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VOLUME 75, NUMBER 17 PHYS ICAL REVIEW LETTERS 23 OcToBER 1995 Quadrupolar Effect in X-Ray Magnetic Circular Dichroism Christine Giorgetti and Elisabeth Dartyge Christian Brouder and Franqois Baudelet and Laboratoire de Metallurgic Physique et Sciences des Materiaux, BP. 239, F-54506 Nancy, France Claire Meyer, Stefania Pizzini, Alain Fontaine, and Rose-Marie Galera Laboratoire de Magnetisme Louis Neel, 23 rue des Martyrs, B.P. 166, F-38042 Grenoble Cedex 9, France (Received 9 June 1995) Quadrupolar (E2) transitions in x-ray magnetic circular dichroism at the L«& edge of Yb in YbFe2 are evidenced through temperature and angular dependences. The choice of Yb is particularly relevant since E2 transitions come as a single peak. The width, position, and intensity of the E2 contribution are determined. The E2 peak appears in the middle of the dipolar signal. These measurements allow for the determination of dipole and octupole moments of the 4f shell, whose angular and temperature dependences were found to be in agreement with calculation. PACS numbers: 78.70.Dm, 78.20.Ls Interpretation of x-ray magnetic circular dichroism (XMCD) at the Lit i it edges of rare earths is still a matter of discussion. Carra and Altarelli pointed out that electric quadrupolar (E2) transitions towards the 4f shell might be significant in these spectra [1]. They showed that this E2 contribution could be ob- served through its angular dependence which is differ- ent from the cos0 variation of dipolar (El) transitions (0 is the angle between the magnetic moment and the x-ray wave vector). Further calculations [2 7] and other spectroscopic techniques [8,9] confirmed the relevance of E2 transitions. After many unsuccessful experiments [10], the first evidence for E2 contributions to XMCD was published recently [11], confirming the idea that the low-energy peak is entirely due to E2 transitions [5]. On the contrary, we show that the E2 peak lies between two El featuves in YbFez. E2 angular dependence can be written as [4, 12 15] o(0) = Acos0 + Bc s o( 05cso0 3), where A. and 8 have different temperature dependences for rare earths. This point of view was confirmed by the change in shape observed in some rare-earth spectra [16]. In this paper, we study the E2 contributions to XMCD at the Limni edge of Yb in YbFe2. Firstly, we show the angular dependence of XMCD at 10 K; secondly, we prove that the peak corresponding to E2 transitions exhibits the temperature dependence calculated from the crystal and exchange fields of the compound. These results enable us to characterize the position, width, and intensity of the E2 transitions and to compare them with the corresponding calculated quantities. The dipole and octupole moments of the 4f shell can be discriminated and measured with this technique. The choice of Yb is particularly relevant to point out E2 transitions, since the E2 contribution to XMCD is made of only one line at the L»& edge and does not exist at the Lii edge. The initial and final state configurations can be written as 2p 4f' and 2p 4f ', respectively. The ground state of Yb + is J = 7/2, and the possible final states are J' = 1/2 at the L i i edge and J' = 3/2 at the Ltit edge. Because of the E2 selection rules ((AJ( 2), only the J' = 3/2 final state can be reached. Since the 2p core hole is deep and the 2p spin-orbit is very large, no external perturbation (exchange or crystal field) can modify the LSJ coupling of the final states. A more detailed analysis, using an expansion into el- ementary spectra [13] or the E2 sum rules [4], shows that the intensity of the E2 line for a powder is given by Eq. (1) for right-circularly polarized (negative helicity) x rays with A = 30I o (M) and 8 = I o ( 4 M 5M3), where (M) and ( 4 M 5M ) are the average value of 185 (J, ) (dipole moment, proportional to the 4f magnetic mo- ment) and ([3J(J + 1) 1]J, 5J ) (octupole moment of the 4f shell) in the initial state (the z axis is along the 4f moment). The advantage of Eq. (1) is that the geometrical factors (cos0) and the details of the ground state ((. .. )) are decoupled so that temperature, magnetic field, or crystal field effects are summarized in the average values. I~0~ is a positive number, proportional to the square of the reduced E2 matrix elements and to the number of holes [4, 13]. According to Eq. (1), when the magnetic moment of Yb + is saturated (M = 7/2) and when the magnetic field and x-ray wave vector are aligned (0 = 0 ), the E2 contribution is zero. It becomes nonzero by rotating the magnetic field or raising the temperature, because the second term of Eq. (1) decreases faster with temperature 3186 0031-9007/95/75(17)/3186(4)$06. 00 1995 The American Physical Society

