Spin Dynamics in the Stripe Phase of the Cuprate Superconductors

Within a model that supports stripe spin and charge order coexisting with a $d_{x^2-y^2}$-wave superconducting phase, we study the self-consistently obtained electronic structure and the associated transverse dynamical spin susceptibility. In the coexisting phase of superconducting and static stripe order, the resulting particle-hole continuum can strongly damp parts of the low-energy spin-wave branches. This provides insight into recent inelastic neutron scattering data revealing the dispersion of the low-energy collective magnetic modes of lanthanum based cuprate superconductors.

Figure 1

(a) Bond-centered spin density $(-1{)}^{i_x}{S}_i^z$ (red), charge density ${\rho }_i$ (blue), and pairing potential ${\Delta }_i^d$ (green) vs site obtained when $U=4.0t$, $V=2.0t$, $t^{\prime }=-0.37t$; (b) the spectral weight $I(\mathbf{k})$ ($\Delta \omega =0.1t$) vs $\mathbf{k}$ for disordered stripes. (c) Plot of the real part of $N_{{\mathbf{Q}}^{*}}(\omega )$ vs energy $\omega$.

Figure 2

Imaginary part of the full spin susceptibility $\mathrm{Im}{\chi }^{+-}(q_x,q_y,\omega )$ at $q_y=\pi$ for $N=8$, $U=4.0t$, $V=0.0t$, and $t^{\prime }=0.0$ (a) and $t^{\prime }=-0.4t$ (b).

Figure 3

$\mathrm{Im}{\chi }^{+-}(q_x,q_y,\omega )$ at $q_y=\pi$ for $N=8$, $U=4.0t$, $V=2.0t$, and $t^{\prime }=-0.2t$ (a) and $t^{\prime }=-0.37t$ (b). The parameters in (b) are identical to those used in Fig. 1