Paramagnetic-resonance spectrum of gadolinium in single crystals of thorium oxide

y . Phys. Chem. ,Solids

Pergamon Press 1958. Vol. 6. pp. 315-323.

P A R A M A G N E T I C - R E S O N A N C E S P E C T R U M OF G A D O L I N I U M IN SINGLE CRYSTALS OF T H O R I U M O X I D E W. LOW* a n d D. SHALTIELt * Department of Physics, The Hebrew University, Jerusalem, Israel t Department of Physics, Israel Institute of Technology, Haifa, Israel (Received 7 ffanuary 1958)

Abstract--The paramagnetic-resonance spectrum of single crystals of ThO2 containing less than 0.01 mol. per cent of Gd 8+ has been analysed at 290 and 90°K at 3 cm wavelength. The positions and intensities of the lines are explained by a crystalline field of cubic symmetry. The ground state is split with an overall separation 8 c - - 2 d = 0"17554-0'0003 cm -1, c = 219.94-0.3 × 10-~ cm -1, d = 1.04-0.3 ×10-4cm -1, g ----1.9913t0.0005 at 290°K; and 8 c - - 2 d = 0"17964-0"0008 cm -1, c = 225"04-0'8 × 10-4 cm -1, d = 1.74-0.8 × 10-4 cm -~, g = 1-991 4-0"001 at T = 90°K. Transitions corresponding to AM = 4-3, AM = 4-4, AM = 4-5 were observed. The narrow line width of less than 1 G permits the detection of the hyperfine structure of the two isotopes 155 and 157. The ratio of the magnetic moments is /q156//~ils7 ----0.7444-0.007 and the spectra are consistent with nuclear spins of 3/2 for both isotopes. It is suggested that there are oxygen vacancies distributed at random throughout the crystal. 1. I N T R O D U C T I O N

show no absorption peaks and presumably have an excess of oxygen ions or t h o r i u m vacancies. T h e magnetic properties of gadolinium make it an almost ideal tracer of the local symmetry. Its paramagnetic-resonance spectrum differs greatly for various symmetries, and it is easy to distinguish, for example, whether the ion is surrounded b y cubic or axial symmetry. BRAUERand GRADINGER(5) and HUND and D~RRWgCHTER(6) have shown that Gd2Oa goes into solid solutions with ThO2 up to about 50 per cent gadolinium without appreciably destroying the regnlarity of the t h o r i u m lattice. Since all commercial thorium oxides, even those of high purity, contain traces of rare-earth elements, we hoped to find a small amount of gadolinium among these impurities. T h i s proved to be indeed so in many of the crystals investigated. T h e spectrum of gadolinium in a cubic field is in itself of considerable interest. T h e ground state of ssTpz is split b y a high-order perturbation under the combined action of the crystal field and spinorbit interaction. T h e exact mechanism responsible for the re* A review of the physics of electron emission from moval of the eightfold degeneracy is still a matter of conjecture. A n u m b e r of possibilities have been ThO2 has been given by DANFORTH.(I) 315 ALTHOUGH the properties of thorium oxide have been studied intensively in view of its importance in the manufacture of filaments in electron tubes, not very much research has been carried out on single crystals of the oxide. T h e few results which have appeared in the literature have i n d i c a t e d a considerable complexity in the optical and electrolytic properties of this crystal. Single crystals of ThO~ are usually red in colour, but can be bleached when heated in vacuum or in hydrogen at about 1000°C. Vacuum firing at higher temperature produces a yellowish cast. On electrolysis at high temperatures, the crystal turns uniformly black and a metallic surface layer is deposited at the cathode end.(2) T h e optical absorption has been studied b y WEINREICH and DANFORTH(3) and b y BODINE and TmESS. (4) T h e latter workers find that crystals heated in vacuum or in hydrogen at 1800°C show an anomalous absorption at about 4000 A, which they attribute to o~.¢gen vacancies or interstitial t h o r i u m ions (oxygen deficient). T h e red crystals

