Evolution of spin dynamics across the discontinuous metal-insulator transition in a deformable lattice

We performed electron spin-resonance (ESR), magnetic, and optical absorption studies of a model system used to investigate the metal-insulator transition in a deformable lattice. The ESR and magnetic studies revealed that the small polarons have no correlation to the conductivity below or above the mobility edge. The conducting transition is marked by the appearance of an asymmetric ESR signal simultaneously with a significant suppression of the small bipolaron optical absorption band indicating that the extended states result from an abrupt dissociation of the small bipolarons. Immediately above the mobility edge competing phases of extended states, small polarons, and small bipolarons coexist. We propose a phase diagram for the charge and spin dynamics of an interacting gas of small (bi)polarons across the discontinuous conducting transition that has implications for understanding the long-standing conundrum of Mooij correlations.

Figure 1

The $n$ dependence of the ESR signal at room temperature. Samples from $n=0.09$ up to 1.00 are fit with two Lorentzian components $c1$ and $c2$. At $n=1.09$, an asymmetric ESR signal is observed, which is fit with a Dysonian component $c3$.

Figure 2

The $n$ dependence of ESR [(a) room temperature FWHM and (b) $g$ value], magnetic [(c) percentage of spin-1/2 magnetic moments], and transport properties [(d) electrical resistivity at 300 K] of ${\mathrm{K}}_n/{\mathrm{K}}_2-\mathrm{P}$. Note that the asymmetric $c3$ component applies only to $n=1.09$.

Figure 3

The temperature dependence of (a) FWHM of the $c1,c2$, and $c3$ components and (b) $\rho$ of $n=0.90$ and 1.09. Component $c3$ applies only to $n=1.09$.

Figure 4

The $n$ dependence of room-temperature optical absorption spectra of ${\mathrm{K}}_n/{\mathrm{K}}_2-\mathrm{P}$ at (a) $n=0.09$ and (b) 0.09–1.09. The solid circles and squares mark the small bipolaron and high-frequency bands, respectively. The broken curve in panel (a) is the fitting of Eq. (1). The tilted straight line and downward arrow in panel (b) provide guides for the eye to observe the evolution of the small bipolaron absorption band.

Figure 5

The proposed phase diagram for extended states and small (bi)polarons in the face of $\lambda ,W,t$, and $U$. See the text for details.