Spin dynamics of edge-sharing spin chains in $\mathrm{SrC}{\mathrm{a}}_{13}\mathrm{C}{\mathrm{u}}_{24}{\mathrm{O}}_{41}$

The low-energy magnetic excitation from the highly Ca-doped quasi-one-dimensional magnet $\mathrm{SrC}{\mathrm{a}}_{13}\mathrm{C}{\mathrm{u}}_{24}{\mathrm{O}}_{41}$ was studied in the magnetic ordered state by using inelastic neutron scattering. We observed the gapless spin-wave excitation, dispersive along the $a$ and $c$ axes but nondispersive along the $b$ axis. Such excitations are attributed to the spin wave from the spin-chain sublattice. Model fitting to the experimental data gives the nearest-neighbor interaction $J_c$ as 5.4 meV and the interchain interaction $J_a=4.4\mathrm{meV}$. $J_c$ is antiferromagnetic and its value is close to the nearest-neighbor interactions of the similar edge-sharing spin-chain systems such as $\mathrm{CuGe}{\mathrm{O}}_3$. Comparing with the hole-doped spin chains in $\mathrm{S}{\mathrm{r}}_{14}\mathrm{C}{\mathrm{u}}_{24}{\mathrm{O}}_{41}$, which shows a spin gap due to spin dimers formed around Zhang-Rice singlets, the chains in $\mathrm{SrC}{\mathrm{a}}_{13}\mathrm{C}{\mathrm{u}}_{24}{\mathrm{O}}_{41}$ show a gapless excitation in this paper. We ascribe such a change from gapped to gapless excitations to holes transferring away from the chain sublattice into the ladder sublattice upon Ca doping.

Figure 1

(a) The spin-ladder sublattice of $\mathrm{S}{\mathrm{r}}_{14-x}\mathrm{C}{\mathrm{a}}_x\mathrm{C}{\mathrm{u}}_{24}{\mathrm{O}}_{41}$ consists of two-leg ladders, and $J_{\mathrm{R}}$ and $J_{\mathrm{L}}$ are exchange interactions along the rungs and the legs. Theory predicts that doped holes form pairs (see the red ellipse), which play important roles in its superconducting phase. (b) On the spin-chain sublattice of $\mathrm{S}{\mathrm{r}}_{14}\mathrm{C}{\mathrm{u}}_{24}{\mathrm{O}}_{41}$, so-called Zhang-Rice (ZR) singlets are formed by a copper hole hybridized with a hole in its neighboring oxygen. The two neighboring $\mathrm{C}{\mathrm{u}}^{2+}$ form spin dimers through the nonmagnetic $\mathrm{C}{\mathrm{u}}^{3+}$ [18]. (c) The holes in highly Ca-doped compounds were primarily driven to the spin-ladder sublattice due to the chemical pressure, which consequently leaves the spin chain nearly undoped. This magnetic system becomes long-range magnetic order at 4.2 K. $J_c$ is the NN exchange interaction while $J_{ac1}$, $J_{ac2}$, and $J_a$ are possible interactions along the $a$ axis.

Figure 2

The low-energy magnetic excitation of $\mathrm{SrC}{\mathrm{a}}_{13}\mathrm{C}{\mathrm{u}}_{24}{\mathrm{O}}_{41}$ measured on PELICAN at 1.5 K. (a) The constant energy cut in the $Q_{\mathrm{K}}-Q_{\mathrm{L}}$ plane by integrating intensity over the energy range from 0.5 to 2 meV. (b) The magnetic excitation in the $Q_{\mathrm{L}}$-E plane with the integrated intensity over the $Q_{\mathrm{K}}$ range from −5 to 0 r.l.u. (c) The 3D view of the magnetic excitation in the $Q_{\mathrm{K}}-Q_{\mathrm{L}}$-E space. (d) The constant energy cuts at 1, 1.5, and 2 meV from panel (b) with a 1-meV window. The curves are intentionally shifted along the intensity axis in order to avoid overlapping.

Figure 3

$Q_{\mathrm{L}}$ scans at energy transfers of 0.5 meV (a), 1 meV (b), 2 meV (c), 3 meV (d), and 3.5 meV (e) through the antiferromagnetic zone center Q (0, 1, 3) at 1.5 K with a fixed-$E_f$ mode on SIKA. (f) An energy scan at Q (0, 1, 3.9), i.e., close to the boundary of the Brillouin zone, with a fixed-$E_f$ mode on SIKA. The solid lines are fitted to the double-Lorentzian cross section convoluted with the instrumental resolution, where the background is shown by the dash-dotted line. The horizontal bar below the peak in panel (f) shows the instrumental resolution at the energy transfer of 4 meV.

Figure 4

$Q_{\mathrm{L}}$ scans at the energy transfer 0.5 meV with $Q_{\mathrm{K}}=0.8$ (a), $Q_{\mathrm{K}}=1.0$ (b), and $Q_{\mathrm{K}}=1.2$ (c). (d) The $Q_{\mathrm{K}}$ scans at the peak position with $Q_{\mathrm{L}}=3$ and off-peak position at $Q_{\mathrm{L}}=2.5$.

Figure 5

$Q_{\mathrm{K}}$ scans at energy transfers of 0.5 meV (a), 1.5 meV (b), and 2.5 meV (c) through Q (0, 0, 3) with a fixed-$E_f$ mode on SIKA. (d) An energy scan at the boundary of the Brillouin zone at Q (1, 0, 3) with a fixed-$E_f$ mode on SIKA. The solid lines are fitted to the double-Lorentzian cross section convoluted with the instrumental resolution. The background is shown by the dash-dotted line. The horizontal bar below the excitation peak in panel (d) shows the instrumental resolution at the energy transfer of 4 meV.

Figure 6

The dispersion curves along the $Q_{\mathrm{L}}$ (a) and $Q_{\mathrm{H}}$ (b) directions. The black dots are experimental data while the red curves are the dispersion relations as obtained by fitting to the right branches of the experimental data while the left branches are plotted symmetrically with the same fitted parameters.