Frustrated spin systems: history of the emergence of a modern physics

Hung The Diep

doi:10.5802/crphys.235

Article de synthèse

Frustrated spin systems: history of the emergence of a modern physics
[Systèmes de spins frustrés : émergence d’une physique moderne]

Hung The Diep ¹

¹ Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, CNRS, UMR 8089, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France

Comptes Rendus. Physique, Volume 26 (2025), pp. 225-251.

Cet article fait partie du numéro thématique Gérard Toulouse, une vie de découvertes et d'engagement coordonné par Bernard Derrida et al..

Résumé
Abstract

En 1977, Gérard Toulouse a introduit le concept nommé « frustration » pour les systèmes de spins dans lesquels une partie des interactions n’est pas satisfaite (cas de spins Ising) ou toutes les interactions ne sont pas satisfaites (cas de spins XY et Heisenberg). En utilisant cette notion, beaucoup de systèmes de spins frustrés ont été créés et étudiés. On peut mentionner quelques modèles populaires : le modèle de Villain, le modèle frustré sur un réseau cubique simple et le modèle antiferromagnétque sur un réseau triangulaire. La frustration dans les deux premiers modèles est due à un mélange des interactions ferromagnétiques et antiferromagnétiques, tandis que la frustration dans le dernier modèle est due à l’incompatibilité de l’interaction avec la géométrie du réseau (on dit alors « frustration par géométrie » ). Les systèmes frustrés ont des propriétés nouvelles et remarquables. Ce qui est frappant est que des méthodes très puissantes telles que le groupe de renormalissation ont du mal à clarifier un certain nombre de points tels que la nature de la phase transition dans des systèmes de spins frustrés, comme on le verra dans cet article de revue. J’ai commencé à étudier des systèmes de spins frustrés au début des années 80, après ma thèse. J’ai bénéficié de nombreuses discussions avec Gérard Toulouse. Je continue mes recherches jusqu’aujourd’hui sur des systèmes frustrés tels que les skyrmions. Dans cette revue, j’évoque mes travaux représentatifs sur des systèmes frustrés, allant des systèmes frustrés de spins Ising exactement résolus aux systèmes de spins XY ou Heisenberg en 2D et 3D. J’évoquerai mes derniers travaux sur les skyrmions résultant de la compétition entre l’interaction d’échange et l’interaction Dzyaloshinskii–Moriya (DM) soumis à un champ magnétique appliqué. Enfin, une théorie quantique de magnons utilisant la méthode de fonction de Green est présentée pour des systèmes frustrés avec des configurations de spin non-colinéaires tels que ceux avec l’interaction DM.

In 1977, Gérard Toulouse has proposed a new concept termed as “frustration" in spin systems. Using this definition, several frustrated models have been created and studied, among them we can mention the Villain’s model, the fully frustrated simple cubic lattice, the antiferromagnetic triangular lattice. The former models are systems with mixed ferromagnetic and antiferromagnetic bonds, while in the latter containing only an antiferromagnetic interaction, the frustration is caused by the lattice geometry. These frustrated spin systems have novel properties that we will review in this paper. One of the striking aspects is the fact that well-established methods such as the renormalization group fail to deal with the nature of the phase transition in frustrated systems. Investigations of properties of frustrated spin systems have been intensive since the 80’s. I myself got involved in several investigations of frustrated spin systems soon after my PhD. I have learned a lot from numerous discussions with Gérard Toulouse. Until today, I am still working on frustrated systems such as skyrmions. In this review, I trace back a number of my works over the years on frustrated spin systems going from exactly solved 2D Ising frustrated models, to XY and Heisenberg 2D and 3D frustrated lattices. At the end I present my latest results on skyrmions resulting from the frustration caused by the competition between the exchange interaction and the Dzyaloshinskii–Moriya interaction under an applied magnetic field. A quantum spin-wave theory using the Green’s function method is shown and discussed.

Reçu le : 2024-11-20
Révisé le : 2025-01-12
Accepté le : 2025-01-17
Publié le : 2025-02-12

DOI : 10.5802/crphys.235

Keywords: Frustrated spin systems, Exactly solved models, Non-collinear spin configuration, Phase transitions, Reentrance, Disorder lines
Mots-clés : Systèmes de spins frustrés, Modèles exactement solvables, Configurations de spin non-colinéaires, Skyrmions, Théorie de Magnons dans des Systèmes Frustrés

Affiliations des auteurs :

Hung The Diep ¹

¹ Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, CNRS, UMR 8089, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Hung The Diep. Frustrated spin systems: history of the emergence of a modern physics. Comptes Rendus. Physique, Volume 26 (2025), pp. 225-251. doi : 10.5802/crphys.235. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.235/

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