316

W. L O W and D. S H A L T I E L of separations of the 7/2, 5/2, 3/2 lines from the central ]/2 line were 10 : 5 : 6.* The spectrum was examined in detail at the 1 , 0 , 0 dircction and also the ] , I , 0 and ] , i , I directions. The parameters c and d were determined most accurately in the I, 0, 0 direction from the separations.

put forward involving spin-orbit interaction and the crystal field matrices in various powers. (7) The variation of the initial splitting with temperature is an important clue. This paper, therefore, reports also the spectrum of Gd 3+ at room and liquid-air temperatures. One of us (W.L.) has recently studied the behaviour of Gd 3+ in CaF2. T h e spectrum could be described by a spin Hamiltonian reflecting the cubic symmetry of CaFz. Despite the fact that Gd 3+ had an excess charge in the fluorite lattice, no distortions to within a few gauss could be observed. A suggestion was put forward that symmetric charge distributions (S states) attract nearest neighbours uniformly and prevent the formation of vacancies or associated interstitial F - ions in the

375

HT/2--H-5/2 = 1 0 c + 3 d . . . .

512

750 CO 5 c + 7 d - - 51---2" a 2

Ha/2--H-1/~. :

6c--7d + 51--2 " a 2

'~--~ ~--~I +750

a2

Hs/2--H-3/2 :

375

~,-.

CO

(1)

c°

-~--~ ~--r,~

~"l

1

56"+ 70 "-5~C"L_H~;~J= 2362.1g---I H_~,2- H3/~. 6C - 7D'~C 3 [~+ ~.~] =1417'2g

Fxo. 1. High-field (AM = q-l) absorption lines of Gd 8+ in ThO=. immediate neighbourhood. It was of interest to see whether this would hold true also in the case where the impurity ion has a smaller valence than the host lattice. The observed spectra showed many interesting aspects. We observed, for the first time to our knowledge, transitions corresponding to A M = 4-3, 4-4, and ± 5 . Moreover, the very narrow line width made it possible to detect and to resolve the hyperfine structure of the two odd isotopes 155 and 157. 2. EXPERIMENTAL RESULTS (a) Strong-field spectrum, A M = ±1 transitions The spectrum was examined at 3 cm at both room and liquid-air temperature, using conventional paramagnetic-resonance techniques. There was one ion per unit cell and the approximate ratios

We use the notation of L o w ; (7) c and d refer to the contributions of the fourth- and sixth-order cubic potential and a = gflH, where H is the external magnetic field and g the spectroscopic splitting factor. A schematic diagram of the observed lines is shown in Fig. 1. The crystals had to be carefully aligned, since the initial splitting was found to be fairly large. Even a small misalignment of less than 1° would cause a reduction in the separations of several gauss. T h e least-square result of several measurements yield the following values: c = 236.5-4-0"3 G d = 1.134-0"3G

l

T=290°K

g = 1.99134-0.0005 * We shall denote by M the M --> M-1 transition.

PARAMAGNETIC-RESONANCE and

c = 242.0±0.8 G

]

d = 1.814-0-8 G

)

T = 90°K

g = 1.991 4-0-001

SPECTRUM

317

OF G A D O L I N I U M

and are indicated in Fig. 2, which gives the variation of the energy levels with the magnetic field, using the strong-field values of c and d. These energy levels in the 1, 0, 0 direction form a closed expression and are given by:

The spectroscopic splitting factor was measured with respect to the D P P H free radical in the 1, 0, 0 direction. The line width of the M = 1/2 line in this direction is narrower than that of the free radical, and AH, the separation between these two lines, could be measured to within 0.2 G. The above value of g = 1"9913 is corrected for second- and third-order shifts. The error includes the uncertainty in AH, in the absolute values of c, d, and H. Adding all these contributions linearly, we arrive at a conservative estimate of 0.0005.

