S. K. KURTZ AN D W. G. NI LSEN

where ) is the spin-orbit coupling constant (positive forless than half-filled shells). In deriving these rela, tions,it is assumed that the lowest orbital level is non-

degenerate, that there is no mixing of this level with

higher orbital states and that spin-spin interactionswithin the ion can be neglected. From the g values givenin Table I, these relations predict D positive and Enegative in agreement with experiment. However, themagnitude of X calculated from the equation for 2D is

significantly larger than the free-ion value" of +92 cm 'in apparent disagreement with the decrease in A usually

'7 D. S. McClure, in Solid State Physics, edited by F. Seitz andD. Turnbull (Academic Press Inc. , New York, 1959), Vol. IX,p. 428.

fpundia, i8, ig in the crystal. This anomaly may indicatethat the eBect of configurational mixing or spin-spininteractions should be taken into account in the deriva-tion of the equations for D and E given above.

ACKNOWLEDGMENTS

The authors wish to thank J. J. Rubin and L. G.Van Uitert for providing the zinc tungstate crystals,J.B.Mock and H. W. Reinbold for assistance in makingthe measurements and Mrs. W. I. Mammel for pro-gramming the energy level calculations. The authorsalso benefited from discussions with J. E. Geusic, E. O.Schulz-DuBois, H. E.D. Scovil, M. Peter, and S. Geller.

's J. Owen, Proc. Roy. Soc. (London) A227, 183 (1955).'s M. Tinkham, Proc. Roy. Soc. (London) A236, 549 (1956).

PHYSICAL REVIEW VOLUME 228, NUMBER 4 NOVEM B ER 15, 1962

Paramagnetic Resonance and Charge Compensation of Tetravalent Uranium (U'+)in Calcium, Strontium, and. Barium Fluorides

AMNON YARIV

Bell Telephone Laboratories, Incorporated, MNrray IA'l/, Rem Jersey

(Received June 12, 1962)

A new electron spin paramagnetic resonance spectrum in CaF2 doped with uranium is attributed to U4+.

The spectrum possesses axial symmetry about the (111)directions and is describable by a spin Hamiltonianwith g&=0+0.15 and gll =3.238&0.005 at 4.2'K. The trigonal symmetry is due to the presence of chargecompensating 0' iona along the (111)directions. The spectrum is absent in crystals grown under reducingconditions. Similar results were also observed in SrF2 and BaF2.

I. INTRODUCTION

't+ARAMAGNETIC resonance studies of uraniumhave been limited mostly to the trivalent ion. ' '

Ghosh, Gordy, and Hill' have reported a resonance in

UF4,. unfortunately, the powder form of the sample andthe high concentration made the interpretation difficult.Paramagnetic resonance on solid solutions of Th02.U'+

has been observed by I lewellyn' with g=2.7. In this

paper we report on a paramagnetic resonance spectrumobserved in single crystals of CaFs doped with 0.1%%u~

of uranium. After accounting for the resonance lines

arising from U'+ ions in sites of fourfold symmetry' andlines due to U'+ ions in sites lacking axial symmetry, weare left with a set of lines possessing a threefold sym-metry about the (111)cube diagonals. This spectrum isassigned to U'+ ions substituting for Ca++ ions. Theextra positive charge (+2e) is believed to be com-

' B.Bleaney, P. M. Llewellyn, and D. A. Jones, Proc. Phys. Soc.(London) A69, 858 (1956).' G. Vincow and W. Low, Phys. Rev. 122, 1390 (1961).

3 C. A. Hutchinson, Jr., P. M. Llewellyn, E. Wong, and B. P.Dorain, Phys. Rev. 102, 292 (1956).

4 S. N. Ghosh, W. Gordy, and D. G. Hill, Phys. Rev. 96, 36(1954).

s P. M. Llewellyn, thesis, Oxford, 1956 (unpublished).

pensated by two 0' ions replacing two F ions alongany of the (111)directions, thus giving rise to the ob-served trigonal spectrum. The assignment of thisspectrum to U'+ ion (Sf') rather than U'+ ions (Sf') isbased on certain features of the paramagnetic resonancewhich can be explained if we assume a low-lying non-Kramer's doublet arising from an even number ofelectrons. This assignment is strengthened further bythe dependence of the U4+ spectrum on the crystalgrowing conditions. The bulk of the investigation wasdevoted to CaF2 host crystals. The presence of U4+ wasdetected also in SrF~ and BaF2.

