PHYSICAL REVIE%' B VOLUME 46, NUMBER 2 1 JULY 1992-II

Low-temperature calorimetric study of magnetic ordering in erbium oxide

Y. J. Tang and X. W. CaoDepartment ofPhysics and National Institute for Auiation Research, Wichita State Uniuersity, Wichita, Kansas 67208

J. C. HoDepartments ofPhysics and Chemistry and National Institute for Auiation Research, Wichita State University, Wichita, Kansas 67208

and Department of Physics, National Tsing Hua Uniuersity, Hsinchu, Taiwan, Republic of China

H. C. KuDepartment ofPhysics, National Tsing Hua Uniuersity, Hsinchu, Taiwan, Republic of China

(Received 30 August 1991;revised manuscript received 19 December 1991)

Low-temperature heat-capacity measurements on erbium oxide show an antiferromagnetic transition

at 3.3 K, which is corroborated by magnetic-susceptibility data. Entropy calculations indicate that the

magnetic ordering is associated with the ground-state doublet of Er'+ ions located at one of their two

nonequivalent sites in the cubic crystal.

Rare-earth elements form the basis of a wide range ofmagnetic alloys and compounds of basic as well as tech-nological importance. They also play a significant role inthe current research on high-transition-temperature su-perconductors. Syntheses of these materials often involverare-earth oxides in the initial stage, which are thermallydecomposed during the various reaction procedures.Minute amounts of these oxides could, however, remainin the final products. It is also possible that oxidation ofrare earths would occur during high-temperature pro-cessing. Such low-level contaminations can usually be ig-nored, except in cases where the intended study on agiven specimen is calorimetric or magnetic in nature, andthe rare-earth oxide impurities undergo magnetic transi-tions in the temperature range of interest. The .

knowledge of these transitions then becomes relevant indata analysis and interpretation. Earlier studies of rare-earth oxides exhibiting magnetic ordering include thoseon, e.g., gadolinium oxide' and ytterbium oxide. Thispaper describes the determination calorimetrically ofsuch a behavior in erbium oxide.

The 0.65-g sample, in the form of a pressed and sin-tered (24 h at 980'C) disk, was prepared from JohnsonMatthey's 99.9o//o-pure powders. X-ray-diffraction pat-terns agreed well with those expected for the cubic com-pound. It was thermally anchored to a thermometer-heater assembly in an adiabatic calorimeter. Heat-capacity measurements were made between 2 and 13 Kwith pulsed Joule heating and germanium thermometry.Heat capacities of the thermometer-heater assemblyalone were separately measured for addenda correction.The overall uncertainty of the results is estimated to beless than 2%%uo.

The results in terms of C versus T are presented in Fig.1. The heat capacities C have units of J/mol deg, where"mol" (191.26 g) refers to the formula ErO& 5 containingone Er + ion. Also included are data from an earlierwork by &estrum and Justice. Their measurements from300 down to 5 K reveal a Schottky anomaly with a broad

10

0

30

0

00ErQ„s

0 This work~ Westrum 8c Justice Ref.4—CL=(1.55xl04 J/mol K4) T~

0

0 ~ 0CD ~ 0 0

000000 0

0 2 4I I I

8 10 12

FIG. 1. Temperature dependence of heat capacity. Thedashed line represents the estimated lattice contribution basedon a Debye temperature of 315 K.

peak near 35 K, but the lowest-temperature results areunreliable because of the extrapolated temperature scalefor a platinum thermometer calibrated only above 10 K.Otherwise, the two sets of data in Fig. 1 agree reasonablywell.

The A,-type anomaly occurs at 3.3 K. This is associatedwith an antiferromagnetic ordering among Er + ions.Verification is given in Fig. 2. Magnetic-susceptibility(y) data from a superconducting quantum interferencedevice (SQUID) magnetometer begin to deviate at 3.3 Kfrom the relation y=C'/(T+8), where the Curie con-stant C'=0.033 cm K/g and the Curie-Weiss tempera-ture 8=9.5 K =2.9T&. An e5'ective magnetic momentof 7.1p& can thus be derived for Er +. Detailed analysisof the magnetic heat capacity requires the subtractionof lattice term (CL ) from the total heat capacity. Thisrelatively small contribution [Cz = ( l.55 X 10 J/mol K ) T ] is approximated by using a same Debye tem-perature of 315 K as that for isomorphic GdO& ~ and

46 1213 1992 The American Physical Society

1214 BRIEF REPORTS 46

2.7

I

O 2.5

2.4—

0~ ~

~ ~ ~~ ~

B. = 20G

E( 0„

0l

P/

P

0/

/

2.3

00 126 8 10

«oo OOOO 0 OOOO)

14

3O

2

FIG. 3. Temperature dependence of magnetic heat capacityin terms of CM /T vs T. The dashed lines represent the assump-tions based on a T' dependence of CM below Tz and a quickdrop-off at higher temperatures. The magnetic entropy changecan be evaluated from the area under the curve.

