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Low-temperature crystal and magnetic structure of $alpha$-RuCl3

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 Added by Huibo Cao
 Publication date 2016
  fields Physics
and research's language is English




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Single crystals of the Kitaev spin-liquid candidate $alpha$-RuCl$_3$ have been studied to determine low-temperature bulk properties, structure and the magnetic ground state. Refinements of x-ray diffraction data show that the low temperature crystal structure is described by space group $C2/m$ with a nearly-perfect honeycomb lattice exhibiting less than 0.2 % in-plane distortion. The as-grown single crystals exhibit only one sharp magnetic transition at $T_{N}$ = 7~K. The magnetic order below this temperature exhibits a propagation vector of $k$ = (0, 1, 1/3), which coincides with a 3-layer stacking of the $C2/m$ unit cells. Magnetic transitions at higher temperatures up to 14~K can be introduced by deformations of the crystal that result in regions in the crystal with a 2-layer stacking sequence. The best fit symmetry allowed magnetic structure of the as-grown crystals shows that the spins lie in the $ac$-plane, with a zigzag configuration in each honeycomb layer. The three layer repeat out-of-plane structure can be refined as a 120$^o$ spiral order or a collinear structure with spin direction 35$^o$ away from the $a$-axis. The collinear spin configuration yields a slightly better fit and also is physically preferred. The average ordered moment in either structure is less than 0.45(5) $mu_B$ per Ru$^{3+}$ ion.



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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.
Revealing the spin excitations of complex quantum magnets is key to developing a minimal model that explains the underlying magnetic correlations in the ground state. We investigate the low-energy magnons in $alpha$-RuCl$_3$ by combining time-domain terahertz spectroscopy under an external magnetic field and model Hamiltonian calculations. We observe two absorption peaks around 2.0 and 2.4 meV, which we attribute to zone-center spin waves. Using linear spin-wave theory with only nearest-neighbor terms of the exchange couplings, we calculate the antiferromagnetic resonance frequencies and reveal their dependence on an external field applied parallel to the nearest-neighbor Ru-Ru bonds. We find that the magnon behavior in an applied magnetic field can be understood only by including an off-diagonal $Gamma$ exchange term to the minimal Heisenberg-Kitaev model. Such an anisotropic exchange interaction that manifests itself as a result of strong spin-orbit coupling can naturally account for the observed mixing of the modes at higher fields strengths.
Polarization-resolved Raman spectroscopy was performed and analyzed from large, high quality, mono-domain single crystal of {alpha}-RuCl3, a proximate Kitaev quantum spin liquid. Spectra were collected with laser polarizations parallel and perpendicular to the honeycomb plane. Pairs of nearly degenerate phonons were discovered and show either a 4-fold or 2-fold polarization angle dependence in their Raman intensity, thereby providing evidence to definitively assign the bulk crystal point group as C2h. The low frequency continuum that is often attributed to scattering from pairs of Majorana fermions was also examined and found to disappear when the laser excitation and scattered photon polarizations were perpendicular to the honeycomb plane. This disappearance, along with the behavior of the phonon spectrum in the same polarization configuration, strongly suggests that the scattering continuum is 2-dimensional. We argue that this scattering continuum originates from the Kitaev magnetic interactions that survives up to room temperature, a scale larger than the bare Kitaev exchange energy of approximately 50 K.
Fractionalized excitations are of considerable interest in recent condensed-matter physics. Fractionalization of the spin degrees of freedom into localized and itinerant Majorana fermions are predicted for the Kitaev spin liquid, an exactly solvable model with bond-dependent interactions on a two-dimensional honeycomb lattice. As function of temperature, theory predicts a characteristic two-peak structure of the heat capacity as fingerprint of these excitations. Here we report on detailed heat-capacity experiments as function of temperature and magnetic field in high-quality single crystals of {alpha}-RuCl3 and undertook considerable efforts to determine the exact phonon background. We measured single-crystalline RhCl3 as non-magnetic reference and performed ab-initio calculations of the phonon density of states for both compounds. These ab-initio calculations document that the intrinsic phonon contribution to the heat capacity cannot be obtained by a simple rescaling of the nonmagnetic reference using differences in the atomic masses. Sizable renormalization is required even for non-magnetic RhCl3 with its minute difference from the title compound. In {alpha}-RuCl3 in zero magnetic field, excess heat capacity exists at temperatures well above the onset of magnetic order. In external magnetic fields far beyond quantum criticality, when long-range magnetic order is fully suppressed, the excess heat capacity exhibits the characteristic two-peak structure. In zero field, the lower peak just appears at temperatures around the onset of magnetic order and seems to be connected with canonical spin degrees of freedom. At higher fields, beyond the critical field, this peak is shifted to 10 K. The high-temperature peak located around 50 K is hardly influenced by external magnetic fields, carries the predicted amount of entropy, R/2 ln2, and may resemble remnants of Kitaev physics.
Motivated by the possibility of an intermediate U(1) quantum spin liquid phase in out-of-plane magnetic fields and enhanced magnetic fluctuations in exfoliated {alpha}-RuCl3 flakes, we study magneto-Raman spectra of exfoliated multilayer {alpha}-RuCl3 in out-of-plane magnetic fields of -6 T to 6 T at temperatures of 670 mK - 4 K. While the literature currently suggests that bulk {alpha}-RuCl3 is in an antiferromagnetic zigzag phase with R3bar symmetry at low temperature, we do not observe R3bar symmetry in exfoliated {alpha}-RuCl3 at low temperatures. While we saw no magnetic field driven transitions, the Raman modes exhibit unexpected stochastic shifts in response to applied magnetic field that are above the uncertainties inferred from Bayesian analysis. These stochastic shifts are consistent with the emergence of magnetostrictive interactions in exfoliated {alpha}-RuCl3.
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