Basu, C

Gupta, R

IACS Institutional Repository

Phys.7SXO),225-22i (2001)U P  Aan international journalMagnetic measurement and crystal-field analyses of the optical and magnetic dataof Tm2(S0 )^3.8H2 0  crystalR Gupta and C Basu"**^Department of Solid State Pl^sics,Indian Association for the Cultivatioii of Science,Jadavpur, Calcutta-700 0'^2, p d iaE-mail sspcbt&’mahcndra laca^res in R e c e iv e d  1 0  J a n u a r y  2 0 0 1 , a c c e p te d  1 9  F e b r u a r y  2 0 0 1Abstract The measurements o f the mean magnetic susccpiibiiity and crystalline anisotropy of Tin, (SO^), 8H ,0  have been carried out in theicmpcralure range 80-300 K. The results of magnetic measurements are explained using a crystal field of C,  ^ symmetry which is the major symmetry ,onfirmcd by optical absorption, Zeeman spectroscopy and para electric resonance experiment All the results show nearly accidentally degenerate SMfk components in the ground state and the presence of the nearly degenerate pair of Stark component within 0 57 ± 0 I cm ‘ in the ground mimifold \ \ci of crystal field parameters are evaluated using a rigorous approach and making consistent interpretation of both the magnetic and optical dataKr>words Crystal-field parameters, magnetic and optical data, Tm,(SOj), 8H ,0 crystalPVrS Nos. 71.70C h, 75 J 0 D gI. IntrtxluctionWc present both theoretical and experimental investigations of the magnetic susceptibility and its variation with temperature ol‘ ihuiiurn sulphate octahydrate crystal. Specifically, wc have measured (he mean magnetic susceptibility together with the principal magnetic susceptibilities (crystalline) and hence, the dmsuiropics over the temperature range 80-300 K. So far, no crystal field analysis of this crystal has been p)crformcd. However, taim a study of the optical absorption spectra of single crystal uf rm^(S0 4 )^.8 H2 0 , Karlow and Gruber [ 1 ] have suggested a low symmetry Cjj  ^of the crystal field. Using this symmetry, we intend to analyse the magnetic data that wc have obtained. It is iniportant to note that this spectroscopic work indicates a nearly accuJcntal degeneracy in the ground stale of tripositive thulium in ihc octahydralcd sulphate salt which has been supported by /cenian spectroscopy and paraelcctric resonance experiments, The degenerate ground level consists of two nearly degenerate l r^ound singlets within 0 . 5 7  ± 0 . 1  cm~*.Our purpose is to investigate whether it is possible to find a ’'ingle set of parameters remaining within the same theoretical framework for both magnetic and optical data mentioned above, specific properties wc would try to correlate are the SarkOirresponding Authorsplitting of excited levels, the accidentally degenerate ground level, the observed spectroscopic splitting factor and the magnetic anisotiopies over the entire temperature range. The theoretical model that wc use, implies the most rigorous approach of direct diagonalisation of the Hamiltonian in a complete basis of states belonging to all the terms of the Tm^^-ion. This mclhod has the advantage that it automatically includes intermediate coupling and different J-mixing under the crystal field. Finally, it may be mentioned that the present theory with a set of fifteen parameters, provides a fair overall description of the magnetic and the optical data.2. Experimental methodsPowdered sample of Tm-sulphalc octahydrate was dissolved in icc cold water. Crystals are formed by very slow evaporation of the solution in a dry atmosphere. For facilitating crysialization few drops of concentrated H^SO^ acid arc also added to the solution. Crystals are needle shaped about (5 