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A study on the magnetic susceptibilities and optical absorption spectra on single crystals of Gd(III) pyrogermanate
78
Journal of Magnetism and Magnetic Materials 86 (1990) 78-84 North-Holland
A STUDY ON THE MAGNETIC SUSCEPTIBILITIES AND OPTICAL ABSORPTION S P E C T R A O N S I N G L E C R Y S T A L S O F Gd(III) P Y R O G E R M A N A T E T. K U N D U , D. G H O S H Solid State Physics Department, Indian Association for the Cultivation of Science, Jadavpur, Calcutta-700 032, India
and B.M. W A N K L Y N Clarendon Laboratory, University of Oxford, UK
Received 3 April 1989; in revised form 1 August 1989
The paper reports for the first time the experimental results of the measurements of magnetic susceptibilities(K± and Kll) and their anisotropy (AK) between 300 and 21.8 K and the optical absorption spectra (UV region) at 12.5 K on single crystals of gadolinium pyrogermanate (GdPG). The anisotropy, which is only 211 × 10-6 emu/mol at room temperature and increases by two orders of magnitude at 21 K, is predominantly a crystal field (CF) effect on the SS7/2 ground term, through higher order perturbations. Interpretation of the observed magnetic data was carried out by considering a conventional spin Hamiltonian (Hs) to derive expressions for K_ and KII in terms of four effective crystal field parameters (ECFP). The values of ECFP were varied to obtain a very close fitting between the theoretical and experimental values of K j , KH, AK and K. The splitting of the SST/2term corresponding to these values of ECFP was found to be large, which suggests a strong CF effect in GdPG, as also observed in other RPG crystal studied earlier. The thermal characteristics of the magnetic anisotropy below 30 K deviate by about 5% which could not be explained by CF effects alone. A series expansion method was adopted to analyse the results of K± and Kll below 30 K, however the corresponding coefficient B2~ and B3a were observed to be unusually high indicating the presence of CF effect even in this temperature region. The Schottky specific heat, Csch, between 300 and 21 K for GdPG has been calculated and this shows a maximum at Trnax = 17 K.
I. Introduction The rare earth p y r o g e r m a n a t e (R2GezO 7 or R P G ) c o m p o u n d s are a new class of crystals in which the rare earth a t o m has a u n i q u e Dsh site symmetry, rarely f o u n d in a 4f n system. Moreover, these c o m p o u n d s are c o n c e n t r a t e d in the rare earth ions [1]. O n a c c o u n t of these facts, crystals of R P G are expected to exhibit interesting magnetic a n d magneto-optical properties at low temperatures. The p y r o g e r m a n a t e crystals form an isomorphous series having high space group symmetry, i.e., P41212, so that the magnetic a n d optical properties of single crystals of these comp o u n d s can be c o n v e n i e n t l y a n d accurately studied a n d interpreted. Very little work has b e e n reported on these R P G , being limited to their struct-
ural investigations [2,3], study of the optical absorption spectra of D y 3÷ a n d Er 3÷ [4] a n d the magnetic susceptibilities of T m 3÷ [5]. Preliminary studies have shown that some of these R P G , viz. Tb, Dy, H o a n d Er, exhibit magnetic ordering at (2.05 + 0.05), (2.15 + 0.05), (1.45 + 0.05) a n d (1.15 +__0.05) K, respectively [1]. However, it m a y be m e n t i o n e d here that in rare earth systems, above liquid h y d r o g e n temperatures, the magnetic susceptibilities, especially their anisotropic properties, are very sensitively d e p e n d e n t o n crystal field (CF) effects caused b y the nearest a n i o n s surr o u n d i n g the rare earth ion. I n fact, magnetic a n i s o t r o p y is a very sensitive p r o b e for studying the crystal field a n d other effects, which influence different physical properties involving the paramagnetic atomic site [6,7]. F u r t h e r m o r e , very small
0304-8853/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
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T. Kundu et al. / Susceptibility and optical absorption of Gd single crystal
values of magnetic anisotropy can be measured very accurately by the torque method as discussed in detail in our previous work on some rare earth compounds [7-9]. The present work on gadolinium pyrogermanate (GdPG) was undertaken because it belongs to this new class of magnetic insulators and also because the small splittings of the ground term of half-filled shells have arisen considerable interest over the last few decades. The ground term for Gd 3+ is 857/2, the splittings of which can only arise due to departures from Russel-Saunders coupling or crystal field mixing of states of different class. The theory of the gadolinium ion in a crystalline environment therefore is very different in character from other rare earth ions and to first order the ground term cannot in principle be split by crystal field alone. Higher order perturbations, involving the simultaneous action of the crystalline field and either the spin-orbit or spin-spin coupling, remove the spin degenaracy of the ground, S = 7/2, term and this in turn makes the magnetic susceptibilities weakly anisotropic around room temperature. This anisotropy increases with lowering the temperature. The rate however, depends on the nature of the eigenvalues and eigenfunctions corresponding to the multiplet splitting of the 8S7/2 term. Thus, by accurately measuring the small magnetic anisotropy, K L -Kit, of G d P G crystals over a wide range of temperature (300-21 K), it was expected to determine very accurately the splitting of the 8S7/2 term from parametrial fitting.
