Chakravarty, A S

Desai, V P

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55PARAMAGNETIC SUSCEPTIBILITIES OF THE 3d" OCTAHEDRAL COMPLEXES V . P. D E SA I AND A . S. C H A K R A V A R T YS a h a  I n s t i t u t e  o f  N u c I iE a h  P h y s i o s ,C a l c u t t a *9 ,  I n d i aBeceivful Aur/ust 24, 1968ABSTRACT. In the 0(‘tahedral <*ompIoxes of the transition metal ions the tomperatum independent high-frequency contribution to parainagnc susceptibilly x'n <'oming from tin* i^r^ t excited configuration has been estimated. This contribution must be differentiated, from the usual high-froquoncy contribution coming from the ground (ionfiguratiou dcmedod h y  X/<. The magnitude of this contribution depending on a parti(*ular ion and a particular (complex vari(js roughly from 1% to 9% of the room temperature susceptibility value and is tluiH quite significant. This means that the magnitudes of tlu' crystal fiekl par'ametor A, the .spju- orbit coupling constant in the crystal etc;, usually obtained from the ground <*onfigurjiti(»n alone will be altered somewhat in the temperatures range 20O'K to 300 K wh(*ii tins additional contribution is also taken into ac(;ount.T N T R O 1) U C T 1 () NDuring the past decade there has hoou a good amount of work on the paia- mzgnetic susceptibilities of tlie (‘omplexi^s of tlie transition inotal ions (Urvu, 1956; (yhakravarty, 1959; Bovso ef al 1960, 1961, 1962), But in all tlu^ so iuvissti- gations the ground configuration has only hoon taken into (‘ousideration on th(^  assumption that the excited configurations will not contributes significantly be- cause of their large energy separations from the ground coiifiguration. It is the purpose of this paper to show that actually it is not so. The second order toiii' poraturo independent Van Vlock susceptibility coming from the first excited con­figuration (first excited configuration corresponds to one electron excitation from the ground configuration) is quite appreciable in the typo of comploxos under consideration. A preliminary theoretical account of this contribution has boon already given by Griffith (1961). But his interest was mainly confined witli showing roughly the effect of this contribution to the Bohr magneton number Butit is easy to realise that the /icff would bo rather insensitive to small alteration of the susceptibility values duo to the contribution coming from the excited fen- figuration. Wo have, however, calculated this contribution for the individual ions Ti®+ through and show that it is roughly between 1% and 9% of the room temperature susceptibility value. In our calculations we have assumed tlic liydrated (complexes of the transition metal ions to be approximately octahedral in symmetry. The reason is that the slight departure of the crystalline electric506Magnetic Susceptibilities of the Complexes 6 0 7fiold from octahedral symmetry will not alter the magnitudes of this contribution very much so that our conclusions will be correct to a very high degree of approxi­mation. This assumption, on the other hand, reduces the labour appreciably.T H E O R E T I C A L  A S P E C T SFor the theoretical aspects one siumld consult Griffiths (1961) and therefore wt' should mention here only the important points. Since the Hamiltonian forfor the magnetics jiorturbation involves tlio orl)ital angular momentum L and het'auso L is one-electron operator, the matrix (‘lenient of the magnetic Hamiltonian is non-vanishing between the terms of tlie ground and first oxcitcKi configuration.But since th(^  orbital angular momentum L of the fiw  ions gets somewhat reduced wlion the ions form the octahedral complexi s xn o must take this fact also into consideration. We denote this orbital rodiudion factor by k. The value of this reduction factor has been assumed to bo 0.9 (0\N"on and Thornloy, 1966). Wc bclicn o this is a reasonable value in the typo of complexes we an^  considering. It should also be noted that wo have czlenlatod this high frecpiency contribution in the strong field approximation (Ballhaiisen, 1962). The final expression which wo have \isod can he shown to beXh "- 3ST*2Lj(1)where is the ground states belonging to the (joiifigurationspin-allowed exciied states belonging to the (*onfiguration Other confi­gurations will have no offoct because L is a one-electron operator. We write x h to differentiate it from the usual high frequency contribution coming from the ground configuratiem which is (justomarily denoted by Xh* E^^^—Eq is the energy sox>aration between the ground and the ex(uiod states. Tlie energy separations have been found from the experimental optical absorption spectra of these com- plexes (see the references at the end of table 1). The strong field wave functions in the crystal field of octahedral symmetry have been derived by us using the methods of Tanabe and Sugano (1954) which we do not present here. The correct- ness of the wave functions was chocked by finding the electrostatic energy matrix elements and comparing them with Tanabe and Sugano