Magnetic field effects in an octupolar quantum spin liquid candidate
Bin Gao, Tong Chen, Han Yan, Chunruo Duan, Chien-Lung Huang, Xu Ping Yao, Feng Ye, Christian Balz, J. Ross Stewart, Kenji Nakajima, Seiko Ohira-Kawamura, Guangy… 展开作者
Bin Gao, Tong Chen, Han Yan, Chunruo Duan, Chien-Lung Huang, Xu Ping Yao, Feng Ye, Christian Balz, J. Ross Stewart, Kenji Nakajima, Seiko Ohira-Kawamura, Guangyong Xu, Xianghan Xu, Sang-Wook Cheong, Emilia Morosan, Andriy H. Nevidomskyy, Gang Chen, Pengcheng Dai
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 for 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.
Recent experiments on the dipolar-octupolar pyrochlore compound Ce$_2$Zr$_2$O$_7$ indicate that it may realize a three-dimensional quantum spin liquid (QSL). In particular, the analyses of available data suggest that the system is in a region of parameter space, where the so-called $π$-flux $U(1)$ octupolar quantum spin ice (QSI) with an emergent photon could be realized. On the other hand, because the system is far from the perturbative classical spin ice regime, it is unclear whether the quantum ground state is primarily a coherent superposition of 2-in-2-out configurations as in the canonic…
We show how a gapless spin liquid with hidden octupolar order arises in an applied magnetic field, in a model applicable to thin films of 3He with competing ferromagnetic and antiferromagnetic (cyclic) exchange interactions. Evidence is also presented for nematic -- i.e., quadrupolar -- correlations bordering on ferromagnetism in the absence of a magnetic field.
In the spin-1/2 frustrated chain with nearest-neighbor ferromagnetic exchange J1 and next-nearest-neighbor antiferromagnetic exchange J2 under magnetic field, magnetic multipolar-liquid (quadrupolar, octupolar, and hexadecapolar) phases are widely expanded from the saturation down to a low-field regime. Recently, we have clarified characteristic temperature and field dependence of the NMR relaxation rate 1/T_1 in the quadrupolar phase. In this paper, we examine those of 1/T_1 in the octupolar phase combining field theoretical method with numerical data. The relevance of the results to quasi on…
Recently there have been a number of experiments on Ce$_2$Zr$_2$O$_7$ and Ce$_2$Sn$_2$O$_7$, suggesting that these materials host a three-dimensional quantum spin liquid with emergent photons and fractionalized spinon excitations. However, the interpretation of the data to determine the precise nature of the quantum spin liquids is still under debate. The Kramers doublet in Ce$^{3+}$ local moment offers unusual pseudo-spin degrees of freedom as the $x$ and $z$ components transform as a dipole and $y$ component as an octupole. This leads to a variety of possible quantum spin liquid (or quantum …
Over the past two decades, the magnetic ground states of all rare earth titanate pyrochlores have been extensively studied, with the exception of Sm$_2$Ti$_2$O$_7$. This is, in large part, due to the very high absorption cross-section of naturally-occurring samarium, which renders neutron scattering infeasible. To combat this, we have grown a large, isotopically-enriched single crystal of Sm$_2$Ti$_2$O$_7$. Using inelastic neutron scattering, we determine that the crystal field ground state for Sm$^{3+}$ is a dipolar-octupolar doublet with Ising anisotropy. Neutron diffraction experiments reve…
The dipolar-octupolar pyrochlore oxides R$_2$M$_2$O$_7$ (R=Ce, Sm, Nd) represent an important opportunity in the search for three dimensional Quantum Spin Liquid (QSL) ground states. Their low energy physics is governed by an alluringly simple XYZ Hamiltonian, enabling theoretical description with only a small number of free parameters. Meanwhile, recent experiments on Ce pyrochlores strongly suggest QSL physics. Motivated by this, we present here a complete analysis of the ground state phase diagram of dipolar-octupolar pyrochlores. Combining cluster mean field theory, variational arguments a…
We study f-electron lattice models which are capable of supporting octupolar, as well dipolar and quadrupolar, order. Analyzing the properties of the Gamma8 ground state quartet, we find that (111)-type combinations of the Gamma5 octupoles Tbeta(111)=Tbeta(x)+Tbeta(y)+Tbeta(z) are the best candidates for octupolar order parameters. Octupolar ordering induces Gamma5-type quadrupoles as secondary order parameter. Octupolar order is to some extent assisted, but in its basic nature unchanged, by allowing for the presence of quadrupolar interactions. In the absence of an external magnetic field, eq…
Recent experiments on Ce$_2$Zr$_2$O$_7$ suggest that this material may host a novel form of quantum spin ice, a three-dimensional quantum spin liquid with an emergent photon. The Ce$^{3+}$ local moments on the pyrochlore lattice are described by pseudospin 1/2 degrees of freedom, whose components transform as dipolar and octupolar moments under symmetry operations. In principle, there exist four possible quantum spin ice regimes, depending on whether the Ising component is in the dipolar/octupolar channel, and two possible flux configurations of the emergent gauge field. In this work, using ex…
