ESR-study of the low-temperature phase transition in KDy(WO4)2

PHYSICA Physica B 240 (1997) 21 25

ELSEVIER

ESR-study of the low-temperature phase transition in KDy(WO4)2 M.T. Borowiec a' *, V. D y a k o n o v b, A. Nabialek a, A. Pavlyuk c, S. Piechota a, A. P r o k h o r o v b, H. Szymczak a "Institute of Physics, Polish Academy of Sciences, Al. Lotnik6w 32/46, PL 02-668, Warsaw, Poland bDonetsk Physico- Technical Institute, Ukrainian Academy of Science. 340114 Donetsk, Ukraine ~Institute of lnorganic Chemistry Russian Academy of Science, Novosibirsk, Russia

Received 4 October 1996; received in revised form 10 March 1997; accepted 19 June 1997

Abstract The low-temperature structural phase transition of the Jahn-Teller type in a KDy(WO4) 2 single crystal has been studied by means of the ESR method. The ESR line width near the point of transition (Tsp, ~ 7 K) is shown to increase from 0.17 T up to a maximum value of 0.24 T and then it decreases to 0.19 T. The width of transition area is about 8 K. The symmetry of g-tensor does not change at the point of the phase transition while the values of the g-tensor components change considerably: g= = 3.13; g~ ~0; gy = 0.82 at T > Tspt; gz = 1.98; gx ~0; gy = 1.19 at T < T s p t. It is suggested that the symmetry of high- and low-temperature phases is identical. Keywords." KDy(WOJ2; ESR; Phase transition; Symmetry; Jahn-Teller effect

1. Introduction Recently, the crystals of double molybdates of rare-earth ions have attracted much attention and are investigated by various methods with regard to their interesting properties. The availability of rareearth ions with closely spaced energy levels in these c o m p o u n d s results in the occurrence of structural phase transitions connected with the manifestation of the cooperative Jahn-Teller effect. The magnetically ordered structure possessing a n u m b e r of features connected with low-dimensional interactions is observed at low temperature [-1-4]. Unlike double molybdates, information on c o m p o u n d s

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with a similar structure, namely, the rare-earth tungstanates is nearly absent. At present, some results of optical studies for KDy(WO4)2 ( K D y W ) are known. N e a r 10 K, the shifts of the optical absorption lines for D y 3+ as a result of the structural phase transition (SPT) were observed. The temperature of the S P T calculated within the framework of the molecular-field theory for two non-degenerate electronic states interacting with one-dimensional distortion is equal to 11.5 K [-5]. Investigation of the R a m a n spectrum in KDy(WO4)2 showed that some peculiarities of the Ran]an spectrum at low temperature (T < 1 0 K ) are connected with an electronic transition in the D y 3 + ion spectrum [6]. An a n o m alous increase of the dielectric constant in KDy(WO4)2 was observed near 10 K [7]. These effects were interpreted as the result of the cooperative Jahn-Teller phase transition.

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M,T. Borowiec et al. / Physica B 240 (1997) 21 25

In studies of the temperature dependence of the specific heat of a KDy(WO4)2 single crystal, a broad anomaly of the specific heat with a peak at Tsp t = 6.38 K has been found [8]. It should be noted that the observed Tsp t value differs from the value reported in papers [5 7]. The study of the Dy 3+ ion ground state at the phase transition which is connected with a manifestation of the cooperative Jahn Teller effect (CJTE) is of significant interest. Therefore, in the present work the features of the low-temperature phase transition in KDy(WO4)2 have been investigated by means of the ESR method.

2. Experimental and samples Potassium dysprosium tungstanate which belongs to a set of the rare-earth tungstanates is characterized by the spatial group C6h = C2/c [-9]. The elementary cell of KDy(WO4)2 contains four formulary units. The lattice constants have the following values: a = 8.05 A, b = 10.32A, c --- 7.52 A. The monoclinic angle is equal to/J = 94°13 '. Dy 3+ is surrounded by oxygen ions forming a distorted dodecahedron in which the two oxygen ions are spaced at a greater distance from the rare-earth ion than the other six oxygen ions. In this crystallographic structure, the oxygen and tungsten atoms are located at common positions. The dysprosium and potassium atoms have twofold rotation axes. The crystals were grown from the melt of potassium ditungstanate (KzW207) by two methods: the modified Czochralski method using an oriented microcrystal (in this case the crystal dimensions were about 20 x 20 x 60 mm) and by the spontaneous crystallization method with a slow temperature decrease (from 950°C with the rate of 3°/h). Using the second method, well-facetted single crystals with a maximum size of about 3 mm having a greenish-yellow color were produced. The crystals could be placed in the resonator of an ESR spectrometer without additional processing. The orientation of crystals was established by X-ray diffraction. Measurements of the ESR spectra were carried out in an X-band spectrometer with high-frequency modulation. The magnetic field was changed from o

o

o

0 to 1 T. The magnetic component of the highfrequency field was perpendicular to the external magnetic field. The rotation of the sample was realized in the resonator in one plane. For the study of the angular dependencies in the various planes the samples were cemented on the quartz holder. Variation of the temperature was obtained by cooled helium gas flow that permitted to vary temperature over a wide range from 4.2 to 300 K.

