Pressure-induced charge orders and their postulated coupling to magnetism in hexagonal multiferroic LuFe₂O₄

Multiferroic materials, possessing simultaneous magnetic and ferroelectric orders, hold significant promise for applications in spintronics and electronic devices. Hexagonal LuFe₂O₄ has emerged as a promising candidate for charge-order driven multiferroicity, exhibiting high charge and spin-ordering temperatures. Previous studies using X-ray diffraction (XRD) and transmission electron microscopy (TEM) have indicated a three-dimensional (3D) charge order at ambient pressure, involving a periodic arrangement of Fe²⁺ and Fe³⁺ ions. While evidence for CO-driven ferroelectricity has been reported, its origin remains a subject of debate. Furthermore, a quasi-two-dimensional (Q2D) ordering of Fe²⁺-Fe³⁺ ions has been observed above the 3D charge ordering temperature, persisting up to ~525 K. Neutron diffraction studies revealed ferrimagnetic order below the Néel temperature (~240 K), suggesting a crucial role for correlations between charge and magnetic order in the multiferroicity of LuFe₂O₄. Applying external pressure offers a powerful tool to investigate the interplay between charge, magnetic, and structural degrees of freedom in frustrated systems like LuFe₂O₄, potentially revealing a range of tunable ground states. However, previous high-pressure studies on LuFe₂O₄ using powder samples had limitations, preventing an accurate description of pressure-induced phases. This study aims to overcome these limitations by using in situ high-pressure single-crystal X-ray diffraction (HP-SXD) and high-pressure X-ray magnetic circular dichroism (HP-XMCD) to investigate the pressure-dependent evolution of charge and magnetic interactions in LuFe₂O₄.

Extensive research has focused on understanding the multiferroic properties of LuFe₂O₄. Early XRD and TEM measurements revealed the existence of 3D charge ordering at ambient pressure, characterized by a periodic arrangement of Fe²⁺ and Fe³⁺ ions, forming a √3 × √3 × 2 superlattice. The possibility of CO-driven ferroelectricity was suggested, although its origin remained controversial. The observation of a Q2D charge ordering above the 3D charge ordering temperature further complicated the picture. Neutron diffraction experiments confirmed ferrimagnetic order below TN (~240 K), highlighting the intricate interplay between charge and spin orders. While previous high-pressure studies using powder samples provided some insights into the pressure-induced modifications of magnetic properties and structural transitions, the lack of single-crystal data hindered a complete understanding of the correlated charge and magnetic phase transitions. Specifically, powder averaging obscured the detailed evolution of superlattice reflections under pressure, leading to ambiguous interpretations of the pressure-induced phases. This study sought to address these limitations by employing single-crystal techniques, aiming to provide a more precise description of the pressure-induced phase transitions.

The study employed in situ high-pressure single-crystal X-ray diffraction (HP-SXD) and high-pressure X-ray magnetic circular dichroism (HP-XMCD) techniques to investigate the pressure-dependent evolution of charge and magnetic orders in LuFe₂O₄. Single crystals of LuFe₂O₄ were grown using the floating-zone method under a controlled atmosphere to ensure optimal stoichiometry. HP-SXD measurements were performed at the Advanced Photon Source (APS) using monochromatic X-rays. The pressure was varied from 0.8 GPa to 14.5 GPa, and diffraction patterns were recorded at various pressure points. Symmetry analysis and structure refinements were conducted using software packages like SARAH and FULLPROF. HP-XMCD spectroscopy measurements were performed at APS to monitor the change in net magnetization under pressure, using a diamond anvil cell to achieve high pressure. The Fe K-edge was chosen for its compatibility with the high-pressure environment. XMCD scans were repeated with opposite applied field directions to eliminate artifacts. Density functional theory (DFT) calculations, using the projector augmented wave (PAW) method implemented in VASP, were used to support the experimental findings and provide insights into the underlying electronic structure and energetics of the different phases. The GGA+U method was employed to account for electron correlation effects. Calculations were performed to determine the enthalpy of each charge-ordered phase at various pressures to construct the phase diagram. The pressure was determined by in situ ruby fluorescence measurements, with an uncertainty of less than 5%.

The HP-SXD measurements revealed a series of pressure-induced charge order phase transitions in LuFe₂O₄. At low pressure (0.8 GPa), a centrosymmetric incommensurate 3D charge order (CO-AP) with a wave vector κAP = (1/3, 1/3, 3/2) was observed, consistent with ferrimagnetic order. As pressure increased, the superlattice peaks broadened along the L-direction, indicating a transition to a quasi-two-dimensional (Q2D) charge order (CO-2D) phase with ferrimagnetism, persisting up to 5.5 GPa. Above 6.0 GPa, a sharp transition to a centrosymmetric commensurate 3D charge order (CO-HP) phase with a wave vector κHP = (1/4, 1/4, 0) was observed, associated with antiferromagnetic order. The HP-XMCD measurements supported these findings, showing a decrease in net magnetization with increasing pressure, consistent with a ferrimagnetic-to-antiferromagnetic transition. The DFT calculations revealed that the pressure-induced compression of Fe-Fe bonds within the [Fe₂O₄] bilayer structure enhances the Coulomb interactions, driving the transition from the (1/3, 1/3) CO to the (1/4, 1/4) CO. This charge redistribution leads to changes in spin-spin interactions, resulting in the observed ferrimagnetic-to-antiferromagnetic transition. The DFT calculations showed that the energy of the different phases are sensitive to pressure, with the CO-AP and CO-2D phases being favored at lower pressures and CO-HP being the most stable at higher pressures.

The results demonstrate a strong coupling between charge and magnetic orders in LuFe₂O₄, where pressure-induced lattice compression plays a crucial role in driving the observed phase transitions. The change from a (1/3, 1/3) to a (1/4, 1/4) charge order is linked to the modification of Coulomb interactions between Fe-Fe bonds, leading to a rearrangement of both charge and spin degrees of freedom. The observed ferrimagnetic to antiferromagnetic transition highlights the sensitivity of the magnetic ground state to subtle changes in the charge distribution. The agreement between experimental findings and DFT calculations reinforces the understanding of the coupling mechanism between charge, spin, and lattice degrees of freedom. The ability to tune the charge and magnetic orders in a controlled manner using pressure opens new avenues for exploring and manipulating multiferroic properties in LuFe₂O₄ and related materials.

This study systematically investigated the pressure-induced phase transitions in LuFe₂O₄, revealing three distinct charge-ordered phases with correlated magnetic order. Pressure-enhanced Coulomb interactions, driven by lattice compression, are identified as the key mechanism driving the transitions between these phases. The strong coupling between charge and magnetic orders highlights the complex interplay of degrees of freedom in this multiferroic material. This work paves the way for further exploration of pressure-tuning of charge and magnetic orders in similar systems, potentially leading to new functionalities in multiferroic materials.

The study focused primarily on the effect of hydrostatic pressure on LuFe₂O₄. Investigating the influence of other parameters such as temperature, magnetic field, and chemical doping could provide a more comprehensive understanding of the phase transitions and their underlying mechanisms. The DFT calculations used approximations in treating electron correlations, and further refinement of theoretical models could enhance the predictive power. The high-pressure experiments involved limitations in the accessible pressure range, potentially missing additional phases at even higher pressures.