E±7/2 --

13c+5d±3a 1 2 q-~ x 140 I t

r

× [(3c--9dT]a)Z-k~-a 2]

E±51~ --

5c+7d±a 1 2 ±~X

X [(5c q- 7dq z 2a) 2+ 12a2)] t

5c-t-7dqZa

(b) Low-field spectrum At any given angle a number of additional lines of smaller intensity were observed at lower magnetic field strengths. These varied in position and intensity as the magnetic field was rotated with respect to the cubic axes. A careful study of these lines was made at and near the 1, 0, 0 direction and six such lines were observed. These correspond to the transitions :

1

/

(2)

X [(5c+7d+2a)2+ 12a2] t 13c+5d+3a

E±I/2 --

2

1 q-~X 140 ] t

I-

X [(3c--9dq-Zaa)Z+--~-a z]

Ho = E51z-+ E-al2 110 = E7/2 ~ E-1/2 Ho -= El12 ~ E-7/2

where E is measured in units of gauss and

Ho = Eal2 ~ E-5/2 Ho = Ell2 ~ E-51z

Ho = hvlgfl.

Ho = E512 ~ E-5/2

A check on the strong-field values of c and d is provided by calculating H0, i.e. hv, the applied microwave frequency. Table 1 shows the experimental results for one particular set of measurements. The average deviation is approximately one part in 1500 within the combined errors of the magnetic

Table 1. Measured low-frequency transitions H0 is calculated using strong-field values c -- 236.5 G, d = 1.13 G.

Transition

5/2--+--3/2 7/2--~--1/2 1/2-+--7/2 3/2--~--5/2 1/2-->--5/2 5/2-*--5/2

Observed H (G)

Ho (talc.) (G)

Relative intensity (measured to within 30 per cent)

Relative intensity (calculated)

944'4 847.1 789"7 645"5 645±5 626-3

3345 3343 3347 3340 3362±20g 3345

28 10 10 20 1.5 1"5

20 10 10 20 1"2 1'2

318

W. L O W and D. S H A L T I E L

z" "6

oe C

Ld

u

L~OO

4OO

EO0 t-mld~

800

1000

1200

gouss

FIG. 2. E n e r g y levels o f G d s+ as a f u n c t i o n of t h e applied external m a g n e t i c field in t h e 1, 0, 0 direction. T h e vertical lines s h o w t h e observed low-field transitions. T h e levels are calculated for c ---- 236"5 G a n d d ---- 1.13 G, c/d > O.

field measurement and the constancy of the microwave frequency between measurements. It is to be noted that the 1/2 --> --5/2 line falls nearly on top of the 3/2 --> --5/2 line and the accuracy is correspondingly poor.

The spins of 3/2 are confirmed. The results are: ~155

--

= 0.744+0.007

bt157

As57 = 5.7a-J-0.12g (c) Hyperfine structure There are two odd isotopes of Gd, 155 and 157, each of approximately 15 per cent abundance. Their hyperfine structure has been detected previously in enriched gadolinium both by paramagnetic resonance(s) and by optical spectroscopy.(9) We have observed the hyperfine structure of both isotopes in their natural abundance in all transitions of the strong-field spectrum and even in some transitions of the low-field spectrum. Fig. 3 shows a recording of the hyperfine structure of the low-field 5 / 2 - - > - - 3 / 2 transition. The reconstruction of the spectrum on a linear scale is directly below. The line width of the individual hyperfine lines is about 1 G, and the relative intensity with respect to the central peak about 1 : 20

A15s = 4.25+0.15g The ratio of the magnetic moment was determined graphically from many recordings and is therefore considerably more accurate than the absolute measurements of the intervals with proton resonance. T h e results should be compared with the previous paramagnetic-resonance results on magnesium bismuth nitrate.(s) /~155

0,75±0.07

]z1-~7

A16~ = 5.34±0.17g ~/155 = 4.0-I-0.3g

PARAMAGNETIC-RES

ONANCE SPECTRUM

and the optical determination(9) ~155

= 0.80±0.02.

~157

Our results are in agreement (within the limits of the combined errors of both measurements) with

OF GADOLINIUM

31~

culated b y KITTEL and LUTTINGER(11) for the 1, 0, 0 direction. Measurements of the line width at half power a r e very difficult, because the hyperfine lines m = ~zl/2 of both isotopes contribute appreciably to the width. Even the ratios of the "effective" h a l f width for various electronic transitions cannot b e obtained without appreciable error, since it i s found that the line width increases with M and t h e contributions to the width of the hyperfine s t r u c ture are larger for larger values of M. We have adopted a somewhat arbitrary method b y measuring the width at 3/4 intensity, where the contribution of the hyperfine lines is very small. Table 2 lists the ratios of the integrated intensity, the ratio. of the amplitudes, and the ratio of the line width. T h e values are averages for each pair of lines.