Quadrupolar Effect in X-Ray Magnetic Circular Dichroism

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Page 1: Quadrupolar Effect in X-Ray Magnetic Circular Dichroism

VOLUME 75, NUMBER 17 PHYS ICAL REVIEW LETTERS 23 OcToBER 1995

Quadrupolar Effect in X-Ray Magnetic Circular Dichroism

Christine Giorgetti and Elisabeth Dartyge

Christian Brouder and Franqois Baudelet

and Laboratoire de Metallurgic Physique et Sciences des Materiaux, BP.239, F-54506 Nancy, France

Claire Meyer, Stefania Pizzini, Alain Fontaine, and Rose-Marie GaleraLaboratoire de Magnetisme Louis Neel, 23 rue des Martyrs, B.P.166, F-38042 Grenoble Cedex 9, France

(Received 9 June 1995)

Quadrupolar (E2) transitions in x-ray magnetic circular dichroism at the L«& edge of Yb in YbFe2are evidenced through temperature and angular dependences. The choice of Yb is particularly relevantsince E2 transitions come as a single peak. The width, position, and intensity of the E2 contributionare determined. The E2 peak appears in the middle of the dipolar signal. These measurements allowfor the determination of dipole and octupole moments of the 4f shell, whose angular and temperaturedependences were found to be in agreement with calculation.

PACS numbers: 78.70.Dm, 78.20.Ls

Interpretation of x-ray magnetic circular dichroism(XMCD) at the Lit i it edges of rare earths is stilla matter of discussion. Carra and Altarelli pointedout that electric quadrupolar (E2) transitions towardsthe 4f shell might be significant in these spectra [1].They showed that this E2 contribution could be ob-served through its angular dependence which is differ-ent from the cos0 variation of dipolar (El) transitions(0 is the angle between the magnetic moment and thex-ray wave vector). Further calculations [2—7] and otherspectroscopic techniques [8,9] confirmed the relevanceof E2 transitions. After many unsuccessful experiments[10], the first evidence for E2 contributions to XMCDwas published recently [11],confirming the idea that thelow-energy peak is entirely due to E2 transitions [5]. Onthe contrary, we show that the E2 peak lies between twoEl featuves in YbFez.

E2 angular dependence can be written as [4,12—15]

o(0) = Acos0 + Bc so(05cso0 —3),

where A. and 8 have different temperature dependencesfor rare earths. This point of view was confirmed by thechange in shape observed in some rare-earth spectra [16].

In this paper, we study the E2 contributions to XMCDat the Limni edge of Yb in YbFe2. Firstly, we showthe angular dependence of XMCD at 10 K; secondly,we prove that the peak corresponding to E2 transitionsexhibits the temperature dependence calculated from thecrystal and exchange fields of the compound. Theseresults enable us to characterize the position, width, andintensity of the E2 transitions and to compare them withthe corresponding calculated quantities. The dipole andoctupole moments of the 4f shell can be discriminatedand measured with this technique.

The choice of Yb is particularly relevant to point out E2transitions, since the E2 contribution to XMCD is madeof only one line at the L»& edge and does not exist atthe Lii edge. The initial and final state configurationscan be written as 2p 4f' and 2p 4f ', respectively. Theground state of Yb + is J = 7/2, and the possible finalstates are J' = 1/2 at the L i i edge and J' = 3/2 at theLtit edge. Because of the E2 selection rules ((AJ( 2),only the J' = 3/2 final state can be reached. Since the2p core hole is deep and the 2p spin-orbit is very large,no external perturbation (exchange or crystal field) canmodify the LSJ coupling of the final states.

A more detailed analysis, using an expansion into el-ementary spectra [13] or the E2 sum rules [4], showsthat the intensity of the E2 line for a powder is givenby Eq. (1) for right-circularly polarized (negative helicity)x rays with A = 30I o (M) and 8 = I o ( 4 M —5M3),where (M) and ( 4 M —5M ) are the average value of185

(J,) (dipole moment, proportional to the 4f magnetic mo-ment) and ([3J(J + 1) —1]J, —5J ) (octupole momentof the 4f shell) in the initial state (the z axis is along the4f moment).

