Rare-earth Orthoferrite Demonstrates Dicke Cooperativity Scaling As sqrt(N) Via Coupled Phonons and Crystal-Field Excitations

The interplay between electronic behaviour and the crystal structure of materials underpins many fascinating physical phenomena, including magnetism and the emergence of ferroelectricity, yet understanding how these interactions scale remains a significant challenge. Fangliang Wu, Xiaoxuan Ma, and Zhongwei Zhang, along with colleagues, now report the direct observation of a specific type of cooperative behaviour, known as Dicke cooperativity, within the rare-earth orthoferrite, ErFeO3. The team employed magneto-Raman spectroscopy to reveal strong coupling between spin, lattice vibrations and electronic states, demonstrating that the strength of interaction between these elements scales with the number of participating ions. This discovery confirms the cooperative nature of interactions between localized electronic excitations and long-range vibrations, offering a potential route to precisely control the electronic and vibrational properties of materials through population management.

Terahertz Phonon Dynamics in ErFeO3

This research investigates the dynamic behavior of vibrations, known as phonons, within single-crystal ErFeO3, a complex material exhibiting both magnetic and vibrational properties. Combining advanced optical measurements with theoretical calculations, scientists explored how these vibrations interact with the material’s magnetic fields, aiming to understand its potential for use in future technologies, including spintronics and materials that exhibit multiple forms of order. A key finding reveals a strong connection between the material’s magnetic and vibrational characteristics, potentially leading to unique quantum phase transitions and enabling novel functionalities. High-quality crystals of ErFeO3 were grown and carefully oriented for precise measurements.

Raman spectroscopy, a technique probing vibrational modes, was used to study the material’s behavior under varying magnetic fields, up to 9 Tesla. Theoretical calculations, based on density functional theory, predicted the vibrational spectrum and underlying physics, accurately representing the material’s electronic structure. This combination of experimental and theoretical approaches provides a comprehensive understanding of the interplay between spin and lattice degrees of freedom in ErFeO3. This research was supported by numerous grants from Chinese and Japanese funding agencies, highlighting the collaborative nature of the project. The team acknowledges contributions from researchers responsible for optical measurements, sample synthesis, theoretical calculations, and data interpretation. This work provides a detailed investigation of the vibrational and magnetic properties of ErFeO3, suggesting its potential for advanced materials applications.

Dicke Cooperativity Links Spin, Lattice, and Orbitals

Scientists directly observed Dicke cooperativity, arising from the interaction between vibrations and electronic excitations within ErFeO3. Using magneto-Raman spectroscopy, they uncovered strongly coupled spin, lattice, and orbital excitations, revealing a fundamental connection between these properties. Researchers identified that the strength of the coupling between vibrations and electronic excitations scales with the square root of the number of electrons in the excited state, demonstrating a collective interaction between local electronic states and long-range vibrations. The team meticulously measured how the coupling between vibrations and electronic excitations changes with temperature, fitting the data with a mathematical model to extract key parameters.

These measurements yielded a coupling strength of 0. 11 terahertz at 10 Kelvin, quantifying the interaction. Further analysis revealed that the energy difference between the vibration and electronic excitation decreases as temperature increases, allowing for precise control over the coupling strength. Remarkably, scientists established a linear relationship between the coupling strength and the square root of the number of electrons in the excited state, even at elevated temperatures up to 90 Kelvin. This linear relationship, a defining characteristic of Dicke-type cooperativity, confirms the collective behavior of the coupled system. The team’s work verifies that Dicke-type scaling extends to models involving localized electronic states, establishing the vibration-electronic excitation coupled system as a viable platform for exploring Dicke physics. This breakthrough opens avenues for solid-state quantum simulation, potentially mirroring multi-mode Dicke models used in cavity quantum electrodynamics, and offers new approaches to controlling material properties like superconductivity and colossal magnetoresistance through population control.

Dicke Cooperativity via Phonon-Crystal-Field Coupling

This research demonstrates the direct observation of Dicke-type cooperativity arising from the interaction between vibrations and electronic transitions within ErFeO3. Through magneto-Raman spectroscopy, scientists identified strongly coupled spin, lattice, and orbital excitations, revealing that the strength of the coupling between vibrations and electronic transitions scales with the square root of the number of electrons in the excited state. These findings confirm the cooperative nature of interactions between localized electronic states and long-range vibrations, establishing a pathway for controlling the electronic and vibrational properties of materials through population management. The significance of this work lies in its verification of Dicke cooperativity within a solid-state material, previously observed primarily in atomic systems. By demonstrating this cooperativity in ErFeO3, the team provides insights into the emergence of collective phenomena and opens possibilities for designing materials with tailored properties.