Generalized Gibbs Phase Rule and Multicriticality Applied to Magnetic Systems

A generalization of the original Gibbs phase rule is proposed in order to study the presence of single phases, multiphase coexistence, and multicritical phenomena in lattice spin magnetic models. The rule is based on counting the thermodynamic number of degrees of freedom, which strongly depends on the external fields needed to break the ground state degeneracy of the model. The phase diagrams of some spin Hamiltonians are analyzed according to this general phase rule, including general spin Ising and Blume–Capel models, as well as q-state Potts models. It is shown that by properly taking into account the intensive fields of the model in study, the generalized Gibbs phase rule furnishes a good description of the possible topology of the corresponding phase diagram. Although this scheme is unfortunately not able to locate the phase boundaries, it is quite useful to at least provide a good description regarding the possible presence of critical and multicritical surfaces, as well as isolated multicritical points.

New Syntheses, Analytic Spin Hamiltonians, Structural and Computational Characterization for a Series of Tri-, Hexa- and Hepta-Nuclear Copper (II) Complexes with Prototypic Patterns

We present a series of pyrazolato-bridged copper complexes with interesting structures that can be considered prototypic patterns for tri-, hexa- and hepta- nuclear systems. The trinuclear shows an almost regular triangle with a μ3-OH central group. The hexanuclear has identical monomer units, the Cu6 system forming a regular hexagon. The heptanuclear can be described as two trinuclear moieties sandwiching a central copper ion via carboxylate bridges. In the heptanuclear system, the pyrazolate bridges are consolidating the triangular faces, which are sketching an elongated trigonal antiprism. The magnetic properties of these systems, dominated by the strong antiferromagnetism along the pyrazolate bridges, were described transparently, outlining the energy levels formulas in terms of Heisenberg exchange parameters J, within the specific topologies. We succeeded in finding a simple Kambe-type resolution of the Heisenberg spin Hamiltonian for the rather complex case of the heptanuclear. In a similar manner, the weak intermolecular coupling of two trimer units (aside from the strong exchange inside triangles) was resolved by closed energy formulas. The hexanuclear can be legitimately proposed as a case of coordination-based aromaticity, since the phenomenology of the six-spins problem resembles the bonding in benzene. The Broken-Symmetry Density Functional Theory (BS-DFT) calculations are non-trivial results, being intrinsically difficult at high nuclearities.

Spin Hamiltonians in Magnets: Theories and Computations

The effective spin Hamiltonian method has drawn considerable attention for its power to explain and predict magnetic properties in various intriguing materials. In this review, we summarize different types of interactions between spins (hereafter, spin interactions, for short) that may be used in effective spin Hamiltonians as well as the various methods of computing the interaction parameters. A detailed discussion about the merits and possible pitfalls of each technique of computing interaction parameters is provided.

Парамагнитные центры Mn-=SUP=-2+-=/SUP=-, Gd-=SUP=-3+-=/SUP=- и Cu-=SUP=-2+-=/SUP=- в легированном хромом монокристалле Li-=SUB=-2-=/SUB=-CaSiO-=SUB=-4-=/SUB=-

In the Li2CaSiO4 crystal, in addition to intense axial centers of Cr4+, the EPR spectra of impurity ions Mn2+ (S = 5/2), Gd3+ (S = 7/2), and Cu2+ (S = 1/2) have been discovered and studied. Manganese and gadolinium ions exhibit spectra of tetragonal symmetry, copper ions are represented by spectra of both axial and triclinic symmetry. The parameters of the spin Hamiltonians of tetragonal centers are determined. It was shown that Mn2+ and Gd3+ ions substitute for calcium ions with an eightfold oxygen environment, copper ions are localized in lithium positions with a tetrahedral environment. The reasons for the appearance of Cu2+ triclinic centers are discussed.

Experimental protection of quantum coherence by using a phase-tunable image drive

The protection of quantum coherence is essential for building a practical quantum computer able to manipulate, store and read quantum information with a high degree of fidelity. Recently, it has been proposed to increase the operation time of a qubit by means of strong pulses to achieve a dynamical decoupling of the qubit from its environment. We propose and demonstrate a simple and highly efficient alternative route based on Floquet modes, which increases the Rabi decay time ($$T_R$$ T R ) in a number of materials with different spin Hamiltonians and environments. We demonstrate the regime $$T_R \approx T_1$$ T R ≈ T 1 with $$T_1$$ T 1 the relaxation time, thus providing a route for spin qubits and spin ensembles to be used in quantum information processing and storage.

Nanolaser-based emulators of spin Hamiltonians

Finding the solution to a large category of optimization problems, known as the NP-hard class, requires an exponentially increasing solution time using conventional computers. Lately, there has been intense efforts to develop alternative computational methods capable of addressing such tasks. In this regard, spin Hamiltonians, which originally arose in describing exchange interactions in magnetic materials, have recently been pursued as a powerful computational tool. Along these lines, it has been shown that solving NP-hard problems can be effectively mapped into finding the ground state of certain types of classical spin models. Here, we show that arrays of metallic nanolasers provide an ultra-compact, on-chip platform capable of implementing spin models, including the classical Ising and XY Hamiltonians. Various regimes of behavior including ferromagnetic, antiferromagnetic, as well as geometric frustration are observed in these structures. Our work paves the way towards nanoscale spin-emulators that enable efficient modeling of large-scale complex networks.

A computer code for topological quantum spin systems over triangulated surfaces

We derive explicit closed-form matrix representations of Hamiltonians drawn from tensored algebras, such as quantum spin Hamiltonians. These formulas enable us to soft-code generic Hamiltonian systems and to systematize the input data for uniformly structured as well as for un-structured Hamiltonians. The result is an optimal computer code that can be used as a black box that takes in certain input files and returns spectral information about the Hamiltonian. The code is tested on Kitaev’s toric model deployed on triangulated surfaces of genus 0 and 1. The efficiency of our code enables these simulations to be performed on an ordinary laptop. The input file corresponding to the minimal triangulation of genus 2 is also supplied.