Thin film strain crystallizes heavy electrons – Verwey returns

Decoding the enigma: Heavy fermion formation without f electrons in spinel oxide LiV₂O₄

June 08, 2023

A joint team of researchers from the Department of Quantum Materials (Takagi) and the Stuttgart Center for Electron Microscopy (StEM) at the Max Planck Institute for Solid State Research has discovered the crystallization of heavy fermions (electrons travelling with extraordinarily large effective mass) into a charge-ordered state in an epitaxially strained film of a mixed-valent spinel oxide, LiV₂O₄. Surprisingly, the observed ordering pattern is reminiscent of the historical proposal by Verwey more than 80 years ago, a pattern yet to be definitively found in spinels. This discovery provides an important hint for resolving the long-standing mystery surrounding the mechanism of heavy fermion formation in LiV₂O₄.

Electrons in solid metals are generally free to move around, as described by the free-electron model. However, in certain solids, a unique phenomenon occurs where electrons become localized and arrange themselves into a distinct regular pattern − a process known as charge ordering. In 1939, Evert J. W. Verwey discovered charge ordering in magnetite (Fe₃O₄), a material with a spinel crystal structure. This material exhibits low resistivity at room temperature, but below a certain threshold, magnetite’s resistivity notably increases. Verwey connected this change in physical properties to the low-temperature ordering of electrons on iron ions, causing distinct valence states (Fe²⁺ and Fe³⁺) within the spinel structure. Verwey’s breakthrough discovery of charge ordering in magnetite represented the first reported instance of a metal-to-insulator transition and considerably advanced our understanding of complex electronic behaviors in condensed matter.

Further studies, however, have shown that the ordering pattern in Fe₃O₄ differs from the Verwey’s initial proposal, sparking further investigations into similar materials. LiV₂O₄, a spinel oxide similar to Fe₃O₄, has attracted attention due to its novel “heavy-fermion” metallic behavior – electrons with effective masses much larger than normal remain mobile within the material. Heavy fermions are usually seen in materials containing lanthanide elements with f-electron orbitals. Yet, it is an enigma as to why LiV₂O₄, which lacks any lanthanide elements, exhibits such behavior. An intriguing scenario suggests that the heavy-fermion state is nearly transitioning into a charge-ordered state but is unable to fully manifest due to geometrical frustration. Inherent to the spinel structure, geometrical frustration restricts charge or spin configurations from achieving an ordered state, resulting in the emergence of numerous energetically close, hidden states. This hints at the potential existence of such hidden and diverse charge-ordered states within LiV₂O₄, which could be uncovered via the application of strain.

To investigate this hypothesis, the research team turned to heteroepitaxy engineering, a technique that fabricates a thin film of a material on top of various substrate materials. Using pulsed laser deposition, they grew LiV₂O₄ thin films on two different substrates, MgO and SrTiO₃. Notably, the strained film on MgO exhibited insulating behavior, while the relaxed film on SrTiO₃ exhibited the typical heavy-fermion behavior. To unravel the origin of the insulating behavior, the team utilized an atomic-resolution microscope technique known as scanning transmission electron microscope (STEM), in conjunction with electron energy loss spectroscopy (EELS). This combination enabled them to examine the valence states of vanadium ions at an atomic scale. To their surprise, the results revealed the existence of charge ordering, featuring alternating layers of tri- and tetra-valent vanadium ions (V³⁺ and V⁴⁺) stacked in the film’s growth direction (Figure). This ordering pattern echoed what Verwey had initially proposed for magnetite, reviving his theories back almost after 80 years and demonstrating the enduring impact of his foundational work.

Right: Schematic diagram of a LiV2O4 thin film grown on an MgO substrate. The lattice mismatch between the two materials causes the LiV2O4 film to undergo biaxial tensile strain, as indicated by the grey arrows. Scanning transmission electron microscopy (STEM) operates by directing a focused electron beam through the sample, thereby producing an atomic-resolution image. Left: A STEM image of the LiV2O4 sample, which unveils a charge ordering pattern consisting of alternating layers of tri- and tetra-valent vanadium ions (V3+ and V4+) stacked in the film’s growth direction. Interestingly, this observed ordering pattern is in line with what Verwey had initially proposed for magnetite. — **Right:** Schematic diagram of a LiV₂O₄ thin film grown on an MgO substrate. The lattice mismatch between the two materials causes the LiV₂O₄ film to undergo biaxial tensile strain, as indicated by the grey arrows. Scanning transmission electron microscopy (STEM) operates by directing a focused electron beam through the sample, thereby producing an atomic-resolution image. **Left:** A STEM image of the LiV₂O₄ sample, which unveils a charge ordering pattern consisting of alternating layers of tri- and tetra-valent vanadium ions (V³⁺ and V⁴⁺) stacked in the film’s growth direction. Interestingly, this observed ordering pattern is in line with what Verwey had initially proposed for magnetite.

© Max Planck Institute for Solid State Research, Stuttgart, Germany

**Right:** Schematic diagram of a LiV₂O₄ thin film grown on an MgO substrate. The lattice mismatch between the two materials causes the LiV₂O₄ film to undergo biaxial tensile strain, as indicated by the grey arrows. Scanning transmission electron microscopy (STEM) operates by directing a focused electron beam through the sample, thereby producing an atomic-resolution image. **Left:** A STEM image of the LiV₂O₄ sample, which unveils a charge ordering pattern consisting of alternating layers of tri- and tetra-valent vanadium ions (V³⁺ and V⁴⁺) stacked in the film’s growth direction. Interestingly, this observed ordering pattern is in line with what Verwey had initially proposed for magnetite.

© Max Planck Institute for Solid State Research, Stuttgart, Germany

This discovery significantly enhances our understanding of novel quantum behaviors in spinel compounds and lays the groundwork for future investigations into related materials and phenomena. The historical Verwey pattern observed within LiV₂O₄ aligns well with the proposed existence of multiple hidden charge-ordered states, as a result of geometrical frustration. This suggests that the heavy fermion state of LiV₂O₄ might be nothing more than a charge-ordered state suppressed by this geometrical frustration. Interestingly, the intriguing effect of geometrical frustration has been proposed as a potential source of quantum magnetism and superconducting states. As exemplified by this study, a thorough examination of the delicate interplay between geometric effects and unique electronic or magnetic properties can pave the way toward breakthroughs in discovering exotic quantum phenomena. Finally, the study highlights the merit of leveraging cutting-edge experimental techniques, such as heteroepitaxial engineering and STEM-EELS. Employed synergistically, these methodologies have the potential to unravel new phenomena and stimulate exciting discoveries in the rapidly expanding field of quantum materials research.