Striped Multiferroic Phase in Double-Exchange Model for Quarter-Doped Manganites

The phase diagram of quarter-hole-doped perovskite manganites is investigated using the double-exchange model. An exotic striped type-II multiferroic phase, where 25% of the nearest-neighbor spin couplings are orthogonal to each other, is found in the narrow-bandwidth region. Comparing with the spiral-spin ordering phase of undoped manganites, the multiferroic Curie temperature of the new phase is estimated to be $\sim 4$ times higher, while the ferroelectric polarization is similar in magnitude. Our study provides a path for noncollinear spin multiferroics based on electronic self-organization, different from the traditional approach based on superexchange frustration.

Figure 1

The zero-$T$ (2D lattice) phase diagram of quarter-doped manganites. SOS denotes the novel multiferroic phase. Full dots denote the couplings where variational results were confirmed by the MC simulation [24] and the zero-$T$ relaxation using a $L=8$ cluster. Open dots are cases where the MC simulation did not provide a clear answer due to strong competition of metastable states.

Figure 2

Spin patterns of the (a) SOS and (b) $C_{1/4}{E}_{3/4}$ phases. The magnetic unit cell of the SOS phase (red square) is $4\sqrt{2}\times 4\sqrt{2}$ ($4\times 4$ in the orthorhombic notation). Shown also are the two possible local $\overrightarrow{P}$ from the DM mechanism (red arrows). The total $\overrightarrow{P}$ is, thus, perpendicular to the stripes [25]. (c) The (common) spin structure factor of these two phases. The characteristic peaks appear at ($1/4$, $1/4$), ($1/8$, $3/8$), and ($3/8$, $1/8$) and their equivalent positions in the $\overrightarrow{q}+(1/2,1/2)$ region. The ideal amplitudes of these three peaks are in the ratio of $2:1:1$. Density-of-states of the (d) SOS and (e) $C_{1/4}{E}_{3/4}$ phases (at $\lambda =0$, fixing the spin pattern). Both of these phases have a gap (0.6, $\sim 0.2–0.3\mathrm{eV}$) at the Fermi level.

Figure 3

Finite-$T$ MC results ($J_{\mathrm{AFM}}=0.18$, $\lambda =0$) for the SOS phase, on the $L=8$ cluster. Left axis: $\overrightarrow{P}$ per site is calculated using $\sum _{⟨i,j⟩}[{\overrightarrow{e}}_{i,j}\times ({\overrightarrow{S}}_i\times {\overrightarrow{S}}_j)]/L^2$, phenomenologically. Thus, $|\overrightarrow{P}|$ per site at zero-$T$ is $\sqrt{2}/4$. The MC average is done on $|\overrightarrow{P}{|}^2$, to avoid strong finite-size fluctuations in $\overrightarrow{P}$, and $⟨|\overrightarrow{P}{|}^2{⟩}^{1/2}$ per site is shown. Right axis: Amplitudes of characteristic peaks in the spin structure factor and their summation are normalized to their zero-$T$ values. Dashed lines indicate the size-dependent high-$T$ asymptotic values of spin structure factors and $|\overrightarrow{P}|$ (i.e., background). Real-space spin correlations at the maximum length $C(L/2,L/2)$ are also shown. Inset: Same properties but on the $L=16$ lattice.

Figure 4

Zero-$T$ charge and orbital ordering of the SOS and $C_{1/4}{E}_{3/4}$ phases. The unit cell of the charge and orbital ordering block shown here is only $1/4$ of that of the spin ordering (dotted regions in Fig. 2). The radius of the circles are proportional to the local $e_g$ charge density. The high (H), medium (M), and low (L) charge density regions are partitioned by the broken lines. For the SOS phase ($\lambda =0$), the $e_g$ density in the H (L) region is $5/6$ ($2/3$). For the $C_{1/4}{E}_{3/4}$ phase at $\lambda =0.8$, the $e_g$ density in the H/M/L sites is $0.95/0.73/0.59$, respectively.