study offers the following picture of spin dynamics in this system. This frustrated magnet is slowly moving through a (very large) manifold of degenerate ground states lacking long-range order. This slow motion is driven by medium- and high-energy spin waves with Bose statistics. We discuss two surprising aspects and their implications for quantum spin liquids in general: the complete lack of sharp quasiparticle excitations in momentum space and the success of the linear spin wave theory. Similar conclusions have been reached independently about a S=3/2 "pyrochlore" antiferromagnet MgCr₂O₄ [4].

[1] R. Moessner and J. T. Chalker, Phys. Rev. Lett. 80, 2929 (1998).
[2] K.W. Plumb et al., Nat. Phys. 15, 54 (2019).
[3] S. Zhang et al., Phys. Rev. Lett. 122, 167203 (2019).
[4] X. Bai et al., Phys. Rev. Lett. 122, 097201 (2019).   

Magnetic field dependence of magnetic correlations in a pyrochlore Heisenberg antiferromagnet

Recent neutron experiments on the S=1 pyrochlore NaCaNi₂F₇ [1] revealed a dynamic structure factor exhibiting pinch points and a continuum of high energy magnetic excitations. These signatures point towards a magnetic ground-state which can be described by an almost ideal Heisenberg antiferromagnet on the pyrochlore lattice. Although a highly degenerate ground state its expected at low temperatures, disorder freezes the spin degrees of freedom so that a specific spin configuration is preferred [2]. How disorder induces a frozen spin state in this Coulomb phase [3] remains to be fully understood. We present here a set of neutron scattering measurements in NaCaNi₂F₇ as a function of external magnetic field. Above a threshold field, H > 2 T, a long-range ordered magnetic field polarized phase emerges. I will discuss the magnetic field and temperature evolution of magnetic correlations in NaCaNi₂F₇ through this polarized phase.

[1] Krizan, J. W. and Cava, R. J., Physical Review B 92, 014406 (2015)
[2] Plumb, K. W. et al, Nat. Phys. 1, 54 (2019)
[3] Henley, C. L., Annu. Rev. Condens. Matter Phys 1, 179 (2010)
  

Ultrasound Velocity Measurements in Bond-Disordered Pyrochlore Magnet NaCaCo2F7

Pyrochlore cobalt fluoride NaCaCo₂F₇ is a geometrically frustrated magnet, which exhibits spin freezing below T_f ~ 2.4 K while the Weiss temperature is θ_W ~ -140 K. The spin-freezing behavior in this compound is considered to be due to the presence of bond randomness which is generated by the random occupation of Na⁺ and Ca²⁺ ions on the pyrochlore A sites. We perform ultrasound velocity measurements in a single crystal of NaCaCo₂F₇. Temperature (T) dependence of the bulk modulus C_B = (C₁₁+2C₁₂)/3 exhibits Curie-type -1/T softening upon cooling below ~ 20 K down to T_f, which should be a precursor to the lattice distortion at T_f. And this softening is suppressed by the application of magnetic field, indicating that the spin freezing is driven by the spin-lattice coupling. For the bond-disordered frustrated NaCaCo₂F₇, the softening in the breathing elastic mode of C_B above T_f suggests that the spin freezing, or the release of frustration is a result of the enhancement of the bond randomness driven by the spin-lattice coupling.   

Low energy excitations in Tb2Ti2O7 with [111] magnetic field

The pyrochlore magnet Tb₂Ti₂O₇ has shown exotic magnetic properties and has been considered to be a quantum spin liquid. Although Tb₂Ti₂O₇ has been studied for decades, low energy experiments with magnetic field along [111] are rare. We perform time-domain terahertz spectroscopy on high quality Tb₂Ti₂O₇ crystal to study the crystal field excitations as a function of magnetic field with very high resolution. The excitations behaves significantly different below and above a critical field, indicating a phase transition around 2.5 T. We also observed the discrepancy between two polarization channels. Our work provides insight into this very intriguing material.   