x 1 x 1 )  mm in size and colourless. For susceptibility measurement, the crystals arc finely ground.The crystals are m onoclinic with space group C?,,, dimensions [2 ] of the unit cell arc a = 18.12 A. /? = 6.67 A, c = 13.43 A and the monoclinic angle fi = 10P^57'. ITie symmetry©2001 lACS226 R G upta and  C  Basu(diad) axis is along h. One of the three principal crystalline susceptibilities ^  i» ^ 2  ’ 3 bes along the symmetry axis and it is denoted by X^*X\  X i  be in the ac plane, X\  being taken to be greater than X i  by convention. For uniaxial symmetry of the ion, the principal ionic susceptibilities arc denoted by A',, andwhich lie parallel and perpendicular to the symmetry axis z respectively i.e. A„ = A,, Aj  ^ = A  ^ = A^.Bleancy et al (3) gives the correlation between ionic and crystalline magnetic anisotropies in a monoclinic crystal with uniaxial symmetry. There arc two sets of equations (3, 4| depending upon whether A„ is greater or less than A ^. For thulium sulphate octahydrate crystals experimental results indicate that A,, > K^ at all temperatures. Noting that there are two rare earth ions per formula unit, the relevant relations for thulium sulphate octahydrate are given as follows :A ',,-A , = (;t , (la)where the sum over / includes all the 4/elcctrons. Terms involve both odd q and even k arc not allowed for point ' symmetry [6,7] and there exist fifteen crystal field paranicici! The matrix of the total Hamiltonian is constructed taking all states arising out of all the atomic terms [7] o f / ^  ionbasis states in the |5 L 7  7 ,) scheme. The energy matrixTm^**^  ion comes out to be of the order of 91 x 9 1. The matrix k then diagonalized with the help of a computer (vax 3 4 (H)) Ti,,^  fifteen crystal field parameters B ^ ’s arc adjusted to in observed crystal field splittings and magnetic data wuh calculated ones. The diagonalization yields thirteen wStark leu n for the ground term. The next higher multiplet is of the oidei oi 5350 cm"' above the ground m ultiplet. The signiiuam contribution to the magnetic susceptibility comes from tlu lowest group of thirteen levels resulting from the diagonali/aiion procedure. Zeeman perturbation is now applied on those slak^  and the paramagnetic susceptibility upto second order and perpendicular to the symmetry axis of the ion at dilkrem temperatures is calculated using Van VIcck’s formula (81.= Oh) 4. Results and discussionEq. (lb) is used to lest whether A„ > A^ using experimental principal crystalline su.sceptibibty values. Further, the general relation between the crystalline and mean ionic susceptibilities isU'Is/f= (X „  + 2 X j / 3  = ^ / 2 . (2)The macroscopic habit of the crystal is such that no crystallographic planes or axes other than the symmetry axis h could be identified. Hence magnetic measurements were done by adopting the m ethod as detailed  in our previous communication [5]. The temperature was kept steady within ± 0 . 1 K. ITie estimated accuracy of the susceptibility measurement i s -5% .3. Theoretical calculationThe effective Hamiltonian for the crystal field energy level calculation of Tm^^ ion in the absence of external field is taken to be consisting of electrostatic energy corresponding to inter electronic repulsion energy, the spin orbit interaction energy and the crystal field energy only. Thus,Only eight |SL]-J levels arc identified including j , 'U,^F\  ^ j in the optical absorption experiment, the level is high in energy to be observed, the spectra of ^H^  and Tl, Ic are obscured by the absorption due to the water molceulrs m the octahydrate complex, the Stark levels ol the ground li, manifold