Spin Glasses Achieve Extensive Degeneracy, Revealing Nonequilibrium Complexity

Spin glasses represent a fascinating puzzle in condensed matter physics, exhibiting collective freezing alongside structural disorder and displaying remarkably slow, history-dependent dynamics. Naeimeh Tahriri, Vahid Mahdikhah, Jahanfar Abouie, and colleagues, from institutions including the Institute for Advanced Studies in Basic Sciences and North Carolina State University, present a comprehensive review of this complex field. Their work integrates the fundamental principles governing spin-glass behaviour, explaining how microscopic factors such as randomness and competing interactions give rise to macroscopic glassiness. This review not only consolidates established theoretical frameworks and experimental characterisation techniques, but also highlights recent advances in materials science and the exciting potential of machine learning to address longstanding challenges in understanding these disordered systems and their behaviour far from equilibrium.

This review presents an integrated account of spin-glass physics, emphasising how microscopic ingredients, quenched randomness, frustration, competing exchange interactions, and random fields, combine to produce macroscopic glassiness. The discussion begins with the canonical Edwards-Anderson and Sherrington-Kirkpatrick formulations, introducing central theoretical ideas that consistently appear throughout the literature, including extensive degeneracy, metastability, and the emergence of long relaxation times.

Spin Glass Transitions in Diluted Magnetic Semiconductors

Diluted magnetic semiconductors (DMS) are materials where a non-magnetic semiconductor host is doped with a magnetic element, aiming to combine semiconductor and magnetic properties for spintronics applications. A significant portion of research focuses on observing and characterizing spin glass behavior in these DMS materials, a disordered magnetic state where magnetic moments are randomly frozen, leading to unusual magnetic properties like a lack of long-range order and a sharp cusp in magnetic susceptibility at a freezing temperature. Investigations cover a wide range of materials, including II-VI semiconductors (CdTe), III-V semiconductors (GaS, GaAs), IV-VI semiconductors (PbTe, SnTe), oxides (ZnO, Fe3O4), chalcogenides, perovskites, and other compounds. Research focuses on identifying spin glass transitions, understanding the origin of spin glass behavior through material composition and interactions, exploring the relationship between structure and magnetism, and investigating electronic structure using techniques like density functional theory. Optical properties and the potential for spintronic devices are also examined, with ongoing research into complex alloys and compounds to achieve robust spin glass states with exceptional thermal stability. Techniques employed include magnetometry, X-ray diffraction, transmission electron microscopy, density functional theory, and optical spectroscopy.

Spin Glass Freezing and Disordered Magnetism

Spin glasses exhibit a unique state of matter where magnetic moments freeze into random orientations while maintaining structural disorder, resulting in slow dynamics influenced by a rugged energy landscape. Formation requires two key conditions: competing interactions between magnetic moments and randomness in those interactions. This combination results in a fundamentally different structure compared to conventional ordered materials, characterized by zero net magnetization despite localized magnetic moments. Scientists have identified a freezing temperature, below which spins become dynamically arrested in disordered orientations, marking the onset of spin glass behavior and a non-ergodic magnetic state lacking long-range order.

Some materials exhibit a reentrant transition, where the system transitions from a magnetically ordered state into a spin glass state upon cooling, and potentially back to magnetic order at even lower temperatures. Detailed analysis reveals the importance of direct exchange, the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, dipolar interactions, and super-exchange. The RKKY interaction, a long-range interaction mediated by conduction electrons, plays a crucial role, with oscillatory behavior observed in the exchange interaction parameter as a function of interatomic distance for alloys like CuMn, AuMn, AuFe, and PtMn.

Spin Glasses, Disorder and Collective Dynamics

This research presents a comprehensive overview of spin glasses, disordered magnetic systems that exhibit unique collective freezing and slow dynamics. The work highlights how microscopic factors, including randomness and competing interactions, contribute to the macroscopic glassy behaviour observed in these materials. Investigations into canonical models, such as the Edwards-Anderson and Sherrington-Kirkpatrick formulations, reveal key concepts like extensive degeneracy and long relaxation times, which manifest as aging and memory effects. The study demonstrates connections between different spin glass materials, including metallic alloys, insulating oxides, and geometrically frustrated systems, emphasizing the role of both intrinsic and induced disorder.

Recent advances in reentrant and room-temperature spin glasses are presented, pushing the boundaries of established theories and motivating further materials exploration. Modern computational techniques, including machine learning and neural network analogies, are connected to longstanding challenges in classifying spin glass phases and understanding their out-of-equilibrium behaviour. Classifying the diverse range of spin glass materials remains a significant challenge, and continued investigation into the relationship between classical and spin glasses represents a promising avenue for future research.