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The spin-lattice relaxation rate $T_1^{-1}$ of $^1$H-NMR has been measured in (CH$_3$)$_2$CHNH$_3$Cu(Cl$_x$Br$_{1-x}$)$_3$ with $x=0$ and 0.35, in order to investigate the microscopic magnetism of systems. Previous macroscopic magnetization and specific heat measurements suggested that these two exist in a singlet-dimer phase. The temperature dependence of $T_1^{-1}$ in an $x=0$ system decreased exponentially toward zero, indicating microscopic evidence of the gapped singlet ground state, which is consistent with the macroscopic experiments. At the same time, in the $x=0.35$ system, $T_1^{-1}$ showed a sharp peak structure at around 7.5 K though no splitting of $^1$H-NMR spectra indicative of the magnetic ordering was observed. We discuss the observed sharp peak structure in the $x=0.35$ system with the soft mode toward the exotic magnetic ground state suggested by the recent $mu$SR experiments.
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Spin-lattice relaxation rate $T_1^{-1}$ of $^1$H-NMR has been measured in (CH$_3$)$_2$CHNH$_3$Cu(Cl$_x$Br$_{1-x}$)$_3$ with $x=0.88$, which has been reported to be gapped system with singlet ground state from the previous macroscopic magnetization and specific heat measurements, in order to investigate the bond randomness effect microscopically in the gapped composite Haldane system (CH$_3$)$_2$CHNH$_3$CuCl$_3$. It was found that the spin-lattice relaxation rate $T_1^{-1}$ in the present system includes both fast and slow relaxation parts indicative of the gapless magnetic ground state and the gapped singlet ground state, respectively. We discuss the obtained results with the previous macroscopic magnetization and specific heat measurements together with the microscopic $mu$SR experiments.
Dc and ac transport properties as well as electric modulus spectra have been investigated for the samples LaMn$_{1-x}$Fe$_{x}$O$_3$ with compositions 0 $leq x leq$ 1.0. The bulk dc resistivity shows a temperature variation consistent with the variable range hopping mechanism at low temperature and Arrhenius mechanism at high temperatures. The ac conductivity has been found to follow a power law behavior at a limited temperature and frequency region where Anderson-localization plays a significant role in the transport mechanism for all the compositions. At low temperatures large dc resistivities and dielectric relaxation behavior for all the compositions are consistent with the polaronic nature of the charge carriers. Scaling of the modulus spectra shows that the charge transport dynamics is independent of temperature for a particular composition but depends strongly on different compositions possibly due to different charge carrier concentrations and structural properties.
We studied the magnetic properties of YCu$_3$(OH)$_6$Br$_2$[Br$_{1-x}$(OH)$_{x}$] ($x$ = 0.33 and 0.45), where Cu$^{2+}$ ions form two-dimensional kagome layers. There is no magnetic order down to 50 mK while the Curie-Weiss temperature is in the order of -100 K. At zero magnetic field, the low-temperature specific heat shows a $T^2$ dependence. Above 2 T, a linear-temperature dependence term in specific heat emerges, and the value of $gamma = C/T$ increases linearly with the field. Furthermore, the magnetic susceptibility tends to a constant value at $T = 0$. Our results suggest that the magnetic ground state of YCu$_3$(OH)$_6$Br$_2$[Br$_{1-x}$(OH)$_{x}$] is consistent with a Dirac quantum-spin-liquid state with linearly dispersing spinon strongly coupled with emergent gauge field, which has long been theoretically proposed as a candidate ground state in the two-dimensional kagome Heisenberg antiferromagnetic system.
Density-functional calculations of lattice dynamics and high-resolution synchrotron powder diffraction uncover antiferroelectric distortion in the kagome francisite Cu$_3$Bi(SeO$_3$)$_2$O$_2$Cl below 115K. Its Br-containing analogue is stable in the room-temperature crystal structure down to at least 10K, although the Br compound is on the verge of a similar antiferroelectric instability and reveals local displacements of Cu and Br atoms. The I-containing compound is stable in its room-temperature structure according to density-functional calculations. We show that the distortion involves cooperative displacements of Cu and Cl atoms, and originates from the optimization of interatomic distances for weakly bonded halogen atoms. The distortion introduces a tangible deformation of the kagome spin lattice and may be responsible for the reduced net magnetization of the Cl compound compared to the Br one. The polar structure of Cu$_3$Bi(SeO$_3$)$_2$O$_2$Cl is only slightly higher in energy than the non-polar antiferroelectric structure, but no convincing evidence of its formation could be obtained.
It has been predicted theoretically and indirectly confirmed experimentally that single-layer CrX$_3$ (X=Cl, Br, I) might be the prototypes of topological magnetic insulators (TMI). In this work, by using first-principles calculations combined with atomistic spin dynamics we provide a complete picture of the magnetic interactions and magnetic excitations in CrX$_3$. The focus is here on the two most important aspects for the actual realization of TMI, namely the relativistic magnetic interactions and the finite-size (edge) effects. We compute the full interaction tensor, which includes both Kitaev and Dzyaloshinskii-Moriya terms, which are considered as the most likely mechanisms for stabilizing topological magnons. First, we instigate the properties of bulk CrI$_3$ and compare the simulated magnon spectrum with the experimental data [Phys. Rev. X 8, 041028 (2018)]. Our results suggest that a large size of topological gap, seen in experiment ($approx$ 4 meV), can not be explained by considering pair-wise spin interactions only. We identify several possible reasons for this disagreement and suggest that a pronounced magneto-elastic coupling should be expected in this class of materials. The magnetic interactions in the monolayers of CrX$_3$ are also investigated. The strength of the anisotropic interactions is shown to scale with the position of halide atom in the Periodic Table, the heavier the element the larger is the anisotropy. Comparing the magnons for the bulk and single-layer CrI$_3$, we find that the size of the topological gap becomes smaller in the latter case. Finally, we investigate finite-size effects in monolayers and demonstrate that the anisotropic couplings between Cr atoms close to the edges are much stronger than those in ideal periodic structure. This should have impact on the dynamics of the magnon edge modes in this class of materials.
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