The magnetic susceptibility of c~Ti(S0,)~ .12H, 0

JOHN A. MACKINNON AND JAMES LEONARD BICKERTON Deparlnient of P/~ysics, Sir George Willht~is University, Montreal, Quebec

Received August 4, 1969

The magnetic susceptibility of CST~(SO,)~. 12H20 (CsTi alum) was measured with a Foner magnetom- eter in the temperature range 4.2 to 300 OK. Emphasis was placed on the liquid-helium to liquid- nitrogen temperature range, since complete measurements for this temperature region have not been reported previously.

The experimental results were interpreted with an expression derived by Kamimura for the effective moment of Ti3+ ions as a fi~nction of temperature in a crystalline electric fieldof trigonal or tetragonal symmetry. A best fit to the experimental data was obtained with values of r2A = -36.7 + 7.1 cm-I and h = 25.2 2 5.0 cm-'. These values indicate the presence of an excited energy state approximately 30 cm-' above the ground state; in addition there is a substantial reduction in the spin-orbit coupling factor from the free-ion value.

Canadian Journal of Physics, 48, 814 (1970)

Introduction

The magnetic properties of the undiluted paramagnetic salt CsTi alum (CsTi(SO,),. 12- H,O) have been the object of interest for many years. Magnetic susceptibility measurements have been made by Van den Handel (1940), Benzie and Cooke (1951), Dutta-Roy et al. (1959), and Figgis et al. (1963). Electron spin resonance (e.s.r.) measurements have been made by Bleaney et al. (1955) and nonresonant relaxation results have been obtained by Gorter et al. (1938) and De Haas and Du PrC (1938).

The susceptibility measured by Van den Handel (1940) deviated from a Curie law in the liquid-helium region. Preliminary measurements of susceptibility by Bleaney et al. (1955) verified the anomalous behavior observed by Van den Handel. Bleaney et al. (1955) suggested the existence of an excited state some tens of cm-' above the ground state as an explanation for their experimental e.s.r. g factors, and the departure from the Curie law at liquid-helium temperatures. In order to explain the fast relaxa- tion times observed for CsTi alum, Van Vleck (1940) has concluded that there must exist an excited state -100 cm-' above the ground state.

The g factors calculated by Bose et al. (1959) from the high-temperature susceptibility work of Dutta-Roy et al. (1959) are markedly different from those obtained from the e.s.r. work at low temperatures. It has led Bose et al. (1959) to suggest that a change in orbital level Structure may take place somewhere between 100 and 4.2 OK. Figgis et al. (1963) repeated the high-

temperature susceptibility work and obtained values of susceptibility which are appreciably higher, and show a larger change in magnetic moment with temperature than those obtained earlier by Dutta-Roy et al. (1959).

We have measured the magnetic susceptibility of CsTi alum in the temperature range 300 to 4.2 OK with a Foner magnetometer. The experi- mental results deviate from a Curie law in the temperature region 30-4.2 OK, and suggest the presence of an excited state - 30 cm- ' above the ground state.

Crystallography of Samples, Sample Preparation, and Storage

The alums are a series of double salts (Lipson and Beevers 1935) with formula

in which Ri is a monovalent metal, Riii a trivalent metal, and R" sulfur, selenium, or tellurium. The crystals belong to the pyritohedral class of the cubic system, with four R'R~~~(R"O,), 12H,O molecules per unit cell.

Recent X-ray crystallographic measurements (Sygusch 1969) have shown that CsTi alum retains its alum structure (space group) down to at least liquid-nitrogen temperatures. Bleaney et al. (1955) have concluded from their e.s.r. experimental results that CsTi alum possesses the usual alum structure at liquid-helium temperatures. There appears to be, then, no ma- jor structure change in CsTi alum in the tempera- ture region 300 to 4.2 OK.

Samples of CsTi alum deteriorate rapidly when

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MACKINNON AND BICKERTON: MAGNETIC SUSCEPTIBILITY O F C ~ T i ( S 0 ~ ) ~ . 1 2 H ~ 0

The magnetic moment (e.m.u./g) of three powdered samples of CsTi alum was obtained as a function of temperature and magnetic field. The susceptibility values were corrected for the diamagnetism of the CsTi alum lattice. In the absence of any experimental values for the diamagnetic susceptibility of CsTi alum, the value for CsAl alum (MacKinnon and Raudorf 1968) -0.5 x e.m.u./g was used.

