ON THE EXISTENCE OF BIPOLARONS IN Ti4O7

Transcription

1 ON THE EXISTENE OF BIPOLARONS IN Ti4O7 B. hakraverty,. Schlenker To cite this version: B. hakraverty,. Schlenker. ON THE EXISTENE OF BIPOLARONS IN Ti4O7. Journal de Physique olloques, 1976, 37 (4), pp < /jphyscol: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1976 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 JOURNAL DE PHYSIQUE olloque 4, supplément au n 10, Tome 37, Octobre 1976, page ON THE EXISTENE OF BIPOLARONS IN Ti B. K. HAKRAVERTY and. SHLENKER Groupe des Transitions de Phases entre National de la Recherche Scientifique B. P. 166, Grenoble edex France Résumé. Nous avons établi dans des études antérieures que les phases basse température (T < 130 K) et intermédiaire (130 K < T < 150 K) de Ti contiennent des paires Ti3+-Ti 3+ On peut considérer que ces paires sont des bipolarons gelés et ordonnés sur un réseau pour T < 130 K, désordonnés et mobiles comme dans un liquide de bipolarons pour 130 K < T < 150 K. Nous montrons maintenant que dans un système comme Ti 4O 7 avec un électron 3d par deux cations, le réseau de bipolarons correspondant à un arrangement ordonné de paires de Ti 3+ et d'ions Ti 4+ est stabilisé à la fois par la répulsion coulombienne intersite entre premiers voisins et par les couplages électrons-phonons. es deux mécanismes peuvent conduire à une interaction effective intersite Vett négative, qui est analogue à la répulsion coulombienne intra-atomique Uen négative, récemment proposée par P. W. Anderson. Nous suggérons aussi, que bien que le mouvement des bipolarons par l'intermédiaire d'un état activé correspondant à la moitié de leur énergie de liaison ne soit pas très probable, il existe un autre mécanisme de transport par l'intermédiaire d'un état excité où les bipolarons sont dissociés en deux polarons séparés. Nous discutons nos résultats de relaxation RPE de centres Ti 3+ et de V 4+ dans (Tii-zV 1)407 en fonction de ce modèle. Abstract. We have previously established that Ti 3+ -Ti 3+ pairs are formed in both the low (T < 130 K) and the intermediate (130 K <T< 150 K) temperature phases of Ti40 7. These pairs may be viewed as bipolarons frozen and ordered on a lattice below 130 K, disordered and mobile for 130 K < T < 150 K, as in a bipolaron liquid. We now show that in a system such as Ti40 7 with one 3d electron per two cations, the bipolaron lattice with an ordered arrangement of Ti 3+ pairs and Ti 4+ ions, is stabilized through both the nearest neighbour intersite oulomb repulsion Fand the electron-phonon coupling. These two mechanisms may lead to a negative effective intersite interaction Vest, which has a strong analogy with the negative effective intraatomic oulomb repulsion Uett recently proposed by P. W. Anderson. We also suggest that, if the motion of bipolarons through an activated state corresponding to half their binding energy is not very likely, another process through an excited state where the bipolarons are dissociated into two separated single polarons should provide an easier transport. We discuss our EPR data of relaxation of Ti 3+ centers and of V 4+ centers in (Tii-sV^O? in the scope of this model. 1. Introduction. Ti is one of the series of the P. W. Anderson and P. Fazekas [4] that the ground magnetic phases of the oxydes of Titanium that state of S = J system is not magnetic but is a covalently show [1] two consecutive first order phase transitions bonded singlet state resonating from site to site. More at 130 K and 150 K. The ground state is insulating and recently, P. W. Anderson [5] has shown that such a quasi-diamagnetic ; the conductivity jump at the 130 K pairing phenomenon is greatly facilitated through local transition is not accompanied with any charge in the bond distortion, as if an effective negative Mottmagnetic susceptibility, while the transition at 150 K Hubbard t/was operative on a bond-site. The resultant leads both to the metallic state and to a Pauli suscepti- pair, stabilized by the lattice distortion can be called a bility. Recently. Schlenker [2] and coll. have done bipolaron. In this communication, we would like to perextensive investigations of this system and have defini- sent arguments that support the existence of bipolarons tely demonstrated that both the low (T < 130 K) and in pure Ti as well as in Ti doped with Vanadium the intermediate temperature (130 K < T < 150 K) We will also discuss briefly the ordered ground state of phases are due to covalently bonded near-neighbour these pairs, as well as the dynamics of their motion. 3d 1 pairs of cations of Ti 3 + and that while the ground state is a perfectly ordered arrangement of these pairs 2. Pair formation. Pair formation is not unique (alternate strands of Ti 3+ and Ti 4+ chains), the inter- to Ti 4 0 7, the other classic example being V0 2 [6]. In mediate phase can be correctly described as a liquid pure V0 2, the 3d 1 V 4+ cations are covalently bonded state of these pairs (Fig. 1). This idea is originally due to in F pairs, just as in H 2 molecule. In an almost locali- P. W. Anderson [3] and it was shown later by zed picture (small band-width limit), the ground state Article published online by EDP Sciences and available at