2. Experimental results 2.1. Magnetic susceptibilities and anisotropies
Single crystals of GdzGe207 were grown by sintering the initial components and using P b O GeO2 as flux [1]. The crystals were practically colourless and grew as thin platelets. The crystal platelets were transparent and the plane (bc) was optically isotropic under a polarising microscope. Detailed investigation of the crystallographic structure performed on Gd2Ge207 revealed considerable deviation from other R P G crystals [3]. A
x
0 oxygen • Er z
Fig. 1. Projection of structure for: (a) ErPG along the c-axis [2]; (b) GdPG along the a-axis [3].
unit cell of GdzGe20 7 contains twelve independent ions of Gd 3+ of which nine are surrounded by seven oxygen ions forming a deformed bipyramidal structure having a common pentagonal base and three Gd 3+ ions have similar bipyramidal environment with eight oxygen ions and a common hexagonal base. The axis of the pyramids or the tetragonal axis nearly coincided with the crystalline a-axis (which is the c-axis for other RPG) shown in fig. 1. The investigated structure of gadolinium in addition contains a triortho group Ge3Oao and an isolated tetrahedron GeO4 as against the other R P G which are of much higher symmetry and contain the regular Ge207 group. Structural investigations reveal that G d P G is triclinic (a = 18.5 ,&, b = c = 6.8 ,~ and a = fl = ), = 90 ° _+ 2.5 o) with space group P1 or P1. However, magnetic measurements along different axes show that the principal magnetic ellipsoid is nearly uniaxial (within 1%) about the a-axis (referred as Kjl axis) and the anisotropy in the bc plane, perpendicular to the a-axis was negligble. Single crystals chosen for magnetic measurements weighed between 25 and 26 mg. The experimental procedure involved very accurate measurement of the crystalline anisotropy, X c - X a ( = K ± - K r l in the present case) between
T. Kundu et al. / Susceptibility and optical absorption of Gd single crystal
80
O.OZ 40
100
T ( K ) 200
300
0.03 30
\ 0~
I
0.01
o 7" ..... J
i
100
T(K)
3OO
200
Fig. 2. Shows theoretical (solid line) and the experimental results of AK (e) and 1/K± (©) for GdPG. Calculated values of AK of GdES ( - - - - - ) is also shown. Inset: Calculated (solid line) and experimental thermal variation of TKII.
300 and 21 K. In order to measure K 1 -KII, each crystal was freely suspended along the b axis by means of fine quartz fibre in a uniform horizontal magnetic field. Under this condition, the greater of the two principal susceptibility tensors in the horizontal plane, i.e., K_ or Kll sets along the field direction and the torque experienced by the fibre is proportional to the anisotropy, K± -Kll. Details of measurement have been reported tJ
t'~
t.O
~r OO
o
r
a
elsewhere [11,12]. The value of the magnetic anisotropy was found to be 211.73 × 10 -6 e m u / m o l at room temperature which increased on cooling and attained the value of 2.5096 × 10 -2 e m u / m o l at 21.8 K (fig. 2). On the other hand magnetic anisotropy measurements in the bc plane showed only a small increase at the lowest temperature and was still negligible compared to the value of K ± - K l l at that temperature. In G d P G it was observed that K± was larger than KIt over the entire temperature range and K_~-KII = AK increased considerably on lowering the temperature (fig. 2). Hence in order to obtain better accuracy the thermal characteristic of K± was measured in an electrodynamically controlled Curie-type balance using the Faraday method [13]. From the measurement of K± and AK, the thermal variation of K = ( 2 K ± + K i l ) / 3 and KII were calculated. The results of AK, TKII and l / K ± are shown in fig. 2.
2.2. Spectroscopic studies The spectra of Gd 3+ are characterised by absence of spectral lines in the visible region but there are sharp lines in the UV region due to the presence of excited t e r m s 6p7/2, 6p5/2, 6p3/2 [14]. The polarised optical absorption (UV) spectra of G d P G at 12.5 K was studied for the first time in a high resolution Carl Zeiss Spectrograph (PGS 2), having a dispersion of 3.5 ,~/mm. The transitions due to the 6p7/2, 6P5/2 and 61)3/2 multiplets were recorded for estimating the CF splitting of the
0-4
9~ t"O
/
20
40
T(K)
60
80
Fig. 3. (a) Polarised absorption spectra with incident light along the a-axis in the UV region at 12.5 K; (b) thermal variation of C~h.
T. Kundu et al. / Susceptibility and optical absorption of Gd single crystal
same. Single crystals of Gd2Ge20 7 were directly fixed to the slit of the crystal holder using conducting grease. The crystal holder was in thermal contact with the cold tip of the closed cycle helium cryocooler (Displex CS202). The absorption lines occurring in the UV range were recorded on thin photographic plates (Illford 6ASA, 9DIN no. 30) which were scanned by a sensitive micro-photometric arrangement incorporating sensitive diodes (LDR), the output of which was amplified and fed to an X Y recorder (Rikadenki RW 201). Fig. 3a shows the recorded absorption spectra o f 6p7/2, 6p5/2, 6 p 3 / 2 multiplets with polarised light incident along the a axis. Due to the shape (and hardness as well) of the crystal it was not possible to record the spectra with the incident polarised light perpendicular to the a axis. Consequently it was not possible to determine the ground term splitting by the usual method of applying selection rules to the different transitions between the ground and excited multiplets in the spectra for different polarisation directions [14]. However, the usual CF pattern for 6pv/2, 6p5/2 and 6P3/2 transition of Gd 3+ compounds were obtained (table 2), and the CF splitting in the PG system was found to be the largest compared to the chloride and ethyl sulphate [14].
3. Discussion
In gadolinium compounds the first excited state lies about 32000 cm -1 above the ground term 8S7/2, hence the magnetic susceptibility and anisotropy, observed in some Gd 3+ compounds is completely a ground term phenomenon. As mentioned earlier, crystal field alone in the first order cannot split the SS7/2 term and theory would predict g = 2. However, EPR studies on several Gd salts have shown a complicated resonance pattern [15], suggesting a small splitting of the S-state similar to that found in Mn 2+ (S-state) compounds [16]. In order to explain the small splitting of the S-state ions, a spin-Hamiltonian having the same symmetry as the crystal field was considered successfully to explain the EPR resonance lines [17]. A spin Hamiltonian method [18] is generally applied to explain magnetic susceptibilities and
81
their anisotropies for 3d n complexes which have a ground orbital singlet or a doublet term [19]. In order to explain the magnetic anisotropy in GdPG, a spin Hamiltonian H s corresponding to Dsh symmetry was considered, as was done for explaining EPR results of other Gd 3÷ compounds of C3h symmetry
H s = gjflH. S + B°(3S~ - S ( S + 1)} + B°(35S 4 - [30S(S + 1 ) - 251Sf
- 6 S ( S + 1 ) + 3 S 2 ( S + 1) 2} + B6°{231S6 - 105SJ[3S(S + 1 ) - 7]
+$2[105S2(S + 1) 2 - 525S(S + 1) + 294] - 5 S 3 ( S + 1) 3 + 40S2(S + 1) 2 5
.
