Magnetic properties of vitreous and crystalline PbV2O6

Journal of Non-Crystalline Solids 84 (1986) 329-336 North-Holland, Amsterdam

329

MAGNETIC PROPERTIES OF VITREOUS AND CRYSTALLINE PbV206 E. AGOSTINELLI *, P. FILACI *, D. FIOKANI *, A. M O N T E N E R O ** and M. BETTINELLI ÷ * 1TSE, Area della Ricerca di Roma, CNR, CP 10, 00016 Monterotondo Stazione, Italy ** lstituto di Strutturistica Chimica, Via Massimo D'Azeglio 85, Parma, Italy + Istituto di Chimica Generale, Padova, Italy

The magnetic properties of the semiconducting system PbV206 have been investigated on the vitreous as well as on the crystalline modification obtained from a very fast and a very slow cooling respectively. The results of magnetic susceptibility measurements, performed in the temperature range 4.2 ~< T~< 250 K, are reported and compared. The differences between the observed magnetic behaviours are attributed to the different j u m p i n g rates of the 3d electron for V 4÷ to V 5+ ions in the vitreous and crystalline samples. The magnetic properties of the vitreous phase are well described in terms of a crystal field model for Iocalised electrons, which on the other hand is inadequate for the crystalline phase, because of the higher electron mo[gility. These results are in agreement with a previous EPR study.

1. Introduction Glasses containing transition metal oxides are a subject of continuous interest because of the possible applications due to their semiconducting properties [1-3]. It is well known that the electron conductivity in this kind of glasses is due to a thermally activated hopping process of d electrons between ions in different valence states. Glasses based on V205 are known to have both V 4÷ and V 5+ ions present. The conduction process has been described as the motion of the unpaired 3d electron from a V 4÷ (3d 1) site to a V 5÷ site [4-5]. This unpaired electron induces a polarization of the lattice around it and the charge carrier is a small polaron [6-9]. The equimolar system P b O - V 2 0 ~ was prepared, characterized and studied previously by electron spin resonance [10]. Different phases are obtained depending on the cooling rate and they are characterised by different electric conductivity. The material can be obtained from the melt either as vitreous phase or as polycrystalline lead metavanadate (PbV206) or as two different mixtures containing both the vitreous phase and the a-PbV207 or ~-PbV207 crystalline phases [10]. In these materials the V4+/Vtot ratio is nearly constant and very low in value ( - 0.05). In this paper we report a low-temperature magnetic study on the two homogeneous phases, the vitreous and the polycrystalline (PbV206). The comparison between the two different magnetic behaviours is also reported and discussed. 0022-3093/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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E. Agostinelli et al. / Vitreous and crystalline PbV206

2. Experimental The vitreous and polycrystalline PbV206 samples were prepared using equimolar amounts of PbO and V205 (Carlo Erba, reagent grade) by melting at T = 800°C and by subsequent cooling down [10]. The vitreous phase was obtained by rapid quenching on a graphite support previously cooled with liquid nitrogen. The polycrystalline phase was instead obtained by very slow cooling. The susceptibility measurements were performed by a Faraday balance (Oxford Instruments cryogenic system) in the temperature range 4.2 ~< T ~< 250 K. The magnetic field H Z and the field gradient 3H/3z were generated by two different superconducting NbTi coils, allowing both H Z and 3H/3z to be set independently of each other. The main coil and gradient coils could be energized to a maximum of 70 kOe and 1 k O e / c m respectively. We use a main field H = 27 kOe and the maximum gradient field. The changes in weight were measured by an electronically controlled vacuum microbalance (Sartorius) with a resolution of 1 #g. The sample was placed inside a quarz sphere suspended by a fine silica wire from the balance. The temperature was measured with a gold ( + 0.03%) - Fe versus chromel thermocouple. The main field was calibrated by using HgCo(CNS)4. The accuracy of our measurements is 5 parts per 103.

3. Results and discussion

3.1. Vitreous Phase The static magnetic susceptibility as X-~ vs T plots for both vitreous and crystalline samples are reported in fig. 1. First let us focus our attention on the virtreous sample. A simple Curie-Weiss law is not followed. The inverse of the susceptibility shows instead a continuous non-linear increase with increasing temperature. The thermal behaviour of the susceptibility should reflect a temperature dependence of the magnetic moment of V 4÷ ions, due to the presence of energy levels thermally accessible, whose population changes with temperature. Structural data on the vitreous phase are not yet available (the analysis of the X-ray radial distribution function is in progress) but the EPR spectrum [10] indicates that V 4÷ ions occupy tetragonally distorted octahedral sites, in analogy with the local environment of the crystalline PbV206 phase, whose structure is reported in ref. [11]. In a crystal field model the ground state 2T2g for a d ~ configuration in octahedral symmetry is splitted into three doubly degenerated levels, for the combined perturbation due to the axial field and the spin-orbit coupling. The application of a magnetic field removes the residual degeneracy. The appropriate Hamiltonian is ()fr0 + )F')~b = E ~b, where ~ o is the Hamiltonian for the system as the cubic crystal field is concerned and Jff' = XL. S + l~'ax, which represents the part of the Hamiltonian for the

