Theoretical studies of the phase transition in the anisotropic 2-D square spin lattice

The phase transition occurring in a square 2-D spin lattice governed by an anisotropic Heisenberg Hamiltonian has been studied according to two recently proposed methods. The first one, the Dressed Cluster Method, provides excellent evaluations of the cohesive energy, the discontinuity of its derivative around the critical (isotropic) value of the anisotropy parameter confirms the first-order character of the phase transition. Nevertheless the method introduces two distinct reference functions (either N\'eel or XY) which may in principle force the discontinuity. The Real Space Renormalization Group with Effective Interactions does not reach the same numerical accuracy but it does not introduce a reference function and the phase transition appears qualitatively as due to the existence of two domains, with specific fixed points. The method confirms the dependence of the spin gap on the anisotropy parameter occurring in the Heisenberg-Ising domain

Decoupling of the S=1/2 antiferromagnetic zig-zag ladder with anisotropy

The spin-1/2 antiferromagnetic zig-zag ladder is studied by exact diagonalization of small systems in the regime of weak inter-chain coupling. A gapless phase with quasi long-range spiral correlations has been predicted to occur in this regime if easy-plane (XY) anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase and a spiral phase. We study the level crossings of the spectrum,the dimer correlation function, the structure factor and the spin stiffness within these phases, as well as at the transition points. As the inter-chain coupling decreases we observe a transition in the anisotropic XY case from a phase with a gap to a gapless phase that is best described by two decoupled antiferromagnetic chains. The isotropic and the anisotropic XY cases are found to be qualitatively the same, however, in the regime of weak inter-chain coupling for the small systems studied here. We attribute this to a finite-size effect in the isotropic zig-zag case that results from exponentially diverging antiferromagnetic correlations in the weak-coupling limit.Comment: to appear in Physical Review

Antisymmetric Magnetic Interactions in Oxo-Bridged Copper(II) Bimetallic Systems

The antisymmetric magnetic interaction is studied using correlated wave-function-based calculations in oxo-bridged copper bimetallic complexes. All of the anisotropic multispin Hamiltonian parameters are extracted using spin-orbit state interaction and effective Hamiltonian theory. It is shown that the methodology is accurate enough to calculate the antisymmetric terms, while the small symmetric anisotropic interactions require more sophisticated calculations. The origin of the antisymmetric anisotropy is analyzed, and the effect of geometrical deformations is addressed.

Theoretical determination of spin Hamiltonians with isotropic and anisotropic magnetic interactions in transition metal and lanthanide complexes

10.1039/c3cp52521

Magnetic Interactions in Molecules and Highly Correlated Materials: Physical Content, Analytical Derivation, and Rigorous Extraction of Magnetic Hamiltonians

10.1021/cr300500

Real space renormalization group with effective interactions: applications to 2-D spin lattices

The Bloch’s theory of effective Hamiltonians has been used to improve the Real Space Renormalization Group approach. The effective interactions between elementary blocks of a periodic lattice can be extracted from the knowledge of the spectrum of the dimers or trimers of blocks. The potentialities of the method are illustrated on a series of quasi 1-D and 2-D problems. The spin gap of two-leg ladders is calculated and an estimate of the impact of ferromagnetic couplings between two-leg ladders on the gap is presented. The method satisfactorily identifies the phase transitions in the 1/5-depleted square lattice as well as in the spin-frustrated Shastry-Sutherland lattice. The J 2 /J 1 checkerboard lattice is studied and a location of the phase transition between the Néel phase and the dimer phase is proposed. Copyright Springer-Verlag Berlin/Heidelberg 2004

Derivation of spin Hamiltonians from the exact Hamiltonian: Application to systems with two unpaired electrons per magnetic site

The foundations and limits of S=1/2 and S=1 spin Hamiltonians for systems with two unpaired electrons in two well-defined orbitals per site are discussed by merging accurate ab initio calculations in binuclear systems with the effective Hamiltonian theory. It is shown that, beyond the usual JijSi.Sj terms, the effective spin Hamiltonian necessarily introduces four-body spin operators in the S=1/2 case and biquadratic terms in the S=1 formalism. The order of magnitude of these additional terms can be rationalized from a quasidegenerate perturbation theory expansion starting from a Hubbard-type Hamiltonian. This permits to discuss the physical mechanisms governing the reduction from the all electron Hamiltonian to the spin-only Hamiltonians and the conditions under which a further reduction from a spin Hamiltonian to the simplest Heisenberg-Dirac-Van Vleck form is possible. The overall discussion is illustrated by numerical calculations of the magnetic coupling between two Ni2+ cations in the K2NiF4 perovskite and between triply bonded carbon atoms in poly-ynes