- 6 0 S ( S + 1)} + Bd{(S x + ,Sy)
5
+ ( S~ - iSy )5} /2, in which 3B° = b °, 60B ° = b°, 1260B° = bg and 275B65 = b65,and b °, b°, bg and b65 are the effective crystal field parameters (ECFP). On application of the above Hamiltonian the diagonal and off-diagonal matrix elements of the matrices spanned by J = _+7/2 were calculated and the matrices were diagonalised to obtain the energy eigenvalues E ° and the corresponding eigenfunctions for the ground multiplet levels. The magnetic perturbation was next applied on these levels to obtain expressions for the magnetic susceptibilities K j_ and KII using the Van Vleck [191 expression
Kj = ( g~Nflz/z) E {[( E,0) ) / k T - 2E/{2)] i
× exp(-Ei
(0)/ k T ) } ,
where E[ m, Ei°) and Ei~2) are, respectively, the zeroth, first and second order perturbed Zeeman energies and the rest have their usual meanings. The principal_ magnetic susceptibilities K . , Kij and finally K = ½(2K 1 + K . ) were calculated separately in terms of the effective crystal field parameters b °, b4°, /96o and b65. In order to fit the observed magnetic susceptibilities and anisotropy data, the values of ECFP
82
72 Kundu et al. / Susceptibility and optical absorption of Gd single crystal
Table 1 Crystal field energy levels (in cm -1) of Ss7/2 in Gd2Ge20 7. ECFP (in cm-1): 6o=0.27, b ° = - 1 . 5 6 , b6°=0.126, b65= + 11.00 Energy levels
Wavefunctions
0 1.058 21.540 27.082 50.340
1.000017/2, _+0.8759 [7/2, - 0.707117/2, 0.482517/2, 0.7071 [7/2,
_+1/2) +_7/2) - 5/2) +_7/2) - 5/2)
290.482517/2, -T-3/2) + 0.707117/2,5/2 ) + 0.875917/2, -T-3/2) +0.7071 [7/2, 5/2)
were varied by small amounts using computer programming. During the process of such variations a number of interesting facts were revealed. (a) The calculated values of AK at room temperature depended very sensitively on the values of b ° so that the latter could be determined very accurately. (b) The rate of increase of AK on cooling could be matched by adjusting the other parameters, of which b4° was the most effective one. (c) At low temperatures i.e., below 80 K the value of AK could be varied by small amounts by adjusting the values of b° and b65. (d) The relative spacing and composition of the eigenvalues and eigenfunctions, respectively, of the components of the ground multiplet depended sensitively on the values of the ECFP. The best set of parameters obtained after fitting the calculated values of K ± , Kit, AK and K simultaneously with the observed ones are given in table 1. The calculated and observed values of K . and Kll were fitted within 1%. The corresponding energy eigenvalues and eigenfunctions are also given therein. The room temperature anisotropy (expressed in 10 6 emu/mol) in G d P G is 211.73 which is large compared to the observed value of 52 in gadolinium sulphate octahydrate [20] or that of the calculated value of 11.4 in GdES obtained on substitution of the values of ECFP reported from EPR studies [15] (fig. 2). This explains the high value of b° in G d P G compared to the other two salts (respective values of b ° being 2700, 1260 and 200.8, all expressed in 10 -4 cm-~). It may be remarked here that in pyrogermanate (PG) sys-
terns studied earlier e.g., Er, Dy and Tm [4,5], the value of the CF parameter B ° was large compared to other compounds for each of these rare earths [14] suggesting a stronger crystal field effect in PG systems. It was observed that for the high values of b2° and b4°, determined by close fitting of the thermal characteristic of AK, the effect of b6° and b65 were negligible (even when changed by two orders). Similarly for GdES (having C3h symmetry) effect of b6° and b66 were found to be small. It is to be borne in mind that unlike all RPG, G d P G contains two different polyhedra (fig. 1), some in penta coordination and others in hexa coordination (as in GdES) in the ratio of 3"1. We had examined the effect of such a mixture assuming that the anisotropy for the two different polyhedra are not very different. Since the contribution to 2xK for each type of polyhedra are not known separately, this approximation had to be made in order to obtain a meaningful interpretation of the results. Furthermore, since the contributions of b6° and b~ or b° and b6 were very small in G d P G or GdES, respectively, the calculated results are not affected appreciably if Dsh site is considered only. Inspection of table 1 shows that the ground multiplet 8S7/2 is decomposed into 5 levels, 2 spin singlets and 3 doublets; the first excited doublet lies very close (1.058 cm -1) to the lowest doublet level. The total splitting AE 1 of 8S7/2 in the present case is 50.34 cm-a which is large corresponding to other Gd 3+ salts (see table 2). It is to be noted that EPR experiments on systems belonging to 4f 7 configuration, viz. Gd 3+, in different crystalline host lattices of ethyl sulphates [15], sulphates [21], double nitrates, trichlorides [22], hydrated trichlorides [23] as well as in CaF z, ThO 2 [24], Hapi crystals [25] and other oxide host lattices like CaO and SrO [26] have revealed a small splitting of the SS7/2 term lying between 0.1 and 10 cm -I [27]. It is to be noted further that the ground term splitting of PG systems studied earlier is large. For example, T m P G exhibited a total ground t e r m ( 3 H 6 ) splitting of 1149.58 cm -~ [5] as against the corresponding splitting of only 307.3 cm-1 in TmES [28]. Inspection of fig. 2 shows that the calculated and observed values of AK deviated by 5% below 30 K. It is relevant to mention here that EPR
T. Kundu et al. / Susceptibility and optical absorption of Gd single crystal
Table 2 Observed spectra of some Gd 3+ salts (in cm -1) State 6P7/z
A E 2 a)
6P5/2
A E 3 a)
6P5/2 AE4 a)
GdPG b) (T=12.5 K) 31874.7 31937.5 31993.0 32056.3 181.60
GdCI3"6H20 c) (T=l.8 K) 32059.6 32091.7 32123.3 32147.6 88.00
GdESc) (T=1.7 K) 32136.07 32135.85 32163.63 32164.56 28.49
32494.5 32559.9 32617.6 123.10
32660.4 32699.9 32740.9 80.50
32737.73 32757.85 32760.18 22.45
33107.1 33170.9 63.80
33254.9 33290.3 35.40
-
a) Multiplet width; b) present work; c) Dieke (1968).
