Research Highlights

Over the past decades, a strong spin-orbit coupling has been recognized as a key ingredient in stabilizing unconventional phases in correlated materials. For 4d and 5d Mott insulators, for instance, there is great interest in the Kitaev materials, which are systems hosting dominant Ising-like bond-dependent interactions for local effective moments j-1/2 in weakly coupled honeycomb layers. If these bond-depended interactions have similar strength, Kitaev exactly established the existence of a quantum spin liquid of gapless Majorana fermions moving in a static Z2 flux background. Remarkably, an infinitesimally small external magnetic field generates chiral Majorana edge modes with half-quantized thermal Hall conductance. Following Kitaev’s seminal work, some layered honeycomb magnets have been synthesized and investigated to find spin-liquid phases. Among those materials, A2IrO3 (A = Na, Li) and α-RuCl3 have been studied in considerable detail: All of them order antiferromagnetically at low temperatures but display several anomalies. Many of these anomalies have been attributed on phenomenological grounds to proximate or field-induced spin-liquid behavior, such as excitation continua in neutron scattering and the approximately half-quantized thermal Hall effect observed in α-RuCl3. In the discussion of spin liquidity, randomness due to crystalline defects or substitutions is an additional relevant ingredient: The compound H3LiIr2O6 has been suggested as a quantum spin-liquid candidate but is likely heavily disordered. For both Na2IrO3 and α-RuCl3, magnetic dilution has been proposed as a route to suppress bulk magnetic order, and α-(Ru{1−x}Ir{x})Cl3 for x > 0.22 has been argued to show spin-liquid-like signatures. In these works, we investigate the role of the defects in the ordered phases, magnetic anisotropies, and the Kitaev spin-liquid, all relevant to understanding the real Kitaev materials.

• E. C. Andrade and M. Vojta, Phys. Rev. B 90, 205112 (2014) (Phys. Rev. B.) (arXiv)

• E. C. Andrade , L. Janssen , and M. Vojta, Phys. Rev. B 102, 115160 (2020) (Phys. Rev. B.) (arXiv)

• V. Dantas, E. C. Andrade, Phys. Rev. Lett. 129, 037204 (2022) (Phys. Rev. Lett.) (arXiv). See also this press release (Portuguese only).

In quantum magnets, the combination of competing exchange interactions and geometric frustration can lead to unconventional magnetic states. In the extreme case, quantum fluctuations can melt the long-range magnetic order, giving rise to quantum spin liquids (QSLs). In chiral spin liquids (CSLs), the ground state preserves the spin-rotation symmetry of the Hamiltonian but supports a finite scalar spin chirality if reflection and time reversal symmetries are spontaneously or explicitly broken. Chiral three-spin interactions provide a route to stabilizing CSL ground states. Microscopically, this type of interaction arises in Mott insulators with a magnetic flux through triangular plaquettes, and their ratio to exchange interactions can be enhanced in the vicinity of the Mott transition On the kagome lattice, a model with dominant three-spin interactions driving a uniform scalar spin chirality harbors the Kalmeyer-Laughlin CSL, a gapped topological phase with anyonic excitations. On the other hand, three-spin interactions that induce a staggered scalar spin chirality favor gapless CSLs, which are striking examples of non-Fermi liquids with Fermi surfaces of fractionalized excitations. We have investigated a spin-1/2 model on the kagome lattice with staggered three-spin interaction as well as frustrated Heisenberg exchange interactions. An important question pertains to the stability of this CSL with respect to magnetic order. Equivalently, from the perspective of the magnetic phases, one may ask how the chiral interaction destabilizes the cuboc order. Combining energy minimization, analytical arguments, and variational Monte Carlo, we were able to uncover a rich phase diagram that could be relevant to the kapellasite.

• F. Oliviero, J. A. Sobral, E. C. Andrade, and R. G. Pereira. SciPost Phys.13, 050 (2022) (SciPost Phys.) (arXiv).