II. EXPERIMENTAL RESULTS

The ground state of tetravalent uranium is 'H4. Thepresence of compensating charges along the (111)directions, which is described in Sec. V, causes the localsymmetry of the U4+ ion, which substitutes for a Ca++ion, to be of the trigonal, Ca„type. The ninefold de-generacy is split into

2A i+A s+3Ei,i.e., into three doublets and three singlets with one of thedoublets lying lowest. The observed paramagnetic

TETRAVALENT U (U4+) IN Ca, Sr, AND BaF 1589

16

14lfJU)D~& 120~ )0

Q

LU

U 6I-

4

Lo cj Fj(c

V=23.587 MC7-42 K

2I

[os] cos' (~s) [i ~oj0'-40 -20 0 20 40 ' 60 80 'IOO

IN DFGREES120 140 160

FIG. 1.Variation of the resonance magnetic Geld for the trigonalsites as a function of the angle between the magnetic field and thetrigonal axis. The magnetic Geld is in the (110}plane. The solidcurve is based on Eq. (2}with 6=0 and gi I =3.238. The circles areexperimental points.

resonance spectrum at low temperatures ((20'K) isdue to transitions between the Zeeman split levels of thelow-lying doublet. The eigenfunctions of this doublet,in perfect C3, symmetry would be made up of an ad-mixture of states with 7=4 and J,=+4, ~1, W2,which is such, as will be discussed in more detail inSec. IV, that in addition to having g&

——0, which isusually the case for non-Kramer's doublets, (n!A!P)is also zero and no transitions should be observed. Theobserved transitions are found to be due to the com-ponent of the microwave 6eld which is parallel to thetrigonal axis. This can be explained if we assume randomlocal departures in the crystal from the perfect C3„symmetry. These distortions will cause an additionaladmixture, most probably of the type AM = ~2 whichintroduces the ! 0) wave function thus making possible53f=0 transitions.

For an arbitrary direction of the dc magnetic field,we find four lines which are due to charge compensationalong each of the four (111)directions. These lines arefully consistent with a Hamiltonian

,'I('. =g((PS,H, +A,S,+A„S„, .

where P is the Bohr magneton. S„S„andS„arethecomponents of the eRective spin vector S with S=-', .H, is the projection of the dc magnetic field along the"s"direction which is the direction of the trigonal axis.gII is the component of the g tensor along the trigonalfield axis. 6 and A„represent the departure from axialsymmetry. Within the framework of the eRective spinHamiltonian, the terms A,S, and A,S, in Eq. (1) causea 65,=~1 admixture, thus making possible 65,=0transitions when the rf magnetic held Hl has a z

component.

TRl GON

I

I

OR F SI&ES————

TR IGONAXIS F

SITE

AXISD

FIG. 2. The location of the four trigonal axes in relation to thecubic structure and the magnetic Geld. The direction of each vectorcan be ascertained from the position of the two black dots. The(110) plane is dotted.

Diagonalization of Eq. (1) yields

[Pg~) 2 +271/2H= )

gimp cosg(2)

where A'=A, '+A„',8 is the angle between the applieddc magnetic field H and the trigonal field (z) axis.

Assuming the distortion parameter lP to have arandom symmetric distribution about some mean valueand recognizing that the strength of the transition for aspin packet characterized by a given lV is proportionalto lV, it follows that spins with a high value of 6' absorbmore energy than the same number of spins with alower value of 6'. This fact, coupled with the depen-dence of H on A' [Eq. (2)7, leads to the observedasymmetric line shape with its steep drop on the high-field side as exemplified by line C in Fig. 3. To obtain

gt&, the dc magnetic field was measured at the base ofthe absorption line on the high-field side, where 6=0, at0=0'. The result is

! g&&! =3.238~0.005 at 4.2'K.