Positions of CF components for GdPG are shown in fig. 3a.
results of some G d 3+ crystals could only be explained by using two different sets of E C F P for room temperature and nitrogen temperatures [29]. The said deviation below 30 K in G d P G m a y be due to such variations or due to high temperature effect of magnetic ordering occurring at a lower temperature as in Gd(OH)3. We attempted to analyse the low temperature results between 20 and 30 K using high temperature series sum method, as in Gd(OH)3, in which case, however, low temperature experimental results of K± and KII were available between 20 and 1.4 K [30]. For G d P G we found that K H= 7 . 3 8 / ( T + 3.10),
K± = 7 . 4 0 / ( T + 1.48).
Hence using the procedure described by Skjeltorp et al. [30], we substituted the values of 011, 0±, A0 in the expressions for 1 / T K ± , 1 / T K , and A((1/KII ) - ( l / K ± ) } . The values of B2~ and B3a for G d P G were then found to be two orders larger than the values of Gd(OH)3. This implied that in G d P G the CF effect was still prominent between 30 and 20 K so that this method is not applicable in this temperature region. Facilities for measurement of K± and KII at lower temperatures are not available with us, but will be very useful in determining the effects, if any, of dipolar or exchange interactions even at 21 K.
83
In conclusion it m a y be remarked that (a) in G d 3+ crystalline compounds the magnetic anisotropy ( A K ) is small around room temperature but quite large around 20 K and is predominantly a CF effect on 8S7/2, through higher order perturbations. In fact, the high temperature thermal characteristic of A K is a finger print of the nature of the crystal field; (b) the observed low values of A K and K± below 30 K, may be due to several possible reasons like magnetic ordering at a lower temperature. Antiferromagnetic ordering due to dipolar or exchange interaction between G d 3+ atoms in the bc plane, would reduce the value of K± which may account for the observed low value of A K at 21.8 K. Measurement of K± and gll at still lower temperatures is essential for confirmation. At low temperatures a possibility of a change in the crystal field effect (i.e., in the values of ECFP), affecting the magnetic susceptibility tensors, cannot be ruled out; (c) in view of a spin doublet lying 1.058 cm-1 above the ground doublet, EPR studies and low temperatures X-ray studies on G d P G shall be very illuminating since the line spectra of Gd 3+ are easily obtained even at room temperature; (d) Thermal characteristics of the Schottky specific heat (C~cn) depend very sensitively on the nature of the low lying electronic levels, as has been demonstrated previously by us and others [9,10] on several rare earth hydroxides, for which accurate experimental data of the specific heat were available. Motivated by this we calculated the thermal characteristics of Csch for G d P G , and the Schottky m a x i m u m was found to be a t T m a x = 17 K (fig. 3b). Direct measurement of specific heat on G d P G will thus be rewarding as it is expected to establish effects of C F on this property and the position of Tmax.
Acknowledgement
The support of the work in part by the Science and Engineering Research Council is acknowledged (BMW).
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T. Kundu et al. / Susceptibility and optical absorption of Gd single crystal
References [1] B.M. Wanklyn, J. Mater. Sci. 8 (1973) 649. [2] Y.I. Smolin, Sov. Phys. Crystallogr. 15 (1970) 36. [3] Y.I. Smolin, Y.F. Shepelev and I.K. Butikova, Sov. Phys. Crystallogr. 16 (1971) 790. [4] M. Wardzynska and B.M. Wanklyn, Phys. Stat. Sol. (a) 40 (1977) 663. [5] A. Sengupta, S. Dasgupta, D. Ghosh and B.M. Wanklyn, Solid State Commun. 67 (1988) 745. [6] B.K. Chaudhari and D. Ghosh, Phys. Stat. Sol. (a) 23 (1974) 649. [7] S. Dasgupta, M. Saha and D. Ghosh, J. Phys. C 19 (1986) 1771. [8] S. Dasgupta, M. Saha, S. Mroczkowski and D. Ghosh, Phys. Rev. B 27 (1983) 6960. [9] T. Kundu, D. Ghosh and S. Mroczkowski, J. Phys. C 21 (1988) 5993. [10] R.D. Chirico, E.F. Westrum Jr., J.B. Gruber and J. Warmkessel, J. Chem. Thermodynamics 11 (1979) 835. [11] D. GuhaThakurta and D. Mukhopadhyay, Ind. J. Phys. 40 (1966) 69. [12] T. Kundu, S. Dasgupta, M. Saha and D. Ghosh, Ind. J. Phys. 60A (1986) 312. [13] D. Ghosh, D. Phil Thesis, Calcutta University (1969) unpublished. [14] G.H. Dieke, Spectra and Energy Levels of Rare Earth Ions in Crystals (Wiley, New York, 1968).
