Effect of correlated disorder on the magnetism of double exchange systems

We study the effects of short-range-correlated disorder arising from chemical dopants or local lattice distortions on the ferromagnetism of $3d$ double exchange systems. For this, we integrate out the carriers and treat the resulting disordered spin Hamiltonian within a local random phase approximation, whose reliability is shown by direct comparison with Monte Carlo simulations. We find large-scale inhomogeneities in the charge, couplings, and spin densities. Compared with the homogeneous case, we obtain larger Curie temperatures $\left(T_C\right)$ and very small spin stiffnesses $\left(D\right)$. As a result, the large variations of $\frac{D}{T_C}$ measured in manganites may be explained by correlated disorder. We also provide a microscopic model for Griffiths phases in double exchange systems.

Figure 1

(Color online) (a) $T_C$ as a function of hole density (clean case). Lines are obtained with the effective Heisenberg Hamiltonian within mean field (dashed line), RPA (dot dashed line), and Monte Carlo (solid line) treatments, and symbols from Monte Carlo simulations of the full double exchange model: MC1 (Ref. 23), MC2 (Ref. 20), and MC3 (Ref. 22) (b) $T_C$ as a function of the on-site potential width $\Delta$ for the Anderson disorder (uncorrelated): The solid line is obtained with the local RPA and symbols are from Monte Carlo simulations (Ref. 23).

Figure 2

(Color online) Top row: real-space picture of the magnetic couplings $2J_{ij}$ of the effective model (correlated disorder), on one layer of the ${12}^3$ cube. The dark (white) regions correspond to large (weak) couplings. Bottom row: real-space distribution of ${\lambda }_i={\lim }_{T\to T_C}\frac{⟨S_i^z⟩}{m}$ on the same layer. From left to right, $n_h=0.1$ (a),(d), 0.3 (b),(e), and 0.5 (c),(f). Parameters are $x=0.3$ and ${ϵ}_D=0.15W$.

Figure 3

(Color online) $T_C$ (symbols) as a function of hole density for the model with correlated disorder calculated by SC-LRPA (averaged over 100 configurations of disorder). Also given are the mean-field (dashed line) and RPA with all couplings identical $J_{ij}=\overline{J}$ (solid line). Parameters are $x=0.3$ and ${ϵ}_D=0.15W$. Calculations are done for sizes ${16}^3$ and ${20}^3$.

Figure 4

(Color online) Dimensionless ratio $D∕a^2{T}_C$ of the spin stiffness to the Curie temperature as a function of the hole density $n_h$, for the correlated and Anderson forms of disorder. The width of the distribution of potentials was chosen to be the same in both cases: ${ϵ}_D=0.15W$ $(x=0.3)$ and $\Delta =0.80W$. Experimental results (Ref. 15) are divided by the lattice constant of $\mathrm{La}\mathrm{Mn}{\mathrm{O}}_3$ squared $(a=3.9\mathrm{\AA })$.