The advantage of Eq. (1) is that the geometrical factors(cos0) and the details of the ground state ((. . .)) aredecoupled so that temperature, magnetic field, or crystalfield effects are summarized in the average values. I~0~

is a positive number, proportional to the square of thereduced E2 matrix elements and to the number of holes[4,13]. According to Eq. (1), when the magnetic momentof Yb + is saturated (M = —7/2) and when the magneticfield and x-ray wave vector are aligned (0 = 0 ), theE2 contribution is zero. It becomes nonzero by rotatingthe magnetic field or raising the temperature, because thesecond term of Eq. (1) decreases faster with temperature

3186 0031-9007/95/75(17)/3186(4)$06. 00 1995 The American Physical Society

Page 2: Quadrupolar Effect in X-Ray Magnetic Circular Dichroism

VOLUME 75, NUMBER 17 PHYSICAL REE VIEW LETTERS 23 OcToBER 1995

than the first term, which v'

ee great advanta e

e magnetic

or other rare earths

reopas q. (1) is als, is

and octu o1 o [17 .c ra shape which is diff

The compound Ybpe cphase M C

e2 crystallizes in theCu 't'"'t"" 't hi htic 'nd Mossbauer me

revi-

t""1'nt 't't' 'f Yb

e ic oy b

11 1 [20J.comp where each sub'

p nsation temper-

moment.su lattice has e ua

lier for T The corn enscomp and

comp= 28 —3 K h

mpensation temperatas been checke

a ure

ermal variation of the by measurin th

CD measurements at the L rrr gont eener dgy pe positron-in ecteL, , rance. The ol

g I at

crystal, focusinse was a

he, w ere the sam 1

poes of

armonics wer e rejected by a mirrample was placed H

a photodiode arrarray detector. Ri hty a mirror positioned b f

'g ' ypo ons ppolarizatio

ariz ed

selected by position rate around 0.6

h bTheT absorption spectra w

sam les iec ra were measure'

n geometr i, in transmissiod on powder

to thepp ied alternativel y parallel (o.+ and cr

y, in a magnetic fi ld

) p ( )

1900 airio, t e spectra are

timp s of measuremments. The

the average of

b 20h Lwere d

Low tern eratur

y le e rjge ato .h'" 1' "034 T p

gy

I,ra measured at thee CD s ectr

1 d d

0

t A o d' toE 1 pand zero for 0 = 0 (atT =OK).

II

e= 66.

1.6

1.2

COCO

XCl0~ 08

04

0.0

-20 20 -20 0 20

E —Eo (eV)

FIG. 1. Yb LJ/I ed e X

E — Eo (eV)

Liii edge XMCD spectra of

re divided by cos66 .and 66 . Spectra for

e A cocomparison of the two s ectrah' ""'ddi"'n 1

bl f 0='

iona peak aroundOK

, which~ p po

spectra have bee ln 1g. 2

departure from th e cosO de endee een reversed. Thee strong

spectrum revealss unambiguousl tpen ence of the rest fs o the

central peak.s y the E2 nature f hre o the

The an ulag ar dependence ields-,-.d f-- h--eoretical arguments. At a tove, the spectra are reversee reversed and are still made of

h''""'"100 d 5contribution. T g p

o lo'

. : (i) a strai htze as

MCD signal (dotted 1

g leone tangent to the

4 eV i'o e line) was drawn

, (u) a Gaussian ron between —5 and

line wanpro eof width o = . u

i h li (doand the

b i d h d'ffhese E1 s ectra

andspectra are composed f

i e sign and ths an angles.

s ape at

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Page 3: Quadrupolar Effect in X-Ray Magnetic Circular Dichroism

VOLUME 75, NUMBER 17 PH YS ICAL REVIEW LETTERS 23 OcTOBER 1995

I I I I [ I I I I[

I I04~ ~

jj0.2—

/C

//

LD

o 0.0C)

XC5O

-0.2— E1~ E2

fit— — -- XMCD

/rj

//

/

-0.4-20 -10 0 10

Energy (eV)

20

FIG. 2. Decomposition of the XMCD spectrum for 50 K and0' (dotted line) as the sum of a Gaussian peak (full line) andan El contribution (dashed line). The dots result from thedifference between the XMCD spectrum and a straight linedrawn between —5 and 4 eV.

35 s

3.0—

2.5—

2.0

1.5—

1.0

0.5E2(0 ) / E2(66')E1(0') / E1(66')

0.00 50 100 150 200 250 300

Temperature (K)

FIG. 3. Ratio of peak intensities of 0 = 0 and 66 for F 1

and E2 contributions. The thick (thin) full line is the calculatedvariation of the E2 (El) contribution.