THz spectroscopy study of the rare-earth pyrochlore Tb2Ti2O7

Tb₂Ti₂O₇ is unique rare-earth pyrochlore in that it does not exhibit theoretically predicted long-range magnetic order down to the lowest measured temperatures below 100 mK. Instead, a fluctuating spin-liquid state with short-range correlations persists, while strong spin-lattice coupling occurs. As a manifestation of this coupling, the two lowest crystal electric field (CEF) level doublets separated by approximately 1.5 meV = 0.42 THz have been shown to couple to a transverse acoustic phonon. Such a vibronic process is accompanied by hybrid magnetoelastic excitations, which have been previously detected by neutron scattering and THz spectroscopy.
We measured absorption of THz radiation in a single crystal at the temperatures 3 K and 60 K combined with magnetic fields up to B = 15 T applied along the local [111] axis. The B dependence of the crystal field excitations gives us the opportunity to accurately describe the CEF spectrum including the vibronic process, and to see how it is transformed by a static magnetic field.   

Probing Multipolar Quantum Spin Liquids in non-Kramers Pyrochlore Materials with Magnetostriction.

Quantum spin liquids (QSLs) and Multipolar ordered states (MPOs) both share the property of being notoriously difficult to detect with conventional probes. Recently, lattice-based techniques are proposed as novel probes to detect MPOs. Motivated by this success, we investigate the possibility of detecting QSL when it arises from interacting multipolar moments. In this talk, we theoretically propose that spin-lattice coupling can be used as a powerful tool to probe such multipolar QSL phases.   

Half-moon quantum spin liquid in a spin-1/2 J1-J2-J3a Heisenberg antiferromagnet on the pyrochlore lattice

We investigate the quantum Heisenberg model on the pyrochlore lattice for spin-1/2 in the presence of antiferromagnetic nearest-neighbor J₁, second nearest-neighbor J₂, and third nearest-neighbor J_3a exchange interactions. By employing the pseudofermion functional renormalization group method, we find, that the quantum Coulomb spin liquid of the J₁ only model is robust along the line J=J₂=J_3a up till J/J₁∼0.22, thus extending its classical region of stability. Similarly, for J/J₁>0.22, we find an absence of long-range magnetic order down to T=J₁/100, however, the bowtie features now give way to half-moons as seen in the static spin susceptibility profile, thus pointing to the realization of a ``half-moon’’ quantum spin liquid. At the point J/J₁=1/2, which features a sub-extensively degenerate classical ground-state manifold, we show that quantum fluctuations fail to break this degeneracy stabilizing a quantum spin liquid. In stark contrast to this finding, in the corresponding classical model, thermal fluctuations are known to select a collinear antiferromagnetically ordered state via the order-by-disorder mechanism. Hence, we present a rare scenario wherein thermal and quantum fluctuations act differently.   

Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore

A quantum spin liquid (QSL) is an exotic state of matter where unpaired electrons’ spins, although being entangled, do not show magnetic order even at the zero-temperature. Because such a state may be important to the microscopic origin of high-transition temperature superconductivity and useful for quantum computation, the experimental realization of QSL is a long-sought goal in condensed matter physics. Although neutron scattering experiments on the two-dimensional QSL candidates ZnCu₃(OD)₆Cl₂ and YbMgGaO₄ have found evidence for the hallmark of a QSL at very low temperature - a continuum of magnetic excitations, the presence of site disorder complicates the interpretation of the data. Recently, the three-dimensional (3D) Ce³⁺ pyrochlore lattice Ce₂Sn₂O₇ has been suggested as a clean, effective spin-1/2 QSL candidate, but the evidence of a spin excitation continuum is missing due to the lack of single crystals. Here we use alternating current magnetic susceptibility, thermodynamic, muon spin relaxation (μSR), and neutron scattering experiments on single crystals of Ce₂Zr₂O₇, a compound isostructural to Ce₂Sn₂O₇, to demonstrate the absence of magnetic ordering/spin-glass down to 20 mK and the presence of a spin excitation continuum at 35 mK. With no evidence of oxygen deficiency and chemical disorder seen by diffuse scattering measurements and neutron diffraction, Ce₂Zr₂O₇ may be a 3D pyrochlore lattice QSL material with minimum magnetic and nonmagnetic chemical disorder.   

