Magnetic form factor of Eu2+ in EuO

~~atrna~ of Magnetism amdMagnetic Materials 5 (1977) 258 -262 o North-Holland Publishing Company

LETTER To

E EDITOR

MAGNETICFORM FACTOR OF Eu2+ IN EuO *

J.W. CABLE and W.C. KOEHLER &Co&d S;ate DhGsion,Oak Ridge NationalLaborertory,Oak Ridge, Tennessee 37830, USA Received 12 May 1977

Polarized neutron measurements of the magnetic form factor of Eu2+ in EuO were made, to checik for possible solid state effects on the radial extent of the 4f wavefunctions in this ferromagnetic insulator. Previous studies show good agteement between thle magnetic form factors observed for the heavy rareearth metals and those calculated for the free ions using relativistic Dirac-Fock wavefunctions. However, the same comparison in this case shows an approximate 9% expansion of the 4%wavefunctions in EuO relative to that calculated for the Eu2+ ion. This apparent solid state effect has the .sazmesign but twice the magnitude of that recently calculated by Byrom, Ellis and Freeman for (EuO~)-~~ clusters.

1. Introduction magnetic moment is all spin moment and, since the 4f shell is half filled, the spin and charge densities are the same. The big disadvantage for neutrons is the high absorption cross section of the Eu (-1600 b at 1 A) ‘which means that small crystals and relatively long counting times are required.

It has long been expected that solid state effects would be unimportant for the 4f electrons in the heavy rare earths and that the 4f charge and spin densities should be well approximated by free ion wavefunctions. This seems to be the case for the heavy rare earth metals Gd and Er for which good agreement is obtained between the observed [ 1,2] neutron magnetic form factors and those cal::ula~ed [2,3] for the tripositive ions using relativistic Dirac-Fock wavefunctions. The situation is less clear for rare earth oxides. Neutron polarization analysis data for Gd2Q3 were originally interpreted +?J to indicate a significant contraction (-10%) of the 4f spin density relative to that in the metal. Although most of this difference has mow been removed by a careful reanalysis [4] including spin correlations, it was this result which provided the original motivation for this nleutron study of the magnetic furm factor of EuO. In many respects IEuO is the ideal rare earth containing insulator for sucF1a neutron study. magnetic [S] m a readily accessible temperature region iTc = 69.3 K) and ha:; the simple rocksalt structure. The Eu is divalent with an 8S7,2 ground state so the

2. IExperimentaJ results The EuO single crystals used in this study were prepared at the IBM Thomas J. Watson Research Center and were kindly supplied to us by Dr. LB. Torrance. They are nominally 1%deficient in Eu and therefore remain insulating at low temperatures [6]. The actual Eu content was established from magnetization measurements made on one of the crystals by Prof. J.S. Kouvel. If x is defined as the fraction of vacant Eu sites, then there are 2x Eu3+ions and (1 - 3x)Eu2+ ions on the Eu sites. The observed magnetization of 6.73 & per Eu site at 4.2 K and 20 kOe corresponds to x = 0.013 assuming 7 flB pe: Eu2+and zero moment for the Eu3+ and 012- ions. In the polarized neutron method, one measures the ratio of intensities at the Bragg positions for incident neutrons polarized parallel and antiparallel to the sample magnetization. With magnetization perpendic-

* Pesearch sponsored by Energy Research and Development Administration ratia,n.

under contract with Union Carbide Corps

258

J. W. Cable, W.C. Koehkr /Magnetic form factor of Eu2+ in EuO

ular to the scat#ering plane, this so-called flipping ratio R is related to $he magnetic structure amplitude FM by

(1) where FN is the nuclear structure amplitude, 6 is the change in nuclear amplitude due to nuclear polarization and the upper signs are for (FM +a)& < 1 while the lower signs are for (FM + ~)/FN > 1. The 6 term is proportional to a Brillouin function of pNH,&T and is usually insignificant. However, because of the large Eu nuclear moments and hyperfiie field, there is some polarization of the Eu nuclei even at 4.2 K so that a small 8 correction must be applied. The correction can be experimentally determined since FM and FN are both temperature independent at low T while 6 follows a Curie law ?-‘-dependence. With 6 determined, FM is then extracted from eq. (1) using known values of FN. In this rocksah structure, FN = &, exp(- I+$, sir&/h*) + be exp(-I+$ sin20/Xf) where 5~~ is the average nuclear scattering amplitude at Eu sites, be = 0.5803 X 1O-l* cm, the I+? are Debye-Waller factors and the f sign is for all even (+) or all odd (-) hkl reflections. Because of resonance scattering, by:, is wavelength dependent and must be determined for each neutron wavelength used in the experiment. Flipping ratio measurements were made on two single crystals of EuO at 4.2 Kin a vertical magnetizing field of 20 kOe. One of these crystals was pillar shaped with dimensions 0.6 X 1.OX 2.5 mm and the other was disc shaped with thickness CL46mm and a diameter of approximately 5 mm. In each case the crystal was mounted with a (110) direction parallel to the applied field and data were collected for the first 21 Bragg reflections at X = 0.75 t8 and for the first 14 reflections at 1.067 8. A Eu filter was used to avoid & beam contamination at 1.067 A anld calculations showed no significant IX correction at either wavelength. Corrections for incomplete incident polarization, flipper efficiency and sample depolarization were applied. Observations on equivalent reflections with different pathlengths through the crystals gave no indication of extinction as should be expected for these highly absorbing crystals. The corrected flipping ratios