E. Agostinelli et aL / Vitreous and crystalline PbV, O~

331

800 •

[ I

•

600

•

o

o

0

T

0

E ~ . 400

0 0 0 0 0

o o

200

C , 0

I 100

,

I 200

T(K) Fig. 1. X -1 vs T plots for the vitreous ( O ) and crystalline ( e ) modification.

pertubation by spin-orbit coupling ( ~ L - S ) and the axial crystal field (K~). The energy of each level, in the absence of a magnetic field, is reported in table 1. The separation between the energy levels depends on the ratio o = A / M where A indicates the energy of the axial distortion and ~. the spin-orbit coupling. Second order effects, coming from contributions of excited states are neglected. Because the system is anisotropic the magnetic moment is given by .=

+

The theoretically predicted temperature dependence of the magnetic moment [12] was compared with our experimental data. In fig. 2 some curves calculated for different values of v, including v = 0 (corresponding to the undistorted octahedral case), are reported. Increasing the za/k ratio the thermal variation of the magnetic moment is progressively reduced. A satisfac-

Table 1 Energies for the 2T2 term after perturbation by spin-orbit coupling and tetragonal crystal field component

E+=x(o-'2) Eo = 2~k[(2 ~ 1 + U ) ~ - ( U 2 + U q- 9 ) 1 / 2 ] E

i 1 + v)-(v 2 + v + ])'/21 = ~X[(2

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E. Agostinelli et al.

/ Vitreous and crystalline PbV20 ~

v=3

1.5

/

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1.0

0.5 I

0

50

J

100

150

200

T(K)

Fig. 2. Temperature dependence of the atomic effective magnetic moment #at for the vitreous ( O ) and crystalline modification (e). The solid curves represent the theoretical curves calculated for different v ( = A / h ) values, assuming a crystal field model for an axially distorted octahedral symmetry. K = 1.0; ~, = 170 c m - 1.

tory agreement between calculated and experimental moments was obtained for v = 1.4, )~ = 170 cm -] ()~ = 250 cm - I for the free ion) and k (the orbital reduction factor) = 1.0. The reduction of the 2~ value with respect to the free ion value is due to the covalent character of the V - O bond. The magnetic properties of the vitreous phase are therefore well described by a crystal field model for localised electrons. Magnetic interactions between V 4+ are very weak in such a magnetically diluted system ( V 4 + / V t o t ~ 0 . 0 5 ) . Our results are well consistent with the EPR spectrum, which shows a well resolved hyperfine structure, due to the interaction between a 3d electron (S = 1/2) and nuclear magnetic moment ( I = 7 / 2 ) for the V 51 nucleus. This indicates that the unpaired 3d electron is Iocalised around a single V 51 nucleus. The hopping process therefore must be much smaller than the hyperfine parameters in frequency units ( - 1 5 0 MHz). Furthermore, it was observed that the EPR spectrum does not change from 150 K up to 380 K. At the latter temperature the spectrum becomes unresolved suggesting a phase transformation which is irreversible. The presence of the well resolved hyperfine structure in the temperature range 150 < T < 380 K indicates that the energy barrier for the hopping W is definitely higher than K T (270 cm-1 for the highest temperature) (from conducibility measurements: W = 0.448 eV, i.e. 3600 cm-1). The high value of W is related to the disordered nature of the glass for which the activation energy W is the sum of two contributions: W = 1 / 2 W D + W h

E. Agostinelli et al. / Vitreous and crystalline PbVeO6

333

[6,13]. The first term W o is the mean energy difference between adjacent vanadium sites, characteristic of the glass state, and the second one, Wh, is the activation energy for the hopping process of the polarons between two identical sites. The jumping frequency of the charge carriers is proportional to e x p ( - W / K T ) and therefore the high value of W freezes the hopping process leading to an electron localisation. This is in agreement with the temperature dependence of the susceptibility, which indicates the presence of isolated V 4÷ ions. 3.2. Crystalline phase

