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We report an electron spin resonance (ESR) study of single crystals of the spin-chain spin-ladder compound (Sr,La,Ca)_{14}Cu_{24}O_{41}. The data suggest that in intrinsically hole doped Sr_{14-x}Ca_xCu_{24}O_{41} only a small amount of holes is transferred from the chains to the ladders with increasing x, resulting in a crossover from spin dimerized to uniform spin chains. In the samples of La_{14-x}Ca_xCu_{24}O_{41} with reduced hole content a very broad signal is observed in the paramagnetic state, indicative of a surprisingly strong anisotropy of the nearest neighbor exchange in the chains.
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The electrodynamic response of the spin-ladder compound Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ ($x=0, 3, 9$) has been studied from radiofrequencies up to the infrared. At temperatures below 250 K a pronounced absorption peak appears around 12 cm$^{-1}$ in Sr$_{14}$Cu$_{24}$O$_{41}$ for the radiation polarized along the chains/ladders (${bf E}parallel {bf c}$). In addition a strongly temperature dependent dielectric relaxation is observed in the kHz - MHz range. We explain this behavior by a charge density wave which develops in the ladders sub-system and produces a mode pinned at 12 cm$^{-1}$. With increasing Ca doping the mode shifts up in frequency and eventually disappears for $x=9$ because the dimensionality of the system crosses over from one to two dimensions, giving way to the superconducting ground state under pressure.
Structural properties of the spin chain and ladder compound Sr$_{14}$Cu$_{24}$O$_{41}$ have been studied using diffraction with hard x-rays. Strong incommensurate modulation reflections are observed due to the lattice mismatch of the chain and ladder structure, respectively. While modulation reflections of low orders display only a weak temperature independence, higher orders dramatically increase in intensity when cooling the sample to 10 K. All observed modulation reflections are indexed within the super space group symmetry and no structural phase transition could be identified between 10 K and room temperature. We argue that these modulation reflections are not caused by a five-fold periodicity of the chain lattice, as claimed by Fukuda et al. Phys. Rev. B 66, 012104 (2002), but that holes localize in the potential given by the lattice modulation, which in turn gives rise to a further deformation of the lattice.
The low energy lattice dynamics of the quasi-periodic spin-ladder cuprate Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ are investigated using terahertz frequency synchrotron radiation. A high density of low-lying optical excitations are present in the 1-3 THz energy range, while at least two highly absorbing excitations stemming from rigid acoustic oscillations of the incommensurate chain and ladder sublattices, are observed at sub-terahertz frequencies. The effects of Ca substitution on the sub-terahertz quasi-acoustic sliding mode gaps is investigated using coherent synchrotron radiation. Analysis of the results suggest increasing substitution of Sr for Ca is accompanied by a transfer of spectral weight between sliding modes associated with different chain-ladder dynamics. The observation is consistent with a transfer of hole charges from the chains to the ladders and modification of the sublattice dimensions following Ca substitution. The results are discussed in context to the significance of low-lying vibrational dynamics and electron-phonon coupling in the superconducting state of certain quasi-periodic systems.
When two quantum systems are coupled via a mediator, their dynamics has traces of non-classical properties of the mediator. We show how this observation can be effectively utilised to study the quantum nature of materials without well-established structure. A concrete example considered is Sr$_{14}$Cu$_{24}$O$_{41}$. Measurements of low temperature magnetic and thermal properties of this compound were explained with long-range coupling of unpaired spins through dimerised spin chains. We first show that the required coupling is not provided by the spin chain alone and give alternative compact two-dimensional spin structures compatible with the experimental results. Then we argue that any mediator between the unpaired spins must share with them quantum correlations in the form of quantum discord and in many cases quantum entanglement. In conclusion, present data witnesses quantum mediators between unpaired spins in Sr$_{14}$Cu$_{24}$O$_{41}$.
Using far-infrared spectroscopy we have studied the magnetic field and temperature dependence of the spin gap modes in the chains of Sr$_{14}$Cu$_{24}$O$_{41}$. Two triplet modes T$_1$ and T$_2$ were found in the center of the Brillouin zone at $Delta_1=9.65$ meV and $Delta_2=10.86$ meV in zero magnetic field. The T$_1$ mode was excited when the electric field vector ${bf E}$ of the light was polarized along the b axis (perpendicular to the planes of chains and ladders) and T$_2$ was excited for ${bf E}parallel {bf a}$ (perpendicular to the chains and along the rungs). Up to the maximum magnetic field of 18 T, applied along the chains, the electron $g$ factors of these two modes were similar, $g_{1c}=2.049$ and $g_{2c}=2.044$. Full linewidth at half maximum for both modes was 1 cm$^{-1}$ (0.12 meV) at 4K and increased with $T$. The temperature dependence of mode energies and line intensities was in agreement with the inelastic neutron scattering results from two groups [Matsuda {it et al.}, Phys. Rev. B {bf 59}, 1060 (1999) and Regnault {it et al.}, Phys. Rev. B {bf 59}, 1055 (1999)]. The T$_1$ mode has not been observed by inelastic neutron scattering in the points of the $k$-space equivalent to the center of the Brillouin zone. Our study indicates that the zone structure model of magnetic excitations of Sr$_{14}$Cu$_{24}$O$_{41}$ must be modified to include a triplet mode at 9.65 meV in the center of the magnetic Brillouin zone.
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