Magnetoelastic Landau Quantization Demonstrates Universal Scaling with a Single Tunable Gap and Equipartition Plateau

The interplay between magnetism, elasticity, and quantum behaviour in materials containing defects presents a long-standing challenge in condensed matter physics, but new research offers a unified understanding of these complex phenomena. Denise Assafrão from Universidade Federal do Espírito Santo, Faizuddin Ahmed from The Assam Royal Global University, and Edilberto O. Silva from Universidade Federal do Maranhão, demonstrate how a single, tunable parameter governs both the thermodynamic properties and quantum oscillations observed in materials with specific types of defects, known as screw dislocations, when exposed to a magnetic field. This work establishes a clear connection between seemingly disparate observations, revealing a fundamental scale that dictates material behaviour, and importantly, provides a pathway to extract crucial information about defect density from a single measurement. The findings promise advancements in diverse fields including caloritronics, microcooling technologies, and precision strain engineering, offering a rational basis for designing materials with tailored properties.

Magnetoelastic Quantization, Thermodynamics, and Precision Measurement

Researchers have developed a comprehensive, single-scale model to describe magnetoelastic Landau quantization, investigating its thermodynamic properties, quantum oscillations, and potential for precise measurements. This new approach overcomes the limitations of traditional two-scale methods, accurately capturing the complex interplay between magnetic fields and strain effects. The investigation utilizes a modified Lifshitz-Kosevich formula, incorporating the influence of both magnetic field and mechanical stress on the electronic band structure. Results demonstrate that the single-scale model accurately predicts the temperature dependence of Shubnikov-de Haas oscillations, aligning closely with experimental observations across various materials. Furthermore, the study reveals a significant enhancement in the sensitivity of quantum oscillations to applied strain, suggesting promising avenues for developing novel strain-based sensors and metrological devices. These theoretical findings provide a comprehensive understanding of magnetoelastic phenomena and establish a foundation for exploring advanced quantum materials with tailored properties.

Thermodynamics and quantum oscillations emerge in electronic systems containing a uniform density of screw dislocations when exposed to a magnetic field. A single, tunable energy gap, determined by both the magnetic field and the crystalline structure, governs all equilibrium properties derived from a compact harmonic-oscillator partition function. These properties, including free energy, internal energy, entropy, heat capacity, magnetization, magnetic susceptibility, and magnetocaloric responses, collapse onto universal hyperbolic kernels when plotted against a normalized energy scale. The investigation identifies a “compensated-field” regime where the energy gap closes and the heat capacity reaches an equipartition value.

Universal Hyperbolic Kernels Govern Dislocated Magnetics

This work establishes a unifying framework for understanding the thermodynamic and oscillatory behavior of electronic systems containing a consistent density of screw dislocations under a magnetic field. Researchers demonstrate that a single, tunable energy gap governs all equilibrium properties, including free energy, internal energy, entropy, heat capacity, magnetization, magnetic susceptibility, and magnetocaloric responses, collapsing them into universal hyperbolic kernels. This simplification arises from a compact harmonic-oscillator partition function, revealing a fundamental connection between seemingly disparate properties. The team identified a “compensated-field” regime where the energy gap closes, leading to an equipartition plateau in heat capacity and providing a distinct signature of magnetoelastic interference.

Furthermore, the same energy scale consistently shifts and compresses patterns observed in Hall effect measurements and de Haas-van Alphen oscillations, enabling a method to determine dislocation density from a single magnetic field sweep. In smaller samples, boundary effects generate predictable oscillations in calorimetric measurements, allowing for the determination of effective magnetic length. Importantly, the researchers found that moderate disorder and weak interactions do not disrupt this fundamental kernel structure, but rather smooth out the observed amplitudes. Future research directions include experimental validation through on-chip calorimetry, torque magnetometry, and transport measurements, as well as exploration of device-level applications in areas like caloritronics, microcooling, and strain engineering. This work provides a powerful theoretical foundation for rational design and optimization of materials and devices leveraging the interplay between magnetism, elasticity, and defects.