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A spin Hamiltonian, which characterizes interatomic interactions between spin moments, is highly valuable in predicting and comprehending the magnetic properties of materials. A deeper understanding of the microscopic origin of magnetic interactions can open new pathways toward realizing nanometer-scale systems for future spintronic devices. Here, we explore a method for explicitly calculating interatomic exchange interactions in non-collinear configurations of magnetic materials considering only a bilinear spin Hamiltonian in a local scenario. Based on density-functional theory (DFT) calculations of dimers adsorbed on metallic surfaces, and with a focus on the Dzyaloshinskii-Moriya interaction (DMI) which is essential for stabilizing chiral non-collinear magnetic states, we discuss the interpretation of the DMI when decomposed into microscopic electron and spin densities and currents. We clarify the distinct origins of spin currents induced in the system and their connection to the DMI. In addition, we reveal how non-collinearity affects the usual DMI, which is solely induced by spin-orbit coupling, and DMI-like interactions brought about by non-collinearity. We explain how the dependence of the DMI on the magnetic configuration establishes a connection between high-order magnetic interactions, enabling the transition from a local to a global spin Hamiltonian., 11 pages, 3 figures

Quantum squeezing is an essential asset in the field of quantum science and technology. In this study, we investigate the impact of temperature and anisotropy on squeezing of quantum fluctuations in two-mode magnon states within uniaxial antiferromagnetic materials. Through our analysis, we discover that the inherent nonlinearity in these bipartite magnon systems gives rise to a conjugate magnon squeezing effect across all energy eigenbasis states, driven by temperature and anisotropy. We show that temperature induces amplitude squeezing, whereas anisotropy leads to phase squeezing. In addition, we observe that the two-mode squeezing characteristic of magnon eigenenergy states is associated with amplitude squeezing. This highlights the constructive impact of temperature and the destructive impact of anisotropy on two-mode magnon squeezing. Nonetheless, our analysis shows that the destructive effect of anisotropy is bounded. We demonstrate this by showing that, at a given temperature, the squeezing of the momentum (phase) quadrature (or equivalently, the stretching of the position (amplitude) quadrature) approaches a constant function of anisotropy after a finite value of anisotropy. Moreover, our study demonstrates that higher magnon squeeze factors can be achieved at higher temperatures, smaller levels of anisotropy, and closer to the Brillouin zone center. All these characteristics are specific to low-energy magnons in the uniaxial antiferromagnetic materials that we examine here.

Novel understanding of the recent nanomagnet tailoring experiments and the possibility to further unveil the mechanisms by which the magnetic interactions arise in an atom by atom fashion covers importance as the demand for spin qubit and quantum state detection architectures increases. Here, we address the spin states of a molecular trimer comprising three localized spin moments embedded in a metallic tunnel junction and show that the pair spin interactions can be engineered through the electronic structure of the molecular trimer. We show that bias and gate voltages induce either a completely ferromagnetic state of the localized moments or a spin frustrated state with different stabilities, and that switching between these states is possible on demand by electrical control. The role of quantum coherence in the molecular trimer is discussed with regards to the spin ordering as well as the interplay among electronic interference and induced dephasing by the metallic leads. This work sets foundations for more robust all electrically controlled spin architectures usable in quantum engineering systems and serves as a test bench for exploring unresolved questions in magnetic ordering and symmetry.

We address scatterings of spin waves off uncorrelated defects in two-dimensional (2D) easy-axis antiferromagnet (AFM) insulators. Although an onsite magnetic anisotropy leads gapped Goldstone modes, such that a long range (AFM) order can be established in 2D, lattice imperfections tend to weaken, and eventually destroy the magnetic ordering. Here, the impact of defects is considered within two limits, single and multiple defects. Using Green's function, we perform self consistent simulations to study magnon properties such as density of states and lifetime of induced resonances. Our findings show that repulsive defects decrease the magnon density of states while attractive ones may enhance it. We provide a comprehensive analysis of how defects can result in a reduction and even closing, the anisotropy induced gap, which weakens the long range (AFM) order parameter in the 2D state. We conclude that a small concentration of random defects can fill the gap of magnon spectrum.