matrices, x h cahm at in this way are presented in table 1 and are compared with the room temperature susceptibility values for the ionic complexes. The calculation for the 3d system has no been done because the ground state of this system is a Aj state and there is no sextet present in the first excited configuration.50 8 V. P. Deaai and A. 8. GhakravartySR-Sa> a>Magnetic Susceptibilities of the 3d^  Complexes 609B T S C US S I O NWe Iiav(v calculated x\ octaUodral complcjxes of tlie trarmitioumotal ions. The sam(^  calculation can also be dolie for the totrahoriral complexes and in those cases the maguitudos of x\ would be even bigger because tlio energy separation appearing in the denominator of eqn. (1) is usually much lessthan that in the octahedral complexes. Tt is evident from table 1 that at tlie room t;omperature the contribution of x\ to the ground ooufiguration total paramagnetic susceptibility varies from 1 % to 0% depending on the particular (^ omph^ x. This contribution from tlie excited configuration will alter the tTvstalliue field para­meters, the offeedive Lande factors as well as the spin-oi*bit coupling parameter somewhat apprecia})ly in tlie temperature range 200''iir—300'K in the manner (ixplaiiK^ d below.Ill calculating the suscoptiliility expn^ssion in the ground configuration, the Hamiltonian tliat is usually (considered is given hy (Abragam and Piytte, 1051)H Ion +  Cubk + A ( l  —V2^ ) — CC^l(2)whore Vcubic the erystalline oleetric field potential of octahedral symmetry,A is tlie strength of the crystal field of tetragonal or trigonal symmotry, —a and a' are the effective Laud6 factors in tho axial and perpendicmlar dinictioiis, Vg is the 5J-eomponont of tlie effective orbital angular momentum, f  ia the spin-orbit (K)upling parameter in tho crystal, A, cc and a' are tho parameters first intro­duced by Abragam and Piyce (1951) for tho orbitalitv dogonorato ground states sucli as in V3+(3(P), Fo2+(3d«) and Co2+(3d7). Now, as soon as tho expressions for tho susceptibility, involving tho parameters A, oc and a' an^  obtained by using tho above Hamiltoniaai, one mak(vs a trial and error calculation to fit the theory with the oxporimentfd susceptibility curve at difft*rent tompe^ raturos. Tn this way one gets the magnitudes of the above mentioned parameters. Tho fitting of tho data are done in most cases within 1% accniracy. Tt is very impeutant to note that tho contribution from the excited configuration whicili varies from 1% to 9% in different cases must bo taken into consideration along with the major contribution from tho ground configuration before interpreting the sus­ceptibility vs. temperature curve. As a result, aU tho parameters appearing in tho above Hamiltonian will have different magnitudes compared wit|i those calculated without considering the said contributions. It is important to note that the magnitudes of the parameters will differ significantly in tho range 100°K to 300°K but not appreciably at temperatures below lOO^ K^ because the luagnitude of susceptibility goes on increasing as tho temperature decreases whereas6 1 0 V. P. Desai and A . 8. CJiakravartythis high-froquoncy contribution from tlio excited configuration is temperature independent and therefore remains the same at all temperatures.. A C K N O W L E D G E M E N TW e are grateful to Professor A.. K . Saha for his kind interest in this work.H E F E R E N C E SAbragam, A. and Pryeo, M. H. L., 1951, Proc, Roy, A205, 135; A206, 173. Ballhausen, 0. .1,, 1962, Infrodnction to Ligand Field Theory, MoOraw-Hill Book (U), Inc., Now York.Hose, A, Chakravarty, A. S. and Chatterjoe, K., 1960, Proc. Roy, .^Voc., A255, 141, 145.-------------------- — ...... . ...........................1961, Proc, Roy. Soc., A261, 43; 207,----------------------------------------------------------  1962, J, Phys. Soc. Japan, 17, 27, B-T.----------------------------- ------  1963, Proc. Roy. Soc„ A261, 43.Chakravarty, A. S., 1959, Proc. Phya. Soc„ 74, 711.Chatterjoo, R., 1962, Indian J. Phys., 36, 660.Droiaoh and Trommor, 1937, Z. Phys. Chem., B37, 40.Griffith, J, S., 1961, The Theory of Transition Metal Iona, Cambridge University Press. Hartmann, H. V., Schlafer, H. L. and Hansen, K. H. 1956, Z. Anorg. U. AUg.. Ghem,, 284, 153.Hartmann, H. and Furlani, C., 1956, Z. Phys. Chem., 9, 162.Hartmann, H. and Schlafer, 1951, Z, Naturforcea, 6A, 762.Holmes and McClure, 1956, J. Chem, Phys., 26, 1688.Jorgensen, C. K., 1954, Acta, Chem. Scand. 8, 1496.Jorgensen, C. K., 1954, Acta. Chem, Scand,, 8, 1507.Jorgensen, C. K., 1955, Acta. Chem. Scand., 9, 1302.Lone, W., 1957, Z. Physik. Chem. (Frankfurt), 13, 107.Owen, J, and Thornley, J. H. M., 1966, Rep. Prog. Phys., 29, Part II, 675.Tanabe, Y., Siigtmo, S., 1954, J. Phys. Soc„ Japan, 9, 753.Uryu, N., 1956, J. Phys. Soc. Japan, 11, 770.

Paramagnetic Susceptibilities of the 3dn Octahedral Complexes

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Paramagnetic Susceptibilities of the 3dn Octahedral Complexes

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