259

were in good agreement for the two crystals so averaged data were used to obtain the (FM t 6)/FN values listed in table 1. This table represents a total of 284 separate measurements with approximately four runs per reflection for each crystal at each wavelength. The quoted errors include the rms deviations and an estimated 50% uncertainty in the instrumental and depolarization corrections. The latter are particularly large for the (002) and (220) reflections which have (FM + 8)jF~ values close to unity. As a check on these data, measurements were made at 96 K for the six innermostreflections at X = 1.067 A. This increase in temperature reduces FM by a factor of about six so that the instrumental and depolarization corrections become unimportant. Values of (FM + ~)/FN for the (002) and (220) reflections obtained at 96 K but normalized to 4.2 K by taking temperature ratios of the (222), (004), (224) and (440) reflections are given in the last column of table 1. These are more reliable than the values actually obtained, at 4.2 K. Table 1 shows larger (& + ~)/FN values at 0.75 A than at 1.067 A. This arises from the aforementioned wavelength dependence of by”. In analyzing these data, we assume that the O*- ions have no moments so that

where &u is the average magnetic scattering amplitude at the Eu sites. From the large (FM + b)lFN values of the ail odd reflections, it is clear that 7;~~is comparable in magnitude to bo. Thus these ratios provide a sensitive determination of bEu when properly normalized. For this normalization, we define r as the ratio of (FM t S)/FN for the odd relative to the even reflections at the same sin 6/X. The FM t6 terms then cancel le,aving I-‘-l -=_ r-1

b. e-(Wo-

W&sin*tY/A*

BEu

(3)

which was least squares fitted to determine 5~” and (W, -- I+,) by using r’s taken from interpolation of the all even data to the sin 0/X positions of the aii odd data. The fitted values are: 5~” = (0.601 t Q.002) X lo- l2 cm ,

wo- WEU = (0.200 rt 0.026) X 1O- l6 cm* , at 0.75 A and

.KW,C&b&,W.C. Koehler /Magnetic formfuctorof Edi

260

Table 1 Magnetic to nudear structure amplitude ratios for EuO at 4.2 K and 20 kOe. --A = 1.067 A &=0.X A lrkt

&+#+6 -

FM’6

f:

111 113 331 333 1ts

1.6 0.7 0.2 0.2 0.2

58.6 26.7 14.1 1.9 7.9 1.295 0.87 2 0.710 0.57 1 0.385 0.27 1 0.226 0.230 0.147 0.129 0.062 0.040 0.035 0.037 0.024 0.006

224 440 442 006 226 008 660 228 662 664

15.02 8.29 4.75 3.07 3.03 1.181 0.801 0.647 0.539 0.338 0.242 0.203 0.212 0.143

0.030 0.035 0.013 0.006 0.003 0.002 0.001 0.001 0.00 1 0.001 0.001 0.002 0.002 0.001 0.001 0.002

f

FN

FN

FN

X=l*OUP FMfS

f

in EuO

0.14 0.09 0.03 0.012 0.01 0.030 0.015 0.007 0.004 0.002 0.001 0.00 1 0.001 0.001

3.049

0.7 89

0.010 0.008

* Data obtained at 96 K to avoid large instrumental and depolarization corrections but normalized to 4.2 K,

5~” = (a.673 5 0.003) X 10-l 2 cm , fz’t, -

V& = (0.225 .k 0.034) X I O- l6 cm2 , .

at 1.067 8. The wavelength dependence of be:” is given by ~~~ = b& + Ab’ + iAb” where I!$!”is the non-reso-

Table 2 Eu nuclear scattering amplitudes at 0.75 A and 1.067 A. h(A)

1b

-Abu b

__

____----

&u

bEu a

Ab

0.75

0.601

0.609

1.06’7

0.5'3 . 0.6>32

-0.323 -0.272

_--__I

-

-0.040 -0.025

a 1;Eu = (1 - X&u, x = 0.013 ’ Caiculated from the Breit-Wigner formula c bEu = b& + Ab’ + iAb”

0 c bEU

0.93 1 0.954

nant amplitude and Ab’ and Ab” are the real and imaginary resonant increments. The latter were calculated by use of the Breit-Wigner formulation using known resonance parameters and the relevant amplitude components are given in table 2. The agreement of the bgu values st the two wavelengths shows that our bEUvalues are consistent with this formulation. Mavingthus established FN at the two wavelengths, only 6 is required to obtain FE” from the data of table L.. ..,.,a ,r cy. 1_ \LJ. f3-I Tl., C r-..-rrL:--.-..e r,lm,, r..,LLrr uy UPG VI lilt: u bvllcc;l.lvIP WilJ UlhGll IlVlll 1IlG temperature dependence of FEu + 6 at thz (662) position where &u is small. From data taken at 1.84,4.2 and 15.6 K, we obtain &u + 6 = 0.20 + 0.020 T-’ which corresponds to 6 = 0.005 X 1O-l2 cm ti 4.2 K. The &corrected magnetic amplitudes are given in table 3 along with Ef values obtained from the expression j&u = 0.27 Ef using the average j!& data.