The rms value of 6 was estimated by assuming aGaussian distribution for (A'), s

(A')& 2&(10i7 cgs 0.1 cm '

Since the highest magnetic field available in thisexperiment was 15 000 G, our estimate of g& was notbased on a direct measurement but rather on the fitbetween the experimental resonance data and thegeneral (g, 40) form of Eq. (2)

6 B.Bleaney, P. M. Llewellyn, M. H. L. Pryce, and G. R. Hall,Phil. Mag. 45, 991 (1954).

[(~)s A271/2

II=p[g„'cos'|/+gi sin'|/7'"

(3)

AM NON YARI V

The result is

8c——p+ cos '(1/%3) = (p+54.76',

8D ——y —cos '(1/K3) = y —54.76',8~= cos '((cosy)/v3),

(3)

where y is the angle between the magnetic field vectorand the i 001j direction.

The solid curves of Fig. 1 were obtained by usingEq. (2) with lg„l=3.238, 6=0 and the respectivevalues of 8 as given by Eqs. (3). When +=0', i.e., whenthe applied magnetic field is parallel to one of the cubeedges, we have

18~I = 18~ I

= i8~I =cos '(1/v3)l,

g~ ——0~0.15.

Figure 1 shows the variation of the observed mag-netic field H as a function of the angle q between theapplied magnetic field and the L001j axis. With themagnetic field applied in the (110)plane, two of the fourtrigonal lines are due to sites whose axes lie in the (110)plane at 54.76' and —54.76'

i icos (1/&3)j withrespect to the L001j direction. The spectra of these sitesare labeled D and C, respectively. The remaining twotrigonal sites are equivalent and give rise to a single linewhich is labeled, in Fig. 1, as F. The position of the fourtrigonal sites in relation to the basic cubic cell contain-ing the uranium ion is shown in Fig. 2.

The angle 9, between the applied magnetic field andeach of the four trigonal axes, is given by

experimental points in Fig. 1 are those of the center ofgravity of the doublet.

Figure 3 shows an absorption run taken at q =40'.No field modulation is employed so that the ordinate isproportional to g"H~, . Only line C and the doublet Fare present at this orientation. Line D occurs at a valueof H which is outside our reach. The crystal orientationis such that the rf magnetic field is nearly perpendicularto the trigonal axes of sites C and D, a fact which ex-plains the relative weakness of their absorption as com-pared to that of the two Ii sites.

The lines labeled as A and 8 arise from the tetragonalU'+ sites discussed by Bleaney et at.' The compensationaxis for the site giving rise to line 8 is the

i 001j direc-tion and is contained, along with the magnetic field, inthe (110)plane. The sites with axes along the (010) and

i100j directions are magnetically equivalent when H is

in the (110) plane and give rise to line A. Small devi-ations from perfect alignment will split this line into adoublet. The remaining lines, X~, X2, X3, X4, and F,belong to yet another site discussed separately in Sec.VI. Since all the crystals investigated had a considerablefraction (ranging from 0.1 to 0.99) of tetragonal sites,we are including in Fig. 4 a plot of the resonance mag-netic field for these sites as a function of p underexperimental conditions identical to those specified forFig. 1. The data of Fig. 4 can be fitted with

l &g~~ l

=3.528+0.005 and

l g& l

= 1.875&0.005. The small dis-crepancy between these values and those reported byBleaney et at' could be due to the fact that our data wereobtained at 4.2 K while theirs were obtained at 20'K.

and the three spectra coincide. The extrema of each ofthe three spectra occur at the maxima and minima oflcos8l as given by Eq. (3). This constitutes sufFicientproof for the trigonal symmetry of the sites.

