arXiv:cond-mat/9606001 · Physical review. B, Condensed matter

Magnetic excitation spectrum of dimerized antiferromagnetic chains

Götz Silvester Uhrig, Heinz J. Schulz

Published Oct 1, 1996• 170 citations

Abstract

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.

DOI: 10.1103/physrevb.54.r9624

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arXiv:cond-mat/9606001 · Physical review. B, Condensed matter

Magnetic excitation spectrum of dimerized antiferromagnetic chains

Götz Silvester Uhrig, Heinz J. Schulz

Published Oct 1, 1996• 170 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1103/physrevb.54.r9624

Related papers

Crossover of spectral features from Dimerized to Haldane behavior in alternating antiferromagnetic-ferromagnetic spin-half chains

Weihong Zheng, Chris J. Hamer, Rajiv R. P. Singh

We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings $J$ and $-|λ|J$ as a power series in $λ$ . For small $|λ|$ , the gapped one-particle spectrum has a maximum at $k=0$ and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As $|λ|$ is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from $k=0$ , the one particle states merge with the bottom of the continuum near $k=0$ , and the spectral weights associated with the one-particle states become very small. Extrapolation of the spectrum to large $|λ|$ confirms that the ground state energy and excitation gap map onto those of the spin-one chain.We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings $J$ and $-|λ|J$ as a power series in $λ$. For small $|λ|$, the gapped one-particle spectrum has a maximum at $k=0$ and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As $|λ|$ is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from $k=0$, the one particle states merge with the bottom of the continuum near $k=0$, and the spectral weights associated with the one-particle states become very small. Extrapolation of the spectrum to large $|λ|$ confirms that the ground state energy and excitation gap map onto those of the spin-one chain.

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M. B. Stone, Yinghao Chen, Daniel H. Reich +4 more

We examine the magnetic field dependent excitations of the dimerized spin-1/2 chain, copper nitrate, with antiferromagnetic intradimer exchange ${J}_{1}=0.44(1)\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ and exchange alternation $\ensuremath{\alpha}={J}_{2}/{J}_{1}=0.26(2)$. Magnetic excitations in three distinct regimes of magnetization are probed through inelastic neutron scattering at low temperatures. At low and high fields there are three and two long-lived magnonlike modes, respectively. The number of modes and the antiphase relationship between the wave-vector dependent energy and intensity of magnon scattering reflect the distinct ground states: A singlet ground state at low fields ${\ensuremath{\mu}}_{0}H<{\ensuremath{\mu}}_{0}{H}_{c1}=2.8\phantom{\rule{0.28em}{0ex}}\mathrm{T}$ and an ${S}_{z}=1/2$ product state at high fields ${\ensuremath{\mu}}_{0}H>{\ensuremath{\mu}}_{0}{H}_{c2}=4.2\phantom{\rule{0.28em}{0ex}}\mathrm{T}$. In the intermediate-field regime, a continuum of scattering for $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}{J}_{1}$ is indicative of a strongly correlated gapless quantum state without coherent magnons.We examine the magnetic field dependent excitations of the dimerized spin-1/2 chain, copper nitrate, with antiferromagnetic intradimer exchange ${J}_{1}=0.44(1)\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ and exchange alternation $\ensuremath{\alpha}={J}_{2}/{J}_{1}=0.26(2)$. Magnetic excitations in three distinct regimes of magnetization are probed through inelastic neutron scattering at low temperatures. At low and high fields there are three and two long-lived magnonlike modes, respectively. The number of modes and the antiphase relationship between the wave-vector dependent energy and intensity of magnon scattering reflect the distinct ground states: A singlet ground state at low fields ${\ensuremath{\mu}}_{0}H<{\ensuremath{\mu}}_{0}{H}_{c1}=2.8\phantom{\rule{0.28em}{0ex}}\mathrm{T}$ and an ${S}_{z}=1/2$ product state at high fields ${\ensuremath{\mu}}_{0}H>{\ensuremath{\mu}}_{0}{H}_{c2}=4.2\phantom{\rule{0.28em}{0ex}}\mathrm{T}$. In the intermediate-field regime, a continuum of scattering for $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}{J}_{1}$ is indicative of a strongly correlated gapless quantum state without coherent magnons.

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Spectrum of elementary and collective excitations in the dimerized S=1/2 Heisenberg chain with frustration

Pavel V. Shevchenko, Valeri N. Kotov, Oleg P. Sushkov

We have studied the low-energy excitation spectrum of a dimerized and frustrated antiferromagnetic Heisenberg chain. We use an analytic approach, based on a description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet $(S=0)$ and triplet $(S=1)$ modes are found as two-particle bound states of the elementary triplets. We have also calculated the contributions of the elementary and collective excitations into the spin structure factor. Our results are in excellent agreement with exact diagonalizations and dimer series expansions data as long as the dimerization parameter \ensuremath{\delta} is not too small $(\ensuremath{\delta}>0.1),$ i.e., while the elementary triplets can be treated as localized objects.We have studied the low-energy excitation spectrum of a dimerized and frustrated antiferromagnetic Heisenberg chain. We use an analytic approach, based on a description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet $(S=0)$ and triplet $(S=1)$ modes are found as two-particle bound states of the elementary triplets. We have also calculated the contributions of the elementary and collective excitations into the spin structure factor. Our results are in excellent agreement with exact diagonalizations and dimer series expansions data as long as the dimerization parameter \ensuremath{\delta} is not too small $(\ensuremath{\delta}>0.1),$ i.e., while the elementary triplets can be treated as localized objects.