[15] B. Bleaney, R.J. Elliott, H.E.D. Scovil and R.S. Trenam, Phil. Mag. (London) 42 (1951) 1062. [16] B. Bleaney and D.J.E. Ingram, Proc. Roy. Soc. A205 (1951) 336. [17] R.J. Elliott and K.W.H. Stevens, Proc. Roy. Soc. A219 (1953b) 387. [18] A. Abragam and M.H.L. Pryce, Proc. Roy. Soc. A205 (1951) 135. [19] J.H. Van Vleck, Theory of Electric and Magnetic Susceptibility (Oxford Univ. Press, London, 1932). [20] K.S. Krishnan and S. Banerjee, Phys. Rev. 59 (1941) 770. [21] G.S. Bogle and H.F. Symmons, Proc. Phys. Soc. 79 (1962) 775. [22] C.A. Hutchinson Jr., B.R. Judd and D.F.O. Pope, Proc. Phys. Soc. P70 (1957) 514. [23] M. Weger and W. Low, Phys. Rev. 111 (1958) 1526. [24] W. Low and D. Shaltiel, J. Phys. Chem. Solids 6 (1958) 315. [25] J.M. Baker and F.I.B. Williams, Proc. Phys. Soc. (London) 78 (1961) 1340. [26] A.J. Shuskus, J. Chem. Phys. 41 (1964) 1885. [27] B.H. Justice and E.F. Westrum Jr., J. Phys. Chem. 67 (1963) 351. [28] E.Y. Wong and I. Richman, J. Chem. Phys. 34 (1961) 1182. [29] W. Low, Paramagnetic Resonance in Solids (1960) p. 121. [30] A.T. Skjeltorp, C.A. Catanese, H.E. Meissner and W.P. Wolf, Phys. Rev. B 7 (1973) 2062.
Journal of Magnetism and Magnetic Materials 86 (1990) 78-84 North-Holland
A STUDY ON THE MAGNETIC SUSCEPTIBILITIES AND OPTICAL ABSORPTION S P E C T R A O N S I N G L E C R Y S T A L S O F Gd(III) P Y R O G E R M A N A T E T. K U N D U , D. G H O S H Solid State Physics Department, Indian Association for the Cultivation of Science, Jadavpur, Calcutta-700 032, India
and B.M. W A N K L Y N Clarendon Laboratory, University of Oxford, UK
Received 3 April 1989; in revised form 1 August 1989
The paper reports for the first time the experimental results of the measurements of magnetic susceptibilities(K± and Kll) and their anisotropy (AK) between 300 and 21.8 K and the optical absorption spectra (UV region) at 12.5 K on single crystals of gadolinium pyrogermanate (GdPG). The anisotropy, which is only 211 × 10-6 emu/mol at room temperature and increases by two orders of magnitude at 21 K, is predominantly a crystal field (CF) effect on the SS7/2 ground term, through higher order perturbations. Interpretation of the observed magnetic data was carried out by considering a conventional spin Hamiltonian (Hs) to derive expressions for K_ and KII in terms of four effective crystal field parameters (ECFP). The values of ECFP were varied to obtain a very close fitting between the theoretical and experimental values of K j , KH, AK and K. The splitting of the SST/2term corresponding to these values of ECFP was found to be large, which suggests a strong CF effect in GdPG, as also observed in other RPG crystal studied earlier. The thermal characteristics of the magnetic anisotropy below 30 K deviate by about 5% which could not be explained by CF effects alone. A series expansion method was adopted to analyse the results of K± and Kll below 30 K, however the corresponding coefficient B2~ and B3a were observed to be unusually high indicating the presence of CF effect even in this temperature region. The Schottky specific heat, Csch, between 300 and 21 K for GdPG has been calculated and this shows a maximum at Trnax = 17 K.
I. Introduction The rare earth p y r o g e r m a n a t e (R2GezO 7 or R P G ) c o m p o u n d s are a new class of crystals in which the rare earth a t o m has a u n i q u e Dsh site symmetry, rarely f o u n d in a 4f n system. Moreover, these c o m p o u n d s are c o n c e n t r a t e d in the rare earth ions [1]. O n a c c o u n t of these facts, crystals of R P G are expected to exhibit interesting magnetic a n d magneto-optical properties at low temperatures. The p y r o g e r m a n a t e crystals form an isomorphous series having high space group symmetry, i.e., P41212, so that the magnetic a n d optical properties of single crystals of these comp o u n d s can be c o n v e n i e n t l y a n d accurately studied a n d interpreted. Very little work has b e e n reported on these R P G , being limited to their struct-
ural investigations [2,3], study of the optical absorption spectra of D y 3÷ a n d Er 3÷ [4] a n d the magnetic susceptibilities of T m 3÷ [5]. Preliminary studies have shown that some of these R P G , viz. Tb, Dy, H o a n d Er, exhibit magnetic ordering at (2.05 + 0.05), (2.15 + 0.05), (1.45 + 0.05) a n d (1.15 +__0.05) K, respectively [1]. However, it m a y be m e n t i o n e d here that in rare earth systems, above liquid h y d r o g e n temperatures, the magnetic susceptibilities, especially their anisotropic properties, are very sensitively d e p e n d e n t o n crystal field (CF) effects caused b y the nearest a n i o n s surr o u n d i n g the rare earth ion. I n fact, magnetic a n i s o t r o p y is a very sensitive p r o b e for studying the crystal field a n d other effects, which influence different physical properties involving the paramagnetic atomic site [6,7]. F u r t h e r m o r e , very small
0304-8853/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
79
T. Kundu et al. / Susceptibility and optical absorption of Gd single crystal
values of magnetic anisotropy can be measured very accurately by the torque method as discussed in detail in our previous work on some rare earth compounds [7-9]. The present work on gadolinium pyrogermanate (GdPG) was undertaken because it belongs to this new class of magnetic insulators and also because the small splittings of the ground term of half-filled shells have arisen considerable interest over the last few decades. The ground term for Gd 3+ is 857/2, the splittings of which can only arise due to departures from Russel-Saunders coupling or crystal field mixing of states of different class. The theory of the gadolinium ion in a crystalline environment therefore is very different in character from other rare earth ions and to first order the ground term cannot in principle be split by crystal field alone. Higher order perturbations, involving the simultaneous action of the crystalline field and either the spin-orbit or spin-spin coupling, remove the spin degenaracy of the ground, S = 7/2, term and this in turn makes the magnetic susceptibilities weakly anisotropic around room temperature. This anisotropy increases with lowering the temperature. The rate however, depends on the nature of the eigenvalues and eigenfunctions corresponding to the multiplet splitting of the 8S7/2 term. Thus, by accurately measuring the small magnetic anisotropy, K L -Kit, of G d P G crystals over a wide range of temperature (300-21 K), it was expected to determine very accurately the splitting of the 8S7/2 term from parametrial fitting.
