Magnetic field effects on spin excitations in the spin-Peierls compound CuGeO 3 B. Grenier, 1 L. P. Regnault, 1 J. E. Lorenzo, 2 J. P. Boucher, 3 A. Hiess, 4 G. Dhalenne, 5 and A. Revcolevschi 5 1 De ´partement de Recherche Fondamentale sur la Matie `re Condense ´e, SPSMS, Laboratoire de Magne ´tisme et de Diffraction Neutronique, CEA-Grenoble, F-38054 Grenoble cedex 9, France 2 Laboratoire de Cristallographie, CNRS, BP 166, F-38042 Grenoble cedex 9, France 3 Laboratoire de Spectrome ´trie Physique, Universite ´ J. Fourier Grenoble I, BP 87, F-38402 Saint Martin d’He `res cedex, France 4 Institut Laue Langevin, BP 156, F-38042 Grenoble cedex 9, France 5 Laboratoire de Physico-Chimie de l’Etat Solide, Universite ´ Paris-Sud, Ba ˆtiment 414, F-91405 Orsay cedex, France Received 27 March 2000 Neutron inelastic scattering measurements on an undoped single crystal of CuGeO 3 and on a doped crystal CuGe 0.997 Si 0.003 O 3 are performed in the presence of a magnetic field H up to 12 T. In the present work, a particular attention is given to the effect of H on the low-energy elementary excitations. This investigation is performed in the three different phases of the spin-Peierls system. In the dimerized D phase, the Zeeman splitting of the acoustic magnon branch is evaluated all along the dispersion branch (0 q 1/2). In the uniform U phase, it is established first that, at finite temperature T 0, the low wave vector ( q →0) spinon modes are little affected by the thermal fluctuations  E T T . Second, the effect of H on the same low-q mode results essentially in a transfer of the fluctuations towards the Zeeman-shifted lower boundary of the spinon continuum. Finally, our measurements on the doped compound establishes that an energy gap occurs in the elementary excitation spectrum of the incommensurate I phase. I. INTRODUCTION The spin-Peierls transition SP remains one of the most fascinating phenomena in solid state physics. It establishes that a three-dimensional lattice of atoms, subjected to the low-energy quantum fluctuations of an internal low- dimensional spin system, can undergo a distortion at suffi- ciently low temperature. 1 As a result, drastic changes occur also in the spin system. In particular, energy gaps open in the fluctuation spectrum. The renewed interest in this remarkable effect, established more than twenty years ago on organic materials, is due to the inorganic compound CuGeO 3 . 2 The high quality of available single crystals has allowed a rather wide set of new experimental investigations. 3 Simulta- neously, new theoretical and numerical analyzes have been proposed. Recently, it has been suggested that the initial adiabatic approach, 1 which results in the occurrence of a phonon soft mode at the transition, would not apply to that compound. To explain the observed SP transition in CuGeO 3 , a nonadiabatic 4 or ‘‘diabatic’’ 5  situation where the transition would be driven by a ‘‘central peak’’ appears as a possible and promising alternative. Whatever the actual model, a close relation between the fluctuations of the lattice and those of the spin system is to be expected. Complete knowledge of all these fluctuations is therefore required. 6 In the present work, however, we limit our interest to the mag- netic fluctuations. More precisely, we focus on the effects of an external magnetic field H on the low-energy excitations of the spin system. The effect of a field H is of crucial impor- tance in the SP phenomenology. 1 As it is well known, a quasiuniversal phase diagram is obtained as a function of H and T, with three distinct phases, denoted hereafter U, D, and I see Fig. 1a. 3,7 These phases are defined with respect to the lattice structure of the spin system. In the U phase, and within the simplest model, this lattice is composed of uni- form chains, and a unique lattice parameter—the distance c between two neighboring spins—needs to be used to de- scribe that structure. In the D phase, the spin chains are dimerized and two parameters, c 1 and c 2 , are now needed to define the spin chain structure. In the I phase, the lattice distortion undergoes a periodic modulation along the chains, with a periodicity which depends directly on the uniform magnetization, i.e., on the value of the applied field H. Ac- cordingly, in the I phase, the lattice distortion is generally incommensurate and characterized by the wave vector com- ponent in the chain direction d =2  m ˜ , where m ˜ is the magnetization per spin  d /2 is expressed in reciprocal lat- tice units r.l.u. and m ˜ is evaluated with respect to the quan- tum spin value, i.e., 0 m ˜ 1/2. Due to these different lat- tice structures, for each phase, a specific spin hamiltonian can be defined. The effects of H analyzed in the present work are common features to all SP systems and therefore they are to be considered as general properties of these models. They should not depend, in an essential way, on the precise Hamil- tonian of the spin system. Our experimental investigation relies on neutron inelastic scattering NIS measurements. They are performed in presence of a relatively large mag- netic field maximum field value H =12 T) and for each phase, new results are presented, which are concerned with the low-energy excitations—and/or fluctuations—of the spin system. They are probed for different wave vectors Q in the reciprocal space of the compound. The basic properties of CuGeO 3 and the experimental conditions are briefly described in the following section. Most of our results have been obtained in the D phase. These results are discussed in Sec. III. The data obtained in the U and I phases are presented in Secs. IV and V, respectively. II. CuGeO 3 AND EXPERIMENTAL DETAILS Both the undoped and the Si-doped single crystals CuGeO 3 and CuGe 1 -x Si x O 3 ( x =0.003), used in the present PHYSICAL REVIEW B 1 NOVEMBER 2000-II VOLUME 62, NUMBER 18 PRB 62 0163-1829/2000/6218/1220610/$15.00 12 206 ©2000 The American Physical Society