To illustrate the nature of the transition, the magnetic susceptibility (e.m.u./g) is plotted against lOOO/T (Fig. 1). In Table I, the magnetic susceptibility values obtained from our experi- ments are shown along with the susceptibility values calculated from an expression derived by Kamimura (1956).

left exposed to the atmosphere. To prevent this deterioration, the samples were kept in the 60

Discussion

-

The change in the slope of the magnetic susceptibility vs. 1000/T curve is attributed to a low-lying excited energy state above the ground state. The presence of a low-lying excited state

mother liquor until the momeilt they were needed for the experiments. The samples were then 55- removed from the solution, powdered, and placed in the sample chamber of the Foner magnetom- 50 - eter rod, the whole operation being carried out in a nitrogen atmosphere. The samples were weighed prior to the insertion of the sample rod j45- into the magnetometer sample chamber and 5 after the completion of the experiment. "40 -

>- Experimental Apparatus and Procedure

The magnetic susceptibility measurements F: were made with a PAR Foner magnetometer in fj30- the temperature region 300 to 4.2 OK. The magnetometer was calibrated with a standard Ni sample (saturation moment o,,, = 58.6 e.m.u./g (Danan et al. 1968)). The calibration was checked with a small current dipole. The magnetic field was supplied by a Varian 12 in., 3603 electro- magnet. The magnetic field was calibrated with a 3 15. Varian F-8 nuclear fluxmeter. The temperature was measured with a copper-constantan thermo- couple with the reference junction immersed in a '0 liquid-helium bath.

Experimental Results

r n / T (OK-$

FIG. 1. The magnetic susceptibility of CsTi alum is shown as a function of 1000/T. The solid line is the theoretical expression for the susceptibility (Kamirnura 1956) with r Z A = -36.7 crn-' and h = 25.2 crn-'.

introduces an appreciable temperature depen- dence in the effective moment of the Ti3+ ions.

Using a crystalline field model Kamimura (1956) calculated the energy levels and the effective moment for a single 3d electron as a function of temperature in a field of trigonal or tetragonal symmetry. The values of the energies of the three Kramers doublets E,(O1, EL('). E3(0) (Fig. 3) and the effective moment parallel perf (11) and perpendicular pef f ( I ) to the crystal field axis of symmetry are expressed in term2 of the two parameters r ? ~ and h, where r 2 = S[f(r)l2r4dr, A is the axial field splitting param- eter, and h the spin-orbit coupling coefficient.

The susceptibility for any temperature is

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CANADIAN JOURNAL OF PHYSICS. VOL. 48, 1970

TABLE I Experimental values of temperature and susceptibility for CsTi alum are given. Theoretical values of susceptibility, pCrrZ(average), p,rrz(ll), and p , r rZ(I ) calculated from expressions derived by Kam- imura (1956) are also indicated. In the theoretical calculations rZA = -36.7 cm- and ?, = 25.2~11-'

Magnetic susceptibility

Experimental Theoretical Temperature ( x lo-6 ( x lo-' pCrrZ(average) pcrrZ(I!) ~ . r ? (+ )

(OK) e.m.u.lg) e.m.u.lg) (theoretical) (theoret~cal) (theoret~cal)

calculated from

The manner in which the average effective moment (peff(average)) changes with temperature is shown in Fig. 2. The moment changes slowly between 300 and 100 OK but more rapidly below 100 OK as redistribution of the Ti3' ions in the ds") manifold of states takes place. At 4.2 OK, the effective moment should be essentially that of the ground state. Kamimura (1956) has calculated the g factors parallel (gll) and perpen- dicular (g,) for the ground state of themanifold @(') in terms of the parameter t = r2A/h. For r2A = - 36.7 cm-' and h = 25.2 cm-' these expressions give g l l = 1.33 and g, = 0.94. The

where N is the number of molecules per g, p the magnetic moment in Bohr magnetons, P the Bohr magneton, and k Boltzmann's constant. Since powdered samples were used in our experiments, an average value for the effective moment was calculated from

~eff~(average) = +~ef f~ ( I I ) + 5peff2( 1)

The parameters I ~ A and h were adjusted to give the best fit to our experimental data (least- squares criterion). The following values were obtained :

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MACKINNON AND BICKERTON: MACINE3 TIC SUSCEPTIBILITY O F C~Ti(S0~)~.12H~0 817

CUBIC AXIAL +

SPIN ORBIT

FIG. 2. The average effective nlonlent of the Ti3+ ions is shown as a function of temperature.

e.s.r. experiments of Bleaney et al. (1955) involve only transitions between the two lowest Zeeman levels. The g factors obtained from these experi- ments were g,, = 1.25 and g, = 1.14 2 0.02. Our calculated values are in general agreement with the experimentally determined e.s.r. values but do not lie within the experimental error quoted by the authors. The experimental error in our results cannot accommodate the discrep- ancy since a change in the parameter t = r 2 A / h shifts the calculated values gll and g, in the same direction.