J. W. Cable, W.C. Koehler /Magnetic form factorof Eu2+ in EuO

261

Table 3 Magnetic amplitudes and cf v&es for EuO at 4.2 K and 20 kOe. -_-_A = 0.75 A

A = 1.067 A

x=1.067BL*

hkl

FEU

f

FEu

f

111 113 331 333 115

1.41 0.88 OS9 0.40 0.40

0.12 0.06 0.04 0.03 0.03

1.44 0.87 0.54 0.37 0.57

0.04 0.03 0.02 0.01 0.01

002 220 222 004 224 440 442 006 226 444 008 446 660 228 662 664

1.519 1.017 0.824 0.659 0.439 0.305 0.253 0.257 0.161 0.141 0.064 0.039 0.034 0.036 0.021 0.002

0.035 0.041 0.015 0.007 0.004 0.003 0.002 0.002 0.001 0.001 0.001 0.002 0.002 0.001 0.001 0.002

1.470 0.992 0.797 0.66 1 0.409 0.290 0.241 0.252 0.167

0.037 0.019 0.009 0.005 0.003 0.002 0.002 0.002 0.002

sin 6

f

FEu

-ii-

0.1685 0.3224 0.4237 0.505 1 1.310 0.982

0.013 0.010

0.1944 0.2749 0.3368 0.3 887 0.476 1 0.5500 0.5832 0.6448 0.6733 0.7767 0.8015 0.8249 0.8473 0.9119

P

f

5.34 3.22 2.02 1.40 1.37

0.14 0.10 0.06 0.04 0.04

5.00 3.65 2.97 2.45 1.572 1.092 0.915 0.943 0.602 0.522 0.237 0.144 0.126 0.133 0.078 0.007

0.04 0.03 0.03 0.02 0.007 0.006 0.005 0.005 0.003 0.004 0.004 0.007 0.007 0.004 0.004 0.007

* 96 K d:Btanormalized to 4.2 K.

3. aiscussion

The observed iif values are plotted versus sin 0/h in fig. 1. These exhibit the smooth variation expected for the spherically symmetric spin density of an S state ion. However, the radial dependence differs from that calculated [7] from relativistic Dirac-Fock wavefunctions for the Eu2+ion. This is shown in fig. 1 where the solid curve is the calculated Dirac-Fock form factor normalized to the average moment of 6.73 pu. The observed form factor falls off more rapidly with spin 0/h and indicates an approximate 9% expansion of the 4f wavefunctions in EuO relative to those in the Eu2+ ion. This is somewhat surprising since the free ion calculations give agreement with the observed form factors for Gd [ 1,3] and Er [2] and also for the Tb3* ion in Tb(OH)3 [8]. However, recent molecular clwster calculations [9] show that small solid state effects may be expected in EuO. The calculations indicate a 4% expansion of the

0

0.2

0.4

0.6 sin

0.6

8f,,

Fig. 1. Averaged Ff data of EuO at 4.2 K and 20 kOe. The open (closed) data points are for all odd (even) hki reflections with the point at the origin taken frcm the bulk magnetization. The solid curve was ~lculated for the Eu2+ ion from relativistic Dirac-Fock wavefunctions (ref. [ 71).

J.1(1. Cat&,W.C.Kixehler /hffrgnctic formfuctor of &i2+inEuO

262

4fwavefmctions in (EuO$*clusters relative to those in the Eu2+ ion. The present results suggest an even targer effect in EuO. c

Acknowledgements The authors are indebted to Dr. LB. Torrance for furnishing the single crlystals used in this study and to

Professor J.S. Kouvel for magnetization measurep:ents on these crystals.

References [l] R.M. Moon, W.C. Krxhler, J.W. Cable and N.R. Child, Phys Rev. BS (1972) 997.

[2]C.Stassis, G.R. Kline, AJ. Freeman and J.P. Desclaux, Phys. Rev. B13 (1976) 3916. 13) A J. Freeman and J.P. DescIaux, International J. Ma8 netism 3 (X972) 311, [4) R.N. Moon and W.C.Koehler, Phys. Rev. Bll(1975) 1609. [S) B.T. Matthias, R.M. Bozorth and J.H. Van Vleck, Phys. Rev. Lett. 7 (1961) 160. [6 ] M.W.Shafer, S.B. Torrance and T. Penney, J. Phys. Chem. sotids 33 (1972) 2251. [7] AJ. Freemanand J.P. Desclaux, private communication. [8] G.H. Lander, T.0. Brun, J.Z. Desclaux and A.J. Freeman, Phys. Rev. B8 (1973) 3237. [9]E. Byrom, D.E. Ellis and A.J. Freeman, Phys. Rev. B14 (1976) 3558.