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arXiv:cond-mat/9906273 · Physical review. B, Condensed matter

High magnetic-field ESR in the Haldane spin chains NENP and NINO

M. Sieling, U. Löw, B. Wolf, S. Schmidt, Sergei A. Zvyagin, B. Lüthi

Published Jan 1, 2000• 25 citations
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Abstract

We present electron spin resonance experiments in the one-dimensional antiferromagnetic $S=1$ spin chains NENP and NINO in pulsed magnetic fields up to 50 T. The measured field dependence of the quantum energy gap for $B||b$ is analyzed using the exact diagonalization method and the density matrix renormalization group method. A staggered anisotropy term $(\ensuremath{-}{1)}^{i}{d(S}_{i}^{x}{S}_{i}^{z}{+S}_{i}^{z}{S}_{i}^{x})$ was considered in addition to a staggered field term $(\ensuremath{-}{1)}^{i}{S}_{i}^{x}{B}_{\mathrm{st}}.$ We show that the spin dynamics in high magnetic fields strongly depends on the orthorhombic anisotropy E.

DOI
10.1103/physrevb.61.88

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We present electron spin resonance experiments in the one-dimensional antiferromagnetic S=1S=1S=1 spin chains NENP and NINO in pulsed magnetic fields up to 50 T. The measured field dependence of the quantum energy gap for B∣∣bB||bB∣∣b is analyzed using the exact diagonalization method and the density matrix renormalization group method. A staggered anisotropy term (\ensuremath−1)id(SixSiz+SizSix)(\ensuremath{-}{1)}^{i}{d(S}_{i}^{x}{S}_{i}^{z}{+S}_{i}^{z}{S}_{i}^{x})(\ensuremath−1)id(Six​Siz​+Siz​Six​) was considered in addition to a staggered field term (\ensuremath−1)iSixBst.(\ensuremath{-}{1)}^{i}{S}_{i}^{x}{B}_{\mathrm{st}}.(\ensuremath−1)iSix​Bst​. We show that the spin dynamics in high magnetic fields strongly depends on the orthorhombic anisotropy E.
Antiferromagnetic spin-1 chains host the celebrated symmetry-protected topological Haldane phase, whose spin-1/21/21/2 edge states were evidenced in bulk by, e.g., electron spin resonance (ESR). To fully reveal and manipulate the spin-1/21/21/2 degree of freedom, one may build on the recent success in assembling effective spin-1 antiferromagnetic chains from nanographene and porphyrin molecules, and on the nascent technique of combined ESR and scanning tunneling microscopy, which is able to measure the spin dynamics site by site with atomic real-space resolution. In this Letter, we combine exact diagonalization and density matrix renormalization group to investigate the local dynamic spin structure factor of the different phases of the bilinear-biquadratic Hamiltonian with single-ion anisotropy in the presence of an external magnetic field. We find that the signature of the Haldane phase is a low-energy peak created by singlet-triplet transitions in the edge-state manifold. We predict that the signature peak is experimentally observable, although for chains of length above N=30N=30N=30 its energy should be first tuned by application of an external magnetic field. We fully characterize the peak in real space and energy, and further show its robustness to weak anisotropy and a relevant range of temperatures.
We investigate the magnetic field behaviour of an antiferromagnetic Heisenberg spin-1 chain with the most general single-ion anisotropy. We discuss the regime in which the magnetic field is below the transition value. The splitting of the Haldane triplet is obtained as a function of a field applied in an arbitrary orientation by means of a Lanczos exact diagonalization of chains of up to 16 spins. Our results are well summarized in terms of a first-order perturbation theory. We explain various level crossings that occur by the existence of discrete symmetries. A discussion is given of the electron-spin-resonance and neutron-scattering experiments on the compound Ni(C 2 H 8 N 2 ) 2 NO 2 ClO 4 (NENP).