The temperature dependence of the intensities of E1and E2 contributions is complex because the sampleis not saturated and changes of magnetic moments areintermingled with anisotropy effects. Therefore we havestudied the temperature dependence of the ratios (0 over66 ) of the El and E2 areas, which are presented inFig. 3. As expected, the El ratios are consistent with aconstant value of 1/ cos66 (thin line). The E2 ratio startsfrom a very small value at 10 K and increases towards theE1 value at high temperature. We have simulated theE2 ratios by calculating I(0 )/I(66') from Eq. (1). The

crystal field and exchange field parameters used for thiscalculation were taken from Ref. [19]. As seen in Fig. 3,the experimental variation is consistent with the calculatedcurve (thick full line), although the experimental pointsare somewhat above the computed values for E2. Thisdiscrepancy can be explained by noticing that, at 0.34 T,the magnetization is not saturated and the sample is adistribution of domains. This distribution can be takeninto account by averaging over 0 around a mean 00 in

Eq. (1) [7].From the width of the E2 peak, we calculated the ab-

solute intensity of E2 transitions using Cowan's program[21], and we normalized them with respect to the edgejump using the absolute E1 cross sections published inRef. [22]. The intensity of the E2 peak obtained for afully saturated Yb ion at 0 K (M = —7/2, p4f 4p, ii)and a polarization rate of 1 is 52 X 10 . XMCD mea-surement for an applied magnetic field of 1 T at 300 K(where p, 4f = 0.63p, ii) yields an E2 peak with inten-sity 4 X 10 . This corresponds to an E2 intensity of25 X 10 at 0 K. The agreement is correct when thecircular polarization rate is taken into account.

The third important parameter is the energy positionof the E2 transitions. The position of the E2 peak withrespect to the E1 white line can be compared with a rela-tivistic ASCF calculation carried out with Desclaux pro-gram [23]. The difference between the 2p 4f' Sd 6s'and 2p 4f '35d 6s' average configuration energies is—10 eV. This is larger than the experimental energy dif-ference between the top of the white line and the E2 peak(—5 eV). This energy shift can be used as a reference forthe calculation of E2 contribution for the other rare earths.It is compatible with the energy difference between dipoleand quadrupole contributions found by Krisch et al. [24].

By studying the angular variation of XMCD given inEq. (1), and by comparing with calculated E2 transitionsshapes, one can determine the dipole and octupole mo-ments of the 4f shell. This is possible because the cal-culation of E2 transitions can be made accurately withatomic structure programs [21] and because all spectra canbe written as the sum of a dipole and octupole momentsmultiplied by a fixed spectral shape [17]. The octupolepart of the E2 transition can be obtained from angulardependent measurement. This allows for the determina-tion of the position and width of E2 transitions. Fromthese parameters we can calculate the dipole moment part[A in Eq. (1)] and extract it from the experimental spec-tra. The quadrupole moment can be determined for cer-tain rare earths with MOssbauer spectroscopy. XMCD is aunique tool for the measurement of the octupole momentwhich can be used to fit the crystal and exchange field pa-rameters of the compound.

The accurate determination of the quadrupole contribu-tion is necessary to obtain a reliable E1 XMCD spectrum.At the L~~~ edge of Yb in YbFe2 the E1 contribution toXMCD spectra is made of two peaks. A similar shape

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Page 4: Quadrupolar Effect in X-Ray Magnetic Circular Dichroism

VOLUME 75, NUMBER 17 PH YS ICAL RE VIE%' LETTERS 23 OCTOBER 1995

was observed at the Lttt edge of the heavy rare earths (R)in RFez compounds [25]. This contradicts the idea that thefirst peak is due to F2 transitions [5]. In XMCD spectra atthe Lt t edge of Yb [26], only one peak is observed, so thatthe statistical ratio of —2 between E1 XMCD signals atthe I ii and I ~iq edges is not satisfied. This is connectedto the spin-orbit effect on the 5d shell.

In conclusion, the F2 transitions in XMCD were ob-served at the I.II~ edge of Yb in Ybpe2. Our results con-firm unambiguously the prediction of Carra and Altarelli[1]. We have extracted the width, intensity, and energyposition of these transitions and compared them with cal-culated values. Temperature variations of the ratios ofF2 terms at 0 and 66' were found to agree with calcula-tions. Dipole and octupole moments of the 4f shell canbe determined from F2 spectra. This opens the way to anaccurate determination of the F1 contribution and to thestudy of 5d magnetism in rare earths.