We study the effects of bond and site disorder in the paradigmatic J1 -J2 Heisenberg model on a square lattice in the order-by-disorder frustrated regime. Combining symmetry arguments, numerical energy minimization, and large-scale classical Monte Carlo simulations, we establish that the finite temperature Ising-like transition of the clean system is destroyed in the presence of any finite concentration of impurities. We explain this finding via a random-field mechanism that generically emerges in systems where disorder locally breaks the same real-space symmetry spontaneously globally broken by the associated order parameter. We also determine that the phase replacing the clean one is a paramagnet polarized in the nematic glass order with a non-trivial magnetic response. To apply these ideas to a relevant experimental setup, we study the impact of quenched disorder (random exchange couplings or site dilution) on easy-plane pyrochlore antiferromagnets. In the clean system, order-by-disorder selects a magnetically ordered state from a classically degenerate manifold. In the presence of randomness, however, different orders can be chosen locally depending on the details of the disorder configuration. Using a combination of analytical considerations and classical Monte-Carlo simulations, we argue that any long-range-ordered magnetic state is destroyed beyond a critical level of randomness where the system breaks into magnetic domains due to random exchange anisotropies, becoming, therefore, a glass of spin clusters, in accordance with the available experimental data. These random anisotropies originate from off-diagonal exchange couplings in the microscopic Hamiltonian, establishing their relevance to other magnets with strong spin-orbit coupling.

• R. Sarkar, J. W. Krizan, F. Brückner, E. C. Andrade, S. Rachel, M. Vojta, R. J. Cava, H.-H. Klauss. Phys. Rev. B 96, 235117 (2017). (Phys. Rev. B.) (arXiv)

• E. C. Andrade, J. A. Hoyos, S. Rachel, M. Vojta, Phys. Rev. Lett. 120, 097204 (2018). (Phys. Rev. Lett) (arXiv)

• M. M. J. Miranda, I. C. Almeida, E. C. Andrade, J. A. Hoyos, Phys. Rev. B 104, 054201 (2021). (Phys. Rev. B) (arXiv)

Defects are ubiquitous in magnets. Often, they contribute a large magnetic response at low temperatures because they induce effective magnetic moments. We consider frustrated Heisenberg antiferromagnets, whose clean-limit ground state is characterized by non-collinear long-range order with non-zero vector chirality, and study the effects of quenched bond disorder (random exchange couplings) and site dilution (vacancies). A single bond induces a dipolar texture in the spin background-independent of microscopic details. Using general analytical arguments as well as large-scale simulations for the classical triangular-lattice Heisenberg model, we show that any finite concentration of such defects destroys long-range order for spatial dimension d ≤ 2 in favor of a glassy state whose correlation length in d = 2 is exponentially large for small randomness. Remarkably, the effect of random site dilution in the same system is much weaker: Vacancies induce an octupolar texture, and long-range order is stable against a small vacancy concentration. However, the zero-field magnetization associated with a vacancy cannot be measured at any finite field; instead, the vacancy moment becomes perfectly screened in the small-field limit by virtue of a singular screening cloud.

• A. Wollny, E. C. Andrade, and M. Vojta, Phys. Rev. Lett. 109, 177203 (2012). (Phys. Rev. Lett.) (arXiv)

• S. Dey, E. C. Andrade, M. Vojta, Phys. Rev. B 101, 020411(R) (2020). (Phys. Rev. B) (arXiv)

• S. Dey, E. C. Andrade, M. Vojta, Phys. Rev. B 102, 125121 (2020). (Phys. Rev. B) (arXiv)

• E. Häußler, J. Sichelschmidt, M. Baenitz, E. C. Andrade, M. Vojta, T. Doert., Phys. Rev. Materials 6, 046201 (2022) (Phys. Rev. Materials) (arXiv)