Small deviations from perfect alignment of the crystalwill spoil the perfect equivalence of the two sites whichgive rise to spectrum F and the latter appears as adoublet. The doublet separation is zero at @=0 andincreases as p is increased from zero toward 90'. The

III. EXPERIMENTAL NOTES

The experiments were conducted at 4.2'K. Strongresonance signals were also observed at 20'K but not at78'K. This is probably due to short thermal relaxationtime at the latter temperature. The paramagneticresonance spectrometer was of the superheterodyne type,with an intermediate frequency of 60 Mc/sec, capableof covering the 21—24 kMc/sec range. The signal and

:aa'?«c::cc?:9a;:;?Cc''? ... :.."..'c?ca«a'?: .:?':': ' »'. ,';;. . . , , ?».. ., ,a. ."c:,. :.::Ccc:c'?»: '.;:;:;Ca??';',:»??::?::&»c:CC

'ale::ci tax 4t"'?c .!'c?Cia'ci'ci'i«ra!:i:",' '' ". '::ici: r?c'"' " 'i::::.;:5c'c:." c::i!'",?':,':,' i:: "..'i'i,'?ciicrciai, :."'.4': ra!ci:

a?ABC«::?ca'''?cr»$'4$»i»" @i'ca:",c .:?'«c?+»i,:.?:c»4%,'-'.i?a?c??Nk'j: .:'c? '.??r;.c ?Ca a

g$ ~'c ~' c"x0+'4!flat 'Pfa, '.» ':«4 i" ' '''a'c'a', , ~«', ta»' .'++?«Ci?r ."i?."?r . '.":!~i'i ~'a? '. '.atc'c', ,'?c'ci'Fa

~'+ xa «N axe ' ' '~?: A~."..::. w.:?acxc:.xra ''a»«?a:.j ', ':.;%.... : »a?«cac .?ca??»ra

. :,. ~' -''. ':-.y", g.':.', :. : .',', . .. .. l;,.'.

. .'

.: .:,I &': ', 3~41~'R~"'&':,"'-:-"4' '' ',"."... ' '-, ' ' ' '

. , ; ' ' ' ."' '~:;":,"'"%':; ',, tI, 4%4'444 7 '&.ll"

FIG. 3. Actual absorption run at @=40'.The ordinate is proportional to y"II1~,is marked by the magnetic Geld values.

»a.

tcjiir! '? '''«ta"'"c:,:::;.,':, ." ',:,",';, i:;::''»i 'ic '?.".'c,:,':,:'.«Sac."",:.:;:;;~''j''»:,','» i''c $'c' '» .'c: '': a c'.

»3

+

'. ~. ::::i'.;.:L:.. . . .:.";:-: ~. ~-''.:::::r:::;-:;::,":4 . . ;

c:aca. ' .a c»

The abcissa

TETRAVALENT U (U4+) IN Ca, Sr, AND BaF

local oscillator power were provided by two stabilized2K33 klystrons. The sample cavity operated in theTED~~ mode with the sample placed at its center. Thesample and cavity orientation were such that the rfmagnetic field at the sample position was always per-pendicular to the dc magnetic field.

The coupling of the cavity as well as the sensitivity ofthe receiver to x" or p' were controlled by a variable-coupling scheme which was previously described byGordon. ' The precision measurements of the magneticfield were performed by a nuclear magnetic resonanceprobe and frequency counters. The rf frequency wasdetermined by measuring the beat frequency obtainedby mixing the signal power with a known harmonic of aquartz crystal stabilized 20-M%ec oscillator. Thecrystals were oriented with the aid of an x-ray goni-ometer.

Magnetic fields of up to 15 kG were provided by a12-in. Varian magnet rotatable about a vertical axis.Linear sweep of the magnetic field was provided by theuse of a function generator. Sinusoidal sweep of up to50-G peak amplitude and at frequencies of up to 100 cpswas used when phase sensitive detection was employedand was provided by Helmholtz coils wound around thepole faces.

