Physical review. B, Condensed matter

Two-magnon states of the alternating-bond ferrimagnetic chain

A. J. M. Medved, B. W. Southern, David A. Lavis

Published Jan 1, 1991• 5 citations

Abstract

In this paper we examine the nature of two-magnon excitations in the alternating-bond ferrimagnetic spin chain for general values S and S' of the two species of spin. Both a direct analytic approach as well as a method based on a scaling transformation are used to study the bound-state branches and their relationship to the two-magnon continuum.

DOI: 10.1103/physrevb.43.816

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Physical review. B, Condensed matter

Two-magnon states of the alternating-bond ferrimagnetic chain

A. J. M. Medved, B. W. Southern, David A. Lavis

Published Jan 1, 1991• 5 citations

Publisher

Abstract

DOI: 10.1103/physrevb.43.816

Related papers

Two-magnon states of the alternating ferromagnetic Heisenberg chain

S C Bell, P. D. Loly, B. W. Southern

Journal of Physics Condensed MatterDec 11, 19899 citations

Three magnon excitations in alternating quantum spin/bond chains

Martinez Cuellar, José Luís

In this thesis we examine the nature of three magnon excitations in alternating spin/bond ferromagnetic chains. We study a Hamiltonian that describes a chain (composed of two non-identical one-dimensional uniform and homogeneous sublattices) with alternating spin magnitudes, S and $S\\sp\\prime$ , and alternating nearest neighbor interactions, $J\\sb1$ and $J\\sb2.$ The Recursion Method is used to locate the bound states and their relationship to the three-magnon continuum. The specific cases studied are the S = $S\\sp\\prime$ = 1/2, S = $2S\\sp\\prime$ = 1, and S = $S\\sp\\prime$ = 1 alternating spin chains. We consider not only the effects of spin alternation but also of varying strengths. For each case, we studied different bond sets, more exactly, $J\\sb1$ = 1 and $J\\sb2$ equal to 0, 1/4, 1/2 and 1.In this thesis we examine the nature of three magnon excitations in alternating spin/bond ferromagnetic chains. We study a Hamiltonian that describes a chain (composed of two non-identical one-dimensional uniform and homogeneous sublattices) with alternating spin magnitudes, S and $S\\sp\\prime$, and alternating nearest neighbor interactions, $J\\sb1$ and $J\\sb2.$ The Recursion Method is used to locate the bound states and their relationship to the three-magnon continuum. The specific cases studied are the S = $S\\sp\\prime$ = 1/2, S = $2S\\sp\\prime$ = 1, and S = $S\\sp\\prime$ = 1 alternating spin chains. We consider not only the effects of spin alternation but also of varying strengths. For each case, we studied different bond sets, more exactly, $J\\sb1$ = 1 and $J\\sb2$ equal to 0, 1/4, 1/2 and 1.

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Götz Silvester Uhrig, Heinz J. Schulz

Motivated by recent measurements on CuGe ${\mathrm{O}}_{3}$ , the spectrum of magnetic excitations of an antiferromagnetic $S=\frac{1}{2}$ chain with alternating coupling strength is investigated. Wave-vector-dependent magnons and a continuum with square-root behavior at the band edges are found. The spectral density of the continua is calculated. Spin-rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. The existence of (anti)bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum a quintuplet.Motivated by recent measurements on CuGe${\mathrm{O}}_{3}$, the spectrum of magnetic excitations of an antiferromagnetic $S=\frac{1}{2}$ chain with alternating coupling strength is investigated. Wave-vector-dependent magnons and a continuum with square-root behavior at the band edges are found. The spectral density of the continua is calculated. Spin-rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. The existence of (anti)bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum a quintuplet.

arXiv:cond-mat/9606001Physical review. B, Condensed matterOct 1, 1996170 citations

S\\sp\\prime

, and alternating nearest neighbor interactions,

J\\sb1

and

J\\sb2.

The Recursion Method is used to locate the bound states and their relationship to the three-magnon continuum. The specific cases studied are the S =

S\\sp\\prime

= 1/2, S =

2S\\sp\\prime

= 1, and S =

S\\sp\\prime

= 1 alternating spin chains. We consider not only the effects of spin alternation but also of varying strengths. For each case, we studied different bond sets, more exactly,

J\\sb1

= 1 and

J\\sb2

equal to 0, 1/4, 1/2 and 1.

S

and ${S}^{\ensuremath{'}},$ or alternating nearest-neighbor couplings,

{J}_{1}

and

{J}_{2}

can be studied using real-space rescaling techniques. These results are then used to investigate three-magnon excitations using the recursion method.

We numerically investigate elementary excitations of the Heisenberg alternating-spin chains with two kinds of spins, 1 and

1/2,

antiferromagnetically coupled to each other. Employing a recently developed efficient Monte Carlo technique as well as an exact-diagonalization method, we verify the spin-wave argument that the model exhibits two distinct excitations from the ground state which are gapless and gapped. The gapless branch shows a quadratic dispersion in the small-momentum region, which is of the ferromagnetic type. With the intention of elucidating the physical mechanism of both excitations, we make a perturbation approach from the decoupled-dimer limit. The gapless branch is directly related to spin 1's, while the gapped branch originates from cooperation of the two kinds of spins.

Motivated by recent measurements on CuGe

{\mathrm{O}}_{3}

, the spectrum of magnetic excitations of an antiferromagnetic

S=\frac{1}{2}

chain with alternating coupling strength is investigated. Wave-vector-dependent magnons and a continuum with square-root behavior at the band edges are found. The spectral density of the continua is calculated. Spin-rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. The existence of (anti)bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum a quintuplet.