2. Experimental results 2.1. Magnetic susceptibilities and anisotropies
Single crystals of GdzGe207 were grown by sintering the initial components and using P b O GeO2 as flux [1]. The crystals were practically colourless and grew as thin platelets. The crystal platelets were transparent and the plane (bc) was optically isotropic under a polarising microscope. Detailed investigation of the crystallographic structure performed on Gd2Ge207 revealed considerable deviation from other R P G crystals [3]. A
x
0 oxygen • Er z
Fig. 1. Projection of structure for: (a) ErPG along the c-axis [2]; (b) GdPG along the a-axis [3].
unit cell of GdzGe20 7 contains twelve independent ions of Gd 3+ of which nine are surrounded by seven oxygen ions forming a deformed bipyramidal structure having a common pentagonal base and three Gd 3+ ions have similar bipyramidal environment with eight oxygen ions and a common hexagonal base. The axis of the pyramids or the tetragonal axis nearly coincided with the crystalline a-axis (which is the c-axis for other RPG) shown in fig. 1. The investigated structure of gadolinium in addition contains a triortho group Ge3Oao and an isolated tetrahedron GeO4 as against the other R P G which are of much higher symmetry and contain the regular Ge207 group. Structural investigations reveal that G d P G is triclinic (a = 18.5 ,&, b = c = 6.8 ,~ and a = fl = ), = 90 ° _+ 2.5 o) with space group P1 or P1. However, magnetic measurements along different axes show that the principal magnetic ellipsoid is nearly uniaxial (within 1%) about the a-axis (referred as Kjl axis) and the anisotropy in the bc plane, perpendicular to the a-axis was negligble. Single crystals chosen for magnetic measurements weighed between 25 and 26 mg. The experimental procedure involved very accurate measurement of the crystalline anisotropy, X c - X a ( = K ± - K r l in the present case) between
T. Kundu et al. / Susceptibility and optical absorption of Gd single crystal
80
O.OZ 40
100
T ( K ) 200
300
0.03 30
\ 0~
I
0.01
o 7" ..... J
i
100
T(K)
3OO
200
Fig. 2. Shows theoretical (solid line) and the experimental results of AK (e) and 1/K± (©) for GdPG. Calculated values of AK of GdES ( - - - - - ) is also shown. Inset: Calculated (solid line) and experimental thermal variation of TKII.
300 and 21 K. In order to measure K 1 -KII, each crystal was freely suspended along the b axis by means of fine quartz fibre in a uniform horizontal magnetic field. Under this condition, the greater of the two principal susceptibility tensors in the horizontal plane, i.e., K_ or Kll sets along the field direction and the torque experienced by the fibre is proportional to the anisotropy, K± -Kll. Details of measurement have been reported tJ
t'~
t.O
~r OO
o
r
a
elsewhere [11,12]. The value of the magnetic anisotropy was found to be 211.73 × 10 -6 e m u / m o l at room temperature which increased on cooling and attained the value of 2.5096 × 10 -2 e m u / m o l at 21.8 K (fig. 2). On the other hand magnetic anisotropy measurements in the bc plane showed only a small increase at the lowest temperature and was still negligible compared to the value of K ± - K l l at that temperature. In G d P G it was observed that K± was larger than KIt over the entire temperature range and K_~-KII = AK increased considerably on lowering the temperature (fig. 2). Hence in order to obtain better accuracy the thermal characteristic of K± was measured in an electrodynamically controlled Curie-type balance using the Faraday method [13]. From the measurement of K± and AK, the thermal variation of K = ( 2 K ± + K i l ) / 3 and KII were calculated. The results of AK, TKII and l / K ± are shown in fig. 2.
2.2. Spectroscopic studies The spectra of Gd 3+ are characterised by absence of spectral lines in the visible region but there are sharp lines in the UV region due to the presence of excited t e r m s 6p7/2, 6p5/2, 6p3/2 [14]. The polarised optical absorption (UV) spectra of G d P G at 12.5 K was studied for the first time in a high resolution Carl Zeiss Spectrograph (PGS 2), having a dispersion of 3.5 ,~/mm. The transitions due to the 6p7/2, 6P5/2 and 61)3/2 multiplets were recorded for estimating the CF splitting of the
0-4
9~ t"O
/
20
40
T(K)
60
80
Fig. 3. (a) Polarised absorption spectra with incident light along the a-axis in the UV region at 12.5 K; (b) thermal variation of C~h.
