An official website of the United States government
We derive the phase structure and thermodynamics of ferromagnets consisting of elementary magnets carrying the adjoint representation of SU(N) and coupled through two-body quadratic interactions. Such systems have a continuous SU(N) symmetry as well as a discrete conjugation symmetry. We uncover a rich spectrum of phases and transitions, involving a paramagnetic and two distinct ferromagnetic phases that can coexist as stable and metastable states in different combinations over a range of temperatures. The ferromagnetic phases break SU(N) invariance in various channels, leading to spontaneous magnetization. Interestingly, the conjugation symmetry also breaks over a range of temperatures and group ranks N, providing a realization of a spontaneously broken discrete symmetry.
more »
« less
This content will become publicly available on May 1, 2026
Ferromagnets from higher SU(N) representations
We present a general formalism for deriving the thermodynamics of ferromagnets consisting of "atoms" carrying an arbitrary irreducible representation of and coupled through long-range two-body quadratic interactions. Using this formalism, we derive the thermodynamics and phase structure of ferromagnets with atoms in the doubly symmetric or doubly antisymmetric irreducible representations. The symmetric representation leads to a paramagnetic and a ferromagnetic phase with transitions similar to the ones for the fundamental representation studied before. The antisymmetric representation presents qualitatively new features, leading to a paramagnetic and two distinct ferromagnetic phases that can coexist over a range of temperatures, two of them becoming metastable. Our results are relevant to magnetic systems of atoms with reduced symmetry in their interactions compared to the fundamental case.
more »
« less
- PAR ID:
- 10599412
- Publisher / Repository:
- Nuclear Physics B
- Date Published:
- Journal Name:
- Nuclear Physics B
- Volume:
- 1014
- Issue:
- C
- ISSN:
- 0550-3213
- Page Range / eLocation ID:
- 116880
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We study the thermodynamics of a non-abelian ferromagnet consisting of “atoms” each carrying a fun-damental representation of SU(N), coupled with long-range two-body quadratic interactions. We uncover a rich structure of phase transitions from non-magnetized, global SU(N)-invariant states to magnetized ones breaking global invariance to SU(N−1) ×U(1). Phases can coexist, one being stable and the other metastable, and the transition between states involves latent heat exchange, unlike in usual SU(2)ferro-magnets. Coupling the system to an external non-abelian magnetic field further enriches the phase structure, leading to additional phases. The system manifests hysteresis phenomena both in the magnetic field, as in usual ferromagnets, and in the temperature, in analogy to supercooled water. Potential applications are in fundamental situations or as a phenomenological model.more » « less
-
The non-Abelian ferromagnet recently introduced by the authors, consisting of atoms in the fundamental representation of , is studied in the limit where becomes large and scales as the square root of the number of atoms . This model exhibits additional phases, as well as two different temperature scales related by a factor . The paramagnetic phase splits into a "dense" and a "dilute" phase, separated by a third-order transition and leading to a triple critical point in the scale parameter and the temperature, while the ferromagnetic phase exhibits additional structure, and a new paramagnetic-ferromagnetic metastable phase appears at the larger temperature scale. These phases can coexist, becoming stable or metastable as temperature varies. A generalized model in which the number of -equivalent states enters the partition function with a nontrivial weight, relevant, e.g., when there is gauge invariance in the system, is also studied and shown to manifest similar phases, with the dense-dilute phase transition becoming second-order in the fully gauge invariant case.more » « less
-
Paramagnetic single-molecule magnets (SMMs) interacting with the ferromagnetic electrodes of a magnetic tunnel junction (MTJ) produce a new system. The properties and future scope of new systems differ dramatically from the properties of isolated molecules and ferromagnets. However, it is unknown how far deep in the ferromagnetic electrode the impact of the paramagnetic molecule and ferromagnet interactions can travel for various levels of molecular spin states. Our prior experimental studies showed two types of paramagnetic SMMs, the hexanuclear Mn 6 and octanuclear Fe–Ni molecular complexes, covalently bonded to ferromagnets produced unprecedented strong antiferromagnetic coupling between two ferromagnets at room temperature leading to a number of intriguing observations (P. Tyagi, et al. , Org. Electron. , 2019, 64 , 188–194. P. Tyagi, et al. , RSC Adv. , 2020, 10 , (22), 13006–13015). This paper reports a Monte Carlo Simulations (MCS) study focusing on the impact of the molecular spin state on a cross junction shaped MTJ based molecular spintronics device (MTJMSD). Our MCS study focused on the Heisenberg model of MTJMSD and investigated the impact of various molecular coupling strengths, thermal energy, and molecular spin states. To gauge the impact of the molecular spin state on the region of ferromagnetic electrodes, we examined the spatial distribution of molecule-ferromagnet correlated phases. Our MCS study shows that under a strong coupling regime, the molecular spin state should be ∼30% of the ferromagnetic electrode's atomic spins to create long-range correlated phases.more » « less
-
With a variable spin state, paramagnetic molecules can affect the impact of magnetic exchange coupling strength between two ferromagnetic electrodes. Our magnetic tunnel junction based molecular spintronics devices (MTJMSD) were successful in connecting paramagnetic single molecular magnet (SMM) between two ferromagnetic electrodes. Isolated SMM exhibited a wide range of spin states. However, it was extremely challenging to identify the SMM spin state when connected to the ferromagnetic electrodes. Our prior experimental and Monte Carlo Simulations (MCS) studies showed that paramagnetic molecules produced unprecedented strong antiferromagnetic coupling between two ferromagnets at room temperature. The overall antiferromagnetic coupling occurred when a paramagnetic SMM made antiferromagnetic coupling to the first electrode and ferromagnetic coupling to the second ferromagnetic electrode. This paper studies the impact of variable molecular spin states of the SMMs, producing strong antiferromagnetic coupling between the ferromagnetic electrodes of MTJMSD. The MTJMSD used in this study was represented by an 11 x 50 x 50 Ising model, with 11 being the thickness of the MTJMSD and 5 x 10 x 50 being each electrode’s size. We employed a continuous MCS algorithm to investigate SMM’s spin state’s impact as a function of molecular exchange coupling strength and thermal energy.more » « less
