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Register a new userDetuning the Honeycomb of the {alpha}-RuCl3 Kitaev lattice: A case of Cr3+ dopant
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Fine-tuning chemistry by doping with transition metals enables new perspectives for exploring Kitaev physics on a two-dimensional (2D) honeycomb lattice of {alpha}-RuCl3, which is promising in the field of quantum information protection and quantum computation. The key parameters to vary by doping are both Heisenberg and Kitaev components of the nearest-neighbor exchange interaction between the Jeff = 1/2 Ru3+ spins, depending strongly on the peculiarities of the crystal structure. Here, we successfully grew single crystals of the solid solution series Ru1-xCrxCl3 with Cr3+ ions coupled to the Ru3+ Kitaev host using chemical vapour transport reaction. The Cr3+ substitution preserves the honeycomb type lattice of {alpha}-RuCl3 with mixed occupancy of Ru/Cr sites, no hints on cationic order within the layers were found by single crystal X-ray diffraction and transmission electron microscopy investigations. In contrast to the high quality single crystals of {alpha}-RuCl3 with ABAB ordered layers, the ternary compounds demonstrate a significant stacking disorder along the c-axis direction evidenced by X-ray diffraction and high resolution scanning transmission electron microscopy (HR-STEM). Raman spectra of substituted samples are in line with a symmetry conservation of the parent lattice upon chromium doping. At the same time, magnetic susceptibility data indicate that the Kitaev physics of {alpha}-RuCl3 is increasingly repressed by the dominant spin-only driven magnetism of Cr3+ in Ru1-xCrxCl3.
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It is widely accepted that topological superconductors can only have an effective interpretation in terms of curved geometry rather than gauge fields due to their charge neutrality. This approach is commonly employed in order to investigate their properties, such as the behaviour of their energy currents. Nevertheless, it is not known how accurately curved geometry can describe actual microscopic models. Here, we demonstrate that the low-energy properties of the Kitaev honeycomb lattice model, a topological superconductor that supports localised Majorana zero modes at its vortex excitations, are faithfully described in terms of Riemann-Cartan geometry. In particular, we show analytically that the continuum limit of the model is given in terms of the Majorana version of the Dirac Hamiltonian coupled to both curvature and torsion. We numerically establish the accuracy of the geometric description for a wide variety of couplings of the microscopic model. Our work opens up the opportunity to accurately predict dynamical properties of the Kitaev model from its effective geometric description.
Kitaev-type interactions between neighbouring magnetic moments emerge in the honeycomb material ${alpha}$-RuCl3. It is debated however whether these Kitaev interactions are ferromagnetic or antiferromagnetic. With electron energy loss spectroscopy (EELS) we study the lowest excitation across the Mott-Hubbard gap, which involves a d4 triplet in the final state and therefore is sensitive to nearest-neighbor spin-spin correlations. At low temperature the spectral weight of these triplets is strongly enhanced, in accordance with optical data. We show that the magnetic correlation function that determines this EELS spectral weight is directly related to a Kitaev-type spin-spin correlator and that the temperature dependence agrees very well with the results of a microscopic magnetic Hamiltonian for ${alpha}$-RuCl3 with ferromagnetic Kitaev coupling.
We study the thermodynamic properties of modified spin-$S$ Kitaev models introduced by Baskaran, Sen and Shankar (Phys. Rev. B 78, 115116 (2008)). These models have the property that for half-odd-integer spins their eigenstates map on to those of spin-1/2 Kitaev models, with well-known highly entangled quantum spin-liquid states and Majorana fermions. For integer spins, the Hamiltonian is made out of commuting local operators. Thus, the eigenstates can be chosen to be completely unentangled between different sites, though with a significant degeneracy for each eigenstate. For half-odd-integer spins, the thermodynamic properties can be related to the spin-1/2 Kitaev models apart from an additional degeneracy. Hence we focus here on the case of integer spins. We use transfer matrix methods, high temperature expansions and Monte Carlo simulations to study the thermodynamic properties of ferromagnetic and antiferromagnetic models with spin $S=1$ and $S=2$. Apart from large residual entropies, which all the models have, we find that they can have a variety of different behaviors. Transfer matrix calculations show that for the different models, the correlation lengths can be finite as $Tto 0$, become critical as $Tto 0$ or diverge exponentially as $Tto 0$. There is a conserved $Z_2$ flux variable associated with each hexagonal plaquette which saturates at the value $+1$ as $Trightarrow0$ in all models except the $S=1$ antiferromagnet where the mean flux remains zero as $Tto 0$. We provide qualitative explanations for these results.
Muon spin rotation measurements have been performed on a powder sample of a-RuCl3, a layered material which previously has been proposed to be a quantum magnet on a honeycomb lattice close to a quantum spin liquid ground state. Our data reveal two distinct phase transitions at 11 K and 14 K which we interpret as originating from the onset of three-dimensional order and in-plane magnetic order, respectively. We identify, with the help of density functional theory calculations, likely muon stopping sites and combine these with dipolar field calculations to show that the two measured muon rotation frequencies are consistent with two inequivalent muon sites within a zig-zag antiferromagnetic structure proposed previously.
We calculate magnon dispersions and damping in the Kitaev-Heisenberg model with an off-diagonal exchange $Gamma$ and isotropic third-nearest-neighbor interaction $J_3$ on a honeycomb lattice. This model is relevant to a description of the magnetic properties of iridium oxides $alpha$-Li$_2$IrO$_3$ and Na$_2$IrO$_3$, and Ru-based materials such as $alpha$-RuCl$_3$. We use an unconventional parametrization of the spin-wave expansion, in which each Holstein-Primakoff boson is represented by two conjugate hermitian operators. This approach gives us an advantage over the conventional one in identifying parameter regimes where calculations can be performed analytically. Focusing on the parameter regime with the zigzag spin pattern in the ground state that is consistent with experiments, we demonstrate that one such region is $Gamma = K>0$, where $K$ is the Kitaev coupling. Within our approach we are able to obtain explicit analytical expressions for magnon energies and eigenstates and go beyond the standard linear spin-wave theory approximation by calculating magnon damping and demonstrating its role in the dynamical structure factor. We show that the magnon damping effects in both Born and self-consistent approximations are very significant, underscoring the importance of non-linear magnon coupling in interpreting broad features in the neutron-scattering spectra.
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