We report the first direct and comprehensive determination of the energy levels involved in the Haldane gap occurrence: the singlet ground state and the first triplet excited state. Precise values of the parameters are obtained from the analysis of the magneto-optical resonance transitions observed in the far infrared for frequencies ranging from 70 to 1000 GHz and magnetic fields up to 18 T. PACS numbers: 76.5a+g, TS.lO.Jm, TS.SO.Ee, 76.9a+dThe great interest in low-dimensional magnetic systems [1] has been strongly renewed recently following a suggestion by Haldane [2] that an energy gap exists in the excitation spectrum of one-dimensional Heisenberg antiferromagnets with integer spins. Numerical simulations [3] and the proof of a solvable model [4] supported the conjecture that a quantum energy gap exists in a linearchain Heisenberg antiferromagnet (LCHA) with integer spin between the singlet ground state and the lowest excited triplet.Several experiments have been performed to confirm the existence of this "Haldane gap." The compound Ni(C2H8N2)2N02C104 (NENP) is to date the best real system approaching the idea! LCHA with 5' = 1. The single-ion anisotropy which in general splits the first excited state for integer S >: 1 and the interchain exchange interaction constant J' responsible for three-dimensional ordering are both small compared to the intrachain exchange interaction constant /, giving the possibility for an energy gap to appear. Susceptibility measurements [5] showed a rounded maximum and an abrupt fall as the temperature was lowered below 15 K. No long-range order was observed down to 1.2 K whatever the field orientation with respect to the crystallographic axes. Two gap energies were obtained for the principal directions parallel and perpendicular to the chain axis. Inelastic neutron-scattering experiments [5] also supported the existence of an energy gap at the boundary of the Brillouin zone with values different from those extracted from the susceptibility data. More recently, magnetization experiments [6,7] in large magnetic fields showed that the magnetization, very small in the low-field region, begins to in-crease sharply at finite fields along the three principal axes giving evidence for the existence of the Haldane gap. Electron paramagnetic resonance (EPR) is generally considered one of the best methods to study the spin system at a microscopic level. It was used to determine the scheme of energy levels [8] and to test the Haldane gap via the introduction of impurities [9]. As a result of the limited ranges of frequencies and fields available only intraexcited triplet transitions were observed in the experiment by Date and Kindo [8] and the energy gap was obtained indirectly. Therefore it seemed useful to extend the EPR measurements to a wider range of fields and frequencies in order to obtain a comprehensive scheme of the energy levels involved in the occurrence of the Haldane gap.We report here the first observation of optical resonance transitions between the ground state and the first...
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