Impurity-Induced Frustration in Correlated Oxides

Using the example of Zn-doped ${\mathrm{La}}_2{\mathrm{CuO}}_4$, we demonstrate that a spinless impurity doped into a nonfrustrated antiferromagnet can induce substantial frustrating interactions among the spins surrounding it. This result is the key to resolving discrepancies between experimental data and earlier theories. Analytic and quantum Monte Carlo studies of the impurity-induced frustration are in a close accord with each other and experiments. The proposed mechanism should be common to other correlated oxides.

Figure 1

The on-site magnetic moment $M(x)$ per Cu normalized by $M(0)$ vs Zn doping $x$. Symbols are neutron scattering [3] (squares) and NQR [4] (diamonds and circles) data, dashed line is their best fit. The dotted line is the classical ($S\to \infty$) result. Solid lines are the QMC [5] and the $T$-matrix results [6], respectively. Inset: slope function (see text) vs $x$ [22].

Figure 2

AF bonds in the (a) dilution-only model, (b) model with impurity-induced frustration (two frustrating bonds are shown). (c) The ${\mathrm{CuO}}_2$ plane with Zn impurity. (d) Schematic level diagram in the impurity-doped system.

Figure 3

(a) and (b): energy ${\epsilon }_{\mathrm{Zn}}$ of the lowest state on the effective “Zn”-site vs ${\Delta }_{\mathrm{Zn}}$ and $t_{\mathrm{Zn}-\mathrm{O}}$, respectively. (c) and (d): $J_{\mathrm{tot}}^{\prime }=4J_{\mathrm{Zn}}^{\prime }+2J_{\mathrm{Zn}}^{\prime \prime }$ vs ${\Delta }_{\mathrm{Zn}}$ and $t_{\mathrm{Zn}-\mathrm{O}}$, respectively. Inset (d): $J_{\mathrm{Zn}}^{\prime \prime }/J_{\mathrm{Zn}}^{\prime }$ vs $t_{\mathrm{Zn}-\mathrm{O}}$. $t_{\mathrm{pd}}=1.5\mathrm{eV}$, $\Delta =3\mathrm{eV}$, $U_d\gg \Delta$.

Figure 4

(a) The slope $R_L$, Eq. (7) vs $1/L$ in systems with and without frustration ($\beta =16$), solid symbols are extrapolated values. Inset: slope increase $\Delta R_L$ due to frustration. (b) Same as inset in Fig. 1 with the $T$-matrix results for $J_{\mathrm{Zn}}^{\prime \prime }=2J_{\mathrm{Zn}}^{\prime }=0.07\mathrm{J}$ and QMC extrapolations of $R(0)$ from Fig. 4a. QMC data provide lower bounds of the slopes.