Short-range spin and charge correlations and local density of states in the colossal magnetoresistance regime of the single-orbital model for manganites

The metal-insulator transition, and the associated magnetic transition, in the colossal magnetoresistance (CMR) regime of the one-orbital model for manganites is studied here using Monte Carlo (MC) techniques in two-dimensional clusters. Both cooperative oxygen lattice distortions and a finite superexchange coupling among the $t_{2g}$ spins are included in our investigations. Charge and spin correlations are studied. In the CMR regime, a strong competition between the ferromagnetic metallic and the antiferromagnetic charge-ordered insulating states is observed. This competition is shown to be important to understand the resistivity peak that appears near the critical temperature. Moreover, it is argued that the system is dynamically inhomogeneous with short-range charge and spin correlations that slowly evolve with MC time, producing the glassy characteristics of the CMR state. The local density of states (LDOS) is also investigated and a pseudogap (PG), identified as a dip in the LDOS at the Fermi energy, is found to exist in the CMR temperature range. The width of the PG in the LDOS is calculated and directly compared to recent scanning-tunneling-spectroscopy (STS) experimental results. The observed agreement between our calculation and the experiment suggests that the depletion of the conductance at low bias observed experimentally is a reflection on the existence of a PG in the LDOS spectra. The apparent homogeneity observed via STS techniques could be caused by the slow time characteristics of this probe. Faster experimental methods should unveil a rather inhomogeneous state in the CMR regime, as already observed in neutron-scattering experiments.

Figure 1

(Color online) The two competing ground states in the one-orbital model at electronic density $n=0.75$, obtained by varying the superexchange coupling $J_{\text{AF}}$, as explained in Ref. 22 and in the text. The FM metallic state is in (a) and the AF/CO insulating state in (b). The arrows denote the classical $t_{2g}$ spins and the open circles are proportional to the electronic density. The full circles in (b) simply denote the location of the holes. The dashed lines in (b) define “spin blocks,” which are discussed later in the text.

Figure 2

(Color online) Resistivity and uniform magnetization upon cooling (black) and heating (red) for $J_{\text{AF}}=0.0325$ (left panel) and $J_{\text{AF}}=0.0335$ (right panel). The result was obtained on a $12\times 12$ square lattice using $\lambda =1.2$, density $n=0.75$, and in the clean limit $\left(\Delta =0\right)$. No hysteresis loop is observed in both quantities.

Figure 3

(Color online) [(a)-(c)] Typical MC snapshots of local charge density and spin correlations on a $8\times 8$ lattice with $J_{\text{AF}}=0.0325$, $n=0.75$, and $\lambda =1.2$ at three different temperatures. In each snapshot, the circle radius is proportional to the local charge density. The 16 holes are represented by filled circles. The length of the arrow at each site $i$ is proportional to the spin–spin correlation $⟨{\mathbf{S}}_0\cdot {\mathbf{S}}_i⟩$, where ${\mathbf{S}}_0$ is a reference point located on a hole site. Presenting this correlation, as opposed to directly showing the classical spins, allows an easier visualization since now most spins are in the plane of the figure. Holes with $\sqrt{5}$ and 2 correlations are highlighted, as well as a couple of well-formed building blocks (see text) at the two highest temperatures. (d) The temperature dependence of the proposed operator $\widehat{O}$ (Eq. (4)). The result of $⟨\widehat{O}⟩$ is averaged over $5\times {10}^4$ MC steps. (e) The building block (see text) of the AF/CO state of the one-orbital model at $n=0.75$. (f) Proposed building block of the AF/CO state in the two-orbital model at $n=0.5$, for completeness.

Figure 4

(Color online) MC results obtained by freezing the phononic degree of freedom (see text for details). Snapshots of initial and final configurations are shown in (a) and (b), respectively. Also shown are the normalized magnetization [in (c)] and resistivity [in (d)]. With frozen charges, the DE mechanism cannot produce the FM state at low temperatures.

Figure 5

(Color online) Characteristic times that illustrate the spin and charge MC dynamics in the one-orbital model are here shown as a function of temperature, together with the resistivity. $t_G$ (circles) is the average MC time that the conductance $G$ remains constant at one of its quantized values. ${\tau }_c$ (squares) is the autocorrelation time of the local charge density. ${\tau }_{\text{s}}$ (diamonds) is the autocorrelation time of the uniform spin structure factor. The resistivity $\rho$ (triangles) is also presented for comparison. The inset contains typical measurements of the conductance as a function of MC time, illustrating the discrete values it takes.

Figure 6

(Color online) (a) MC-time evolution of $\left|\overline{S}\right|$, $\text{cos}\Theta$, and the normalized magnetization $m$. The MC simulation is initialized by a configuration with short-distance AF/CO order [similar to that shown in Fig. 1b] but the simulation occurs at very low temperature, where a FM ground state is stable [similar to that shown in Fig. 1a]. (b) MC-time evolution of $\left|\overline{S}\right|$ and $\text{cos}\Theta$ at shorter MC-time scales than in (a). Three snapshots of a typical block of spins in the early stages of MC evolution are also shown.

Figure 7

(Color online) Left: Density of states $N\left(\omega \right)$ at various temperatures in the CMR regime. A pseudogap develops in both the PM insulating and FM metallic states. Right: temperature evolution of $N^{-1}\left(\omega =\mu \right)$ and the resistivity $\rho$.

Figure 8

(Color online) Temperature dependence of the site-averaged width $\Delta E$ of the pseudogap in the LDOS. Also shown is the resistivity (black diamonds) at the same model parameters. Inset: $\Delta E$ rescaled by the critical temperature of the MI transition $T_{\text{MI}}$. Also shown as black squares are the experimentally determined “polaronic gaps” (extracted from Ref. 26) rescaled by $T_{\text{MI}}$.

Figure 9

(Color online) Statistics of the width of the LDOS pseudogap $\Delta E_i$. (a) A general Gaussian probability distribution of $\Delta E_i$ at various temperatures in both the FM metallic and PM insulating phases is observed when MC-averaged over long times. (b) The standard deviations of $\Delta E_i$. The system behaves more inhomogeneously in shorter MC-time scales.

Figure 10

(Color online) (a) Distribution of the width of the LDOS pseudogap $\Delta E_i$ at different MC-time scales. Real space images of $\Delta E_i$ measured under $50000$ and 100 MC steps at $T/t=0.02$ are also provided in (b) and (c), respectively. The radius of each circle is proportional to the local $\Delta E_i$ value at that site. Open circles corresponds to $\Delta E_i/t\ge 0.2$, whereas solid (red/gray) ones corresponds to $\Delta E_i/t<0.2$.