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arXiv:1406.7596 · Physical Review B

Magnons and continua in a magnetized and dimerized spin- 12 chain

M. B. Stone, Yinghao Chen, Daniel H. Reich, C. Broholm, Guangyong Xu, John R. D. Copley, Jeremy C Cook

Published Sep 29, 2014• 10 citations
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Abstract

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.

DOI
10.1103/physrevb.90.094419

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We examine the magnetic field dependent excitations of the dimerized spin-1/2 chain, copper nitrate, with antiferromagnetic intradimer exchange J1=0.44(1)meV{J}_{1}=0.44(1)\phantom{\rule{0.16em}{0ex}}\mathrm{meV}J1​=0.44(1)meV and exchange alternation \ensuremathα=J2/J1=0.26(2)\ensuremath{\alpha}={J}_{2}/{J}_{1}=0.26(2)\ensuremathα=J2​/J1​=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 \ensuremathμ0H<\ensuremathμ0Hc1=2.8T{\ensuremath{\mu}}_{0}H<{\ensuremath{\mu}}_{0}{H}_{c1}=2.8\phantom{\rule{0.28em}{0ex}}\mathrm{T}\ensuremathμ0​H<\ensuremathμ0​Hc1​=2.8T and an Sz=1/2{S}_{z}=1/2Sz​=1/2 product state at high fields \ensuremathμ0H>\ensuremathμ0Hc2=4.2T{\ensuremath{\mu}}_{0}H>{\ensuremath{\mu}}_{0}{H}_{c2}=4.2\phantom{\rule{0.28em}{0ex}}\mathrm{T}\ensuremathμ0​H>\ensuremathμ0​Hc2​=4.2T. In the intermediate-field regime, a continuum of scattering for \ensuremathℏ\ensuremathω\ensuremath≈J1\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}{J}_{1}\ensuremathℏ\ensuremathω\ensuremath≈J1​ is indicative of a strongly correlated gapless quantum state without coherent magnons.
The density matrix renormalization group and quantum Monte Carlo methods are used to describe coupled trimer chains in a magnetic field hhh. The Hamiltonian contains exchange terms involving the intratrimer coupling J1{J}_{1}J1​ (taken as the unit of energy) and the intertrimer coupling J2{J}_{2}J2​, plus the Zeeman interaction for a magnetic field hhh along the zzz direction. Results for the magnetization per trimer mmm are calculated in regimes of positive and negative values of the ratio J=J2/J1J={J}_{2}/{J}_{1}J=J2​/J1​, from which the rich field-induced ground state phase diagram hhh versus JJJ is derived, with the presence of a Luttinger liquid, the 1/3 plateau (m=1/2m=1/2m=1/2), and the one of fully polarized magnetization (m=3/2m=3/2m=3/2). Also, zero-field Lanczos calculation of the spin-wave dispersion from the 1/3 plateau for Sz=1{S}^{z}=1Sz=1 is shown at the previous regimes of JJJ values. In addition, we also report on the decay of correlation functions of trimers along open chains, as well as the average two-magnon distribution. The ground state is ferrimagnetic for $0<J\ensuremath{\le}1$, and is a singlet for $\ensuremath{-}1\ensuremath{\le}J<0$. In the singlet phase, the spin correlation functions along the legs present an antiferromagnetic power-law decay, similar to the spin-1/2 linear chain, thus suggesting that the ground state is made of three coupled antiferromagnetically oriented chains. In the singlet phase, the dimensionless thermal magnetic susceptibility per site normalized by 1/∣J∣1/|J|1/∣J∣ gets closer to $1/{\ensuremath{\pi}}^{2}$ as the temperature $T\ensuremath{\rightarrow}0$. For the ferrimagnetic phase, we fit the susceptibility to the experimental data for the compound Pb3Cu3(PO4)4{\mathrm{Pb}}_{3}{\mathrm{Cu}}_{3}{({\mathrm{PO}}_{4})}_{4}Pb3​Cu3​(PO4​)4​ and estimate the model exchange couplings: J1=74.8K{J}_{1}=74.8\phantom{\rule{4pt}{0ex}}\text{K}J1​=74.8K and J=0.4J=0.4J=0.4. These values imply a range of energies for the magnon excitations that are in accord with the data from neutron scattering experiments on Pb3Cu3(PO4)4{\mathrm{Pb}}_{3}{\mathrm{Cu}}_{3}{({\mathrm{PO}}_{4})}_{4}Pb3​Cu3​(PO4​)4​ for two excitation modes. The 1/3 plateau closes only at 1/∣J∣=01/|J|=01/∣J∣=0 with J<0J<0J<0.
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We measure by inelastic neutron scattering the spin excitation spectra as a function of applied magnetic field in the quantum spin-ladder material (C5H12N)2CuBr4. Discrete magnon modes at low fields in the quantum disordered phase and at high fields in the saturated phase contrast sharply with a spinon continuum at intermediate fields characteristic of the Luttinger-liquid phase. By tuning the magnetic field, we drive the fractionalization of magnons into spinons and, in this deconfined regime, observe both commensurate and incommensurate continua.
Inelastic neutron scattering experiments on the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependence of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q(parallel) = pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev, Phys. Rev. B 68, 134438 (2003)].
Inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependece of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q=pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev et al., Phys. Rev. B 68, 134438 (2003)].