ABSTRACT
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.
ABSTRACT
Quantum spin liquids (QSLs) have been at the forefront of correlated electron research ever since their proposal in 1973, and the realization that they belong to the broader class of intrinsic topological orders. According to received wisdom, QSLs can arise in frustrated magnets with low spin S, where strong quantum fluctuations act to destabilize conventional, magnetically ordered states. Here, we present a Z2 QSL ground state that appears already in the semiclassical, large-S limit. This state has both topological and symmetry-related ground-state degeneracy, and two types of gaps, a "magnetic flux" gap that scales linearly with S and an "electric charge" gap that drops exponentially in S. The magnet is the spin-S version of the spin-1/2 Kitaev honeycomb model, which has been the subject of intense studies in correlated electron systems with strong spin-orbit coupling, and in optical lattice realizations with ultracold atoms.
ABSTRACT
We show that the off-diagonal exchange anisotropy drives Mott insulators with strong spin-orbit coupling to a classical spin liquid regime, characterized by an infinite number of ground states and Ising variables living on closed or open strings. Depending on the sign of the anisotropy, quantum fluctuations either fail to lift the degeneracy down to very low temperatures, or select noncoplanar magnetic states with unconventional spin correlations. The results apply to all 2D and 3D tricoordinated materials with bond-directional anisotropy and provide a consistent interpretation of the suppression of the x-ray magnetic circular dichroism signal reported recently for ß-Li_{2}IrO_{3} under pressure.
ABSTRACT
Iridium oxides with a honeycomb lattice have been identified as platforms for the much anticipated Kitaev topological spin liquid: the spin-orbit entangled states of Ir(4+) in principle generate precisely the required type of anisotropic exchange. However, other magnetic couplings can drive the system away from the spin-liquid phase. With this in mind, here we disentangle the different magnetic interactions in Li2IrO3, a honeycomb iridate with two crystallographically inequivalent sets of adjacent Ir sites. Our ab initio many-body calculations show that, while both Heisenberg and Kitaev nearest-neighbour couplings are present, on one set of Ir-Ir bonds the former dominates, resulting in the formation of spin-triplet dimers. The triplet dimers frame a strongly frustrated triangular lattice and by exact cluster diagonalization we show that they remain protected in a wide region of the phase diagram.
ABSTRACT
It is well known that the low-energy sector of quantum spin liquids and other magnetically disordered systems is governed by short-ranged resonating-valence bonds. Here we show that the standard minimal truncation to the nearest-neighbor valence-bond basis fails completely even for systems where it should work the most, according to received wisdom. This paradigm shift is demonstrated for the quantum spin-1/2 square kagome, where strong geometric frustration, similar to the kagome, prevents magnetic ordering down to zero temperature. The shortest tunneling events bear the strongest longer-range singlet fluctuations, leading to amplitudes that do not drop exponentially with the length of the loop L, and to an unexpected loop-six valence-bond crystal, which is otherwise very high in energy at the minimal truncation level. The low-energy effective description gives in addition a clear example of correlated loop processes that depend not only on the type of the loop but also on its lattice embedding, a direct manifestation of the long-range nature of the virtual singlets.
ABSTRACT
With large spin-orbit coupling, the electron configuration in d-metal oxides is prone to highly anisotropic exchange interactions and exotic magnetic properties. In 5d(5) iridates, given the existing variety of crystal structures, the magnetic anisotropy can be tuned from antisymmetric to symmetric Kitaev-type, with interaction strengths that outsize the isotropic terms. By many-body electronic-structure calculations we here address the nature of the magnetic exchange and the intriguing spin-glass behavior of Li2RhO3, a 4d(5) honeycomb oxide. For pristine crystals without Rh-Li site inversion, we predict a dimerized ground state as in the isostructural 5d(5) iridate Li2IrO3, with triplet spin dimers effectively placed on a frustrated triangular lattice. With Rh-Li anti-site disorder, we explain the observed spin-glass phase as a superposition of different, nearly degenerate symmetry-broken configurations.
ABSTRACT
The Skyrme-particle, the skyrmion, was introduced over half a century ago in the context of dense nuclear matter. But with skyrmions being mathematical objects--special types of topological solitons--they can emerge in much broader contexts. Recently skyrmions were observed in helimagnets, forming nanoscale spin-textures. Extending over length scales much larger than the interatomic spacing, they behave as large, classical objects, yet deep inside they are of quantum nature. Penetrating into their microscopic roots requires a multi-scale approach, spanning the full quantum to classical domain. Here, we achieve this for the first time in the skyrmionic Mott insulator Cu2OSeO3. We show that its magnetic building blocks are strongly fluctuating Cu4 tetrahedra, spawning a continuum theory that culminates in 51 nm large skyrmions, in striking agreement with experiment. One of the further predictions that ensues is the temperature-dependent decay of skyrmions into half-skyrmions.
ABSTRACT
By many-body quantum-chemical calculations, we investigate the role of two structural effects--local ligand distortions and the anisotropic Cd-ion coordination--on the magnetic state of Cd(2)Os(2)O(7), a spin S = 3/2 pyrochlore. We find that these effects strongly compete, rendering the magnetic interactions and ordering crucially dependent on these geometrical features. Without trigonal distortions, a large easy-plane magnetic anisotropy develops. Their presence, however, reverses the sign of the zero-field splitting and causes a large easy-axis anisotropy (D ≃ -6.8 meV), which in conjunction with the antiferromagnetic exchange interaction (J ≃ 6.4 meV) stabilizes an all-in-all-out magnetic order. The competition uncovered here is a generic feature of pyrochlore magnets.
