Coherent and Dynamic Small Polaron Delocalization in CuFeO$_{2}$

Abstract

Small polarons remain a significant bottleneck in the realization of efficient devices using transition metal oxides. Routes to engineer small polaron coupling to electronic states and lattice modes to control carrier localization remain unclear. Here, we measure the formation of small polarons in CuFeO$_{2}$ using transient extreme ultraviolet reflection spectroscopy and compare it to theoretical predictions in realistically parameterized Holstein models, demonstrating that polaron localization depends on its coupling to the high-frequency versus low-frequency components of the phonon bath. We measure that small polaron formation occurs on a comparable ~100 fs timescale to other Fe(III) compounds. After formation, a dynamic delocalization of the small polaron occurs through a coherent lattice expansion between Fe-O layers and charge-sharing with surrounding Fe(IV) states. Our simulations of polaron formation dynamics reveal that two major factors dictate polaron formation timescales: phonon density and reorganization energy distributions between acoustic and optical modes, matching experimental findings. Our work provides a detailed, real-time observation of how electronic-structural coupling in a polaron-host material can be leveraged to suppress polaronic effects for various applications.

Figures (7)

• Figure 1: A comparison of the (A) delafossite crystal structure of CuFeO$_2$ where Cu atoms are inserted between Fe-O layers and (B) hematite ($\alpha$-Fe$_2$O$_3$). (C) The projected density of states shows that the conduction bands are dominated by Fe orbital character while the valence bands are mixed with Cu-O orbitals. (D) The band structure of CuFeO$_2$ -- where red (blue) stars indicate the VBM (CBM). The weights indicate the extent to which each supercell Bloch state contributes to the corresponding primitive cell state.
• Figure 2: Transient XUV reflection-absorption spectra of CuFeO$_2$ (A) following photoexcitation with a 400 nm pump. The red and blue colors represent increased and decreased absorption after photoexcitation, respectively. Four main spectral features are labeled in the plot. At pump-probe overlap (t$_0$), a series of positive and negative peaks are observed (label 1). Immediately after photoexcitation, an ultrafast spectral blue shift is observed around 55 eV (label 2), which is attributed to octahedra expansion and small polaron formation. At longer pump-probe time delays, spectral intensity and energy oscillations are observed (label 3), which is attributed to polaron induced coherent acoustic phonons. At higher XUV transition energies, increased XUV absorption is observed and attributed to photoinduced Fe(IV) states (label 4). Experimental lineouts (B) at 30 fs (blue), 180 fs (red), and 2.04 ps (green) which correspond to dynamics in label 1, label 2, and label 3, respectively.
• Figure 3: Experimental lineouts (solid lines) (A) compared to BSE theory (dashed lines) for immediately after photoexcitation (blue), following polaron formation (green), and the change to the polaron spectrum following lattice expansion (red), which correspond the label 1, label 2, and labels 3 and 4 in Fig. \ref{['fig2']}A, respectively. Ligand-field theory (B) for differing oxidation states of iron. The blue trace corresponding to Fe(IV) appears at the same energy as Fig. \ref{['fig2']}A, label 4. The spectral oscillations (C) in the main negative feature at $\sim$55 eV in Fig. \ref{['fig2']}A label 3. The oscillations in the red box were Fourier transformed (d) and demonstrate Cu-(Fe-O) c-axis acoustic modes at 1.4 THz and a mixture of Fe-O modes at 5.3 THz.
• Figure 4: Kinetics plot of the charge transfer (blue), polaron (green), and lattice expansion (red) states with "best fit” lines to visualize the kinetics chosen dynamics while disregarding the coherent phonon oscillations.
• Figure 5: Schematic representation of the polaron formation mechanism in CuFeO$_2$. The formation of Fe$^{4+}$ states around polaron sites and the expansion of the lattice enables delocalization of the polarons on a ps timescale.