Crossover Behavior of Magnetic Excitations in the Anisotropic Haldane Antiferromagnet under High Magnetic Fields

Abstract

Field-induced magnetic phases are investigated in the one-dimensional S = 1 Haldane system with the easy-plane anisotropy under external magnetic fields along an arbitrary direction, using the density-matrix renormalization group method. At a critical field the system exhibits the quantum phase transition from the nonmagnetic Haldane phase to a magnetic phase. It is found that the quantum analog of the classical soliton bearing system is induced except for the case where the field is applied perpendicular to the easy plane. In the exceptional case, Tomonaga-Luttiger spin-fluid state is realized. The angle dependence of the critical field is discussed in connection with two consecutive field-induced phase transitions observed in NDMAP. Possible implications for such novel transitions are given. §1. IntroductionQuantum fluctuations play important roles in antiferromagnetic spin chains and are usually enough to destroy the classical Néel ordering even at zero temperature. An S = 1 spin chain with nearest neighbor exchange interactions, the so-called Haldane chain, is a typical example and has the so-called Haldane gap. Recently, there is a growing interest in the study of gapped quantum-spin chains in strong external magnetic fields, 1) which drive the staggered Néel ordering by suppressing the quantum fluctuations.In magnetic fields, we have to consider carefully the symmetry in the spin space. A typical Haldane system, Ni(C 5 H 14 N 2 ) 2 N 3 (PF 6 ), abbreviated hereafter as NDMAP, has the rather large easy-plane anisotropy since S = 1 chains consist of Ni 2+ ions. Honda et al. 2) are the first to realize experimentally the field-induced Néel ordering in NDMAP and to point out a strong impact of the anisotropy on the phase diagrams: the phase diagrams depend crucially on the relative orientation of the field and the principal axes of the anisotropy tensor. 3) Now, it is known that, when the field is applied perpendicular to the easy plane, the ground state above the critical field is the critical state, the Tomonaga-Luttinger (TL) spin-fluid state, which shows various critical phenomena such as the power-law decay of the spin correlation, while, when the field is applied parallel to the easy plane, the state above the critical field is the Ising-like state, which is the quantum analog of the classical soliton bearing system. It is still challenging to observe such exotic phenomena, although usually these are smeared more or less by the three-dimensional ordering in real materials.The aim of this paper is to clarify, with respect to the field direction, the nature of the magnetic states appearing above the critical field h c1 , at which the gap is closed. Another critical field h c2 , above which the magnetization is saturated, is far from the * )