Impurity-induced spin pseudogap in $\mathrm{SrCu}{\mathrm{O}}_2$ doped with Mg, Zn, or La

The low energy magnetic excitations spectra of the pristine and doped quasi-one-dimensional spin chains cuprates $\mathrm{SrCu}{\mathrm{O}}_2$ have been investigated by inelastic neutron scattering. The momentum-integrated magnetic dynamical structure factor yields a constant integrated intensity with regard to energy in the pure compound, while it shows a strong decay, at low energies, in the compounds doped with nonmagnetic impurities, namely, $\mathrm{SrC}{\mathrm{u}}_{0.99}{\mathrm{M}}_{0.01}{\mathrm{O}}_2$ (with $M=\mathrm{Zn}$ or Mg) and $\mathrm{S}{\mathrm{r}}_{0.99}\mathrm{L}{\mathrm{a}}_{0.01}\mathrm{Cu}{\mathrm{O}}_2$ ($\mathrm{C}{\mathrm{u}}^{+}$ carrying $S=0$ created within the chains). These results evidence the opening of a spin pseudogap in the two-spinon continuum of $\mathrm{SrCu}{\mathrm{O}}_2$ upon doping, stemming from disruptions of the spin chains by quantum impurities.

Figure 1

(a) Crystal structure of $\mathrm{SrCu}{\mathrm{O}}_2$. (b) Projection on the $bc$ plane of the structure that shows the zigzag chains of $\mathrm{C}{\mathrm{u}}^{2+}$ ions. $J_{\mathrm{AFM}}$ and $J_{\mathrm{FM}}$ refer to the coupling constants of the antiferromagnetic and ferromagnetic superexchange interactions in the chains, respectively, as described in the text.

Figure 2

(a) Typical ($Q, \omega$) color map of the low energy magnetic excitations spectrum obtained by INS in the Mg-doped $\mathrm{SrCu}{\mathrm{O}}_2$. The white dashed line shows the center of the spin excitations spectrum. (b) Constant energy scans following the trajectory $Q\left(10l\right)$ with $l=[0.3-0.7]$ at $T=1.5\mathrm{K}$, on the TAS 4F1. (c) Comparison of the imaginary part of the dynamical magnetic susceptibility obtained by fits to the constant $E$ scans on the TAS 4F1 (1.5 K) and 2T1 (4 K) and the energy scan at $Q$(1 0 0.5) on the TAS 4F1 (1.5 K).

Figure 3

(a)–(d) Comparison of the measured dynamical structure factors for the pristine $\mathrm{Mg}-,\mathrm{Zn}-$, and $\mathrm{La}-$ doped $\mathrm{SrCu}{\mathrm{O}}_2$ (violet triangles), respectively, with the theoretical $S$(ω) for an infinite chain (black line) and for a 1 and $x\%$-doped chain (green and blue lines, respectively).

Figure 4

Log-log plot of the evolution of Im ${\chi }_L\left(\omega \right)/F_{\mathrm{\Delta }}\left(\omega \right)$ versus $\hslash \omega /k_{b}T$. Data collected at 1.5, 4, 40, and 100 K for $\mathrm{SrC}{\mathrm{u}}_{0.99}\mathrm{M}{\mathrm{g}}_{0.01}{\mathrm{O}}_2$ after normalization by the envelope function $F_{\mathrm{\Delta }}\left(\omega \right)$ [Eq. (4)].

Figure 5

(a) Neutron diffraction patterns of a grinded single crystal of $\mathrm{SrCu}{\mathrm{O}}_2$ at temperatures ranging from 1.5 to 80 K. (b) Typical structural Rietveld refinement result ($\mathrm{SrCu}{\mathrm{O}}_2$ at $T=1.5\mathrm{K}$).

Figure 6

Magnetic susceptibility measured along the spins chains ($c$ axis) for the pristine $\mathrm{Mg}-,\mathrm{Zn}-$, and $\mathrm{La}-$ doped $\mathrm{SrCu}{\mathrm{O}}_2$ and their fits.

Figure 7

(a) ($Q, \omega$) color map of the low energy magnetic excitations spectrum obtained through INS in the pristine $\mathrm{SrCu}{\mathrm{O}}_2$; the white dashed line shows the center of the spin excitations spectrum. (b) Constant energy scans following the trajectory $Q$ (1 0 $l$) with $l=[0.3-0.7]$ at $T=4\mathrm{K}$ on the TAS IN22. (c) Comparison of the imaginary part of the dynamical magnetic susceptibility obtained by fits to the constant $E$ scans and the energy scan at $Q$(1 0 0.5).

Figure 8

(a) ($Q, \omega$) color map of the low energy magnetic excitations spectrum obtained through INS in the Zn-doped $\mathrm{SrCu}{\mathrm{O}}_2$; the white dashed line shows the center of the spin excitations spectrum. (b) Constant energy scans following the trajectory $Q$ (1 0 $l$) with $l=[0.4-0.6]$ at $T=6\mathrm{K}$ on the TAS 4F1. (c) Imaginary part of the dynamical magnetic susceptibility obtained by fits to the constant $E$ scans.

Figure 9

(a) ($Q, \omega$) color map of the low energy magnetic excitations spectrum obtained through INS in the La-doped $\mathrm{SrCu}{\mathrm{O}}_2$; the white dashed line shows the center of the spin excitations spectrum. (b) Constant energy scans following the trajectory $Q$ (1 0 $l$) with $l=[0.4-0.6]$ at $T=1.5\mathrm{K}$ on the TAS 4F1. (c) Comparison of the imaginary part of the dynamical magnetic susceptibility obtained by fits to the constant $E$ scans and the energy scan at $Q$(1 0 0.5).