We are grateful to M. Perroux who prepared the samplein the high pressure setup of the Laboratoire de Cristal-lographie (CNRS, Grenoble) and thank Ph. Sainctavit,H. Maruyama, and J. Lang for their comments andsuggestions.

[1] P. Carra and M. Altarelli, Phys. Rev. Lett. 64, 1286(1990).

[2] P. Carra et al. , Phys. Rev. Lett. 66, 2495 (1991).[3] J.C, Lang et a/. , Phys. Rev. B 46, 5298 (1992).[4] P. Carra et al. , Physica (Amsterdam) 192B, 182 (1993).[5] X.D. Wang et al. , Phys. Rev. B 47, 9087 (1993).[6] X.D. Wang et al. , J. Appl. Phys. 75, 6366 (1994).[7] J. C. Lang et al. , Phys. Rev. B 49, 5993 (1994).[8] J.P. Hannon et al. , Phys. Rev. Lett. 61, 1245 (1988).[9] K. Hamalainen et al. , Phys. Rev. Lett. 67, 2850 (1991).

[10] Ho&Fe, O, z [14,15,27], GdzCo &z [28], ErzCo &z [28],ErzFe, 4B [3], HoFez [29,30], DyFez [30], ErFez [30,]YIG [15], and YbFez [16].

[11) J.C. Lang et al. , Phys. Rev. Lett. 74, 4935 (1995).[12] Ch. Brouder, X ray Absorption -Fine Structure (Ellis

Horwood, New York, 1991),pp. 106-108.[13] Ch. Brouder, Compte rendu des -Journees Grand Est, -

edited by J.-P. Kappler (University of Strasbourg, Stras-bourg, 1994), p. 53-7.

[14] K. Shimomi et al. , Jpn. J. Appl. Phys. 32, Suppl. 32-2,314 (1993).

[15] H. Yamazaki et al. , Jpn. J. Appl. Phys. 32, Suppl. 32-2,317 (1993).

where

x g('IT&'I )(—1) S"(2J+ a+ I)!

/2 a 2~ (I 1 2)~1 1 2l~, qm —n m') ~, qA p, m) qA' p,

' m')

This equation describes the quadrupole contribution toXAFS as a sum of spectral shapes weighted by groundstate properties of the 4f shell ((i~!T '

~i)) [31],and by thepolarization state of the x rays (S('l ). For powders,the relevant terms are So = I/(10~5) and To = 1 for

(O) (0)

the isotropic spectrum and

(t) l(6 x E )z (3) t(E. x E )z(5kSp and Sp10/30 10/70

3)

To =2J, and TtI~ =4[5J, —3J(J + 1) + I]Jz

[19][20]

[21]

[22]

[23][24][25][26][27][28][29]

[30][31]

for the MCD spectrum.C. Meyer et a/. , J. Phys. 38, 1449 (1977).C. Meyer et al. , J. Phys. 40, 403 (1979).J.J.M. Franse and R. J. Radwanski, in Handbook ofMagnetic Materia/s, edited by K. H. J. Buschow (Elsevier,New York, 1993), Vol. 7.R. D. Cowan, The Theory of Atomic Structure and Spectra(University of California Press, Berkeley, 1981).E.B. Saloman et al. , At. Data Nucl. Data Tables 3S, 1

(1988).J. Desclaux, Comput. Phys. Commun. 9, 31 (1975).M. H. Krisch et al. , Phys. Rev. Lett. 74, 4931 (1995).Ch. Giorgetti, Ph. D. thesis, University of Orsay, 1994.Ch. Giorgetti et al. (unpublished).P. Fischer et al. , Solid State Commun. 82, 857 (1992).P. Fischer et al. , J. Appl. Phys. 69, 6144 (1991).F. Baudelet et al. , J. Electron. Spectrosc. Relat. Phenom.62, 153 (1993).J.C. Lang et al. , Phys. Rev. B 50, 13 805 (1994).L. C. Biedenharn and J.D. Louck, Angular Momentum inQunatum Physics (Addison-Wesley, London, 1981).

[16] Ch. Giorgetti et al. , Physica (Amsterdam) 208 2-09B, 777(1995).

[17] The general formula for quadrupole transitions at the L ~~ ~&,

edges of rare earths is [13]

rr~(to) = zr nhaz —k P(2a + 1) P(—1)J3 J J J'

X l(J'llr'C"'IIJ)l'a(E, —E, —h~)

3189