We have performed inelastic neutron scattering on a single crystal sample of ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ to study the spin dynamics of the ${\mathrm{Cu}}_{2}{\mathrm{O}}_{3}$ spin ladder layers and ${\mathrm{CuO}}_{2}$ chains. Our data are best fitted with a dispersion which has a spin gap of $32.5\ifmmode\pm\else\textpm\fi{}0.1\mathrm{meV}$ and a maximum of $193.5\ifmmode\pm\else\textpm\fi{}2.4\mathrm{meV}$, consistent with a coupling along the ladders, ${J}_{\ensuremath{\parallel}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}130\phantom{\rule{0ex}{0ex}}\mathrm{meV}$ and a rung coupling ${J}_{\ensuremath{\perp}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}72\mathrm{meV}$. Excitations with an energy transfer of approximately 11.5 meV arise from a dimer chain with an antiferromagnetic intradimer coupling ${J}_{1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}11.2\mathrm{meV}$ between next-nearest-neighbor Cu ions, and a ferromagnetic interdimer coupling ${J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1.1\mathrm{meV}$. The dimer chains have a periodicity of five units.
We have performed inelastic neutron scattering on a single crystal sample of Sr14Cu24O41 to study the spin dynamics of the Cu2O3 spin ladder layers and CuO2 chains. Our data are best fitted with a dispersion which has a spin gap of 32.5\ifmmode±\else\textpm\fi0.1meV and a maximum of 193.5\ifmmode±\else\textpm\fi2.4meV, consistent with a coupling along the ladders, J\ensuremath∥=130meV and a rung coupling J\ensuremath⊥=72meV. Excitations with an energy transfer of approximately 11.5 meV arise from a dimer chain with an antiferromagnetic intradimer coupling J1=11.2meV between next-nearest-neighbor Cu ions, and a ferromagnetic interdimer coupling J2=\ensuremath−1.1meV. The dimer chains have a periodicity of five units.
We have performed inelastic-neutron-scattering and dc susceptibility measurements on a polycrystalline sample of (Sr0.8Ca0.2)14Cu24O41, which has a complex crystal structure comprising alternating layers containing isolated CuO2 chains and Cu2O3 two-legged ladders. The observed excitation spectrum is consistent with a spin gap for the ladder of 35 meV. At lower energy transfers we have observed a broad, nondispersive, feature centered on 10 meV that corresponds to singlet-triplet excitations in the CuO2 chains. We see some evidence in our susceptibility and neutron-scattering measurements to suggest that portions of the CuO2 chains are dimerized, or broken up into larger finite chains by nonmagnetic CuO2 units.
Inelastic neutron scattering measurements have been performed on the S=1/2 quasi-one-dimensional system ${\mathrm{Sr}}_{14\mathrm{\ensuremath{-}}\mathit{x}}$YxCu24O41, which has both simple chains and two-leg ladders of copper ions. Strong magnetic inelastic peaks, which originate from the simple chains, have been observed at 9--14 meV in Sr14Cu24O41. These spin gaps have been confirmed to originate from a dimerized state of the chain. The dimers are formed between spins which are separated by 2 and 4 times the distance between the nearest-neighbor copper ions in the simple chain. In addition, a weaker magnetic inelastic peak around 11 meV, which originates from a dimerized state in the ladder, has also been observed. These dimers are formed between the nearest-neighbor copper ions which are connected by the interladder coupling. We have also studied the effect of Y3+ substitution for Sr2+ site on the dimerized states. It was found that the yttrium substitution suppresses the gap energies drastically. Possible origins of the dimerized ground state and the excitations are discussed. \textcopyright{} 1996 The American Physical Society.
This thesis describes the neutron scattering measurements of magnetic excitations in \nspin-chains and ladders. The first part discusses an experimental investigation of the copper oxide family Srâ â Cuâ â Oâ â composed of edge-sharing chains and spin-ladders. \nThe study of Laâ Srâ â Cuâ â Oâ â comprises a slightly hole-doped chain and an undoped ladder structure where the chain can be modeled by a ferromagnetic nearest and an \nantiferromagnetic next-nearest neighbor coupling. The hole effects are apparent in gaps in the dispersion relation and can be described by a charge-density wave agreeing with the commensuration of the dispersion. Investigating the undoped ladder establishes \nthe exchange constants including a cyclic exchange manifested by the two-magnon \ncontinuum and the suppression of the S = 1 bound mode. An orbital consideration \nprovides an explanation for the exchanges including the different sizes of rung and \nleg coupling. The excitation spectrum of the doped ladder in Caâ .â Srâ â .â Cuâ â Oâ â can be \ndescribed by a direct comparison with the undoped ladder and the differences consisting \nof a higher energy mode and subgap scattering can be successfully modeled by the charge spectrum of the ladder calculated from the free electron model. The second part of the thesis investigates the alternating chain material Cu(NOâ )â · 2.5D2O and establishes the gapped one-magnon dispersion, the two-magnon continuum and for the first time the S =1 bound mode. Applying magnetic field drives the system through two critical field transitions, condensation of magnons into the ground state and saturation. The modes beyond saturation can be modeled by spin wave theory and the excitations at the first critical field follow Luttinger Liquid behavior. Additionally investigated are the temperature effects with the excitations being of a different nature but containing the signature of a strong correlated system. For an outlook the measurements including temperature and field are provided with further theoretical descriptions necessary.