3 B. K. HAKRAVERTY AND. SHLENKER can be further lowered through pair or bond formation, the decrease of energy of the pair being - t U. The situation is however completely different in Ti407 where one has only one available d-electron for band formation for every two cations. The ground state of such a system, if the near neighbour coulomb repulsion were zero, is shown in figure 3a, the lower Hubbardband being half-filled. If we now turn on the nearneighbour oulomb repulsion V, the system can still lower the ground state energy (Fig. 3b), by avoiding FIG. l@). - rystal structure of the low-temperature ordered phase of Ti407 showing only the Ti chains. (6) Structure with the disordered Ti3+ and Ti4+ chains for the liquid intermediate phase. of such a system with one 3d electron per cation, is a Mott-insulator (Fig. 2a), the ground state energy of an ion being E, + V/2, where E, is the free energy and V FIG. 2(a). - Energy level diagram for a Mott insulator with one 3d electron per cation, an intraatomic oulomb repulsion U and an intersite nearest-neighbour interaction V. is the free ion energy. (6) Same as (a) with the ground state lowered by bond formation between nearest-neighbours. t is the intersite hopping integral. FIG. 3(a). - Energy diagram for a system with one 3d electron per two cations and a zero nearest-neighbour interaction. (b) Same as (a) with a nearest neighbour interaction V. The ground state corresponds to a Verwey order. to have near-neighbour electrons ; at T = 0, this ground state is the Verwey state. In the case of Ti,O,, it would correspond to an alternative arrangement of Ti3+ and Ti4+ ions. In such a situation a near-neighbour pair costs an energy V and even if we form a covalent bond, we will get back only t '/U; since V > t2/u, a covalent pair will never form. If no other interactions are present, the ground state of such a half-filled band will be a Verwey state in the narrow band limit (V > t) or a metal in the wide band regime (V < t), but in neither limit we can hope to get the pairing in Ti40,. It is in this context, that deformation induced pair formation mechanism of P. W. Anderson [5] becomes of great relevance to such a system. We need not assume a negative U. In fact, for Ti,07, U could be large and positive, since we have no experimental evidence of double occupation i. e. Ti2+ cations, in this system. However, for the pair formation, what we need is a negative V and we can write, in the spirit of the Anderson Hamiltonian (static part) : the repulsive near-neighbour interaction. We assume U > V > t wliere U is the on-site Mott-Hubbard repulsion and t is the inter-site hopping integral. It is evident that for such a system, the ground state energy where i and j are near-neighbour sites

