Exotic Low-Energy Excitations Emergent in the Random Kitaev Magnet Cu_{2}IrO_{3}

Magnetocaloric effect of topological excitations in Kitaev magnets

Traditional magnetic sub-Kelvin cooling relies on the nearly free local moments in hydrate paramagnetic salts, whose utility is hampered by the dilute magnetic ions and low thermal conductivity. Here we propose to use instead fractional excitations inherent to quantum spin liquids (QSLs) as an alternative, which are sensitive to external fields and can induce a very distinctive magnetocaloric effect. With state-of-the-art tensor-network approach, we compute low-temperature properties of Kitaev honeycomb model. For the ferromagnetic case, strong demagnetization cooling effect is observed due to the nearly free Z2 vortices via spin fractionalization, described by a paramagnetic equation of state with a renormalized Curie constant. For the antiferromagnetic Kitaev case, we uncover an intermediate-field gapless QSL phase with very large spin entropy, possibly due to the emergence of spinon Fermi surface and gauge field. Potential realization of topological excitation magnetocalorics in Kitaev materials is also discussed, which may offer a promising pathway to circumvent existing limitations in the paramagnetic hydrates.

High-temperature magnetic anomaly via suppression of antisite disorder through synthesis route modification in a Kitaev candidate Cu2IrO3

By incorporating inert KCl into the Na2IrO3+ 2CuCl → Cu2IrO3+ 2NaCl topochemical reaction, we significantly reduced the synthesis temperature of Cu2IrO3from the 350 °C reported in previous studies to 170 °C. This adjustment decreased the Cu/Ir antisite disorder concentration in Cu2IrO3from ∼19% to ∼5%. Furthermore, magnetic susceptibility measurements of the present Cu2IrO3sample revealed a weak ferromagnetic-like anomaly with hysteresis at a magnetic transition temperature of ∼70 K. Our research indicates that the spin-disordered ground state reported in chemically disordered Cu2IrO3is an extrinsic phenomenon, rather than an intrinsic one, underscoring the pivotal role of synthetic chemistry in understanding the application of Kitaev model to realistic materials.

Beyond Kitaev physics in strong spin-orbit coupled magnets

We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To this end, we present a comprehensive overview of the key exchange interactions in candidate materials with a specific focus on systems featuring effectiveJeff=1/2magnetic moments. This includes, but not limited to,5d5iridates,4d5ruthenates and3d7cobaltates. Our exploration covers the microscopic origins of these interactions, along with a systematic attempt to map out the most intriguing correlated regimes of the multi-dimensional parameter space. Our approach is guided by robust symmetry and duality transformations as well as insights from a wide spectrum of analytical and numerical studies. We also survey higher spin Kitaev models and recent exciting results on quasi-one-dimensional models and discuss their relevance to higher-dimensional models. Finally, we highlight some of the key questions in the field as well as future directions.

Possible realization of three-dimensional quantum spin liquid behavior in HoVO4

The study of geometrically frustrated magnetic systems with unusual crystal field ground states offers a possibility of realizing the new aspects of physics of disordered systems. In this study, we report our results of structural, magnetic susceptibility, heat capacity measurements, along with density functional theory (DFT) calculations on HoVO₄; a compound in which the presence of a distorted kind of HoO₈polyhedral leads to multiple magnetic interaction paths. The observed broad maximum below 10 K in the temperature response of DC susceptibility curves implies the presence of short-range correlations. AC susceptibility rules out the possibility of any kind of spin freezing. Temperature dependent heat capacity measurement at zero field indicate towards the absence of long-range ordering, along with the presence of a broad maximum centered around 14 K. The residual heat capacity exhibits a characteristic power-law (T^α) behavior with the exponentαnearly equal to 2, which is analogous to that observed for other three-dimensional (3D) quantum spin liquid (QSL) systems. The DFT calculations signify the presence of dominant second and third nearest neighbor interactions, which in turn lead to magnetic frustration in our system. Our investigations suggest that HoVO₄can be a candidate for realizing a 3D QSL state.