T. Kundu et al. / Susceptibility and optical absorption of Gd single crystal
same. Single crystals of Gd2Ge20 7 were directly fixed to the slit of the crystal holder using conducting grease. The crystal holder was in thermal contact with the cold tip of the closed cycle helium cryocooler (Displex CS202). The absorption lines occurring in the UV range were recorded on thin photographic plates (Illford 6ASA, 9DIN no. 30) which were scanned by a sensitive micro-photometric arrangement incorporating sensitive diodes (LDR), the output of which was amplified and fed to an X Y recorder (Rikadenki RW 201). Fig. 3a shows the recorded absorption spectra o f 6p7/2, 6p5/2, 6 p 3 / 2 multiplets with polarised light incident along the a axis. Due to the shape (and hardness as well) of the crystal it was not possible to record the spectra with the incident polarised light perpendicular to the a axis. Consequently it was not possible to determine the ground term splitting by the usual method of applying selection rules to the different transitions between the ground and excited multiplets in the spectra for different polarisation directions [14]. However, the usual CF pattern for 6pv/2, 6p5/2 and 6P3/2 transition of Gd 3+ compounds were obtained (table 2), and the CF splitting in the PG system was found to be the largest compared to the chloride and ethyl sulphate [14].
3. Discussion
In gadolinium compounds the first excited state lies about 32000 cm -1 above the ground term 8S7/2, hence the magnetic susceptibility and anisotropy, observed in some Gd 3+ compounds is completely a ground term phenomenon. As mentioned earlier, crystal field alone in the first order cannot split the SS7/2 term and theory would predict g = 2. However, EPR studies on several Gd salts have shown a complicated resonance pattern [15], suggesting a small splitting of the S-state similar to that found in Mn 2+ (S-state) compounds [16]. In order to explain the small splitting of the S-state ions, a spin-Hamiltonian having the same symmetry as the crystal field was considered successfully to explain the EPR resonance lines [17]. A spin Hamiltonian method [18] is generally applied to explain magnetic susceptibilities and
81
their anisotropies for 3d n complexes which have a ground orbital singlet or a doublet term [19]. In order to explain the magnetic anisotropy in GdPG, a spin Hamiltonian H s corresponding to Dsh symmetry was considered, as was done for explaining EPR results of other Gd 3÷ compounds of C3h symmetry
H s = gjflH. S + B°(3S~ - S ( S + 1)} + B°(35S 4 - [30S(S + 1 ) - 251Sf
- 6 S ( S + 1 ) + 3 S 2 ( S + 1) 2} + B6°{231S6 - 105SJ[3S(S + 1 ) - 7]
+$2[105S2(S + 1) 2 - 525S(S + 1) + 294] - 5 S 3 ( S + 1) 3 + 40S2(S + 1) 2 5
.
- 6 0 S ( S + 1)} + Bd{(S x + ,Sy)
5
+ ( S~ - iSy )5} /2, in which 3B° = b °, 60B ° = b°, 1260B° = bg and 275B65 = b65,and b °, b°, bg and b65 are the effective crystal field parameters (ECFP). On application of the above Hamiltonian the diagonal and off-diagonal matrix elements of the matrices spanned by J = _+7/2 were calculated and the matrices were diagonalised to obtain the energy eigenvalues E ° and the corresponding eigenfunctions for the ground multiplet levels. The magnetic perturbation was next applied on these levels to obtain expressions for the magnetic susceptibilities K j_ and KII using the Van Vleck [191 expression
Kj = ( g~Nflz/z) E {[( E,0) ) / k T - 2E/{2)] i
× exp(-Ei
(0)/ k T ) } ,
where E[ m, Ei°) and Ei~2) are, respectively, the zeroth, first and second order perturbed Zeeman energies and the rest have their usual meanings. The principal_ magnetic susceptibilities K . , Kij and finally K = ½(2K 1 + K . ) were calculated separately in terms of the effective crystal field parameters b °, b4°, /96o and b65. In order to fit the observed magnetic susceptibilities and anisotropy data, the values of ECFP
82
72 Kundu et al. / Susceptibility and optical absorption of Gd single crystal
Table 1 Crystal field energy levels (in cm -1) of Ss7/2 in Gd2Ge20 7. ECFP (in cm-1): 6o=0.27, b ° = - 1 . 5 6 , b6°=0.126, b65= + 11.00 Energy levels
Wavefunctions
0 1.058 21.540 27.082 50.340
1.000017/2, _+0.8759 [7/2, - 0.707117/2, 0.482517/2, 0.7071 [7/2,
_+1/2) +_7/2) - 5/2) +_7/2) - 5/2)
290.482517/2, -T-3/2) + 0.707117/2,5/2 ) + 0.875917/2, -T-3/2) +0.7071 [7/2, 5/2)
were varied by small amounts using computer programming. During the process of such variations a number of interesting facts were revealed. (a) The calculated values of AK at room temperature depended very sensitively on the values of b ° so that the latter could be determined very accurately. (b) The rate of increase of AK on cooling could be matched by adjusting the other parameters, of which b4° was the most effective one. (c) At low temperatures i.e., below 80 K the value of AK could be varied by small amounts by adjusting the values of b° and b65. (d) The relative spacing and composition of the eigenvalues and eigenfunctions, respectively, of the components of the ground multiplet depended sensitively on the values of the ECFP. The best set of parameters obtained after fitting the calculated values of K ± , Kit, AK and K simultaneously with the observed ones are given in table 1. The calculated and observed values of K . and Kll were fitted within 1%. The corresponding energy eigenvalues and eigenfunctions are also given therein. The room temperature anisotropy (expressed in 10 6 emu/mol) in G d P G is 211.73 which is large compared to the observed value of 52 in gadolinium sulphate octahydrate [20] or that of the calculated value of 11.4 in GdES obtained on substitution of the values of ECFP reported from EPR studies [15] (fig. 2). This explains the high value of b° in G d P G compared to the other two salts (respective values of b ° being 2700, 1260 and 200.8, all expressed in 10 -4 cm-~). It may be remarked here that in pyrogermanate (PG) sys-