4 ON THE EXISTENE OF BIPOLARONS IN Ti Ri being the cationic position i, c = a relevant elastic constant, zi = the atomic energy at the site i, V = the near-neighbour interaction (we omit spin indices). Note that i and'j refer here to true atomic sites and we are supposing that the Mott-Hubbard term U is sufficiently large and positive that H,,, operates only in the lower Hubbard band. The three eigen values are just as in the Anderson model : (a) E = 0, ni = 0, nj = 0, /l2 (b) E = Ei - -for ni = 1, nj = 0, or ni = 0, (2) constructed as has been recently done by Heydock [g] (Fig. 4). The activated state of the bipolaron indicated by :)G is seen to lie, at an energy &,l2 i. e. at half the bipolaron binding energy E, just as in the case of i, j being near-neighbours. We note that the nearest-neighbour bonded pairstate is pbssible only if 2 A2/c > V. In the event this happens, the pair state would be the ground state of the system, rather than the Verwey state (b) (ni = 1, nj = 0). The two widely separated polarons have total energy 2,l2 2 ci --, the bipolaron has an energy (y- V) i. e. a negative effective pair-wise interaction energy V,,, = ---- "- V. Thus we can postulate that the bonded-pairs in Ti,07 are bipolarons, with a bonding energy V,,,. 3. Bipolaronic phases and its transports In Ti,O,, in the absence of bipolaron-bipolaron interaction, the bipolaron band is half-full. The system lowers further the ground state energy by going into a lattice state (Fig. la), of ~i~+-ti~+ strands alternating with ~i~+-ti~+ strands. The free energy of this system has been calculated ref. [7] and one can conclude that : (a) Melting of the bipolaron lattice could be either a first or a second order transition. (b) The ground state energy of the lattice state vis-ci-vis the liquid state, is almost identical so that with small change of external conditions, the bipolaron lattice disorders completely. This, we believe, is what happens with slight addition of V: with only 0.06 % V, the liquid phase is stabilized at T = For larger Vanadium concentration, a transition to a glassy state at low temperature, is to be anticipated. 3.2 Transport of the bipolarans is not completely understood yet. In analogy with single polarons, one may presume that bi,polarons at low temperatures tunnel in a band-motion from bond to bond with their own deformation and smoothly goes over to hopping process (non-diagonal transport) at elevated temperatures. A potential energy diagram of the bipolaron motion between two paired sites can be FIG Potential energy diagram for the bipolarons motion. The main minima correspond to two paired sites and the hori- zontal axis to the relative distortion of these two sites. A is the initial state of the B is the activated state of the bipolaron!j$, is a state with two separated polarons a 0. single polaron transport [10]. There is however an alternative activated state, lower in energy, and not considered by Heydock ; it corresponds to two separated single polarons indicated in figure 4 (state ) by and must provide a faster transfer between two pair sites. The energy of these two polarons compared to the bipolaron state is : w1 = v,,, = 2 A2/c - v. State should be separated from state A by apotential barrier of height W,. In the present state, it is difficult to evaluate W,. Two conclusions can be drawn from figure 4. (a) The chemical equilibrium between bi- and single - polarons gives : ng = ng exp -- [ ZT] (b) onductivity through these single polarons would be given by 0.- (ng + ng) with a mobility 3.3 The study of the E. P. R. line from either a Ti3+ center, of a V4+ center when doped with Vanadium, has provided us some valuable insights, to the formation and motion of bipolarons. In the ordered phase of pure Ti407, the exponential increase of the width of a Ti3 + line with temperature with an activation energy ev [2] may be directly correclated with a Korringa-type relaxation of the center through the single polarons. W,/2 is then 0.08 ev. Since the

5 4-356 B. K. HAKRAVERTY AND. SHLENKER electrical conductivity has an activation energy of 0.17 ev, we get W, ev TIME (mn) FIG Intensity of the V4+ and Ti3f EPR lines versus time after a quenching process down to the ordered low-temperatures phase as measured in (Ti1-~V-)&07 with X = 0.2 % [S]. In the V-doped sample, simultaneous study of the Ti3+ and v4+ signal and its time development 1111 (Fig. 5) can only be interpreted if the disappearance of a V4+ unpaired electron is associated with the formation of a V4+ - Ti3' bipolaron ; the porcess releases a Ti3+ center, whose line intensity must increase constantly with time. This after-efect seems to be a precursor to the formation of the bipolaronic glass phase. In conclusion, we would like to indicate that bipolarons i. e. deformation induced bonded-pair state must exist in Ti40, and give rise ot its different thermodynamic and transport properties. Acknowledgements. - The authors would like to thank R. Buder, S. Lakkis, R. Gourmala and S. Ahmed who have contributed to the experimental results. One of the authors (B. K. hakraverty) would like to thank Dr. Roger Heydock of avendish Laboratory, ambridge, for some stimulating discussions over the bipolarons. References [l] MAREZIO, M., MWHAN, D. B., DERNIER, P. D. and REMEIXA, J. P., Phys. Rev. Lett. 28 (1972) [2] LAKKIS, S., SHLENKER,., HAKRAVERTY, B. K., BUDER, R. and MAREZIO, M., Phys. Rev. B 14 (1976) [3] ANDERSON, P. W., Mater. Res. Bull. 8 (1973) 153. [4] FAZEKAS, P. and ANDERSON, P. W., Phil. Mag. 30 (1974) 423. [5] ANDERSON, P. W., Phys. Rev. Lett. 34 (1975) 953. [6] POUGET, J. P., LAUNOIS, H., RIE, T. M., DERNIER, P., GOSSARD, A., VILLENEUVE, G. and HAGENMULLER, P., Phys. Rev. B 10 (1974) [7] HAKRAVERTY, B. K., TO be submitted for publication [8] SHLENKER,., HAKRAVERTY, B. K., BUDER, R., Int. onf. on the Physics of Semiconductors, Rome (August 30-September ). [9] HEYDOK, R., TO be submitted for publication. [l01 AUSTIN, I. G. and MOTT, N. F., Adv. Phys. 18 (1969) 51. [l11 SHLENKER,., BUDER, R., LAKKIS, S., GOURMALA, M., olloque Ampere, Budapest (25-29 Aug~~st 1975) (unpublished).