Electronic Structure Evolution across the Peierls Metal-Insulator Transition in a Correlated Ferromagnet

Transition metal compounds often undergo spin-charge-orbital ordering due to strong electron-electron correlations. In contrast, low-dimensional materials can exhibit a Peierls transition arising from low-energy electron-phonon-coupling-induced structural instabilities. We study the electronic structure of the tunnel framework compound ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$, which exhibits a temperature-dependent ($T$-dependent) paramagnetic-to-ferromagnetic-metal transition at $T_C=180\mathrm{K}$ and transforms into a ferromagnetic insulator below $T_{\mathrm{MI}}=95\mathrm{K}$. We observe clear $T$-dependent dynamic valence (charge) fluctuations from above $T_C$ to $T_{\mathrm{MI}}$, which effectively get pinned to an average nominal valence of ${\mathrm{Cr}}^{+3.75}$ (${\mathrm{Cr}}^{4+}:{\mathrm{Cr}}^{3+}$ states in a $3:1$ ratio) in the ferromagnetic-insulating phase. High-resolution laser photoemission shows a $T$-dependent BCS-type energy gap, with $2G(0)\sim 3.5(k_B{T}_{\mathrm{MI}})\sim 35\mathrm{meV}$. First-principles band-structure calculations, using the experimentally estimated on-site Coulomb energy of $U\sim 4\mathrm{eV}$, establish the necessity of strong correlations and finite structural distortions for driving the metal-insulator transition. In spite of the strong correlations, the nonintegral occupancy (2.25 $d\text{−}\text{electrons}/\mathrm{Cr}$) and the half-metallic ferromagnetism in the $t_{2g}$ up-spin band favor a low-energy Peierls metal-insulator transition.

Popular Summary

Transition-metal oxides exhibit a fascinating variety of structural, electronic, and magnetic properties based on the competition between localization and delocalization of their electrons. Here, we study the chromium-based material ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$, which consists of quasi-one-dimensional chains and tunnels. ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$ exhibits ferromagnetism below ${\mathrm{T}}_c=180\mathrm{K}$ and a ferrometal-to-ferroinsulator transition (i.e., an increase in electrical resistivity) below ${\mathrm{T}}_{\mathrm{MI}}=95\mathrm{K}$. While its quasi-one-dimensional nature is believed to lead to a Peierls-type insulating state due to a structural distortion, the accompanying ferromagnetism within the metallic and insulating states is difficult to explain. Here, we discover an unusual aspect of the electronic structure of ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$ that helps to solve the puzzle of its ferrometal-to-ferroinsulator transition.

We study the electronic structure changes of polycrystalline ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$ across ${\mathrm{T}}_c$ and ${\mathrm{T}}_{\mathrm{MI}}$ using a combination of experimental probes (electron spectroscopy) and theoretical calculations (first-principles band-structure calculations). Based on precise measurements, we uncover clear temperature-dependent dynamic valence fluctuations of the ${\mathrm{Cr}}^{3+}$ and ${\mathrm{Cr}}^{4+}$ states across the paramagnetic-metal-to-ferromagnetic-metal transition, which has been completely missed in previous studies. The valence fluctuations get pinned in the low-temperature Peierls insulating state below ${\mathrm{T}}_{\mathrm{MI}}=95\mathrm{K}$. This behavior is in contrast to all known systems that exhibit a Peierls transition and constitutes a novel phase of temperature-dependent valence (charge) fluctuations in the presence of ferromagnetic (spin) order.

We expect that our results will motivate others to search for such unusual transitions in quasi-one-dimensional and two-dimensional magnetic materials.

Figure 1

The tunnel framework structure of the hollandite ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$. As seen in the $ab$ plane, the hollandite structure consists of tunnels made out of double chains of ${\mathrm{CrO}}_6$ octahedra, stacked along the $c$ axis. The average valency of Cr ions is ${\mathrm{Cr}}^{3.75+}$, which formally corresponds to ${\mathrm{Cr}}^{4+}(d^2)$ and ${\mathrm{Cr}}^{3+}(d^3)$ states in a $3:1$ ratio (2.25 $d\text{electrons}/\mathrm{Cr}$). The ground state has comparable contributions from $d^n\underset{\_}{L^0}$ ($\equiv$ $d^n$) and $d^{n+1}\underset{\_}{L^1}$ ($\underset{\_}{L^1}:\text{ligand}\text{hole}$) for the ${\mathrm{Cr}}^{3+}$ and ${\mathrm{Cr}}^{4+}$ states.

Figure 2

Soft X-ray valence-band photoemission spectroscopy (PES) of ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$. Valence band PES spectra of ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$ obtained using (a) $h\nu =1200\mathrm{eV}$ and (b) $h\nu =578.05\mathrm{eV}$ and compared with the calculated Cr $3d$ partial DOS. (c) Resonant-PES measured across the Cr $2p-3d$ threshold at 20 K using photon energies indicated by tick marks (A-K) on the Cr $L_3$ XAS curve shown in the inset.

Figure 3

DOS and band gap from first-principles calculations. (a) The atom and spin-projected DOS calculated using $\mathrm{GGA}+U$ ($U=4\mathrm{eV}$) gives a metallic phase for the high-temperature structure. (b) Introducing a structural distortion in the presence of $U$ opens up a gap at zero energy (${\mathrm{E}}_F$) (see text for details). (c) Band gaps calculated using $\mathrm{HF}+U$ and $\mathrm{GGA}+U$ methods for different values of $U$, assuming a structural tetramerization (tet) without and with polaronic (pol) distortions.

Figure 4

Cr 1s core-level spectra of ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$. (a) $T$-dependent Cr 1s core-level spectra obtained using HAXPES show clear changes across the paramagnetic-metal (PMM)-to-ferromagnetic-metal (FMM) transition, but negligible change is seen between 80 K and 20 K in the Peierls ferromagnetic-insulating phase. The observation indicates that the average Cr valence gets pinned to ${\mathrm{Cr}}^{+3.75}$ in the Peierls phase. The inset shows the estimated average Cr valency as a function of $T$. (b) The $T=20\text{−}\mathrm{K}$ spectrum can be synthesized using the ${\mathrm{Cr}}^{4+}$ and ${\mathrm{Cr}}^{3+}$ spectra calculated using a cluster model and added in a ratio of $3:1$, representing the average valency.

Figure 5

Temperature-dependent laser photoemission of ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$. (a) $T$-dependent VB spectra at and near ${\mathrm{E}}_F$, obtained using laser PES. The 0.2-eV feature is evident; the inset shows resolution-convoluted Fermi-Dirac (FD) function fit to the 140-K spectrum confirming a metallic Fermi edge. (b) The spectral intensity at ${\mathrm{E}}_F$ gets depleted gradually when decreasing $T$, indicative of a $T$-dependent gap formation. (c) DOS obtained upon symmetrizing the VB spectra at each $T$. (d) The gap vs $T$ shows a BCS-like dependence, suggestive of a second-order phase transition.

Figure 6

Schematic electronic structure of ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$. ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$ exhibits a charge-transfer-type half-metallic ground state with $U>\mathrm{\Delta }$ in the high-$T$ ferromagnetic metal phase, as shown in the top panel. On reducing $T$, it undergoes a Peierls metal-insulator transition below $T_{\mathrm{MI}}=95\mathrm{K}$, with a gradual depletion of spectral weight at and near ${\mathrm{E}}_F$, consistent with a second-order BCS-like temperature-dependent gap (lower panel).