We propose an exactly solvable model for $j_{\text{eff}}=\frac32$ local moments on the honeycomb lattice. Our construction is guided by a symmetry analysis and by the requirement of an exact solution in terms of a Majorana fermion representation for multipole operators. The main interaction in the model can be interpreted as a bond-dependent quadrupole-quadrupole interaction. When time reversal symmetry is explicitly broken, we obtain a gapped spin liquid with a single chiral Majorana edge mode. We also investigate another solvable model in which the time-reversal-invariant spin liquid is coup…
Experimental identification of quantum spin ice (QSI), a U(1) quantum spin liquid on the pyrochlore lattice hosting emergent photons, is a major challenge in frustrated magnets. In this work, we propose ultrasound measurements as a novel tool for probing the emergent photons of various QSI phases. Our analysis includes QSI phases in non-Kramers doublet compounds such as $\rm{Pr}_2 \rm{Zr}_2 \rm{O}_7$ as well as dipolar-octupolar Kramers doublet compounds such as $\rm{Ce}_2 \rm{Zr}_2 \rm{O}_7$. The latter may host emergent photons associated with an octupolar component which renders them diffic…
Dipolar-octupolar pyrochlore magnets in a strong external magnet field applied in the [110] direction are known to form a `chain' state, with subextensive degeneracy. Magnetic moments are correlated along one-dimensional chains carrying effective Ising degrees of freedom which are noninteracting on the mean-field level. Here, we investigate this phenomenon in detail, including the effects of quantum fluctuations. We identify two distinct types of chain phases, both featuring distinct subextensive, classical ground state degeneracy. Focussing on one of the two kinds, we discuss lifting of the c…
Recent experiments on URu2Si2 show that the low-pressure hidden order is non-magnetic but it breaks time reversal invariance. Restricting our attention to local order parameters of 5f2 shells, we find that the best candidate for hidden order is staggered order of either Tz(beta) or Txyz octupoles. Group theoretical arguments for the effect of symmetry-lowering perturbations (magnetic field, mechanical stress) predict behavior in good overall agreement with observations. We illustrate our general arguments on the example of a five-state crystal field model which differs in several details from …
Single Crystal Diffuse Neutron Scattering Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce$_2$Zr$_2$O$_7$: No Apparent Octupolar Correlations Above $T = 0.05$ K
本研究通过单晶漫散射中子衍射测量与数值连接团簇计算，发现在 $T = 0.05$ K 时 Ce$_2$Zr$_2$O$_7$ 仅表现出偶极自旋冰关联，未观察到八极关联散射的证据。
Notable non-Fermi liquid and quantum critical behaviors are observed in rare-earth metallic systems with non-Kramers local moments supporting a number of different multipolar moments. A prominent example is $\text{Pr(Ti,V)}_{2}\text{Al}_{20}$, where the non-Kramers doublet of the $\text{Pr}^{3+}$ ion allows quadrupolar and octupolar moments, but lacks a dipolar moment. Previous theoretical studies show that a single impurity Kondo problem with such an unusual local moment leads to novel non-Fermi liquid states. In this work, we investigate possible quantum critical behaviors arising from the c…
Symmetry plays a fundamental role in our understanding of both conventional symmetry breaking phases and the more exotic quantum and topological phases of matter. We explore the experimental signatures of symmetry enriched U(1) quantum spin liquids (QSLs) on the pyrochlore lattice. We point out that the Ce local moment of the newly discovered pyrochlore QSL candidate Ce$_2$Sn$_2$O$_7$, is a dipole-octupole doublet. The generic model for these unusual doublets supports two distinct symmetry enriched U(1) QSL ground states in the corresponding quantum spin ice regimes. These two U(1) QSLs are du…
We point out the experimental relevance and the detection scheme of symmetry enriched U(1) quantum spin liquids (QSLs) outside the perturbative spin-ice regime. Recent experiments on Ce-based pyrochlore QSL materials suggest that the candidate QSL may not be proximate to the well-known spin ice regime, and thus differs fundamentally from other pyrochlore QSL materials. We consider the possibility of the $π$-flux U(1) QSL favored by frustrated transverse exchange interactions rather than the usual quantum spin ice. It was previously suggested that both dipolar U(1) QSL and octupolar U(1) QSL ca…
Motivated by the recent development in strong spin-orbit-coupled materials, we consider the dipole-octupole doublets on the triangular lattice. We propose the most general interaction between these unusual local moments. Due to the spin-orbit entanglement and the special form of its wavefunction, the dipole-octupole doublet has a rather peculiar property under the lattice symmetry operation. As a result, the interaction is highly anisotropic in the pseudospin space, but remarkably, is uniform spatially. We analyze the ground state properties of this generic model and emphasize the hidden multi…
