Structure of the Spin-Glass State of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$: The Spiral Theory

Starting from the $t\mathrm{\text{−}}J$ model, we derive the effective field theory describing the spin dynamics in insulating ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$, $x\lesssim 0.055$, at low temperature. The theory results in a disordered spiral ground state, in which the staggered component of the copper spins is confined in a plane determined by the spin anisotropies. The static spin structure factor obtained in our calculations is in perfect agreement with neutron scattering data over the whole range of doping in both, the Néel and the spin-glass phase. We show that topological defects (spin vortex-antivortex pairs) are an intrinsic property of the disordered spiral ground state.

Figure 1

Characteristic ground state configuration of a particular realization at $x=0.05$. The system (a) without defects has higher energy than the same system (b) with a vortex-antivortex pair (squares). The impurity pseudospins $l_i$ are oriented along the $c$ axis. Full (open) circles correspond to values $-\frac{1}{2}$ ($+\frac{1}{2}$). Small arrows represent the $\overrightarrow{n}$ field. The system forms domains stretched along the $a$ direction, in which all pseudospins are aligned in parallel.

Figure 2

(a) $⟨n^b⟩$ as a function of doping $x$. For $\kappa =0.4$, Néel order is destroyed at $x_c\approx 0.02$, in agreement with experiments. For pointlike impurities ($\kappa \to \infty$), there is no phase transition at least up to $x=0.05$. (b) Neutron scattering probability $S_{\mathbf{q}}$ for $x=0.04$. Dots correspond to experimental observations taken from Fig. 4 in Ref. 6, with normalized intensities. The curve represents our simulation, containing no fitting parameters. (c) Incommensurability $\delta$ (in reciprocal lattice units of the tetragonal lattice) as a function of doping. Our calculations (dots) are in good agreement with experimental measurements (squares) taken from Ref. 3, 5, 24, see Fig. 6 of Ref. 3. Theoretical points for the Néel phase are taken from Ref. 14.