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AIP conference proceedings

Novel treatment of the Heisenberg spin-1 chain: Application to Ni(C2H8N2)2NO2(ClO4)α

Alexei M. Tsvelik

Published Jan 1, 1990• 0 citations
Publisher

Abstract

We suggest a new field theory treatment of the Heisenberg spin‐1 chain with a single‐ion anisotropy as a theory of three Majorana (real) fermions. We calculate the static and dynamic magnetic susceptibilities and eliminate the reported contradiction between excitation gaps deduced from high‐field magnetization measurements and neutron scattering data.

DOI
10.1063/1.39738

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We suggest a new field theory treatment of the Heisenberg spin‐1 chain with a single‐ion anisotropy as a theory of three Majorana (real) fermions. We calculate the static and dynamic magnetic susceptibilities and eliminate the reported contradiction between excitation gaps deduced from high‐field magnetization measurements and neutron scattering data.
We suggest a new field-theory treatment of the Heisenberg spin-1 chain with a single-ion anisotropy as a theory of three Majorana (real) fermions. We calculate the static and dynamic magnetic susceptibilities. We show that our results are in a good agreement with the experimental data for NENP [Ni(C2{\mathrm{C}}_{2}C2​H8{\mathrm{H}}_{8}H8​N2{\mathrm{N}}_{2}N2​)NO2{\mathrm{NO}}_{2}NO2​ClO4{\mathrm{ClO}}_{4}ClO4​] compound. In particular, we eliminate the reported contradiction between excitation gaps deduced from high-field magnetization measurements and neutron scattering.
The magnetization process of a single crystal of the spin (S) one linear-chain Heisenberg antiferromagnet, Ni(C2H8N2)2NO2(ClO4), under very high magnetic field has been measured. The magnetization is very small in the low-field region and begins to increase sharply at a finite field for all three of the principal axes. The transition field (HT) above which the system becomes magnetic depends on the direction of the applied field. These experimental results are consistent with the picture that (i) the ground state of S=1 linear chain Heisenberg antiferromagnet is a singlet and (ii) the system becomes magnetic above HT due to closing of the quantum energy gap. The experimental results are analyzed based on a simple energy level scheme. The anisotropy in HT is successfully explained by the theory using the following parameters; the Haldane gap energy EG=17K and the single ion anisotropy constant |D|=16K. These values of EG and D are close to those obtained from other experiments. Using the theory developed in analyzing the magnetization data, we can also explain the behavior of the excitation spectrum of this compound in external magnetic fields determined from the neutron inelastic scattering experiment.
The magnetization process of a single crystal of the spin (S) one linear-chain Heisenberg antiferromagnet, Ni(C2HsN2)2N02(ClO.), under very high magnetic field has been measured. The magnetization is very small in the low-field region and begins to increase sharply at a finite field for all three of the principal axes. The transition field (HT) above which the system becomes magnetic depends on the direction of the applied field. These experimental results are consistent with the picture that (i) the ground state of S = 1linear chain Heisenberg antiferromagnet is a singlet and (ii) the system becomes magnetic above HT due to closing of the quantum energy gap. The experimental results are analyzed based on a simple energy level scheme. The anisotropy in HT is successfully explained by the theory using the following parameters; the Haldane gap energy EG=17 K and the single ion anisotropy constant IDI=16 K. These values of EG and D are close to those obtained from other experiments. Using the theory developed in analyzing the magnetization data, we can also explain the behavior of the excitation spectrum of this compound in external magnetic fields determined from the neutron inelastic scattering experiment.
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).
We study a Heisenberg antiferromagnetic chain of spin S=1 with nearest-neighbor exchange interaction J and easy-plane single-ion anisotropy D. We follow the splitting of the Haldane gap into two components as a function of the anisotropy. Chains of length up to 16 sites are studied by a Lancz\"os method and longer chains up to 32 sites have been investigated by a quantum Monte Carlo simulation for D/J=0.10, 0.15, 0.20, and 0.25. A careful finite-size scaling treatment of our data leads to values that are directly relevant to the interpretation of experiments on 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). We discuss the relationship between our results and the magnetic-susceptibility measurements as well as the inelastic-neutron-scattering data and on the Haldane conjecture. Values are proposed for the parameters D and J in the case of NENP.