Discovery of novel spin-orbital entangled quantum ground states paves an important avenue for controllable quantum materials via unique couplings to the lattice and other external perturbations. In this work, motivated by recent experiments on cubic heavy fermion materials with multipolar local moments, we theoretically investigate strongly-interacting spin-orbital entangled quantum ground states in multipolar quantum impurity systems. Here itinerant electrons are interacting with the local moments carrying quadrupolar and octupolar moments, in contrast to the conventional Kondo problem with d…
Classical symmetry enriched topological orders and distinct monopole charges for dipole-octupole spin ices
International Center for Quantum Materials, Peking University（北京大学量子材料中心）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；The University of Hong Kong, Shenzhen Institute of Research and Innovation（香港大学深圳研究院）；Beijing Key Laboratory of Quantum Devices, Peking University（北京大学量子器件北京市重点实验室）
Neutron scattering is a powerful tool to study magnetic structures and dynamics, benefiting from a precisely established theoretical framework. The neutron dipole moment interacts with electrons in materials via their magnetic field, which can have spin and orbital origins. Yet in most experimentally studied cases the individual degrees of freedom are well described within the dipole approximation, sometimes accompanied by further terms of a multipolar expansion that usually act as minor corrections to the dipole form factor. Here we report a unique example of neutrons diffracted mainly by mag…
In this paper, based on the formulation of an O(3) non-linear sigma model, we study the two-dimensional Pi-flux Hubbard model at half-filling. A quantum non-magnetic insulator is explored near the metal-insulator transition that may be a possible candidate of the spin liquid state. Such quantum non-magnetic insulator on square lattice is not induced by frustrations. Instead, it originates from quantum spin fluctuations with relatively small effective spin moments. In the strong-coupling limit, our results of the spin velocity and spin order parameter agree with results obtained from earlier ca…
We use the constrained random phase approximation (cRPA) to derive from first principles the Ru-$t_{2g}$ Wannier function based model for the Kitaev spin-liquid candidate material $α$-RuCl$_3$. We find the non-local Coulomb repulsion to be sizable compared to the local one. In addition we obtain the contribution to the Hamiltonian from the spin-orbit coupling and find it to also contain non-negligible non-local terms. We invoke strong coupling perturbation theory to investigate the influence of these non-local elements of the Coulomb repulsion and the spin-orbit coupling on the magnetic intera…
The spin-liquid candidate $κ$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$ has been studied by measuring the uniaxial expansion coefficients $α_{i}$, the specific heat, and magnetic susceptibility. Special emphasis was placed on the mysterious anomaly around 6 K - a potential spin-liquid instability. Distinct and strongly anisotropic lattice effects have been observed at 6 K, clearly identifying this feature as a second-order phase transition. Owing to the large anomalies in $α_{i}$, the application of Grüneisen scaling has enabled us to determine the corresponding specific heat contribution and the ent…
Ba4NbIr3O12, a previously unreported material with a triangular planar geometry of Ir3O12 trimers, is described. Magnetic susceptibility measurements show no magnetic ordering down to 1.8 K despite the Curie-Weiss temperature of -13 K. The material has a very low effective magnetic moment of 0.80 μB/f.u. To look at the lower temperature behavior, the specific heat (Cp) was measured down to 0.35 K; it shows no indication of magnetic ordering and fitting a power law to Cp vs. T below 2 K yields the power α = 3/4. Comparison to the previously unreported trimer compound made with the 4d element Rh…
We study the ground state properties, the electronic excitations and lattice dynamics in spin-liquid candidate TbInO$_3$. By employing polarization resolved Raman spectroscopy we define the inter- and intra-multiplet excitations, and establish the low-energy crystal-field (CF) level scheme. In particular, we demonstrate that the ground state of the Tb$^{3+}$ ions is a non-Kramers doublet, and relate the enhanced linewidth of the CF modes to the magnetic fluctuations near the spin-liquid ground state. We identify all 38 allowed Raman-active phonon modes at low temperature. Moreover, we observe …
We report measurements of the specific heat and magnetization of single crystal samples of the spin-1/2 kagome compound ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ (herbertsmithite), a promising quantum spin-liquid candidate, in high magnetic fields and at low temperatures. The magnetization was measured up to $μ_{0}H$ = 55 T at $T$ = 0.4 K, showing a saturation of the weakly interacting impurity moments in fields above $\sim10$ T. The specific heat was measured down to $T < 0.4$ K in magnetic fields up to 18 T, revealing $T$-linear and $T$-squared contributions. The $T$-linear contribution is surprisingly l…
