Nanoclustering phase competition induces the resistivity hump in colossal magnetoresistive manganites

Using a two-band double-exchange model with Jahn-Teller lattice distortions and superexchange interactions, supplemented by quenched disorder, at an electron density $n=0.65$, we explicitly demonstrate the coexistence of the $n=1/2$-type $\left(\pi ,\pi \right)$ charge-ordered and the ferromagnetic nanoclusters above the ferromagnetic transition temperature $T_{\mathrm{c}}$ in colossal magnetoresistive (CMR) manganites. The resistivity increases due to the enhancement of the volume fraction of the charge-ordered and the ferromagnetic nanoclusters upon decreasing the temperature down to $T_{\mathrm{c}}$. The ferromagnetic nanoclusters start to grow and merge, and the volume fraction of the charge-ordered nanoclusters decreases below $T_{\mathrm{c}}$, leading to the sharp drop in the resistivity. By applying a small external magnetic field $h$, we show that the resistivity above $T_{\mathrm{c}}$ increases, as compared with the case when $h=0$, a fact that further confirms the coexistence of the charge-ordered and the ferromagnetic nanoclusters. In addition, we show that the volume fraction of the charge-ordered nanoclusters decreases upon increasing the bandwidth, and consequently the resistivity hump diminishes for large bandwidth manganites, in good qualitative agreement with experiments. The obtained insights from our calculations provide a complete pathway to understand the phase competition in CMR manganites.

Figure 1

(a) Schematic low-temperature phase diagram of manganites $R_{1-x}{A}_x{\mathrm{MnO}}_3$ for different $R$ (rare-earth) and $A$ (alkaline-earth) elements (adopted from Ref. [23]). $F,A$, and CE-type phases near $x=1-n=0.35$ are of interest in the present study, and they denote ferromagnetic (FM), $A$-type antiferromagnetic, and CE-type antiferromagnetic phases, respectively. (b) Schematic to illustrate the temperature dependence of the resistivity for different bandwidth manganites at $x=1-n\sim 1/3$. The same symbols in (a) and (b) are used to indicate the combination of $R$ and $A$. (c) Schematic to show the phase coexistence between charge-ordered (red diamonds) and ferromagnetic (blue triangles) nanoclusters without and with a small external magnetic field $h$ above the FM $T_{\mathrm{c}}$. The direction of a triangle implies the overall spin orientation in each FM nanoclusters (see the text for details).

Figure 2

(a) $n$ dependence on $\mu$ for two different temperatures $T=0.01$ and 0.07. (b) The $n\text{−}T$ phase diagram, containing the CO and FM phases. PS, $I$, and $M$ denote phase separation, insulator, and metal, respectively. The corresponding phase boundaries at $T=0.01$ are indicated in (a) using the same symbols as in (b). $\mathrm{\Delta }=0$ in (a) and (b). $T$ dependence of (c) the FM structure factor $S(0,0)$ and (d) the resistivity $\rho$ in units of $\hslash a/\pi e^2$ at $n=0.65$ for different $\mathrm{\Delta }$ values indicated in (c). The inset in (c) shows the $\mu$ vs $T$, required to set the desired $n=0.65$. The inset in (d) shows the enlarged plot at low temperatures. $\lambda =1.7$ for all figures.

Figure 3

$T$ dependence of the volume fraction of the CO nanoclusters V(CO) and resistivity $\rho$ (in units of $\hslash a/\pi e^2)$ for (a) $\mathrm{\Delta }=0.05$ and (c) $\mathrm{\Delta }=0.1$. The volume fraction of FM nanoclusters V(SO) vs $T$ for (b) $\mathrm{\Delta }=0.05$ and (d) $\mathrm{\Delta }=0.1$. Filled symbols indicate $T_{\mathrm{c}}$. $n=0.65$ and $\lambda =1.7$ for all figures. See the text for dotted lines with star symbols.

Figure 4

$T$ dependence of the volume fraction of (a) FM nanoclusters V(SO) and (b) CO nanoclusters V(CO) with and without an external magnetic field $h$ for $\lambda =1.7$ and $\mathrm{\Delta }=0.05$. Resistivity $\rho$ in units of $\hslash a/\pi e^2$ vs $T$ with and without $h$ for (c) $\lambda =1.7$ and $\mathrm{\Delta }=0.05$, and (d) $\lambda =1.5$ and $\mathrm{\Delta }=0.1$. Filled symbols in (a)–(c) highlight that V(SO) and V(CO) remain unaffected, but the resistivity increases for $T=0.05$ and 0.055 with $h$.

Figure 5

$T$ dependence of (a) the resistivity $\rho$ in units of $\hslash a/\pi e^2$ and (b) V(CO) for $\lambda =1.75$, 1.7, and 1.5. $\mathrm{\Delta }$ values are mentioned in the figure. Legends in (a) and (b) are the same.

Figure 6

(a)–(c) $T$ dependence of the resistivity $\rho$ in units of $\hslash a/\pi e^2$ for different parameters (indicated in the figures). In (a), the dashed line is for $\mathrm{\Delta }=0$. (d) Temperature dependence of V(CO) for the same set of parameters used in (c). Legends in (c) and (d) are the same.