arXiv:cond-mat/9901302Physical review. B, Condensed matterAug 1, 199923 citations

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A. Dobry, David Ibaceta

We study a model of a spin-Peierls material consisting of a set of antiferromagnetic Heisenberg chains coupled with phonons and interacting among them via an interchain elastic coupling. The excitation spectrum is analyzed by bosonization techniques and the self-harmonic approximation. The elementary excitation is the creation of a localized domain structure where the dimerized order is the opposite to the one of the surroundings. It is a triplet excitation whose formation energy is smaller than the magnon gap. Magnetic internal excitations of the domain are possible and give the further excitations of the system. We discuss these results in the context of recent experimental measurements on the inorganic spin-Peierls compound ${\mathrm{CuGeO}}_{3}.$ We study a model of a spin-Peierls material consisting of a set of antiferromagnetic Heisenberg chains coupled with phonons and interacting among them via an interchain elastic coupling. The excitation spectrum is analyzed by bosonization techniques and the self-harmonic approximation. The elementary excitation is the creation of a localized domain structure where the dimerized order is the opposite to the one of the surroundings. It is a triplet excitation whose formation energy is smaller than the magnon gap. Magnetic internal excitations of the domain are possible and give the further excitations of the system. We discuss these results in the context of recent experimental measurements on the inorganic spin-Peierls compound ${\mathrm{CuGeO}}_{3}.$

arXiv:cond-mat/9712239Physical review. B, Condensed matterAug 1, 19987 citations

Excitation Spectrum of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain

Kazuo Hida

The natural explanation of the excitation spectrum of the spin-1 antiferromagnetic Heisenberg chain is given from the viewpoint of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain. The energy spectrum of the latter is calculated with fixed momentum k by numerical diagonalization of finite size systems. It consists of a branch of propagating triplet pair (triplet wave) and the continuum of multiple triplet waves for weak ferromagnetic coupling. As the ferromagnetic coupling increases, the triplet wave branch is absorbed in the continuum for small k, reproducing the characteristics of the spin-1 antiferromagnetic Heisenberg chain.The natural explanation of the excitation spectrum of the spin-1 antiferromagnetic Heisenberg chain is given from the viewpoint of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain. The energy spectrum of the latter is calculated with fixed momentum k by numerical diagonalization of finite size systems. It consists of a branch of propagating triplet pair (triplet wave) and the continuum of multiple triplet waves for weak ferromagnetic coupling. As the ferromagnetic coupling increases, the triplet wave branch is absorbed in the continuum for small k, reproducing the characteristics of the spin-1 antiferromagnetic Heisenberg chain.

Jan 1, 199423 citations

Motivated by recent measurements on CuGe

{\mathrm{O}}_{3}

, the spectrum of magnetic excitations of an antiferromagnetic

S=\frac{1}{2}

We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings

J

and

-|λ|J

as a power series in

λ

. For small

|λ|

, the gapped one-particle spectrum has a maximum at

k=0

and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As

|λ|

is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from

k=0

, the one particle states merge with the bottom of the continuum near

k=0

, and the spectral weights associated with the one-particle states become very small. Extrapolation of the spectrum to large

|λ|

confirms that the ground state energy and excitation gap map onto those of the spin-one chain.

We examine the magnetic field dependent excitations of the dimerized spin-1/2 chain, copper nitrate, with antiferromagnetic intradimer exchange

{J}_{1}=0.44(1)\phantom{\rule{0.16em}{0ex}}\mathrm{meV}

and exchange alternation $\ensuremath{\alpha}={J}_{2}/{J}_{1}=0.26(2)$. Magnetic excitations in three distinct regimes of magnetization are probed through inelastic neutron scattering at low temperatures. At low and high fields there are three and two long-lived magnonlike modes, respectively. The number of modes and the antiphase relationship between the wave-vector dependent energy and intensity of magnon scattering reflect the distinct ground states: A singlet ground state at low fields ${\ensuremath{\mu}}_{0}H<{\ensuremath{\mu}}_{0}{H}_{c1}=2.8\phantom{\rule{0.28em}{0ex}}\mathrm{T}$ and an

{S}_{z}=1/2

product state at high fields ${\ensuremath{\mu}}_{0}H>{\ensuremath{\mu}}_{0}{H}_{c2}=4.2\phantom{\rule{0.28em}{0ex}}\mathrm{T}$. In the intermediate-field regime, a continuum of scattering for $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}{J}_{1}$ is indicative of a strongly correlated gapless quantum state without coherent magnons.

(S=0)

and triplet

(S=1)

modes are found as two-particle bound states of the elementary triplets. We have also calculated the contributions of the elementary and collective excitations into the spin structure factor. Our results are in excellent agreement with exact diagonalizations and dimer series expansions data as long as the dimerization parameter \ensuremath{\delta} is not too small $(\ensuremath{\delta}>0.1),$ i.e., while the elementary triplets can be treated as localized objects.

{\mathrm{CuGeO}}_{3}.