We propose an experiment to use the magneto-optical Faraday effect to probe the dynamic Hall conductivity of spin liquid candidates. Theory predicts that an external magnetic field will generate an internal gauge field. If the source of conductivity is in spinons with a Fermi surface, a finite Faraday rotation angle is expected. We predict the angle to scale as the square of the frequency rather than display the standard cyclotron resonance pattern. Furthermore, the Faraday effect should be able to distinguish the ground state of the spin liquid, as we predict no rotation for massless Dirac sp…
The Kitaev quantum spin liquid displays the fractionalization of quantum spins into Majorana fermions. The emergent Majorana edge current is predicted to manifest itself in the form of a finite thermal Hall effect, a feature commonly discussed in topological superconductors. Here we report on thermal Hall conductivity $κ_{xy}$ measurements in $α$-RuCl$_3$, a candidate Kitaev magnet with the two-dimensional honeycomb lattice. In a spin-liquid (Kitaev paramagnetic) state below the temperature characterized by the Kitaev interaction $J_K/k_B \sim 80$ K, positive $κ_{xy}$ develops gradually upon c…
The organic conductor $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_{3}$ seems to form a quantum spin liquid, although at low temperatures unusual properties are seen in the charge, spin and lattice degrees of freedom. Here we report results of X-band ESR studies of $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_{3}$ single crystals as a function of temperature and angle. We find indications of two anisotropic relaxation mechanisms at low temperatures and compare them to the spin-liquid behavior observed in other strongly correlated systems. In addition, we can recognize charge inhomogeneities in the copper ions of the anion …
The thermal conductivity $κ$ of the quasi-2D organic spin-liquid candidate EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ (dmit-131) was measured at low temperatures, down to 0.07 K. We observe a vanishingly small residual linear term $κ_0/T$, in $κ/T$ vs $T$ as $T \to 0$. This shows that the low-energy excitations responsible for the sizeable residual linear term $γ$ in the specific heat $C$, seen in $C/T$ vs $T$ as $T \to 0,$ are localized. We conclude that there are no mobile gapless excitations in this spin liquid candidate, in contrast with a prior study of dmit-131 that reported a large $κ_0/T$ value [Yam…
Long-range entanglement in quantum spin liquids (QSLs) lead to novel low energy excitations with fractionalised quantum numbers and (in 2D) statistics. Experimental detection and manipulation of these excitations present a challenge particularly in view of diverse candidate magnets. A promising probe of fractionalisation is their coupling to phonons. Here we present Raman scattering results for the S = 1/2 honeycomb iridate Cu2IrO3, a candidate Kitaev QSL with fractionalised Majorana fermions and Ising flux excitations. We observe anomalous low temperature frequency shift and linewidth broaden…
The search for quantum spin liquid (QSL) materials has attracted significant attention in the field of condensed matter physics in recent years, but until now only a handful of them are considered as candidates hosting QSL ground state. Owning to their geometrically frustrated structure, Kagome materials are ideal system to realize QSL. In this study, we synthesized the kagome structured material Claringbullite (Cu$_4$(OH)$_6$FCl) and then performed Zn doping to form Cu$_3$Zn(OH)$_6$FCl. Comprehensive measurements reveal that doping Zn$^{2+}$ ions transforms magnetically ordered Cu$_4$(OH)$_6$…
The low-temperature state of the quantum spin liquid candidate $κ$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$ emerges via an anomaly at $T^{*}\sim6$ K. Although signatures of this anomaly have been revealed in various quantities, its origin has remained unclear. Here we report inelastic neutron scattering measurements on single crystals of $κ$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$, aiming at studying phonon renormalization effects at $T^{*}$. A drastic change was observed in the phonon damping across $T^{*}$ for a breathing mode of BEDT-TTF dimers at $E=4.7$ meV. The abrupt change in the phonon damping i…
We construct a generalized multiplicative renormalization group transformation to study the low energy dynamics of a heavy particle tunneling among $M$ different positions and interacting with $N_f$ independent conduction electron channels. Using a $1/N_f$-expansion we show that this M-level scales towards a fixed point equivalent to the $N_f$ channel $SU(M) \times SU(N_f)$ Coqblin-Schrieffer model. Solving numerically the scaling equations we find that a realistic M-level system scales close to this fixed point (FP) and its Kondo temperature is in the experimentally observable range $1-10 K$.