terns studied earlier e.g., Er, Dy and Tm [4,5], the value of the CF parameter B ° was large compared to other compounds for each of these rare earths [14] suggesting a stronger crystal field effect in PG systems. It was observed that for the high values of b2° and b4°, determined by close fitting of the thermal characteristic of AK, the effect of b6° and b65 were negligible (even when changed by two orders). Similarly for GdES (having C3h symmetry) effect of b6° and b66 were found to be small. It is to be borne in mind that unlike all RPG, G d P G contains two different polyhedra (fig. 1), some in penta coordination and others in hexa coordination (as in GdES) in the ratio of 3"1. We had examined the effect of such a mixture assuming that the anisotropy for the two different polyhedra are not very different. Since the contribution to 2xK for each type of polyhedra are not known separately, this approximation had to be made in order to obtain a meaningful interpretation of the results. Furthermore, since the contributions of b6° and b~ or b° and b6 were very small in G d P G or GdES, respectively, the calculated results are not affected appreciably if Dsh site is considered only. Inspection of table 1 shows that the ground multiplet 8S7/2 is decomposed into 5 levels, 2 spin singlets and 3 doublets; the first excited doublet lies very close (1.058 cm -1) to the lowest doublet level. The total splitting AE 1 of 8S7/2 in the present case is 50.34 cm-a which is large corresponding to other Gd 3+ salts (see table 2). It is to be noted that EPR experiments on systems belonging to 4f 7 configuration, viz. Gd 3+, in different crystalline host lattices of ethyl sulphates [15], sulphates [21], double nitrates, trichlorides [22], hydrated trichlorides [23] as well as in CaF z, ThO 2 [24], Hapi crystals [25] and other oxide host lattices like CaO and SrO [26] have revealed a small splitting of the SS7/2 term lying between 0.1 and 10 cm -I [27]. It is to be noted further that the ground term splitting of PG systems studied earlier is large. For example, T m P G exhibited a total ground t e r m ( 3 H 6 ) splitting of 1149.58 cm -~ [5] as against the corresponding splitting of only 307.3 cm-1 in TmES [28]. Inspection of fig. 2 shows that the calculated and observed values of AK deviated by 5% below 30 K. It is relevant to mention here that EPR
T. Kundu et al. / Susceptibility and optical absorption of Gd single crystal
Table 2 Observed spectra of some Gd 3+ salts (in cm -1) State 6P7/z
A E 2 a)
6P5/2
A E 3 a)
6P5/2 AE4 a)
GdPG b) (T=12.5 K) 31874.7 31937.5 31993.0 32056.3 181.60
GdCI3"6H20 c) (T=l.8 K) 32059.6 32091.7 32123.3 32147.6 88.00
GdESc) (T=1.7 K) 32136.07 32135.85 32163.63 32164.56 28.49
32494.5 32559.9 32617.6 123.10
32660.4 32699.9 32740.9 80.50
32737.73 32757.85 32760.18 22.45
33107.1 33170.9 63.80
33254.9 33290.3 35.40
-
a) Multiplet width; b) present work; c) Dieke (1968).
Positions of CF components for GdPG are shown in fig. 3a.
results of some G d 3+ crystals could only be explained by using two different sets of E C F P for room temperature and nitrogen temperatures [29]. The said deviation below 30 K in G d P G m a y be due to such variations or due to high temperature effect of magnetic ordering occurring at a lower temperature as in Gd(OH)3. We attempted to analyse the low temperature results between 20 and 30 K using high temperature series sum method, as in Gd(OH)3, in which case, however, low temperature experimental results of K± and KII were available between 20 and 1.4 K [30]. For G d P G we found that K H= 7 . 3 8 / ( T + 3.10),
K± = 7 . 4 0 / ( T + 1.48).
Hence using the procedure described by Skjeltorp et al. [30], we substituted the values of 011, 0±, A0 in the expressions for 1 / T K ± , 1 / T K , and A((1/KII ) - ( l / K ± ) } . The values of B2~ and B3a for G d P G were then found to be two orders larger than the values of Gd(OH)3. This implied that in G d P G the CF effect was still prominent between 30 and 20 K so that this method is not applicable in this temperature region. Facilities for measurement of K± and KII at lower temperatures are not available with us, but will be very useful in determining the effects, if any, of dipolar or exchange interactions even at 21 K.
83
In conclusion it m a y be remarked that (a) in G d 3+ crystalline compounds the magnetic anisotropy ( A K ) is small around room temperature but quite large around 20 K and is predominantly a CF effect on 8S7/2, through higher order perturbations. In fact, the high temperature thermal characteristic of A K is a finger print of the nature of the crystal field; (b) the observed low values of A K and K± below 30 K, may be due to several possible reasons like magnetic ordering at a lower temperature. Antiferromagnetic ordering due to dipolar or exchange interaction between G d 3+ atoms in the bc plane, would reduce the value of K± which may account for the observed low value of A K at 21.8 K. Measurement of K± and gll at still lower temperatures is essential for confirmation. At low temperatures a possibility of a change in the crystal field effect (i.e., in the values of ECFP), affecting the magnetic susceptibility tensors, cannot be ruled out; (c) in view of a spin doublet lying 1.058 cm-1 above the ground doublet, EPR studies and low temperatures X-ray studies on G d P G shall be very illuminating since the line spectra of Gd 3+ are easily obtained even at room temperature; (d) Thermal characteristics of the Schottky specific heat (C~cn) depend very sensitively on the nature of the low lying electronic levels, as has been demonstrated previously by us and others [9,10] on several rare earth hydroxides, for which accurate experimental data of the specific heat were available. Motivated by this we calculated the thermal characteristics of Csch for G d P G , and the Schottky m a x i m u m was found to be a t T m a x = 17 K (fig. 3b). Direct measurement of specific heat on G d P G will thus be rewarding as it is expected to establish effects of C F on this property and the position of Tmax.
Acknowledgement
The support of the work in part by the Science and Engineering Research Council is acknowledged (BMW).
84
T. Kundu et al. / Susceptibility and optical absorption of Gd single crystal
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