Unravelling the signatures of effective spin1/2moments in CeVO4: magnetization and heat capacity study

The realization of an effective spin (J_eff) ½ state at low temperatures offers a platform to study the enthralling physics behind the disordered states in certain systems. Here, we report the signatures of magnetic ground state associated withJ_eff= ½ in CeVO₄. Our studies confirm the absence of any ordering or freezing down to 1.8 K. In the low temperature region, the Curie-Weiss fit of the inverse DC susceptibility indicate towards the presence of antiferromagnetic correlations among the Ce³⁺spins. The calculated value of effective moment (∼1.16μB) corresponds toJ= ½ withg_J∼ 1.20. Further, the field dependent magnetization curve at 2 K follows a behaviour corresponding toJ= ½ Brillouin function withg_J∼ 1.13. Magnetic field dependent heat capacity fits very well with two-level Schottky scheme. Our investigations suggest that CeVO₄can be a promising candidate to realiseJ_eff= ½ properties among 3D spin systems.

Metastable Kitaev Magnets

Nearly two decades ago, Alexei Kitaev proposed a model for spin-1/2 particles with bond-directional interactions on a two-dimensional honeycomb lattice which had the potential to host a quantum spin-liquid ground state. This work initiated numerous investigations to design and synthesize materials that would physically realize the Kitaev Hamiltonian. The first generation of such materials, such as Na2IrO3, α-Li2IrO3, and α-RuCl3, revealed the presence of non-Kitaev interactions such as the Heisenberg and off-diagonal exchange. Both physical pressure and chemical doping were used to tune the relative strength of the Kitaev and competing interactions; however, little progress was made towards achieving a purely Kitaev system. Here, we review the recent breakthrough in modifying Kitaev magnets via topochemical methods that has led to the second generation of Kitaev materials. We show how structural modifications due to the topotactic exchange reactions can alter the magnetic interactions in favor of a quantum spin-liquid phase.

Néel ordering in the distorted honeycomb pyrosilicate: C-Er2Si2O7

The rare-earth pyrosilicate family of compounds (RE2Si2O7) hosts a variety of polymorphs, some with honeycomb-like geometries of the rare-earth sublattices, and the magnetism has yet to be deeply explored in many of the cases. Here we report on the ground state properties of C-Er2Si2O7. C-Er2Si2O7crystallizes in the C2/m space group and the Er3+atoms form a distorted honeycomb lattice in thea-bplane. We have utilized specific heat, DC susceptibility, and neutron diffraction measurements to characterize C-Er2Si2O7. Our specific heat and DC susceptibility measurements show signatures of antiferromagnetic ordering at 2.3 K. Neutron powder diffraction confirms this transition temperature and the relative intensities of the magnetic Bragg peaks are consistent with a collinear Néel state in the magnetic space group C2'/m, with ordered moment of 6.61μBcanted 13° away from thec-axis toward thea-axis. These results are discussed in relation to the isostructural quantum dimer magnet compound Yb2Si2O7.

Orbital Effects in Solids: Basics, Recent Progress, and Opportunities

The properties of transition metal compounds are largely determined by nontrivial interplay of different degrees of freedom: charge, spin, lattice, and also orbital ones. Especially rich and interesting effects occur in systems with orbital degeneracy. For example, they result in the famous Jahn-Teller effect, leading to a plethora of consequences for static and dynamic properties, including nontrivial quantum effects. In the present review, we discuss the main phenomena in the physics of such systems, paying central attention to the novel manifestations of those. After shortly summarizing the basic phenomena and their descriptions, we concentrate on several specific directions in this field. One of them is the reduction of effective dimensionality in many systems with orbital degrees of freedom due to the directional character of orbitals, with the concomitant appearance of some instabilities that lead in particular to the formation of dimers, trimers, and similar clusters in a material. The properties of such cluster systems, which are largely determined by their orbital structure, are discussed in detail, and many specific examples of those in different materials are presented. Another big field that has acquired special significance relatively recently is the role of the relativistic spin-orbit interaction. The mutual influence of this interaction and the more traditional Jahn-Teller physics is treated in detail in the second part of the review. In discussing all of these questions, special attention is paid to novel quantum effects.

