OPTICAL INVESTIGATIONS OF THE COOPERATIVE JAHN-TELLER EFFECT IN THE MIXED CRYSTAL SYSTEM (Tbx, Dy1-x) VO4

The phase diagram of (Tb,, Dyl-,) V04 was studied by crystal optical methods. The low-temperature properties of the mixed crystals are found to depend on the different distorted structures of the pure substances. In (Tb0.4, Dyo.6) VOr, two phase transitions are observed, resulting in a superposition of the two distortion types. DyV04 and TbV04 are well-known examples of a structural phase transition caused by a cooperative Jahn-Teller (JT) effect. Above TD, they have the same tetragonal crystal structure and nearly the same lattice parameters. The distortion directions below TD are either parallel to one of the crystallographic aaxes (DyV04) or parallel to the bisectrix of the a-axes, henceforth called saxis, (TbV04) , yielding two different low temperature structures for the two pure substances. Because of the equivalence of the two a-axes, there are two distortion directions in DyVO, as well as in TbVO4, leading to crystallographic domains. The structure of these domains can be observed in a polarising microscope. The domain walls lie at an angle of 45' with respect to the distortion direction [I, 21, so the orientation of the domains gives a hint to the distortion type. The magnetic easy axes coincide with the distortion directions. Therefore an external magnetic field, applied in one of these directions, favours one domain type and the crystal becomes single domained. Thus measurement of the linear optical birefringence (LOB) can be applied to determine the order parameter (distortion), and observation of the crystal in a conoscopic light path can be used to find the distortion types which determine the optical properties. The crystals of (Tb,, Dyl-,) VO4 used in the experiments were flux grown [3] in our Department. For the investigations of the domain structure and the conoscopic interference patterns, the crystals were placed between crossed polarisers. The LOB was mea sured at different wavelengths X in the visible region using a modulation technique [4]. The Dy-rich crystals (concentrations 0.1 5 x 5 0.3) behave like DyVO, diluted with a JT inactive ion. The domain structure of the crystals is similar to that of DyVO, [I] with the walls parallel to the saxes and typical domain sizes of 300 x 20jim2 in the (a, a')plane. The conoscopic interference patterns of singledomained crystals show the distortion along a. The Tb-rich crystals (0.45 < x < 0.9) , on the other hand, behave like TbV04 diluted with a JT inactive ion. The domain structure (with somewhat larger sizes) and the conoscopic interference pattern correspond to crystals with distortion along x. For x = 0.35 and z = 0.4, two phase transitions are observed. Below the higher transition temperature, T D ~ , the domain structure corresponds to that of TbV04. Below the lower transition temperature, T D ~ , the investigations in the polarising microscope indicate a macroscopic superposition of the two distortion types. Because of the finer domain structure of DyVO,, in comparison with that of TbV04, the former domain type is more clearly discernible. The conoscopic interference pattern, which had to be taken in non-zero magnetic field, depends on the field direction. With field along x, a dispersion of the indicatrix axes is observed for T 5 TD2 which results from different and wavelength-dependent influences of the two distortion types on the birefringence. A dispersion of the indicatrix axes is typical for crystals having a symmetry lower than orthorhombic. So the observations reflect the superposition of the distortion types. For temperatures just above T D ~ , the indicatrix axes turn to the crystal Paxes. With fields along a, the Dy-type distortion is favoured. For T < T D ~ , the conoscopic interference pattern resembles that of DyVO, and no dispersion of the indicatrix axes is observed. In a small temperature region above TD2, the superposition of the Tb-type distortion with the remnants of the Dy-type distortion results again in a dispersion of the indicatrix. Summarising these results, the phase diagram of the mixed system (Tb,, Dyl-,) VO4 is a superposition of the phase diagram of diluted DyVO, with that of diluted TbV04 (Fig. 1). The transition temperatures are taken from the measured LOB, Sn (T) , using the extreme points of d (Sn) /dT in different magnetic fields and extrapolating these values to zero field. Within the error bars of the experiment, they coincide with the transition temperatures obtained by specific-heat measurements. Details of these investigations will be published elsewhere [5, 61. Three low temperature regions may be distinguished: a region with a distortion Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888404 C8 892 JOURNAL DE PHYSIQUE Fig. 1. Phase diagram of the mixed system (Tb,, Dyl.-,)V04. Squares: transitions of the Dy-type distortion, triangles: transitions of the Tb-type distortion, full symbolti: taken from birefringence measurements, open symbols: taken from specific heat measurements [6]. Full lines: TD in mean-field approximation. like DyVO,, a region with a distortion like TbV04 and a superposition of the two distortion types. The transition temperatures of the Tb-diluted DyV04 lie a little lower than those of an y3+ [7] and considerably higher than those of a ~ d ~ + dilution [8] of DyVO,. The transition temperatures of the Dy-diluted TbV04, on the other L~and, are approximately equal to those of a ~ d ~ + [8] and distinctly higher than those of a ~ m ~ + or yb3+ dilution [9] of TbV04. The results of the birefringence will only be discussed briefly. For details we refer to a forthcoming publication [5]. In the Tb-rich crystals as well as in pure TbVCh, the curves measured at different wavelength X are not proportional to each other. An exarnple is given in figure 2. The reason for this behaviour is that, due to special Xand %dependences, the linear parts of the different contributions to the LOB may cancel almost completely (see e.g. [4]). Thus higherorder effects become visible. Mean-field calculations of the ordeir parameter e (T) and an ansatz 6n = Le + ~e~ for thfe birefringence show good agreement with the experiments. For the Dy-rich crystals, the curves measured for different X are proportional to each other. For pure DyVO,, the measured LOB represents the course of the distortion [lo], as was shown by calculations using the compressible Ising model 1111. In the diluted crystals, increasing divergences between the measured curves and the model calculations are found which are caused by a special contribution of the ~ b ~ + ions to the LOB, as well as by short-range JT couplings of the D ~ ~ + ions combined with the statistical distribution of the ions in the mixed crystals. Fig. 2. Birefringence of (Tb0.9, Dye.,) VO4, scaled to its extreme value S at T = 7 K. Triangles: X = 436 nm, S = 3 5 . 6 ~ loM4; dots: X = 578 nm, S = -0.62 x lo-,; crosses: X = 633 nm, S = +2.47 x lo-,. [I] Kasten, A. and Becker, P. J., Int. J . Magn. 5 (1973) 157. [2] Kasten, A., Berndts, P. and Kahle, H. G., Physica B 80 (1975) 258. [3] Hintzmann, W. and Miiller-Vogt, G., J. Cryst. Growth 5 (1969) 274. [4] Pilawa, B., Hess, G., Kahle, H. G. and Kwten, A., Phys. Status Solidi B 145 (1988) 729. [5] Hess, G., to be published. [6] Dammann, M. et al., to be published. [7] Harley, R. T., Hayes, W., Perry, A. M., Smith, S. R. P., Elliott, R. J. and Saville, I. D., J. Phys. C 7 (1974) 3145. [8] Bingham, D., Morgan, M. J. and Cashion, J. D., Solid State Commun. 44 (1982) 517. [9] Kasten, A., Kahle, H. G., Klijfer, P. and SchiiferSiebert, D., Phys. Status Solidi B 144 (1987) 423. [lo] Gehring, G. A., Harley, R. T. and Macfarlane, R. M., J. Phys. C 13 (1980) 3161. [ l l ] Page, J. H., Smith, S. R. P., Taylor, D. R. and Harley, R. T., J. Phys. C 1 2 (1979) L 875.