Magnetism of hole-doped $\mathrm{Cu}{\mathrm{O}}_2$ spin chains in ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$: Experimental and numerical results

We study the magnetism of the hole-doped $\mathrm{Cu}{\mathrm{O}}_2$ spin chains in ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ by measuring the Electron Spin Resonance (ESR) and the static magnetization $M$ in applied magnetic fields up to $14\mathrm{T}$. In this compound, the dimerized ground state and the charge order in the chains are well established. Our experimental data suggest that at low temperatures the Curie-like increase of $M$ as well as the occurrence of the related ESR signal are due to a small amount of paramagnetic centers that are not extrinsic defects but rather unpaired Cu spins in the chain. These observations qualitatively confirm recent ab initio calculations of the ground state properties of the $\mathrm{Cu}{\mathrm{O}}_2$ chains in ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$. Our complementary quantum statistical simulations yield that the temperature and field dependence of the magnetization can be well described by an effective Heisenberg model in which the ground state configuration is composed of spin dimers, trimers, and monomers.

Figure 1

(Color online) Magnetization of ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ versus temperature for a constant magnetic field of $B=1\mathrm{T}$ (a) and versus an applied magnetic field for $2.5\mathrm{K}⩽T⩽20\mathrm{K}$ (b). $B$ was applied along the $c$ axis. Lines are fits to the data (see the text).

Figure 2

Temperature dependence of the $g$ factor along the $c$ and $b$ axis, respectively, as obtained from ESR data. Dashed lines extrapolate $g$ of the dimers. Below $\sim 20\mathrm{K}$, the response is due to small deviations from the perfectly dimerized state.

Figure 3

(Color online) Magnetization divided by the $g$ factor and corrected by anisotropic Van-Vleck magnetism along the respective axes of ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ for a constant magnetic field $B=1\mathrm{T}$ versus temperature.

Figure 4

Exchange parameters used for the exact diagonalization: $J=-134\mathrm{K}$, $J_{\Vert }=15\mathrm{K}$, and $J_{NN}=100\mathrm{K}$.

Figure 5

Building blocks of the hole-doped $\mathrm{Cu}{\mathrm{O}}_2$ chains: open circles denote hole sites, arrows denote spin sites. The first block contains a single spin $\left(s\right)$, the second a dimer $\left(d\right)$, and the third block hosts three spins $\left(t\right)$, which form a short chain.

Figure 6

(Color online) Magnetization versus temperature for $B=1\mathrm{T}$: Experimental data ($\vec{B}\Vert c$ axis) are given by crosses. The results of a complete numerical diagonalization are depicted by a solid curve for $N_s=17$ and $N_h=26$ as well as by a dashed curve for $N_s=17$ and $N_h=25$.

Figure 7

(Color online) Magnetization versus applied field for $T=2.5\mathrm{K}$ and $T=4.2\mathrm{K}$: Experimental data ($\vec{B}\Vert c$ axis) are given by symbols. The results of a complete numerical diagonalization are depicted by solid curves for $N_s=17$ and $N_h=26$ as well as by dashed curves for $N_s=17$ and $N_h=25$.