H3LiIr2O6 is the first honeycomb-lattice system without any signs of long-range magnetic order down to the lowest temperatures, raising the hope for the realization of an ideal Kitaev quantum spin liquid. Its honeycomb layers are coupled by interlayer hydrogen bonds. Static or dynamic disorder of these hydrogen bonds was proposed to strongly affect the magnetic exchange and to make Kitaev-type interactions dominant. Using dielectric spectroscopy, here we provide experimental evidence for dipolar relaxations in H3LiIr2O6 and deuterated D3LiIr2O6, which mirror the dynamics of protons and deutero…
Quantum spin liquids (QSLs) are exotic states of matter characterized by emergent gauge structures and fractionalized elementary excitations. The recently discovered triangular lattice antiferromagnet YbMgGaO$_4$ is a promising QSL candidate, and the nature of its ground state is still under debate. Here, we use neutron scattering to study the spin excitations in YbMgGaO$_4$ under various magnetic fields. Our data reveal a dispersive spin excitation continuum with clear upper and lower excitation edges under a weak magnetic field ($H=2.5$ T). Moreover, a spectral crossing emerges at the $Γ$ po…
We construct and analyze a microscopic model for insulating rock salt ordered double perovskites, with the chemical formula A$_2$BB'O$_6$, where the B' atom has a 4d$^1$ or 5d$^1$ electronic configuration and forms a face centered cubic (fcc) lattice. The combination of the triply-degenerate $t_{2g}$ orbital and strong spin-orbit coupling forms local quadruplets with an effective spin moment $j=3/2$. Moreover, due to strongly orbital-dependent exchange, the effective spins have substantial biquadratic and bicubic interactions (fourth and sixth order in the spins, respectively). This leads, at …
The insulating honeycomb magnet $α$-RuCl$_{3}$ exhibits fractionalized excitiations that signal its proximity to a Kitaev quantum spin liquid (QSL) state, however, at $T=0$, fragile long-range magnetic order arises from non-Kitaev terms in the Hamiltonian. Spin vacancies in the form of Ir$^{3+}$ substituted for Ru are found to destabilize this long-range order. Neutron diffraction and bulk characterization of Ru$_{1-x}$Ir$_{x}$Cl$_{3}$ show that the magnetic ordering temperature is suppressed with increasing $x$ and evidence of zizag magnetic order is absent for $x>0.3$. Inelastic neutron scat…
Measurements of the coefficient of thermal expansion on the spin-liquid candidate $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ have revealed distinct and strongly anisotropic lattice effects around 6 K - a possible spin-liquid instability. In order to study the effects of a magnetic field on the low-temperature spin-liquid state, dilatometric measurements have been conducted both as a function of temperature at \emph{B} = const. and as a function of field at \emph{T} = const. While the 6 K anomaly is found to be insensitive to magnetic fields \emph{B} $\leq$ 10 T, the maximum field applied, surprisingly s…
Proposed effective Hamiltonians from the literature for the material $α$-RuCl${}_3$ are used to compute the magnon thermal Hall conductivity, $κ_{xy}$, using linear spin wave theory for the magnetically ordered state. No model previously proposed that was tested explains published experimental data. Models with Kitaev interaction $K>0$ are seen to predict $κ_{xy}\gtrsim 0$, which is inconsistent with the data. Fluctuations toward a Kitaev-type spin liquid would have the wrong sign to explain the data. However, a slight variant of a previously proposed model predicts a large $κ_{xy}$, demonstra…