I I I I ~ I ~ I I I ~ I I I ~ I ~ I ~00 10 20 30 40 50 60 70 80 90 100

FIG. 2. Temperature dependence of magnetic susceptibilityin an applied magnetic field B,=20 6, showing (aj an antiferro-magnetic transition at 3.3 K and (b) a Curie-Weiss fit at highertemperatures.

YbO& 5. The difference plot in Fig. 3 represents the tem-perature dependence of CM/T, where CM =C—CL. Thearea under the curve gives magnetic-entropy changeASM= f (CM/T)dT. In principle, for Er + with J= —", , atotal magnetic entropy should be R In16, with R beingthe gas constant. However, a complete excitation fromthe ground state requires much higher temperatures thanthe range being covered here. The magnetic heat capaci-ty in Fig. 3 is likely induced only by the antiferromagnet-ic ordering with a Neel temperature Tz =3.3 K, plus thelow-temperature end of anomalies centered around 35 Kor higher. Such anomalies are associated with crystal-field split tings.

Assumptions are made to have a rather quick drop-offfor CM at higher temperatures and CM = (0.23J/mol K ) T as an approximation below 2.3 K, based onthe antiferromagnetic spin-wave model. Entropy associ-ated with the magnetic ordering can now be estimatedfrom Fig. 3 by integrating the area under the smoothcurve drawn through the C~/T data, as well as the

dashed-line extrapolations. This gives a b,S~ value of4.14 J/mol K between 0 and g K, which is smaller thanR ln2=5. 76 J/rnol K as expected for a ground-state dou-blet. The difference is too large to be accounted for bythe uncertainties introduced through the data extrapola-tions.

The more likely explanation to this observation may beas follows: As pointed out by Westrum and Justice,there are two crystallographically nonequivalent Er +

sites in the lattice. Both sites are coordinated to six oxideions at the corners of a cube, but with the two unoccu-pied corners located either on a body diagonal (for Er +-Ipossessing diagonal axial symmetry) or on a face diagonal(for Er +-II possessing diagonal axial symmetry), respec-tively, in the ratio of 1:3. Since the symmetry of theligand field profoundly affects the splitting of the magnet-ic ion state, Er +-I and Er +-II could have different ener-gy levels. The observed b,S~ is indeed close to 75% ofR ln2. It is therefore concluded that the heat-capacityanomaly at 3.3 K arises from the antiferromagnetic or-dering among Er +-II. Ordering of Er +-I may occur attemperatures below 2 K. The occurrence of twin-peakanomalies of this type has been reported earlier for iso-morphic GdO& &. Similar effects also prevail in manypure rare-earth metals. For example, neodymium hastwo distinctive ordering temperatures at 8 and 19 K, re-spectively, for the magnetic moments at two nonequiva-lent sites in a double-hexagonal-close-packed structure.

The work at Wichita State University was supportedby Ametek, Inc. and Kansas Technology Enterprise Cor-poration; the work at National Tsing Hua University wassupported by the National Science Council of R.O.C. un-der Contract No. NSC81-0208-M007-003.

BRIEF REPORTS 1215

L. T. Crane, J.Chem. Phys. 36, 10 (1962).O. V. Lounasmaa, Phys. Rev. 129, 2460 (1963).W. E. Henry, Phys. Rev. 98, 226 (1955).

4E. F. Westrum, Jr. and B. H. Justice, J. Phys. Chem. 67, 659(1963).

58. H. Justice and E. F. %estrum, Jr., J. Phys. Chem. 67, 345(1963).

See, e.g., C. B. Zimm, P. M. Ratzmann, J. A. Barclay, G. F.Green, and J. N. Chafe, Adv. Cryog. Eng. 36, 763 (1990).