Table 2. Relative intensity amplitudes and line" widths of the fine-structure spectrum

Transition

1/2 -+ - - 1/2 4-3/2 .+ 4-1/2 4-5/2 --->4-3/2 +7/2 --> 4-5/2 I

I

II

II

I

Ratio of Ratio of Ratio of integrated amplitude line width intensity (accuracy (accuracy (accuracy 3 per cent) 10 10 per cent) p e r cent) 16 16"5 14 7-6

16 14"1 12"5 7"1

1 1.13 1.3 1"4

I

Fzo. 3. Hyperfine structure of Gd 155 (dotted line) and Gd 157 (full line) for the low-field transition 5/2-+ .+ --3/2. The top figure gives the observed derivatives of the absorption line and the lower figure is the r e constructed spectrum. the paramagnetic-resonance measurements, but the optical measurement is somewhat high. (d) Line width and intensities T h e line width and relative intensities of some ions of the S state have shown marked deviations from the theoretical values.(10) These intensities are calculated by evaluating the matrix elements. I ( m]J,]n } 12/h. F o r the strong-field transitions this is equal to J~[S(S+I)--M(M--1)]. F o r other transitions these matrix elements have been cal-

It is seen that to a first approximation the i n tensities and amplitudes conform to the theoretical ratio 16 : 15 : 12 : 7. T h e absolute full w i d t h between points of m a x i m u m slope for the M = 1/2. transition is 1 " 5 + 0 - 2 G . T h e low-field line 5 / 2 - + - - 3 / 2 has a width of 1"1-4-0"1 G. T h e uniformity and jitter of the magnetic field is. estimated to be about 0"3 G at 3000 G or about one part in 10,000. T h i s explains in part the differencein line width. T h e line width is probably less than 1 G if the contributions from hyperfine structure and magnetic field inhomogeneity are subtracted. Table 2 shows that the line width is a function o f the electronic q u a n t u m number. I t was also soon found that the line width was a function of the angle which the cubic axes made with the external; field, being very narrow at the 1, 0, 0 direction

320

W. L O W and D. S H A L T I E L

Fig. 4 shows the variation of the full width at half power as a function of the angle for the M = 5/2 line for a large crystal (0"5 cc). The line width increases and reaches a limiting value at about 15 ° from the 1, 0, 0 direction. Similar variations with angle were observed for the other transitions. One possible explanation for this behaviour is that there are a number of single crystals with slightly different orientations.

rather than of the difference between the energy levels. More work along these lines might possibly lead to the discovery of a method for investigating misalignments within a crystal. The relative intensities of the forbidden transitions are given in Table 1. There is one notable discrepancy in that the 5/2 -+ --3/2 line is of much

Seporat3on of transition

t5

Line w{dth {n gouss

4

\

-3

\

-2

//

3 2 - 30 °

"i2.5°-10°-76 ° - g ° - 2 ' . ¢ o

2'.5° 5° 7:5" ~0° ~.5 °

Degrees from the 1OO direction FIO. 4. Variation of the full width at half power of the 5/2 ~ 3/2 line as a function of the angle which the external field makes with the 1, 0, 0 axis. This would give only a small contribution near the 1, 0, 0 direction, but a large contribution at other angles. To a rough approximation this change can be found from Fig. 5, which shows the variation of the separation M = 5 / 2 - M = 1/2 with angle for two crystals misaligned by about 2"5 °. T h e effective line width is indicated by vertical lines. Between 10 ° and 30 ° the line width caused by misalignments is approximately constant. T h e slope of the 5/2 ~ 3/2 line at 10 ° is about 30 G/degree. The maximum change of the line ~idth is about 3 G and the mean misalignments must be less than 1/5 °. To a first approximation the change in line width would be proportional to the separation of the line from the central line. This is indeed observed, except for the M ~- 3/2 and M---- --1/2 transitions, which are somewhat narrower than the M = 5/2 and M = - - 3 / 2 transitions. The line width is probably a function of the variations of the energy levels with angle