Motivated by recent experiments on Ni(C2H8N2)2Ni(CN)4\mathrm{Ni}({\mathrm{C}}_{2}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}(\mathrm{CN}{)}_{4}Ni(C2​H8​N2​)2​Ni(CN)4​ (commonly known as NENC), we study the electron spin resonance in the critical high-field phase of the antiferromagnetic S=1S=1S=1 chain with strong planar anisotropy and show that the ESR spectra exhibit several peculiarities in the critical phase. Possible relevance of those results for other gapped spin systems is discussed.
Abstract A spin-1/2 Heisenberg antiferromagnetic chain is one of the most important paradigmatic models in quantum magnetism. Its ground state is a spin singlet, while the excitation spectrum is formed by gapless fractional excitations, spinons. The presence of alternating g-tensors and/or the staggered Dzyaloshinskii-Moriya interaction results in opening the energy gap Δ∝H2/3\varDelta \propto H^{2/3}Δ∝H2/3 Δ ∝ H 2 / 3 , once the magnetic field H is applied. A fairly good understanding of this phenomenon was achieved in the framework of the sine-Gordon quantum-field theory, taking into account the effective transverse staggered field induced by the applied uniform field. The theory predicts solitons and antisolitons as elementary excitations, as well as their bound states, breathers. Here, I review recent high-field electron spin resonance spectroscopy studies of such systems, focusing on peculiarities of their spin dynamics in the sine-Gordon regime and beyond.
A systematic field-theory approach to electron spin resonance (ESR) in the S=1/2S=1/2S=1/2 quantum antiferromagnetic chain at low temperature T (compared to the exchange coupling J) is developed. In particular, effects of a transverse staggered field h and an exchange anisotropy (including a dipolar interaction) \ensuremath{\delta} on the ESR line shape are discussed. In the lowest order perturbation theory, the linewidth is given as $\ensuremath{\propto}{\mathrm{Jh}}^{2}{/T}^{2}$ and $\ensuremath{\propto}(\ensuremath{\delta}{/J)}^{2}T,$ respectively. In the case of a transverse staggered field, the perturbative expansion diverges at lower temperature; nonperturbative effects at very low temperature are discussed using exact results on the sine-Gordon field theory. We also compare our field-theory results with the predictions of Kubo-Tomita theory for the high-temperature regime, and discuss the crossover between the two regimes. It is argued that a naive application of the standard Kubo-Tomita theory to the Dzyaloshinskii-Moriya interaction gives an incorrect result. A rigorous and exact identity on the polarization dependence is derived for certain class of anisotropy, and compared with the field-theory results.
A one-dimensional S=1 Heisenberg antiferromagnet in a magnetic field H (\ensuremath{\parallel}z axis) at T=0 is studied by numerical diagonalizations up to N=16. We give the magnetization curve at the thermodynamic limit, and derive an anomaly at Hc1{\mathit{H}}_{\mathit{c}1}Hc1​ (=\ensuremath{\Delta}), where \ensuremath{\Delta} is the Haldane gap. It is also found that the transverse spin correlation has the asymptotic form 〈S0x{\mathit{S}}_{0}^{\mathit{x}}S0x​Srx{\mathit{S}}_{\mathit{r}}^{\mathit{x}}Srx​〉\ensuremath{\sim}(-1)r{)}^{\mathit{r}})r${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\eta}}}$, and the transverse staggered susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{st}}^{\mathit{x}\mathit{x}}$ diverges between Hc1{\mathit{H}}_{\mathit{c}1}Hc1​ and Hc2{\mathit{H}}_{\mathit{c}2}Hc2​ (=4). The exponent \ensuremath{\eta} has a minimum (\ensuremath{\eta}\ensuremath{\simeq}0.3) at magnetization m\ensuremath{\simeq}1/3 and \ensuremath{\eta}\ensuremath{\simeq}0.5 at Hc1{\mathit{H}}_{\mathit{c}1}Hc1​ and Hc2{\mathit{H}}_{\mathit{c}2}Hc2​. If the system is quasi-one-dimensional, even small interchain couplings can create a canted N\'eel order, within a mean-field approximation for interchain interactions. This is consistent with a recent NMR measurement for Ni(C2{\mathrm{C}}_{2}C2​H8{\mathrm{H}}_{8}H8​N2{\mathrm{N}}_{2}N2​)2{)}_{2})2​NO2{\mathrm{NO}}_{2}NO2​(ClO4{\mathrm{ClO}}_{4}ClO4​) (NENP) at low temperature.