Physical review. B, Condensed matter

Multimagnon excitations in alternating spin/bond chains

B. W. Southern, J. L. Martínez Cuéllar, David A. Lavis

Published Oct 1, 1998• 6 citations

Abstract

The nature of multimagnon excitations in alternating spin/bond ferromagnetic chains are studied using a combination of scaling methods and the recursion method. Two-magnon excitations for a Heisenberg chain with either alternating spin magnitudes, $S$ 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.

DOI: 10.1103/physrevb.58.9156

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Three magnon excitations in alternating quantum spin/bond chains

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Two-magnon states of the alternating ferromagnetic Heisenberg chain

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Physical review. B, Condensed matter

Multimagnon excitations in alternating spin/bond chains

B. W. Southern, J. L. Martínez Cuéllar, David A. Lavis

Published Oct 1, 1998• 6 citations

Publisher

Abstract

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.

DOI: 10.1103/physrevb.58.9156

Related papers

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.

Jun 1, 19970 citations

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

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Dynamical structure factors of S=1 bond-alternating Heisenberg chains

Takahumi Suzuki, Sei-ichiro Suga

We calculate the dynamical structural factor of the $S=1$ bond-alternating Heisenberg chain. In the Haldane phase, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~{q}_{c}$ and the one-magnon mode in ${q}_{c}<~q<~\ensuremath{\pi}.$ As the system approaches the gapless point, ${q}_{c}$ shifts towards $q=\ensuremath{\pi}$ and the largest integrated intensity of the one-magnon mode is decreased. In the singlet-dimer phase, the one-magnon mode appears in $0<~q<~{q}_{c}.$ As the bond-alternation becomes strong, ${q}_{c}$ shifts towards $q=\ensuremath{\pi}.$ In the antiferromagnetic-ferromagnetic bond-alternation region with a strong ferromagnetic coupling, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~0.2\ensuremath{\pi}$ and $0.8\ensuremath{\pi}<~q<~\ensuremath{\pi},$ and the one-magnon mode appears in $0.2\ensuremath{\pi}<q<0.8\ensuremath{\pi}.$ The largest integrated intensity of the one-magnon mode is $93%,$ which is slightly smaller than that in the $S=1$ Haldane-gap system. We further discuss the dynamical structural factor in connection with the inelastic neutron-scattering experiments.We calculate the dynamical structural factor of the $S=1$ bond-alternating Heisenberg chain. In the Haldane phase, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~{q}_{c}$ and the one-magnon mode in ${q}_{c}<~q<~\ensuremath{\pi}.$ As the system approaches the gapless point, ${q}_{c}$ shifts towards $q=\ensuremath{\pi}$ and the largest integrated intensity of the one-magnon mode is decreased. In the singlet-dimer phase, the one-magnon mode appears in $0<~q<~{q}_{c}.$ As the bond-alternation becomes strong, ${q}_{c}$ shifts towards $q=\ensuremath{\pi}.$ In the antiferromagnetic-ferromagnetic bond-alternation region with a strong ferromagnetic coupling, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~0.2\ensuremath{\pi}$ and $0.8\ensuremath{\pi}<~q<~\ensuremath{\pi},$ and the one-magnon mode appears in $0.2\ensuremath{\pi}<q<0.8\ensuremath{\pi}.$ The largest integrated intensity of the one-magnon mode is $93%,$ which is slightly smaller than that in the $S=1$ Haldane-gap system. We further discuss the dynamical structural factor in connection with the inelastic neutron-scattering experiments.

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S L M Cyr, B. W. Southern, David A. Lavis

The spectra of both two- and three-magnon excitations in Heisenberg spin chains with next-nearest-neighbour (NNN) interactions are studied using scaling methods and the recursion method respectively. Both two-spin and three-spin couplings are considered for general spin S. In the three-magnon case, the asymptotic behaviour of the recursion coefficients can be used to directly identify the presence of bound states in the spectrum. Both integrable and non-integrable models can be studied, and the integrable models display special features in the bound-state spectra. Our results for the three-magnon bound states of S = 1 chains differ appreciably from those obtained in previous studies based upon an integral equation approach.The spectra of both two- and three-magnon excitations in Heisenberg spin chains with next-nearest-neighbour (NNN) interactions are studied using scaling methods and the recursion method respectively. Both two-spin and three-spin couplings are considered for general spin S. In the three-magnon case, the asymptotic behaviour of the recursion coefficients can be used to directly identify the presence of bound states in the spectrum. Both integrable and non-integrable models can be studied, and the integrable models display special features in the bound-state spectra. Our results for the three-magnon bound states of S = 1 chains differ appreciably from those obtained in previous studies based upon an integral equation approach.

Journal of Physics Condensed MatterJun 24, 19964 citations

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Shaon Sahoo, V. M. L. Durga Prasad Goli, Diptiman Sen +1 more

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ( $J_1^F$ ) and antiferromagnetic ( $J_1^A$ ) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction ( $J_2^F$ ). In this model frustration is induced by the non-zero $J_2^F$ and the effect of dimerization is realized by changing the strength of $J_1^A$ for a fixed value of $J_1^F$ . The model with site spin $s$ behaves like a Haldane spin chain with site spin 2 $s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$ . We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of $J_1^A-J_2^F$ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ($J_1^F$) and antiferromagnetic ($J_1^A$) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction ($J_2^F$). In this model frustration is induced by the non-zero $J_2^F$ and the effect of dimerization is realized by changing the strength of $J_1^A$ for a fixed value of $J_1^F$. The model with site spin $s$ behaves like a Haldane spin chain with site spin 2$s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of $J_1^A-J_2^F$ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

May 29, 20130 citations

Two-magnon states of the alternating-bond ferrimagnetic chain

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

Physical review. B, Condensed matterJan 1, 19915 citations

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.

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.

We calculate the dynamical structural factor of the

S=1

bond-alternating Heisenberg chain. In the Haldane phase, the lowest excited states form the lower edge of the multimagnon continuum in

0<~q<~{q}_{c}

and the one-magnon mode in ${q}_{c}<~q<~\ensuremath{\pi}.$ As the system approaches the gapless point,

{q}_{c}

shifts towards $q=\ensuremath{\pi}$ and the largest integrated intensity of the one-magnon mode is decreased. In the singlet-dimer phase, the one-magnon mode appears in

0<~q<~{q}_{c}.

As the bond-alternation becomes strong,

{q}_{c}

shifts towards $q=\ensuremath{\pi}.$ In the antiferromagnetic-ferromagnetic bond-alternation region with a strong ferromagnetic coupling, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~0.2\ensuremath{\pi}$ and $0.8\ensuremath{\pi}<~q<~\ensuremath{\pi},$ and the one-magnon mode appears in $0.2\ensuremath{\pi}<q<0.8\ensuremath{\pi}.$ The largest integrated intensity of the one-magnon mode is

93%,

which is slightly smaller than that in the

S=1

Haldane-gap system. We further discuss the dynamical structural factor in connection with the inelastic neutron-scattering experiments.

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (

J_1^F

) and antiferromagnetic (

J_1^A

) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (

J_2^F

). In this model frustration is induced by the non-zero

J_2^F

and the effect of dimerization is realized by changing the strength of

J_1^A

for a fixed value of

J_1^F

. The model with site spin

s

behaves like a Haldane spin chain with site spin 2

s

in the limit of vanishing

J_2^F

and large

J_1^F/J_1^A

. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of

J_1^A-J_2^F

is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.