20 °

" \

,

I 0°

oo

\ _1o°

_2o ~

_30 ° d

FIO. 5. Variation of the separation of the M -----5/2--M = 1/2 with angle when the magnetic field is rotated with respect to the 1, 0, 0 axis. The dotted line show* another crystal misaligned by about 2"5°. The vertical lines indicate the separation between the eentre$ of gravity of the two lines. larger intensity and amplitude than the 3/2 --5/2 line. Theoretically they should be approximately of the same order of magnitude. The ratio of the intensity of the 5/2 ~ --3/2 line is of the order of 0.05-0.03 of the 1/2 ~ --1/2 transition. (e) Radiation damage

We have exposed two small crystals (150 mg) to a 60Co source and to X-rays (150 kV, 25 mA for 3 hr). No marked change in the spectrum was observed. No additional lines stronger than I ~ of the 1/2 ~ - - 1 / 2 transition was observed. The many lines observed by FIELDS eta/.(lz) on irradiated ThOz powder must be attributed to additional impurities in these samples or to imperfect reduction of Th(NOa)4 to ThO2. Further work on irradiated ThOz is continuing in the hope of detecting an F centre spectrum, which ought to give a very sharp line.

PARAMAGNETIC-RESONANCE SPECTRUM OF GADOLINIUM 3. DISCUSSION

and

We shall divide the discussion into two parts: (a) T h e significance of these results for the understanding of the magnetic properties of gadolinium. (b) T h e evaluation of these results in relation to the solid-state properties of ThO2. (a) W e have already indicated(7) the difficulties encountered in establishing the mechanism which causes the splitting of the S state. T h e small changes in c and d as a function of temperature are indicative of the fact that the perturbation must be linear in the cubic potential and of the form

( (XT/zIL " SI

Y7/2))4
or

((X7/21L" sI YT/2))o(XT/21 vI Y7/2>, where ( X 7 / 2 I L " sI Y7/~>

(x7A v[ Y~/~) are matrix elements of the spin-orbit interaction or crystalline potential connecting states X and Y. T h e cubic potential varies inversely as 1/a 5, where a is the effective cation-anion distance. Even small changes in this distance due to contraction at low temperatures will cause a relatively large increase in the crystalline potential. Perturbations involving < I V [ > to a high power would show a larger temperature-dependence of c and d. T h i s small temperature-dependence of the cubic-field splitting seems to be a general property of all S-state ions, as seen in Table 3. T h i s is in contra distinction to the axial terms in these crystals, which change radically with temperature. T h e overall splitting of 0.175 cm -1 is somewhat larger than that of 0.1488 cm -1 for CaF2. T h i s is probably caused b y the stronger interaction of the eight O = ions with the G d 3+ than the eight F - ions with this ion.

Table 3. Cubic-field splitting parameter as a function of temperature in S states

Crystal

T (°K)

Fe z+ : KAI(SeO4)2 " 12H20

90 20

Mn 2+ : ZnSiF6 • 6HzO

290 195 90 20

Gd 3+ : CaF2

290 70

Gd 3+ : Th09

321

290 90

Cubic-field constant (c in cm-0

Reference

--0"0127 ±2 --0"0127 ±1

13

0"00075 ±1 0'0010 ±2 0"0011 -/-2 0"0009 ±2

13

0'0185 ±5 0.0197 ±10

7

0"02199 ±3 0"02250 ±8

Present work

W. L O W and D. S H A L T I E L

322

A puzzling feature is that both c and d are of the same sign. Since the thorium occupies the body centre of a cube (Fig. 6), the potential is of the form:

+B[ YeO+C7/2(Y~4+ y6-4)].

1,

v

• Thorium (3 Oxygen

Fie. 6. Crystal structure of ThO2. The thorium ions form a face-centred lattice. Each thorium ion is surrounded by eight oxygen ions.