Completely different magnetic behaviour was observed for the PbV206 crystalline phase. As shown in the X-lVS T plot the susceptibility presents a pronounced variation at low temperature, while a very weak temperature dependence is observed in the high temperature range. Furthermore the susceptibility is much weaker than that of the vitreous phase. The difference between the magnetic properties of the vitreous and of the crystalline phase are clearly evidenced by the comparison of the thermal variation of the magnetic moments. There are two types of vanadium ions bonded to six oxygen atoms in the structure of PbV206 [11]; they form two sets of translationally equivalent distorted octahedra. We then tried to fit the thermal variation of the magnetic moment by using a crystal field model, as done for the vitreous phase, assuming an axially distorted octahedral symmetry. The temperature dependence of the magnetic moment cannot be fitted for any u, k, 2~ set values. Given the presence of two types of V 4÷ ions for which the axial distortion is slightly different, the comparison with the theoretical curves calculated for a unique set of parameters is clearly inadequate. However, a crystal field model for Iocalised electrons cannot in any way describe the thermal variation of the magnetic moment, in particular in the high temperature range. The EPR spectrum is also very different with respect to that of the vitreous phase [10]. The spectrum, which does not change with temperature from room temperature down to 150 K, shows a superposition of two lines of different width, but approximately centered at the same g value. (1.932). One of these lines is strongly narrowed by exchange while the other shows a large, not well resolved hyperfine pattern. The presence of these two lines was explained assuming the existence of two different sites, giving two different energy barriers W for the hopping process. The behaviour of the susceptibility will be the sum of the two different magnetic contributions. At the site with a higher activation energy, i.e. a lower jumping frequency, the electrons are more localised and they are responsible of the large resolved hyperfine structure and should determine the marked dependence of the susceptibility in the low temperature range. On the other hand the electrons leaving from sites with lower activation energy are more delocalised because of the higher hopping frequency. The hopping process is responsible for the exchange narrowed line.

E. Agostinelli et al, / Vitreous and crystalline PbV20~

334

y14.0

0.08

/

/o

0.06

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/

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/ .,6

/

/

/

/

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/ /

rn

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Fig. 3. Field-dependent magnetization measurements for the vitreous (O) and crystalline modification ( A O, A) at different temperatures (K).

54.8 K

.,.-: t'~

0.01

1

3

H (koe / T ,-2--,

Fig. 4. M vs H / T c u r v e s for the crystalline modification.

5

E. AgostineUi et al. / Vitreous and crystalline PbV, O6

335

The higher electron mobility in the crystalline phase with respect to the vitreous one should be responsible for the lower value of the susceptibility and of its smooth variation with the temperture in the high temperature range. As this line remains unchanged in the temperature range 150 < T < 300 K, the activation energy for the electrons with higher mobility is W < KT (105 c m - 1 for the lowest temperature). Isothermal magnetization measurements were performed as a function of the field on both the crystalline and the vitreous sample (fig. 3). The magnetization curves show a weak curvature at low temperature. For the crystalline sample the measurements were performed at three different temperatures and the data are reported also in the form of M vs H / T plots (fig. 4). The absence of superposition of the different curves, expected for a pure paramagnetic behaviour, confirms the inadequacy of a description in terms of localised electrons for the crystalline phase.

4. Conclusions The magnetic properties of vitreous and crystalline PbV206 samples have been studied and compared by the analysis of the susceptibility measurements, performed down to 4.2 K. A crystal field model accounts for the features of the magnetic behaviour of the vitreous phase, indicating that the 3d 1 electron is localised on the V 4+ nucleus. This is in agreement with the well resolved hyperfine structure exhibited by the EPR spectrum, as found in other V 4÷ diluted glasses based on V205 (for instance vanadium phosphate glasses [2]). It is known that the structureal disorder leads to an Anderson localisation [14] of the charge carriers, the jumping frequency being much smaller in the glass than in the crystalline phase. In the amorphous V205 the jumping frequency was found ten times smaller than in the crystalline oxide [15]. For the same reasons it was not possible for the crystalline phase to obtain agreement between crystal field model and experiment, because of the appreciable electron delocalization. This is confirmed by the EPR spectrum where the hopping process between adjacent sites gives an exchange narrowed line, together with a broad, not well resolved hyperfine structure.

References [1] [2] [3] [4] [5] [6] [7]

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[8] M. Sayer, A.M. Mansingh, J.Y. Reyes and G. Rosenblatt, J. Appl. Phys. 42 (1971) 2857. [9] J. Haemers, E. Baetens and J. Vennik, Phys. Star. Sol. (a) 20 (1973) 381. [10] F. Momo, A. Sotgiu, E. Baiocchi, M. Bettinelli and A. Montenero, J. Mater. Sci. 17 (1982) 3221. [11] B.D. Jordan and C. Calvo, Can. J. Chem. 52 (1974) 2701. [12] F.E. Mabbs and D.J. Machin, Magnetism and Transition Metal Complexes (Chapman and Hall, London, 1973). [13] G.N. Greaves, J. Non-Cryst. Solids 11 (1973) 427. [14] P.W. Anderson, Phys. Rev. 109 (1958) 1492. [15] L. Rivoalen, A. Revcolevschi, J. Livage and R. Collongues, J. Non-Cryst. Solids 21 (1976) 171.