We report comprehensive Cu NMR studies on single crystals of ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41},$ which contain simple CuO2 chains and two-leg Cu2O3 ladders. From measurements of the 63Cu NMR shift, it is clear that the spin gap in the ladders decreases with isovalent Ca substitution from $\ensuremath{\Delta}=550\ifmmode\pm\else\textpm\fi{}30$ K for Sr14Cu24O41 (Sr14) to $350\ifmmode\pm\else\textpm\fi{}30$ K, $280\ifmmode\pm\else\textpm\fi{}30$ K, and $270\ifmmode\pm\else\textpm\fi{}30$ K for x=6 (Ca6), x=9 (Ca9), and x=11.5 (Ca11.5), respectively. The exponential decrease of the nuclear spin-lattice relaxation rate 1/T1 below \ensuremath{\sim}130 K is consistent with the presence of the spin gap in the spin excitation spectrum. In the T range higher than $\ensuremath{\sim}200$ K, we observed the following dependences: 1/T1=const and the square of Gaussian spin-echo decay time, ${T}_{2G}^{2}\ensuremath{\propto}T$ which are consistent with the scaling theory for the S=1/2 one-dimensional (1D) Heisenberg model. The value of T2G/T1T is compatible with the theoretical prediction of an exchange constant along the leg ${J}_{\ensuremath{\parallel}}\ensuremath{\sim}1800$ K for Ca6 and ${J}_{\ensuremath{\parallel}}\ensuremath{\sim}1500$ K for Ca9 and Ca11.5. A notable finding is that the magnitude of the spin gap remains nearly constant and characteristics of novel 1D-like spin dynamics are maintained in the content varying from Ca9 to Ca11.5. On the other hand, the charge transport changes with increasing Ca content so that the more conductive Ca11.5 exhibits pressure-induced superconductivity exceeding 3.5 GPa. We have found that T2G2, which is proportional to the inverse spin correlation length ${\ensuremath{\xi}}^{\ensuremath{-}1}$, deviates from a linear T dependence upon cooling and is described by $A+BT\mathrm{exp}(\ensuremath{-}\ensuremath{\Delta}/T)$, regardless of the Ca substitution. We point out that the value of T2G2(T=0)=A is proportional to the finite value of ${\ensuremath{\xi}}_{0}^{\ensuremath{-}1}=\ensuremath{\Delta}{/c}_{1D},$ where ${c}_{1D}=(\ensuremath{\pi}{/2)J}_{\ensuremath{\parallel}}$ is the spin-wave velocity. From the result that the values of ${A}^{\ensuremath{-}1}\ensuremath{\sim}{\ensuremath{\xi}}_{\mathrm{eff}}$ for Ca6, Ca9, and Ca11.5 are significantly reduced compared to that for Sr14, it is suggested that ${\ensuremath{\xi}}_{\mathrm{eff}}$ is dominated at low T by an average distance d among mobile holes obeying the relation ${\ensuremath{\xi}}_{\mathrm{eff}}\ensuremath{\sim}d={\ensuremath{\xi}}_{h}.$ From an estimate of ${\ensuremath{\xi}}_{0}/a\ensuremath{\sim}$ 5.2 for Sr14, where a is the Cu-Cu distance along the leg, ${\ensuremath{\xi}}_{h}/a$ is obtained as $\ensuremath{\sim}3.5$, 2.3, and 2.0, and hole content x as $\ensuremath{\sim}0.14$, 0.22, and 0.25 per Cu2O3 ladder for Ca6, Ca9, and Ca11.5, respectively. These values were consistent with x= 0.14, 0.2, and 0.22 for Ca6, Ca9, and Ca11 estimated from the optical conductivity experiment by Osafune et al. [Phys. Rev. Lett. 78, 1980 (1997)]. The ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ compounds are thus hole-doped two-leg spin-ladder systems which reveal the metallic behavior dominated by the 1D-like spin dynamics at high T and accompanied by the spin gap formation at low T. For Ca11.5, as the spin gap is formed upon cooling below $\ensuremath{\sim}180$ K, the resistivity increases in the direction perpendicular to the ladder, whereas the conductivity along the ladder remains metallic, followed by the localization of mobile holes in both directions below ${T}_{L}\ensuremath{\sim}60$ K. We point out that preformed pairs are confined in each ladder and localized below $\ensuremath{\sim}60$ K at an ambient pressure.
The novel quantum magnet BaCu2V2O8 was recently discovered to be a rare physical realization of a one-dimensional antiferromagnetic-ferromagnetic dimerized chain which displays strongly correlated phenomena at elevated temperatures [E. S. Klyushina et al., Phys. Rev. B 93, 241109(R) (2016)]. This paper presents an extended study of the Hamiltonian of BaCu2V2O8 at base temperature. Static susceptibility and inelastic neutron scattering data are compared to several theoretical models. An analytical relation for the dynamic structure factor of the complex unit cell of BaCu2V2O8 is derived and used to identify the intrachain exchange paths. Further analysis using the first moment of the dynamic structure factor was employed to determine the exchange path responsible for the intradimer interaction. This analysis reveals that the dimer chain is formed by a dominant antiferromagnetic exchange interaction Jintra=40.92meV which is realized via the Cu-O-V(II)-O-Cu superexchange path and a weak ferromagnetic coupling ${J}_{\mathrm{inter}}=\ensuremath{-}11.97$ meV which arises within the copper-oxygen double plaquettes.