One would expect c and d to be of the opposite sign. This again only points to the complexity of the mechanism responsible for the splitting of the ground state Assuming that in the main the 6P7/2 state is admixed to the sS7/2 state, we can estimate the deviation of the g factor from the free spin value, i.e. g -~- (1 -- o~2)g(sS7/2 ) Jr o~2g(6P7/2). The Lande g factor of the g(sS7/2) = 2.0023 and that of 6P7/2 = 1"716 and therefore 0~2 = 0"0384 or ~ = 0"197. This seems to be of the right order of magnitude, as

(sST/2[L" S]6P7/2)

e~-es V'14)t

,-~

E~--Es

1550 x ¢ 1 4 32,000

tions make this crystal an almost ideal substance for a multi-level maser. A close inspection of Fig. 2 and similar diagrams for other orientations shows that one can find suitable multi-level transitions for which the substance acts as a frequency converter in the microwave, U.H.F., or even in the radio-frequency range. Investigations along these lines are in progress. (b) T h e narrow lines (less than 1 G) and the general behaviour of the spectrum show that the cubic symmetry is preserved to a high order, despite the fact that gadolinium has a smaller valence than the lattice host. In order to maintain the neutrality of the crystal, either there are some additional positive ions or negative vacancies randomly distributed throughout the crystal. Evidence for the latter possibility comes from the X-ray measurements of HOND and DORCHW.~CHTER.(6) If this is so, our results indicate that these vacancies are not in the immediate neighbourhood of the paramagnetic ion. In this connection we should like to point out that all red crystals showed the Gd a+ spectrum, whereas one white and one black crystal showed no spectrum which could be attributed to Gd a+. If Gd a+ is present, it must be less than 10-4 tool. per cent. However, a bleached crystal showed no change in the line width or intensity of the paramagnetic resonance of Gd a+. Investigations of the variation of the spectrum with heat-treatment and electrolysis are planned. Finally we should like to suggest that the properties of thoriated tungsten filaments may be influenced by the presence of the rare-earth impurities. It is conceivable that during the activation process some of these rare-earth ions may be converted to the metal a n d diffuse to the surface. It may be well worthwhile to investigate the properties of thoriated tungsten with intentionally added rareearth impurities.

,4cknowledgernent--We should like to thank Dr. W. E. ,-~0.181,

where ~ is the spin-orbit coupling (approximately 1550 cm -1) and E~-Es is the Separation of the P state from the S state. Finally we should like to point out an almost obvious result. T h e narrow spectral lines and the relatively large intensities of the A M = -4-4 transi-

DANFORTH, of the Bartol Foundation, and Dr. G. FINLAY, of the NortonCompany, for kindly supplying a few crystals. REFERENCES

1. Dx~OarH W. E. Advances in ElectronicsVol. 5, p. 169. Academic Press, New York (1953). 2. D,~x~Om'HW. E. Phys. Rev. 86, 416 (1952). 3. WEm'~IeH O. H. and DXN~OaTHW. E. Phys. P~o. 88, 953 (1952).

PARAMAGNETIC-RESONANCE 4. ]]ODII~ J. H. and TmFss F. B. Phys. Rev. 98, 1532 (1955). 5. B~uma G. and GRADINOI~tH. Z. anorg. Chem. 276, 209 (1954). 6. HtrND F. and DtYacHw~,cI-l'I~a W. Z. anorg. Chem. 265, 67 (1952). 7. L o w W. Phys. Rev. 108, March 15, 1958 (1958). 8. L o w W. Phys. Rev. 103, 1305 (1956).

SPECTRUM

OF GADOLINIUM

323

9. SPECK D. R. Phys. Rev. 101, 1725 (1956). 10. L o w W. Proc. Phys. Soc. Lond. B69, 1169 (1956). 11. KITTEL C. and LUTTINGERJ. M. Phys. Rev. 73t 162 (1948). 12. Ftmms P., FreEDMAN A., S~tALLEa B. and Low W. Phys. Rev. 105, 756 (1957). 13. BOWERSK. D. and OWEN J. Rep. Progr. Phys. 18, 305 (1955).