were deduced from the temperature dependent spcciia Consequently, no crystal field analysis of the Stark spliiiiiu^ was performed. However, in our calculation we have considcfui all the levels arising out of all the atomic terms of  ^ ion W. have evaluated the crystal field parameters from our magnciiL susceptibility data consistent with available spectral data .nui maintaining fair agreement between theoretical and o b scm il  values of separation between the nearly degenerate gmumi singlets in the ground manifold and the observed spcctroseopu  splitting factor. After an extensive trial, we arrived at tin following set of parameters which gives the best pos.sible In \o magnetic data, available wStark splittings and also explains tin’ spectroscopic .splitting factor and the separation between iIk nearly degenerate ground singlets.//y  + f / .4^// </ * (3)Taking the point group symmetry of the Tm ion to be C,, ,^ the crystal field Hamiltonian is written in terms of tensor operators C* as defined by Judd [6 ] and Wybourne |7] ask^ 2A,<>E ' == 6 6 0 6 .9 8 8 5  cm  ' E^ =: 34.581 cm  *E ’ == 6 6 7  9 9 3 5  cm  ' i  = -  2 7 0 0  cm  '=  6 6 1 .5 2  ±  22  cm  ' B j j =  359 .78  ± 21 e n rB ,. , =  34 .82  ±  12 c m - ' B..,, -  4 4 0  00  ± 31 cm» 4 : =  314  28 *  4  c m - 'B 4.2 = - 1100 0 0  ±  6  cm  ' B44 = 383 .43  ±  5 cm  'B 4.4 =  2 0 9 .5 2  i  8 cm  ' B «, = 7 1 2 .1 0  ± 10 cm  *=  51 ,5 8  ±  15 cm  ' B *2 = 500 ,39  ±  12 cm  *B m =  .307.93 ±  5  c m - ' Be.4 = 115.47 ±  2  cm  '=  2 3 0 .1 8  ±  12 c m - ' B ..6 :r - 1 5 9 .3 6  ± 14 cmM agnetic measurem ent and cry^stal-field analysis etc 227The observed mean susceptibility values of the powdered I i^inplc together with the experimentally observed X\ ^^ t^ dv.ilacs of Tm -  sulphate octahydrate crystals at different j^ .piptTaiures are shown in Figure 1. The agreement between the ,hservcci and theoretically computed thermal variation of the jnean limic susceptibility K and principal ionic susceptibilities A’, and j are shown in Figure 2. The figure shows that the .iijrt’cnicnt is fairly good for all three quantities. The deviationFiKurt* 1. Thermal vanalion of X * X \ and X i  for thulium sulphate 'Hiahydratc A cxperimcnlal points of X  * O - experimental points ot1^. • experimental points of X .\ (Solid lines arc fit to aid the eye)of the calculated values from the observed ones arc (0 .6 % ~ 7.5%K (2.2%-9.1%) and (2,1% -  lO.CF/i) for K\ and respectively, within the temperature range of 300 to 80K.The calculated first order crystal field splittings together with available observed splittings for the J manifolds are given in 1 able {. The values of the calculated and observed scperaiion A h' (say) between the ground singlets are quoted below for comparisonAw  (observed) = 0.57±0.01 cm ’.Aw (calculated) = 0.5756cmT ab le  1. Crystal iicld splitting ol Tm,(SO^)  ^ 8H,0level2. T herm al variation  o f  m ean ionic suscep tib ility  K and principal s u s c e p t ib i l i t ie s  ATn a n d  f o r  th u l iu m  s u lp h a te  o c ta h y d ra te .  ‘ d ieoretical cu rv e . A ~  e x p e r im e n ta l p o in ts  o f  O -  e x p e rim en ta l P^ i^nts o f  a:,, . ex p e rim en ta l p o in ts  o f  K .ppiricullabelF:\pcriincntal energy levels (cm ')Center of gravity (cm ')Relative observed splittings (cm ')Relative calculated splittings (cm ')z, 0 0z, 0 57 0 549z, 102 101 3z . 24 3 10 3 6Z, 255 277 8Z. 309 3 10 6Z, 363 361 9Z» 437 389 3z„ 461 404 5A, 12623 12778 5 -1 5 5  5 -183  8A , 12648 -1 3 0  5 -1 6 7A , 12742 36 5 -121 8A . 