Topological Metal-Insulator Transition within the Ferromagnetic state

Abstract

A major challenge in condensed matter physics is integrating topological phenomena with correlated electron physics to leverage both types of states for next-generation quantum devices. Metal-insulator transitions (MITs) are central to bridging these two domains while simultaneously serving as 'on-off' switches for electronic states. Here, we demonstrate how the prototypical material of K2Cr8O16 undergoes a ferromagnetic MIT accompanied by a change in band topology. Through inelastic x-ray and neutron scattering experiments combined with first-principles theoretical calculations, we demonstrate that this transition is not driven by a Peierls mechanism, given the lack of phonon softening. Instead, we establish the transition as a topological MIT within the ferromagnetic phase (topological-FM-MIT) with potential axionic properties, where electron correlations play a key role in stabilizing the insulating state. This work pioneers the discovery of a topological-FM-MIT and represents a fundamentally new class of topological phase transitions, revealing a unique pathway through which magnetism, topology, and electronic correlations interact.

Figures (4)

• Figure 1: The crystal structure of K$_2$Cr$_8$O$_{16}$. (a) Tetragonal (smaller) and monoclinic (bigger) crystal structures of K$_2$Cr$_8$O$_{16}$, outlined by solid black lines. The shaded blue areas highlight the chimney building blocks, which comprise a square arrangement of four corner sharing CrO$_6$ octahedra that propagate along the c - axis. Here, $\mathbf{a}$ ($\mathbf{a}_\mathrm{M}$), $\mathbf{b}$ ($\mathbf{b}_\mathrm{M}$) and $\mathbf{c}$ ($\mathbf{c}_\mathrm{M}$) denotes lattice vectors of the tetragonal (monoclinic) phase. The shaded red areas highlight the double chain (inter-chimney) interactions made from Cr-Cr interacting through edge sharing CrO$_6$ octahedra. (b) Structure model showing only the magnetic Cr atoms. The bonding interactions, $J_2$ and $J_3$, are shown in the top panel, while $J_1$ is shown in the bottom panel. The chimneys are made up of $J_3$ and $J_1$ and represent intra-chimney interactions while $J_2$ is the inter-chimney interaction. The magnetic structure determined from ND and angle dependent magnetisation is included in (b) as black arrows. (c) Angle-dependent magnetisation at $T=120$ K, plotted in units of emu/mol for several applied magnetic fields (see legend). Dashed lines represent sinusoidal fits to the data for each applied magnetic field. The arrow marks the easy axis orientation, approximately $22.5^\circ$ relative to the principal axis ($0^\circ$).
• Figure 2: Neutron scattering data of K$_2$Cr$_8$O$_{16}$. (a) Neutron powder diffraction pattern collected at $T=10$ K, including the structural and magnetic refinements. The green ticks denote the allowed reflections and the blue line represents the difference between the model and the data. The main magnetic peak {1,2,1} is highlighted in blue (see SM Fig. S3 for high temperature patterns). The inset shows a comparison between measured ($I_{\rm obs}$) and calculated ($I_{\rm calc}$) intensities from single-crystal magnetic refinement on datasets obtained from subtracting a selection of peaks at 10 K from the peaks at 200 K. (b) The (2,1,1) and (1,2,1) neutron diffraction peak intensities as a function of temperature. The solid line corresponds to the best fit using $I=I_0(1-T/T_{\rm C})^\beta$. (c, d) Collected powder inelastic neutron scattering spectra with the incident energy $E_i=9$ meV at 5 K and 130 K, respectively. The red dashed lines highlight the spurious-unknown dispersion discussed in SM. (e,f) The best fit results obtained using the Heisenberg Hamiltonian for 5 K and 130 K. Fitting and analysis procedures are described in SM.
• Figure 3: First-principles theoretical calculations. (a) Shows one of the distorted Cr-O octahedra that is compressed along the $z$-direction and the mirror symmetry is parallel to the $ab$-plane. $x$, $y$ and $z$ refer to the local axes of the oc-ta-he-dron. (b) Dots denote the pairs of Weyl points in the first Brillouin zone of the tetragonal phase calculated in the monoclinic lattice supercell, defined by the $\mathbf{a}_\mathrm{M}$, $\mathbf{b}_\mathrm{M}$ and $\mathbf{c}_\mathrm{M}$ lattice vectors, located on the nodal plane of $k_c = \pi/c$. The vector, $\bm q_{\rm nest}$, shows how the Weyl points are nested. (c,d) show the DFT band structures of the tetragonal ($U=0.0$ eV) and monoclinic ($U=4.0$ eV) phases, respectively, with respect to the Fermi level ($E_F$). The color bar represents their projections on the $t_{2g}$-like Wannier orbitals. In (c), the small green arrow points to the approximate location of one of the Weyl points. Its inset shows the first BZ of the monoclinic lattice and the $\mathbf{k}$-path along which the band structures (in c,d) are plotted, with the shaded surface being the $k_c = \pi/c$ plane as shown in (b).
• Figure 4: Inelastic x-ray scattering data of K$_2$Cr$_8$O$_{16}$. (a) The inelastic x-ray scattering spectra collected in transverse geometry at 20 K (blue), 95 K (green) and 115 K (red). The scans were performed from $E=-10$ to 30 meV at $\bm q=h\bar{h}2$ for $h$=0.45. The solid black line represents the overall fit (Sec. 1 in SM). (b) The integrated elastic scattering intensity collected along $\bm q=h\bar{h}0$ between $h = 4.45$ and 4.55, $i.e.$ across $\bm q_{\rm CDW}$. Four scans were made and the errorbar represents the standard deviation. The solid line is a fit using the mean field expression: $I(T)=I_0(1-T/T_{C})^\beta$. (c, d) Phonon dispersion along $q\bar{q}l$, collected at $T=$ 20, 95, 115 K in transverse and longitudinal geometries, respectively. One scan performed at 130 K is included as well. (e) Experimentally measured (symbols) and calculated (solid red lines) phonon dispersion from $\Gamma$ to M in folded configuration. Green and black symbols represent the longitudinal and transverse phonon modes, respectively.