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Progress of Theoretical Physics Supplement

A Quantum Spin Chain in High Magnetic Fields

K. Katsumata, H. Hori, Tetsuya Takeuchi, Munekazu Date, Akio Yamagishi, Taturu Yosida, Jean‐Pierre Renard

Published May 16, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.1143/ptp.101.503

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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.
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)].
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).
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)].
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.