The Heisenberg-Kitaev model is a paradigmatic model to describe the magnetism in honeycomb-lattice Mott insulators with strong spin-orbit coupling such as A₂IrO₃ (A = Na, Li) and α-RuCl₃. Here, we study in detail the physics of the Heisenberg-Kitaev model in an external magnetic field. Using a combination of Monte Carlo simulations and spin-wave theory, we map out the semiclassical phase diagram for different directions of the magnetic field. Broken SU(2) spin symmetry renders the magnetization process somewhat complicated, with sequences of phases and metamagnetic transitions. In particular, we find various large-unit-cell and multi-Q phases, including a vortex crystal phase for a field in the [111] direction, in contrast to spin models with Heisenberg symmetry, where collinear zero-field states typically turn into simple canted states. This demonstrates the potential of Kitaev interactions to produce topologically nontrivial magnetic states. We also discuss quantum corrections in the high-field phase and in a number of ordered phases to compute phase boundaries at the next-to-leading order in 1/S and show that quantum corrections substantially modify the classical phase diagram, suppressing large-unit-cell phases. More broadly, our work presents a consistent route to investigate the leading quantum corrections in spin models that break spin-rotational symmetry.

• L. Janssen, E. C. Andrade, M. Vojta, Phys. Rev. Lett 117, 277202 (2016). (Phys. Rev. Lett.) (arXiv)

• L. Janssen, E. C. Andrade, M. Vojta, Phys. Rev. B 96, 064430 (2017). (Phys. Rev. B.) (arXiv)

• P. M. Cônsoli, L. Janssen , M. Vojta, E. C. Andrade, PhysRevB 102 155134 (2021) (Phys. Rev. B) (arxiv)

Motivated by the intrinsic non-Fermi-liquid behavior observed in the heavy-fermion quasicrystal Au₅₁Al₃₄Yb₁₅, we study the low-temperature behavior of dilute magnetic impurities placed in metallic quasicrystals. We find that a large fraction of the magnetic moments is not quenched down to very low temperatures T, leading to a power-law distribution of Kondo temperatures P(T_K) ~ T_K^α-1, with a nonuniversal exponent α, in remarkable similarity to the Kondo-disorder scenario found in disordered heavy-fermion metals. For α < 1, the resulting singular P(T_K) induces non-Fermi-liquid behavior with diverging thermodynamic responses as T → 0. Also inspired by a recent experimental observation of superconductivity in the Al-Zn-Mg quasicrystal, we study the low-temperature behavior of electrons moving in the quasiperiodic potential of the Ammann–Beenker tiling in the presence of a local attraction. Using the mean-field Bogoliubov–de Gennes approach for approximants of different sizes, we calculate the local pairing amplitude. Due to the lack of periodicity of the octagonal tiling, the resulting superconducting state is inhomogeneous, but we find no evidence of the superconductivity islands, as observed in disordered systems. In the weak-coupling regime, we find that Tc depends appreciably on the approximant size only if the Fermi energy sits at a pseudogap in the noninteracting density of states, with Tc decreasing as the system size increases. These results are in line with the experimental observations for the Al-Zn-Mg quasicrystal, and they suggest that, despite their electronic structure, quasicrystals are prone to display conventional BCS-like superconductivity. Nevertheless, in the presence of a uniform magnetic field, an FFLO-like state can still emerge, showing that these systems are certain to provide many more surprises.

• E. C. Andrade, A. Jagannathan, E. Miranda, M. Vojta, V. Dobrosavljević, Phys. Rev. Lett 115, 0364031 (2015). (Phys. Rev. Lett.) (arXiv)

• R. N. Araújo, E. C. Andrade, Phys. Rev. B 100, 014510 (2019). (Phys. Rev. B) (arXiv)

Strongly correlated materials with strong spin-orbit coupling hold promise for realizing topological phases with fractionalized excitations. An exciting avenue for quantum spin liquids comes from Mott insulators with heavy d5 ions in edge-sharing octahedral. In this case, the single electron in the open shell occupies a low-energy j = 3/2 quadruplet. Despite the larger moment, j = 3/2 systems are not necessarily more classical than their j = 1/2 counterparts since they can exhibit unexpected continuous symmetries that enhance quantum fluctuations. For instance, the effective spin model for heavy-element double perovskites with d1 configuration contains bond-dependent interactions with a hidden SU(2) symmetry. This SU(2) symmetry is made explicit when the model is expressed in terms of pseudospin and pseudo-orbital operators, and its effects motivated the proposal of a quantum spin-orbital liquid in double perovskites. Even more surprisingly, it was recently shown that the spin model for j = 3/2 moments on several tricoordinated lattices, including the honeycomb and hyper-honeycomb, has an emergent SU(4) symmetry. This result is remarkable given that SU(N) symmetries with larger values of N are known to favor quantum disordered states. We then propose several spin-liquid candidates for j=3/2 systems --- not only Mott insulators but also the twisted bilayer graphene --- discussing their physical properties, what can be immediately contrasted to experiments. Furthermore, we test the viability of our candidates by employing Variational Monte Carlo calculations.