3. Experimental results and discussion The Dy 3+ ion has the electronic 4f 9 configuration. T h e 6H15/2 multiplet is split into eight Kramers doublets by the low-symmetry crystal field. An ESR spectrum consisting of one line of width 0.2 T was observed for the lowest spin-doublet state. The resonance line is observed both above and below the structural phase transition temperature. Fig. 1 illustrates the angular dependence of the resonance field in the AC plane in both phases. In the high-temperature phase (T > 12 K), the main direction of the g-factor lies in the AC plane and the components are as follows: 9max = 3.13, gr~in ~ 0 and g8 = 0.82 (along a direction of b axisC2). It should be noted that the ,(:/max direction deviates 20 ° from the crystallographic c-axis. The directions of the main axes of the g-tensor in the low-temperature phase (T = 4.2 K) are the same 1.0

0.8 t.-0.6

"I0,4

0-2_8(

I

I

I

I

-40

L

I

}

1

0

i

I

l

i

40

I

I

I

80

grad Fig. 1 Angular dependence of the ESR line of Dy 3+ in KDy(WO4)2 in the AC plane in the high- and low-temperature phase.

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M.22 Borowiec et al. / Physica B 240 (1997) 21-25

within the experimental error but the components of the g-tensor change significantly: gmax = 1.98, gmin ~ 0, gb --'~ 1.19. The behavior of the ESR line in magnetic fields is described by the operator of Zeeman energy with spin S - ½ H = gx fiHxSx + g),[3HySy + g=[3HzSz,

3.4 O 3.0

2.6

(1) 2.2

where the gmax-Z,gb-Y, gmin-X directions are taken as z-, y- and x-axis, respectively. The values of the g-factor satisfy the standard expression

I

1.8

I

i

I

)

I

I

(2) where 6; is the angle between the z-axis and the xy plane, and qo is the angle between the x and y-axis. The angular dependence of the g-factor in the zy plane in the low-temperature phase is shown in Fig. 2. In the transition region which has a sufficiently wide temperature interval (about 8 K), a smooth change of the g-factor with temperature is observed. This dependence, shown in Fig. 3, is well described by the following function: To)] + d,

(3)

I

I

I

10

I

I

I

I

3O

20

g2 = g2 COS2 6) jr_ g2 sin 2 6) COS2(/) _}_ g2 sin 2 6) sin 2 (p,

g = a tanh [½ b ( T -

~G

-r [K] Fig. 3 Temperature dependence of the 9-factor along the direction of its maximum value (z-axis) in the AC plane (20 from the c-axis).

0.25 0.23

I--- 0.21

o

"r-

o

o

0.19

0.17 0.15

0

J

I

I

I

[

I

[

I

I

[

20

10

I

I

I

30

T [K]

2.00

Fig. 4 Temperature dependence of the width of the ESR line obtained from the inflection points of absorption line. The permanent magnetic field is directed along ,qmax.

1.75

b 1.50

1.25 -50

0

50

100

150

200

grad Fig. 2 Angular dependence of the ,q-factor in the plane containing both C2-axis and the (4maxdirection in the AC plane (20': from the c-axis) in the low-temperature phase (T = 4.2 K). The points were determinated from the experiment. The solid line is the calculated curve (Eq. (2)).

where a = 0.58, b = 1 K - l , To = 7.6 K, d = 2.55. The parameters To and d characterize the inflection point of the g(T) curve. A similar dependence is observed along C2(b ). The change of ESR line width measured for the inflection points of the absorption line is of interest (Fig. 4). The line width is equal to 0.17 T in the region far from the transition and it increases to a maximum value of 0.24 T at 7 K. Further decrease of the temperature causes the line width to

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M.T. Borowiec et al. / Physica B 240 (1997) 21-25

narrow up to 0.19 T at 4.2 K. The line width dependence on temperature in the vicinity of transition is qualitatively similar to the change of the temperature dependence of the specific heat measured in the previous work [8]. The width of the ESR line is mainly determined by spin spin interactions of the Dy 3+ ions as well as the spread of the crystal-field parameters for the ground state. It is known that the spin-spin interactions are determined both by the magnetic dipole dipole interactions and the exchange interactions. We shall approximately estimate the contribution of dipole dipole interaction to the width of ESR line. As a detailed measurement of the KDy(WO4)2 structure has not yet been carried out at present, we shall take the coordinates of ions from the structural data for KGd(WO4)2 [10]. For double tungstanate the Dy (Gd) ions are placed in chains parallel to the a-axis, where the distance between neighboring ions is equal to 4 A. The following chain parallel to the first one is displaced along the b- and c-axis by a half-period. The Dy (Gd) ions placed in neighboring chains are located in the planes parallel to bc plane and are shifted relative to each other by 0.5a. For a magnetic field Ho directed along the z (gmax) axis, the line connecting ions in the chain parallel to an axis will be located at an angle of 70 ° and the line connecting ions in different chains will be located at an angle of 48 ° with the direction of the permanent magnetic field. The energy of the magnetic dipole-dipole interaction between two ions at an angle of O with the direction of magnetic field equals E = 92 fi2(1 - 3cos 2 0 ) / R 3.