Competing antiferromagnetic-ferromagnetic states in a d7 Kitaev honeycomb magnet

The Kitaev model is a rare example of an analytically solvable and physically instantiable Hamiltonian yielding a topological quantum spin liquid ground state. Here we report signatures of Kitaev spin liquid physics in the honeycomb magnet Li3Co2SbO6, built of high-spin d 7 (Co2+) ions, in contrast to the more typical low-spin d 5 electron configurations in the presence of large spin-orbit coupling. Neutron powder diffraction measurements, heat capacity, and magnetization studies support the development of a long-range antiferromagnetic order space group of C C 2/ m , below T N   =   11 K at μ 0 H   =   0 T . The magnetic entropy recovered between T   =   2 and 50 K is estimated to be 0.6 R ln2 , in good agreement with the value expected for systems close to a Kitaev quantum spin liquid state. The temperature-dependent magnetic order parameter demonstrates a β value of 0.19(3), consistent with XY anisotropy and in-plane ordering, with Ising-like interactions between layers. Further, we observe a spin-flop-driven crossover to ferromagnetic order with space group of C 2/ m under an applied magnetic field of μ 0 H   ≈   0.7 T at T   =   2   K . Magnetic structure analysis demonstrates these magnetic states are competing at finite applied magnetic fields even below the spin-flop transition. Both the d 7 compass model, a quantitative comparison of the specific heat of Li3Co2SbO6, and related honeycomb cobaltates to the anisotropic Kitaev model further support proximity to a Kitaev spin liquid state. This material demonstrates the rich playground of high-spin d 7 systems for spin liquid candidates and complements known d 5 Ir- and Ru-based materials.

Signatures of a Spin-1/2 Cooperative Paramagnet in the Diluted Triangular Lattice of Y_{2}CuTiO_{6}

We present a combination of thermodynamic and dynamic experimental signatures of a disorder driven dynamic cooperative paramagnet in a 50% site diluted triangular lattice spin-1/2 system: Y_{2}CuTiO_{6}. Magnetic ordering and spin freezing are absent down to 50 mK, far below the Curie-Weiss scale (-θ_{CW}) of ∼134  K. We observe scaling collapses of the magnetic field and temperature dependent magnetic heat capacity and magnetization data, respectively, in conformity with expectations from the random singlet physics. Our experiments establish the suppression of any freezing scale, if at all present, by more than 3 orders of magnitude, opening a plethora of interesting possibilities such as disorder stabilized long range quantum entangled ground states.

Randomly Hopping Majorana Fermions in the Diluted Kitaev System α-Ru_{0.8}Ir_{0.2}Cl_{3}

dc and ac magnetic susceptibility, magnetization, specific heat, and Raman scattering measurements are combined to probe low-lying spin excitations in α-Ru_{1-x}Ir_{x}Cl_{3} (x≈0.2), which realizes a disordered spin liquid. At intermediate energies (ℏω>3  meV), Raman spectroscopy evidences linearly ω-dependent Majorana-like excitations, obeying Fermi statistics. This points to robustness of a Kitaev paramagnetic state under spin vacancies. At low energies below 3 meV, we observe power-law dependences and quantum-critical-like scalings of the thermodynamic quantities, implying the presence of a weakly divergent low-energy density of states. This scaling phenomenology is interpreted in terms of the random hoppings of Majorana fermions. Our results demonstrate an emergent hierarchy of spin excitations in a diluted Kitaev honeycomb system subject to spin vacancies and bond randomness.

Nonmetallic metal toward a pressure-induced bad-metal state in two-dimensional Cu3LiRu2O6

The two-dimensional honeycomb layered nonmetallic metal Cu₃LiRu₂O₆ exhibits Pauli-like paramagnetic and Mott variable range hopping semiconduction behaviors, which can be significantly suppressed toward a bad-metal state by pressure up to 35 GPa.

Thermodynamic Evidence of Proximity to a Kitaev Spin Liquid in Ag_{3}LiIr_{2}O_{6}

Kitaev magnets are materials with bond-dependent Ising interactions between localized spins on a honeycomb lattice. Such interactions could lead to a quantum spin-liquid (QSL) ground state at zero temperature. Recent theoretical studies suggest two potential signatures of a QSL at finite temperatures, namely, a scaling behavior of thermodynamic quantities in the presence of quenched disorder, and a two-step release of the magnetic entropy. Here, we present both signatures in Ag_{3}LiIr_{2}O_{6} which is synthesized from α-Li_{2}IrO_{3} by replacing the interlayer Li atoms with Ag atoms. In addition, the dc susceptibility data confirm the absence of a long-range order, and the ac susceptibility data rule out a spin-glass transition. These observations suggest a closer proximity to the QSL in Ag_{3}LiIr_{2}O_{6} compared to its parent compound α-Li_{2}IrO_{3} that orders at 15 K. We discuss an enhanced spin-orbit coupling due to a mixing between silver d and oxygen p orbitals as a potential underlying mechanism.