127.S5 ~23 5 -53 9A, 12767 - 1 1 5 18 7A„ 12803 24.5 -1 2A , 12835 56 5 129 4A, 12899 1 20 5 151 3A„ 12935 156 5 265 8B, 14512 14580 -6 8  3 -110  2B, 14573 -7  3 0 3B, 14576 -4 ,3 3 0B. 14579 1 3 18 2B, 14583 2.7 18 3B. 14601 20 7 31 3B, 14638 57.7 39 0C, 15134 15213 -79.6 -5 5  9c. 15161 -5 2 .6 -4 4  0C, 15207 - 6 6 -27.1C. 15268 54 4 58 4c. 15298 84 4 68 4228 R Gupta and C BasuT a b le  1. Cont dv»iulev e lE m p ir ic a llabelE x p e r im e n ta l  en e rg y  lev e ls  (c m  ')C e n te r  o f  g ra v i ty(cm  ')R e la tiv e  o b se rv e d  sp li t t in g s  (cm  ’)R e la tiv ec a lc u la te dsp l i t t in g s( c m ’)% E , 2 7 9 3 4 2 8 0 1 3 .4 - 7 9  4 - 5 5  9Ea 2 7 9 7 1 - 4 2  4 " 4 4  0E. 2 8 0 0 7 - 6  4 - 2 7  1E. 2 8 0 7 5 6 1 .6 5 8 .4E, 2 8 0 8 0 6 6 .6 6 8 .4■P, ", 3 6 4 2 0 3 6 4 9 5  7 - 7 5  7 - 9 0 . 7" , 3 6 4 6 4 - 3 1 .7 6 .2" , 3 6 6 0 3 107  3 8 3 .83 8 0 9 2 3 8 2 3 4 - 1 4 2 164  21 , 3 8 1 4 6 - 8 8 128 91, 3 8 2 3 0 - 4 - 2 4  21. 3 8 3 2 6 9 2 - 1 2 2  11 , 3 8 3 7 6 14 2 - 1 4 6  6Next, we proceed to calculate the spectroscopic splitting factor. Karlow and Gruber (1 ] has confined the nearly degenerate ground singlets in the ground manifold of Tm sulphate octahydrate by Zeeman spectroscopy 111 and PER experiments [ 1 ]. From Zeeman measurements, they inferred that the Zeeman splittings in Tm^tSO^ij.SHjO is due entirely to the magnetic interaction between the nearly degenerate ground Stark levels. The spectroscopic splitting factor calculated from their experiment yields the value 13.4 L.U for the splitting factor. We have calculated theoretically the first and second order Zeeman energies of the two nearly degenerate ground Stark levels. After introducing the magnetic interaction the energy values W ,,of the two levels upto second order in energy are given by W, = + 6.124810^  W - 1.957505()3 W )\tVj = W/'®* -  6.120041 p H - \  .9548where and are the Stark energies of ihccomponents in the absence of magnetic field H. Remcmbcntm that these two nearly degenerate levels were initially separaity by a small amount (~ 0.5756 cm“‘) in zero magnetic field, du additional splitting between these two levels due to Zeciium interaction only comes out to be 12.24215 L.U.However, we may conclude that though the assunipiion o| Cy  ^symmetry for Tm- sulphate octahydrate is very appruximau one, the crystal field parameters evaluated on the basis ol th^  symmetry, can more or less explain the magnetic data, availabk optical data and Zeeman splitting.AcknowledgmentThanks are due to Prof. R. Bhattacharyya for his assistance n the experimental measurements.References[ I J  E  A K arlow  and J B G r u b e r . /  Chem Phys 55  AIM)[21 V S  Ivanov  Knstalloi>rufiya 9 655  ( I % 4 )[3 ]  B B lcancy , R P P en ro se  and  B I P lu m io n  P m r  Ro\ Sot AP>: 4 0 6  (1 9 4 9 )[4 ]  D  C u b a  T h a k u ra ta  an d  1) M u k h o p a d h y ay  fmium J P(m 40 (t ( 1 9 6 6 )[5 ]  R G u p ta . S BiswUvS, U S G h o sh  and  C  B asu  Euro J Ph\s 1110 ( 1 9 9 9 )[6 ]  B R J u d d  Operator Technufues in Atomn SpectioMop\York . M cG raw  H ill) (1 9 6 5 )[7 ]  B G  W y b o u rn c  Spectrostopu Properties of Rare-Emtin Y ork • In te rs c ie n c e )  (1 9 6 5 )[8 ]  J H Van V lcck  Electric and Magnetic Susceptihiiitics (Oxli'iil O x fo rd  U n iv e rs ity  P re s s )  (1 9 3 2 )

Magnetic Measurement and Crystal-Field Analysis of the Optical and Magnetic Data of Tm2(SO4)3.8H2O Crystal

http://arxiv.iacs.res.in:8080/jspui/bitstream/10821/5790/1/Magnetic%20Measurement%20and%20Crystal-Field_By%20R%20Gupta.pdf

Magnetic Measurement and Crystal-Field Analysis of the Optical and Magnetic Data of Tm2(SO4)3.8H2O Crystal

Abstract

Similar works

Full text

Available Versions

IACS Institutional Repository