IV. THEORY

The crystalline electric field at the site of the uraniumion possesses a threefold C3, symmetry. The electricfield can be expanded in terms of the generalizedLegendre polynomials I' "(g,oo). Since we are dealingwith a Sf configuration, only terms with ts(6 yieldnonzero matrix elements. The terms with odd e areomitted because of parity considerations. ' The per-turbation Hamiltonian has the form'

V =A os' os+A o'I'os+Ass(F s'+ V—s')

+A o'I'o'+As'(I's'+ I'-s')

+Ass(Vos+ F' s'). (4)

The ninefold degeneracy of the sH4(5 fs) ground statecan be shown by group-theoretical methods to be splitinto three doublets and three singlets. The observedabsorption is due to transitions between the Zeemansplit levels of the lowest doublet. The wave functionsfor the doublet are made up of linear combinations ofthe J=4 manifold wave functions. If the linear com-bination is dominated by a single member IM) we

expect the relation

to hold, where A is the Lande-g factor. For 'II4 A. =0.8and since gii =3.238, 3f=2. The wave functions of the

' J. P. Gordon, Rev. Instr. 32, 658 (1961).' W. Low, Paramagnetic Resonance in Solids (Academic PressInc. , New York, 1960), p. 12.' R. J. Elliot and K. W. H. Stevens, Proc. Roy. Soc. (London)A215, 437 (1952).

10

8—

I—Uj

4

V= 23.587 MC

T = 4.2oK

OTI001]

I

-40 -20 0 20 40 60 80 100 120IN DEGREES

140 160

FzG. 4. The resonance magnetic field for the tetragonal sites ofU'+ as a function of the angle between the magnetic field and theL001] direction. The magnetic Geld is in the (110) plane.

doublet are thus dominated byI2) and

I

—2). Sinceadmixture of AM =~3, &6 is allowed by the perturba-tion Hamiltonian for Cs„symmetry LEq. (4)$. Thetotal wave functions can be written as'

V. THE CHARGE COMPENSATION

The replacement of an ion belonging to the hostcrystal by an impurity ion with a different net charge

's B.R. Jndd, Proc. Roy. Soc. (London) A232, 458 (]955).

where a&c and b(c. The minus sign preceding theI

—1) ket is necessary in order to make

gs ——2(tsl L,+2S,I p) =0.

The paramagnetic resonance data are not suflicient to.solve for a, b, c. We can only write two equations:

ps+ $2+cs —1

which is the normalization condition and

g„=2(PIJ,IP)=4a'+b' —2c'=3.238

for the three unknowns a, 6, and c. To solve for a, b, andc, it is necessary to use optical absorption data in orderto evaluate the "A" parameters in the spin Hamil-tonian. We have neglected the added admixture fromthe 'II5 level.

As mentioned earlier, the matrix element, (crIJ,

lp)' is

zero when ln) andI p) are given by Eq. (5). The effec-

tiveness of the "s"component of the rf magnetic field ininducing transitions is attributed to further admixture,caused by local departures from C3, symmetry, whichmakes possible AM=0 transitions. This assumption iscorraborated by the asymmetric resonance line shape as,discussed in Sec. II.

i592 A M NON YA R I V

requires charge compensation to restore the electro-static charge neutrality. The crystal structure of CaF2is O~' which can be described as a cubic lattice of F ionswith Ca~ ions at every other body center. Thus eachuranium ion, substituting for a Ca~, is at the center ofa cube of eight F ions. The tetragonal spectrum of U'+in CaF& was explained by Bleaney et al.' as being due toan interstitial F ion occupying the otherwise vacantcenter of nearest cube along any of the (100) axes. Thepossibility of charge compensation via the replacementof one of the nearest F ions by an 0' ion was sug-gested by Feofilov and Stepanov. ""This scheme givesrise to spectra possessing threefold symmetry about the(111) directions. Experimental verification for thiscompensation scheme in CaF2.0d'+ was provided bySierro." Additional confirmation for the existence ofthis mechanism was provided by the work of Forresterand Hempstead'4 on CaF2 ..Tb'+. Cubic sites in CaF2.U'+were described by Vincow and I.ow. ' In the case ofCaF2.U4+ the excess +2t, charge, introduced into thelattice when a U4+ ion replaces a Ca~, has to be com-pensated. This can take place by having two F ionswhich are on opposite sides of the U4+ ion along the cubediagonal, replaced by 02 ions. A second mechanism,less likely but one we couM not rule out, involves theoccupation of the first cube center (normally vacant)along any of the (111)directions by an 02 ion.