(4)

For neighboring ions located along the a-axis, the splitting A of a pair of spectral lines is equal to 0.03 T and for ions located in the neighboring chains A = 0.012 T. According to data in Ref. [11] the splitting in a linear chain of identical ions approximately characterizes the pair interaction multiplied by a factor of 2. Thus, the broadening of the ESR line connected with magnetic dipole-dipole interaction is equal to 0.08 T. If we take into account the fact that the ESR line width

of non-interacting rare-earth ions in diluted crystals does not exceed a value of 0.01 T it is possible to infer that the remaining part of the line width ( ~0.08 T) is determined by the exchange interaction between the Dy 3+ ions. A more detailed consideration of the interaction mechanisms can be carried out in studies of pair spectra in a diluted KY(WO4)2 + Dy 3+ single crystal. The significant broadening of absorption line during the process of the phase transition is most probably connected with the disorder of the crystal lattice that causes a spread of parameters of crystal field acting on the rare-earth ion. Both the absence of jumps of the spectrum parameters and the large temperature interval of the SPT confirm the assumption of second-order character of the phase transition. The results of the present ESR-study give no possibility of making a single-valued conclusion about symmetry of the crystal lattice in the lowtemperature phase. However, both the absence of inequivalent positions of rare-earth ions and the preservation of the directions of the main axes of the g-tensor testify in favor of a structural phase transition in which the symmetry of the initial hightemperature phase is not disrupted and a smooth distortion of the lattice in some direction occurs. As an example, one may mention the data on the low-temperature transition in cerium etylesulfate having the C3h symmetry [12]. In this compound, the energy distance between the ground and first excited doublets changes smoothly from 6.7 to 3 c m - 1 without change of symmetry in the temperature range of 2.5-10 K. In the present paper, the low-temperature second-order structural phase transition of KDy(WO4)2 has been investigated by ESR on the Dy 3 + ions. The components of the g-tensor change smoothly without space-orientation change in a wide temperature range near the structural phase transition (4.2 12 K). The observed behavior of absorption line in the process of phase transition is connected with the disorder of the crystal lattice. The absence of magnetically inequivalent positions of paramagnetic ions in both phases (above and below the structural phase transition) makes this material rather convenient for further studies of magnetic properties of both concentrated and

IVLT~ Borowiec et al. / Physica B 240 (1997) 21-25

diluted (by diamagnetic ions) crystals (for example, KY(WO4)2 4- rare-earth ion).

Acknowledgements This work was supported in part by the Polish State Committee on Science (KBN) (Project No. 2 P03B 071 08). References 1-1] V.I. Kut'ko, M.1. Kobets, V.A. Pashchenko, E.N. Khats'ko, Low Temp. Phys. 21 (1995) 345. 1-2] P. Stefanyi, A. Feher, A. Orendacova, J. Phys. C: Condens. Matter. 1 (1989) 7529. [3] P. Stefanyi, A. Feher, Physica B 165 (1990) 465.

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[4] I.M. Vitebsky, S.V. Zherlitsin, A.U. Zviagin, A.A. Stepanov, V.D. Fil', Soy. J. Low Temp. Phys. 12 (1986) 1108. I-5] I.V. Skorobogatova, A.I. Zviagin, Sov. J. Low Temp. Phys. 4 (1978) 800. I-6] Yu.A. Popkov, V.I. Fomin, L.N. Pelikh, Sov. J. Low Temp. Phys. 8 (1982) 1210. [7] L.N. Pelikh, A.A. Gurskas, Sov. Phys. solid state 21 (1979) 128. 1-8] M.T. Borowiec, V. Dyakonov, A. J~drzejczak, V. Markovich, H. Szymczak, Phys. Solid State 38 (1996) 1229. [9] P.V. Klevtsov, L.P. Kozeeva, Soy. Phys. Dokl. 14 (1969) 185. El0] Yu.K.Vishakas, I.V.Mochalov, A.V.Mikhailov, R.F.Klevtsova, A.V.Lyubimov, Lithua. Physical Collection 28 (1988) 224. 1-11] I.M. Krygin, A.M. Prokhorov, JETP 92 (1987) 549, Sov. Phys. Solid State 29 (1987) 368. [12] S.N. Lukin, A.M. Prokhorov, O.P. Teslia, Soy. Phys. JETP 73 (1991) 1072.