• W. M. H. Natori, E. C. Andrade, E. Miranda, R. G. Pereira, Phys. Rev. Lett 117, 017204 (2016). (Phys. Rev. Lett.) (arXiv)

• W. M. H. Natori, E. C. Andrade, R. G. Pereira, Phys. Rev. B 98, 195113 (2018). (Phys. Rev. B) (arXiv)

• W. M. H. Natori, R. Nutakki, R. G. Pereira, E. C. Andrade, Phys. Rev. B 100, 205131 (2020). (Phys. Rev. B) (arXiv)

Stripe order is a common phenomenon in doped magnetic insulators made from transition metal oxides; stripe order is e.g. well-known to occur in cuprate high-temperature superconductors. Such stripe phases often display unusual magnetic excitations in the form of so-called "hourglass" spectra. We have modeled in detail the microscopic physics of the material La_5/3Sr_1/3CoO₄, which allowed us to establish links between crystallographic disorder, magnetic frustration, spin-glass behavior, and the "hour-glass" spectra, with excellent agreement with experimental data

• E. C. Andrade, and M. Vojta, Phys. Rev. Lett. 109, 147201 (2012) (Phys. Rev. Lett.) (arXiv)

• S. M. Gaw, E. C. Andrade, M. Vojta, C. D. Frost, D. T. Adroja, D. Prabhakaran, A. T. Boothroyd, Phys. Rev. B. 88, 165121 (2013) (Phys. Rev. B.) (arXiv)

Fermi liquid theory is known to successfully describe the leading low-temperature behavior of metals, even in instances of very strong correlations. In the presence of perturbations that break translational symmetry, such as impurities and defects, the Fermi liquid readjusts itself, producing a spatially inhomogeneous pseudopotential "seen" by quasiparticles. Here the wave nature of the electrons is manifested by the formation of "ripples", the Friedel oscillations, surrounding the perturbation. Scattering processes of quasiparticles off these ripples then produce new corrections to the T dependence in transport quantities. We study how these well-known effects of the long-ranged Friedel oscillations are affected by strong electronic correlations. In general, our analytical results indicate that a prominent role of Friedel oscillations is relegated to weakly interacting systems.

• E. C. Andrade, E. Miranda, and V. Dobrosavljević, Phys. Rev. Lett. 104, 236401 (2010) (Phys. Rev. Lett.) (arXiv)

The effects of disorder on quantum criticality prove to be much more dramatic than in classical systems, where some critical points can be described by an ‘‘infinite randomness fixed point’’ (IRPF) and the associated quantum Griffiths phase. Such exotic behavior is well established in insulating quantum magnets with discrete internal symmetry of the order parameter but may or may not survive in other models or in the presence of dissipation due to conduction electrons. In this study, we investigate the effects of weak and moderate disorder on the Mott metal-insulator transition at half-filling in two dimensions at T=0. Our results demonstrate that: (i) for a sufficiently weak disorder, the transition retains the second-order Mott character, where electrons gradually turn into localized magnetic moments; (ii) disorder-induced spatial inhomogeneities give rise to an intermediate electronic Griffiths phase that displays IRFP character at criticality, even when the transition is approached by increasing the interaction at weak disorder; (iii) the renormalized disorder "seen" by quasiparticles is strongly screened only at low energies, resulting in pronounced energy-resolved inhomogeneity of local spectral functions.

• E. C. Andrade, E. Miranda, and V. Dobrosavljević, Phys. Rev. Lett. 102, 206403 (2009) (Phys. Rev. Lett.) (arXiv)