It has been shown that the e.s.r. spectrum from a particular alum corresponds to the structural groupinga, P, y to which it belongs (Dionne and MacKinnon 1968). The g factors of com- plex type 111 of another P alum, Ti3+-doped CSAI(SO,)~. 1 2 H z 0 were measured by Woonton and MacKinnon (1968) and found to be gil =

FIG. 3. In a cubic crystal field, the 10-fold degenerate 2D term of the Ti3+ ions splits into a 4-fold and a 6-fold degenerate state with the 6-fold degenerate state lowest. Spin-orbit coupling and an axial field further split the 6-fold degenerate state into three Kranlers doublets. In our calculation, the magnetic dcublet E3(O' lies lowest. The energy-level splittings for r 2 A = -36.7 cm-I and h = 25.2 cm-' are shown.

1.241 5 0.011 and g, = 0.931 5 0.036. The g factors of the ground state calculated from our experimental results are i11 relatively good agreement with the experimental g factors obtained from these more recent e.s.r. experi- ments.

The ~ i ~ + ions in the P alums CsTi alum and CsAl alum are strongly coupled to the lattice. This is indicated by the low g factors and fast relaxation times. Van Vleck (1935) has shown that a d ' ion in an octahedral complex, although not taking part in o bonding, can take part in n bonding. There is little evidence of such bonding in the hydrated iron-group compounds, but of all the iron-group ions, it is most likely to occur in Ti3+ which has a very spreading 3d radial wave function. A substantial reduction in the spin-orbit coupling factor from the free-ion value of 154 cm-I is not difficult to reconcile in light of the large amount of covalent bonding which appears to be present in the P alums.

Our experimental results are in essential

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818 CANADIAN JOURNAL O F PHYSICS. VOL. 48, 1970

agreement with the high-temperature magnetic assistance through Grant No. 815. One of us susceptibility results of Figgis et al. (1963) and (James L. Bickerton) wishes to acknowledge Dutta-Roy et al. (1959). Where a comparison financial assistance received from the National can be made, the magnetic susceptibility measure- Research Council of Canada in the form of a ments obtained in our experiments are -30% studentship while carrying on studies toward the higher than those of Figgis et al. (1963). M.Sc. degree.

Conclusions

A change in the slope of the magnetic suscep- tibility versus 1000/T curve was observed at approximately 30 OK. The experimental data were fitted with a single set of parameters over the temperature range 300-4.2 OK; the presence of an excited energy state -30 cm-' above the ground state, as well as a substantial reduction in the spin-orbit coupling coefficient from the free-ion value, is indicated.

The experimental results obtained are con- sistent with the high-temperature magnetic susceptibility data of Figgis et al. (1963) and Dutta-Roy et al. (1959), and the g factors calculated from the expressions used in the interpretation (Kamimura 1956) are in general agreement with the low-temperature e.s.r. g factors obtained by Bleaney et al. (1955).

Acknowledgments

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BLEANEY, B., BOGLE, G. S., COOKE, A. H., DUFFUS, R. J., O'BRIEN, M. C. M., and STEVENS, K. W. H. 1955. Proc. Phys. Soc. (London), Ser. A, 68, 57.

BOSE, A., CHAKRAVARTY, A. S., and CHATTERJEE, R. 1959. Indian J. Phvs. 33. 325.

DANAN, H., HERR, A., and MEYER, J. P. 1968. J. Applied Phys. 39, 669.

DE HAAS, W. J. and DU PRB, F. K. 1938. Physica, 5, 501, 969

DIONNE,'G. F. and MACKINNON, J. A. 1968. Phys. Rev. 172. 325.

DUTTA~ROY, S. K., CHAKRAVARTY, A. S., and BOSE, A. 1959. Indian J. Phys. 33, 483.

FIGGIS, B. N., LEWIS, J., and MABBS, F. 1963. J. Chen~. SOC. 2473.

GORTER, C. J., TEUNISSEN, P., and DIJKESTRA, L. J. 1938. Physica, 5, 1013.

KAMIMURA, H. 1956. J. Phys. Soc. Japan, 11, 1171. LIPSON, H. and BEEVERS, C. A. 1935. Proc. ROY. Soc.

o on don), Ser. A, 148, 664. MACKINNON, J. A. and RAUDORF, T. 1968 (unpublished

work) McGill University. SYGUSCH, J. 1969. Private communication. VAN DEN HANDEL, J. 1940. Ph.D. Thesis, Leiden Univer-

sity, Leiden,-l ether lands. VAN VLECK. J. H. 1935. J. Chem. Phvs. 3. 807. < ,

1940. Phys. Rev. 57, 426. The wish thank the =TON, G. A. and MACKINNON, J. A. 1968. Can. J.

Research Council of Canada for financial Phys. 46, 59.

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