arXiv:cond-mat/9910322 · Physical review. B, Condensed matter

Optical absorption of spin ladders

Christoph Jurecka, Wolfram Brenig

Published Jun 1, 2000• 28 citations

Abstract

We present a theory of phonon-assisted optical two-magnon absorption in two-leg spin ladders. Based on the strong intra-rung-coupling limit we show that collective excitations of total spin $S=0,1,$ and 2 exist outside of the two-magnon continuum. It is demonstrated that the singlet collective state has a clear signature in the optical spectrum.

DOI: 10.1103/physrevb.61.14307

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arXiv:cond-mat/9910322 · Physical review. B, Condensed matter

Optical absorption of spin ladders

Christoph Jurecka, Wolfram Brenig

Published Jun 1, 2000• 28 citations

arXiv HTML PDF

Abstract

We present a theory of phonon-assisted optical two-magnon absorption in two-leg spin ladders. Based on the strong intra-rung-coupling limit we show that collective excitations of total spin

S=0,1,

and 2 exist outside of the two-magnon continuum. It is demonstrated that the singlet collective state has a clear signature in the optical spectrum.

DOI: 10.1103/physrevb.61.14307

Related papers

Observation of Two-Magnon Bound States in the Two-Leg Ladders of (Ca,La)14Cu24O41

Marco Windt, M. Grüninger, Tamara S. Nunner +8 more

Phonon-assisted two-magnon absorption is studied in the spin- $1/2$ two-leg ladders of $(\mathrm{Ca},\mathrm{La}{)}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ for $E\ensuremath{\parallel}c$ (legs) and $E\ensuremath{\parallel}a$ (rungs). We verify the theoretically predicted existence of two-magnon singlet bound states, which give rise to peaks at $\ensuremath{\approx}2140$ and $2800{\mathrm{cm}}^{\ensuremath{-}1}$. The two-magnon continuum is observed at $\ensuremath{\approx}4000{\mathrm{cm}}^{\ensuremath{-}1}$. Two different theoretical approaches (Jordan-Wigner fermions and perturbation theory) describe the data very well for ${J}_{\ensuremath{\parallel}}\ensuremath{\approx}1020--1100{\mathrm{cm}}^{\ensuremath{-}1}$, ${J}_{\ensuremath{\parallel}}{/J}_{\ensuremath{\perp}}\ensuremath{\approx}1--1.2$. At high energies, the magnetic contribution to $\ensuremath{\sigma}(\ensuremath{\omega})$ is strikingly similar in the ladders and in the undoped high- ${T}_{c}$ cuprates, which emphasizes the importance of strong quantum fluctuations in the latter.Phonon-assisted two-magnon absorption is studied in the spin- $1/2$ two-leg ladders of $(\mathrm{Ca},\mathrm{La}{)}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ for $E\ensuremath{\parallel}c$ (legs) and $E\ensuremath{\parallel}a$ (rungs). We verify the theoretically predicted existence of two-magnon singlet bound states, which give rise to peaks at $\ensuremath{\approx}2140$ and $2800{\mathrm{cm}}^{\ensuremath{-}1}$. The two-magnon continuum is observed at $\ensuremath{\approx}4000{\mathrm{cm}}^{\ensuremath{-}1}$. Two different theoretical approaches (Jordan-Wigner fermions and perturbation theory) describe the data very well for ${J}_{\ensuremath{\parallel}}\ensuremath{\approx}1020--1100{\mathrm{cm}}^{\ensuremath{-}1}$, ${J}_{\ensuremath{\parallel}}{/J}_{\ensuremath{\perp}}\ensuremath{\approx}1--1.2$. At high energies, the magnetic contribution to $\ensuremath{\sigma}(\ensuremath{\omega})$ is strikingly similar in the ladders and in the undoped high- ${T}_{c}$ cuprates, which emphasizes the importance of strong quantum fluctuations in the latter.

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Christoph Jurecka, Wolfram Brenig

We present an analytic theory for the energy spectrum of a two-leg spin ladder doped with two holes. Starting from a pseudo-fermion-bond-boson representation of the corresponding $t_{1,2}-J_{1,2}$ Hamiltonian we apply a diagrammatic approach adapted to the limit of strong rung coupling, which includes both, the coupling of holes to the spin background as well as the two-hole interactions. The two-hole spectrum is calculated and the formation of bound states is discussed. Additionally the evolution of the spin gap of the ladder upon doping is analyzed. A comparison with existing exact diagonalization data is presented and good agreement is found.We present an analytic theory for the energy spectrum of a two-leg spin ladder doped with two holes. Starting from a pseudo-fermion-bond-boson representation of the corresponding $t_{1,2}-J_{1,2}$ Hamiltonian we apply a diagrammatic approach adapted to the limit of strong rung coupling, which includes both, the coupling of holes to the spin background as well as the two-hole interactions. The two-hole spectrum is calculated and the formation of bound states is discussed. Additionally the evolution of the spin gap of the ladder upon doping is analyzed. A comparison with existing exact diagonalization data is presented and good agreement is found.

arXiv:cond-mat/0107365Jul 17, 20010 citations

We present a theory of phonon-assisted optical two-magnon absorption in two-leg spin ladders. Based on the strong intra-rung-coupling limit we show that collective excitations of total spin

S=0,1,

and 2 exist outside of the two-magnon continuum. It is demonstrated that the singlet collective state has a clear signature in the optical spectrum.

Phonon-assisted two-magnon absorption is studied in the spin-

1/2

two-leg ladders of

(\mathrm{Ca},\mathrm{La}{)}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}

for $E\ensuremath{\parallel}c$ (legs) and $E\ensuremath{\parallel}a$ (rungs). We verify the theoretically predicted existence of two-magnon singlet bound states, which give rise to peaks at $\ensuremath{\approx}2140$ and $2800{\mathrm{cm}}^{\ensuremath{-}1}$. The two-magnon continuum is observed at $\ensuremath{\approx}4000{\mathrm{cm}}^{\ensuremath{-}1}$. Two different theoretical approaches (Jordan-Wigner fermions and perturbation theory) describe the data very well for ${J}_{\ensuremath{\parallel}}\ensuremath{\approx}1020--1100{\mathrm{cm}}^{\ensuremath{-}1}$, ${J}_{\ensuremath{\parallel}}{/J}_{\ensuremath{\perp}}\ensuremath{\approx}1--1.2$. At high energies, the magnetic contribution to $\ensuremath{\sigma}(\ensuremath{\omega})$ is strikingly similar in the ladders and in the undoped high-

{T}_{c}

cuprates, which emphasizes the importance of strong quantum fluctuations in the latter.

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

) and triplet (

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

) excitations are found as quasiparticle bound states. Thus it is demonstrated that the spectrum consists of one elementary triplet, one composite triplet, and one composite singlet.

We present an analytic theory for the energy spectrum of a two-leg spin ladder doped with two holes. Starting from a pseudo-fermion-bond-boson representation of the corresponding

t_{1,2}-J_{1,2}

Hamiltonian we apply a diagrammatic approach adapted to the limit of strong rung coupling, which includes both, the coupling of holes to the spin background as well as the two-hole interactions. The two-hole spectrum is calculated and the formation of bound states is discussed. Additionally the evolution of the spin gap of the ladder upon doping is analyzed. A comparison with existing exact diagonalization data is presented and good agreement is found.