Interplay between magnetic exchange, multipolar interactions and virtual crystal field fluctuations in non-Kramers pyrochlore magnets

It has been shown that multipolar degrees of freedom can play a vital role in causing exotic phases in pyrochlore magnets, such as octupoles in Kramers Nd³⁺ or Ce³⁺ ions and quadrupoles in non-Kramers Pr³⁺ and Tb³⁺ ions. Terbium-based pyrochlores are peculiar for hosting virtual crystal field excitation (VCFE) due to the small energy separation between the two low-lying crystal electric field doublets. Here we consider a two-doublets system with magnetic bilinear exchange and electric quadrupole-quadrupole interaction. Via a mean field approach, we show that the proposed model exhibits complex dipolar and quadrupolar phases. Different dipolar order parameters coexist due to VCFE, which also leads to a “parasitic” ferroquadrupolar order accompanying the dominant antiferroquadrupolar order. We find for a set of model parameters locating the system near the dipolar/quadrupolar phase boundary that, upon cooling, such system may undergo a two-step thermal transition into the ultimate low-temperature dipolar phase with an intermediated quadrupolar ordered state. We also propose a range of acceptable parameters for the Tb₂Ge₂O₇ pyrochlore that allows us to reproduce some of the main inelastic neutron scattering features.   

Crystal Field Excitations in Raman Spectra of Pr-based Pyrochlores

Interplay of strong electron correlations and spin-orbit coupling leads to exotic magnetic phases in rare earth pyrochlores. Here we present a study of Pr₂Ir₂O₇ and Pr₂Zr₂O₇, which show magnetic interactions but no ordering down to low temperatures [1-3]. We performed low temperature Raman scattering spectroscopy study of Pr₂Ir₂O₇ and Pr₂Zr₂O₇ single crystals to probe crystal field excitations and phonons. A comparison of crystal field excitations in these two materials reveals a splitting in the Pr³⁺ crystal field doublet at 57 meV in Pr₂Zr₂O₇, possibly originating from the magneto-elastic coupling induced vibronic state. An anomalous broadening of this crystal field excitation is observed in Pr₂Ir₂O₇. A comparison of phonon spectrum to the density functional theory calculations demonstrates an anomalous broadening/splitting of the E_g phonon mode corresponding to the Ir-O-Ir (Zr-O-Zr) bending. We discuss relevance of our findings to magnetic properties of these materials.

[1] S. Nakatsuji, et al., Phys. Rev. Lett 96.8 (2006) 087204.
[2] Y. Machida, et al., Nature 463.7278 (2010) 210.
[3] K. Kimura et al., Nat. Commun. 4 (2013) 1934   

Probing Emergent Excitations in Pr2Hf2O7 with Thermal Conductivity

Pr₂Hf₂O₇ (PHO) is a quantum spin ice candidate with a non-Kramers doublet ground state that displays evidence of dynamic spin ice behaviour [1][2]. We report thermal conductivity measurements of single crystal samples of PHO as a function of temperature between 50 mK and 50 K and magnetic field up to 12 T. A combination of high magnetic field measurements and measurements of different sized samples are used to identify the lattice contribution. We interpret our results considering current theoretical predictions for exotic excitations in quantum spin liquids, such as emergent photons, magnetic monopoles and visons [3].

[1] V. K. Anand et al., Phys. Rev. B 94, 144415 (2016).
[2] R. Sibille et al., Phys. Rev. B 94, 024436 (2016).
[3] M. Gingras and P. McClarty, Rep. Prog. Phys. 77, 056501 (2014).