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NEAR-BOUNDARY AND BULK REGIONS OF A SEMI-INFINITE TWO-DIMENSIONAL HEISENBERG ANTIFERROMAGNET

Niina Voropajeva, A. Sherman

Published Jan 1, 2009• 1 citation
OpenAlex

Abstract

Using the spin-wave approximation elementary excitations of a semi-infinite two-dimensional $S=\frac12$ Heisenberg antiferromagnet are considered. The spectrum consists of bulk modes -- standing spin waves and a quasi-one-dimensional mode of boundary spin waves. These latter excitations eject bulk modes from two boundary rows of sites, thereby dividing the antiferromagnet into two regions with different dominant excitations. As a result absolute values of nearest-neighbor spin correlations on the edge exceed the bulk value.

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Using the spin-wave approximation elementary excitations of a semi-infinite two-dimensional S=12S=\frac12S=21​ Heisenberg antiferromagnet are considered. The spectrum consists of bulk modes -- standing spin waves and a quasi-one-dimensional mode of boundary spin waves. These latter excitations eject bulk modes from two boundary rows of sites, thereby dividing the antiferromagnet into two regions with different dominant excitations. As a result absolute values of nearest-neighbor spin correlations on the edge exceed the bulk value.
Using the spin-wave approximation elementary excitations of a semi-infinite two-dimensional S = ½ Heisenberg antiferromagnet are considered. The spectrum consists of bulk modes — standing spin waves and a quasi-one-dimensional mode of boundary spin waves. These latter excitations eject bulk modes from two boundary rows of sites, thereby dividing the antiferromagnet into two regions with different dominant excitations. As a result, absolute values of nearest-neighbor spin correlations on the edge exceed the bulk value.
Elementary excitations are studied near the Ising limit close to the degenerate point in the one-dimensional anisotropic Heisenberg antiferromagnets with up to next-nearest-neighbor interactions. Solitons in the Néel and (2,2) antiphase states and triplet-dimer excitations in the dimer state are found as propagating modes. These excitations are found to dominate the shape of the central peak in dynamical spin correlation functions, through the comparison with the numerical results by an exact diagonalization method for finite chains. The temperature dependence of the static correlation function is also discussed, and the shape is found to change gradually with increasing temperature, approaching the zero-temperature correlation function at the degenerate point.
The elementary excitations of the one-dimensional spin-S Heisenberg antiferromagnet near saturation are explained, with special attention to the soft mode, in terms of a gas of interacting magnons. Recent numerical studies of the antiferromagnet in a magnetic field uncovered the presence of the soft mode at a magnetization-dependent wave number for large magnetizations. We show that very near saturation and for large spins the antiferromagnet can be written in terms of a gas of magnons interacting via repulsive \ensuremath{\delta}-function potentials, a system with a known Bethe-ansatz solution. The soft mode can then be explained as a Kohn-anomaly-type excitation above a quasi-Fermi-sea. Other elementary excitations form a particle-hole-type double continuum. The soft mode's apparent physical observability is indicated by a shoulder at the appropriate wave number in the integrated longitudinal intensity.
A heterostructure of a semi-infinite metal and a Mott insulator is considered. It is supposed that both materials have an identical lattice spacing and hopping integrals and differ in the Hubbard repulsion which is negligible in the metal and exceeds the critical value for the Mott transition in the insulator. At half-filling and for low temperatures the insulator has long-range antiferromagnetic order. Its low-lying elementary excitations are standing spin waves and a spin-wave mode which is localized near the interface and has a two-dimensional dispersion. This mode ejects bulk modes from the boundary region. The antiferromagnetic ordering of the insulator induces an antiferromagnetic order in the metal where the magnetization decays exponentially with distance from the interface. This decay is characterized by the correlation length of about 6 lattice spacings.
We discuss the excitation spectrum of a disordered, isotropic, and translationally invariant spin state in the two-dimensional Heisenberg antiferromagnet. The starting point is the nearest-neighbor resonating-valence-bond state which plays the role of the vacuum of the theory, in a similar sense as the N\'eel state is the vacuum for antiferromagnetic spin-wave theory. We discuss the elementary excitations of this state and show that these are not Fermionic spin-1/2 ``spinons'' but spin-1 excited dimers which must be modeled by bond bosons. We derive an effective Hamiltonian describing the excited dimers which is formally analogous to spin-wave theory. Condensation of the bond bosons at zero temperature into the state with momentum $(\ensuremath{\pi},\ensuremath{\pi})$ is shown to be equivalent to antiferromagnetic ordering. The latter is a key ingredient for a microscopic interpretation of Zhang's SO(5) theory of cuprate superconductivity.
Results are derived for the dynamic correlation functions between a pair of spin operators at any two sites within a semi-infinite Heisenberg ferromagnet at low temperatures, T<<Tc. The correlation functions are found to contain terms describing the effects of the bulk spin-wave modes and the surface spin-wave modes, together with appropriate weighting factors. The results are employed to evaluate the spin deviation in the ferromagnet as a function of temperature and distance from the surface.