We introduce a new method for analysing the Bose-Hubbard model for an array of bosons with nearest neighbor interactions. It is based on a number-theoretic implementation of the creation and annihilation operators that constitute the model. One of the advantages of this approach is that it facilitates computation with arbitrary accuracy, enabling nearly perfect numerical experimentation. In particular, we provide a rigorous computer assisted proof of quantum phase transitions in finite systems of this type. Furthermore, we investigate properties of the infinite array via harmonic analysis on the multiplicative group of positive rationals. This furnishes an isomorphism that recasts the underlying Fock space as an infinite tensor product of Hecke spaces, i.e., spaces of square-integrable periodic functions that are a superposition of non-negative frequency harmonics. Under this isomorphism, the number-theoretic creation and annihilation operators are mapped into the Kastrup model of the harmonic oscillator on the circle. It also enables us to highlight a kinship of the model at hand with an array of spin moments with a local anisotropy field. This identifies an interesting physical system that can be mapped into the model at hand., Comment: 12 pages, 3 figures; submitted; accepted in Quantum

The monolayer halides CrX$_3$ (X=Cl, Br, I) attract significant attention for realizing 2D magnets with genuine long-range order (LRO), challenging the Mermin-Wagner theorem. Here, we show that monolayer CrCl$_3$ has the unique benefit of exhibiting tunable magnetic anisotropy upon applying a compressive strain. This opens the possibility to use CrCl$_3$ for producing and studying both ferromagnetic and antiferromagnetic 2D Ising-type LRO as well as the Berezinskii-Kosterlitz-Thouless (BKT) regime of 2D magnetism with quasi-LRO. Using state-of-the-art density functional theory, we explain how realistic compressive strain could be used to tune the monolayer's magnetic properties so that it could exhibit any of these phases. Building on large-scale quantum Monte Carlo simulations, we compute the phase diagram of strained CrCl$_3$, as well as the magnon spectrum with spin-wave theory. Our results highlight the eminent suitability of monolayer CrCl$_3$ to achieve very high BKT transition temperatures, around 50 K, due to their singular dependence on the weak easy-plane anisotropy of the material., 6 pages (4 figures) + 4 pages (6 figures)

In contrast to conventional assumptions, we show that the Dzyaloshinskii-Moriya interaction can be of non-relativistic origin, in particular in materials with a non-collinear magnetic configuration, where non-relativistic contributions can dominate over spin-orbit effects. The weak antiferromagnetic phase of Mn$_{3}$Sn is used to illustrate these findings. Using electronic structure theory as a conceptual platform, all relevant exchange interactions are derived for a general, non-collinear magnetic state. It is demonstrated that non-collinearity influences all three types of exchange interaction and that physically distinct mechanisms, which connect to electron- and spin-density and currents, may be used as a general way to analyze and understand magnetic interactions of the solid state.

The experimental realization of a coupled spin pair has been reported by Heiko Webber et.al and its theoretical description has been previously discussed including the condition that local magnetization of the junction is required for the individual moments to affect the electrons in the molecular ligand through the Kondo interaction. Here in this work, we show that when the couple spin pair is placed in an interferometry set up of the Aharonov-Bohm type additional features related to the switching behavior of the coupled spin pair emerge. This features lead to a phase dependent exchange magnetic field coming from the ferromagnets in proximity with the molecule, a phase dependent commutation of the singlet/triplet ground state around zero bias and it leads to variations in the voltage dependent effective exchange profile between the spin pair. These predictions contribute to the acceptance of the hypothesis that spin polarization can be harvested from quantum coherence in molecular quantum mechanics

We investigate numerically the magnetisation dynamics of an array of nano-disks interacting through the magneto-dipolar coupling. In the presence of a temperature gradient, the chain reaches a non-equilibrium steady state where energy and magnetisation currents propagate. This effect can be described as the flow of energy and particle currents in an off-equilibrium discrete nonlinear Schr\"odinger (DNLS) equation. This model makes transparent the transport properties of the system and allows for a precise definition of temperature and chemical potential for a precessing spin. The present study proposes a novel setup for the spin-Seebeck effect, and shows that its qualitative features can be captured by a general oscillator-chain model