Spin Excitations in Fluctuating Stripe Phases of Doped Cuprate Superconductors

Using a phenomenological lattice model of coupled spin and charge modes, we determine the spin susceptibility in the presence of fluctuating stripe charge order. We assume the charge fluctuations to be slow compared to those of the spins, and combine Monte Carlo simulations for the charge order parameter with exact diagonalization of the spin sector. Our calculations unify the spin dynamics of both static and fluctuating stripe phases and support the notion of a universal spin excitation spectrum in doped cuprate superconductors.

Figure 1

Snapshots of the charge order parameters $|{\psi }_{x,y}|$ and the resulting charge modulation ($Q_x+Q_y$), obtained from MC simulations for bond-centered fluctuating stripes on ${32}^2$ sites, using a ${\psi }^6$ action ${\mathcal{S}}_{\psi }$; see text. (a) Strong repulsion between ${\psi }_x$ and ${\psi }_y$, sharp domain walls. (b) Weak repulsion, smooth domain walls with checkerboard structure. (c) Weak attraction, fluctuating checkerboard order.

Figure 2

Dynamic susceptibility ${\chi }^{\prime \prime }(\overrightarrow{q},\omega )$ for bond-centered fluctuating stripes [31] on ${40}^2$ sites. Left/middle: cuts at a constant energy, slightly below/above the resonance energy, $E_{\mathrm{res}}$, as function of momentum. Right: cuts along ($q_x$, $\pi$) as a function of $q_x$ and energy, showing the universal hour-glass spectrum. The couplings are ${\lambda }_1={\lambda }_3/2=5E_{\mathrm{res}}/|\psi {|}_{\mathrm{typ}}$, ${\lambda }_2={\lambda }_4=0$. (a) Strong repulsion between ${\psi }_x$ and ${\psi }_y$, correlation length $\xi \approx 30$. (b) Weak repulsion, $\xi \approx 20$. (c) Weak attraction, $\xi \approx 20$.

Figure 3

Evolution of ${\chi }^{\prime \prime }(\overrightarrow{q},\omega )$ with decreasing stripe correlation length $\xi$, for a situation with strong repulsion between ${\psi }_x$ and ${\psi }_y$, as in Fig. 2a.

Figure 4

Dynamic susceptibility slightly below the resonance energy, for fluctuating stripes in the presence of an in-plane anisotropy. From (a) to (c) the anisotropy is increasing: the ratio of the gradient coefficients for ${\psi }_{x,y}$ in the charge action ${\mathcal{S}}_{\psi }$ is (a) 1.005, (b) 1.01, (c) 1.02.