Partial confirmation for the validity of the mechanismproposed above was provided by the dependence of theconcentration of U4+ on the crystal-growing conditions.The crystals were grown by W. A. Hargreaves of Opto-vac Inc. , using the Stockbarger —Bridgeman method inwhich a graphite crucible containing molten CaF2 anduranium was gradually lowered through a heatinginduction coil. If the crucible and the melt were keptat 100'C above the melting temperature for 2 hbefore cooling, no trace of U'+ was found in the crystal.This is probably due to the reduction action of thegraphite crucible. The compensation mechanism postu-lated above depends on the presence of oxygen in themelt. If the oxygen is removed by the carbon, com-pensation cannot take place and the uranium enters thecrystal as U'+ in tetragonal sites and the compensationis achieved by interstitial F ions.

It may be of interest to note in this connection thatthe present investigation arose from an eAort to lower

" P. P. Feo6lov, J. phys. radium 17, 656 (1956).""P. P. Feollov, Doklady Akad. Nauk. USSR 99, 731 (1954)."I.V. Stepanov and P. P. Feo61ov, Soviet Phys. —Doklady 1,350 (1956).

"Jerome Sierro, J. Chem. Phys. 34, 2183 (1961).'4 P. A. Forrester and C. F. Hempstead, Phys. Rev. 126, 923

(1962).

the threshold for optical maser action in CaF2.U'+ andthat only after the complete elimination of the U'+ ionsdid the threshold become low enough so that continuousoperation, rather than pulsed was achieved. "

VII. RESONANCE IN SrF&'.U4+ AND BaF~'.U4+

Trigonal spectra attributed to U'+ were also observedin SrF2 and BaF2 doped with uranium. Due to the largeamount of strain in the crystals, the lines were verybroad which decreased the accuracy with which the spinHamiltonian parameters could be determined. Theseparameters are:

SrFg ..U'+

BaF2.U4+gl ~

= 2.85+0.05, g~ 0, at 4.2'K;

gii 3, gg 0 at 4.2 K.

A brief account of this work was given by the authorat the First International Conference on ParamagneticResonance, Jerusalem, Israel, July, 1962.

ACKNOWLEDGMENTS

It is a pleasure to acknowledge the extremely helpfulcommunication with Professor B. Bleaney who firstsuggested the possibility of the U4+ spectrum. W. A.Hargreaves of "Optovac Inc. ,

" provided the manycrystals investigated and was instrumental in establish-ing the correlation between the growing conditions andthe U+ concentration. We have also benefited frommany discussions with Dr. J. P. Gordon and from theable experimental assistance of J. !hi. Dziedzic.

'~ G. D. Boyd, R. J. Collins, S. P. S. Porto, and W. A. Har-greaves, Phys. Rev. Letters 8, 269 (1962)."S. P. S. Porto and A. Yariv, J. Appl. Phys. 33, 1620 (1962).

VI. NONAXIAL SITES

In the course of this investigation we found, in addi-tion to the tetragonal U'+ and the trigonal U4+ spectra,an additional group of lines shown in Fig. 3 as Xz, X2,Xs, and I'. The optical spectrum of the sites giving riseto these lines occupies the same general spectral regionas that of the CaF~.U'+ tetragonal sites. The lines areconsequently believed to arise from U'+ ions in a newsite which lacks an axis of symmetry and which gets itscharge compensation from F ions in the next nearestinterstitial cube center. Fuller details on these sites willbe given in a separate paper.

We have referred to the trigonal spectrum on twoprevious occasions"" as being due to U'+. This assign-ment, as made evident by the present paper, was inerror and should be corrected to CaF2..U4+.