Neutron diffraction study of magnetically ordered TbAsO4

~EUTRG~

~IF~CTrO~ STUDY OF MAGNETICALLY ORDERED ‘&A&3., W. 5k&‘mr and 0. WILL

~~~~s

Iastitutder

~njv~i~t Bonn, Lehretuhl Mr Minerabgie tmd K~s~i~~hie S&lo& 53M) Ban 1, West Germany

Poppelsdorfer

(Received 22 May I!+?&accepted I1 September 1978) moment undergoesa magneticphase transition at TN = 13 K into a helical an~e~om~tic with the propagation vector alo~~&aOl] end the moments perpendicular to[oOlJ. The pupation period is 1972 12 A, divot to 31 zk2unit cell constaats. The neutron d~~~t~n results are discussed in connectionwith previouslymeasuredmacroscopicdata. Abstract-T%As&

contignration. Thespiralis planar,

1. UWROINYCMON

Karlsruhe,had been groundfrom crystals grown by a flux method[M]. For neutron diffraction the material was contained in an Al-cylinderof 7 mm diameter and M mm height. The diagrams (Fig.‘1) wete taken at tlte DID0 research reactor in Jtllkh on the powder d~~~tomet~ KATINKA[lSl in steps of 0.1’ in 28 with a neutron wave le@b of 1.203A. The 4.2K pattern was measured with a feud better statistics than the I.1 K pattern. For the low tempernture diffraction measurements at 1.1K the sample was mounted in a 3He-cryostat with ‘He exchange gas surrounding the sample. After precooling the sampIe to 1.5K by puck ou the liquid 4He-reservoir and simultaneousIycondensing the ‘He, temperatures down to 1.1K were reached by pumping with a charcoal aeon pump on the %e-bath. Because the ‘He could not be regenerated con~~sly the coolingprocedure had to be repeated several times in order to receive a complete diiraetion diagramat 1.1K.

The series of the rare earth compounds RRXO,, with RE = rare earth, X = P, V or As, has been extensively studied recently by optical methods, specitk heat ~~~e~nts and susc~b~i~ using. The maininterest centeres on the magneticorderingobserved at low temperatures TN,preceded by a crystallogmphic phase ~sitiun at Td caused by a cooparative JahnTeller distortion. The magnetic ordering and the magnetic seethes can reliably studied only by Yukon di&action[l]. At present only in compounds in which the ordered magnetic moments are not parallel to the c-axis undergo a e~s~I~phi~ phase trnnsition at 7” r TN to lower symmetry: DyVO,[2], DyAsO,[3], TbI%[Ql. When the moments are oriented along the c-axis (optical axis) no reduction in symme~ could be observed: DyPU&j. GdVG,jfil, GdAsCkP]. In this paper we wish to report on the magnetic structure of TbAsO+as studied by neutron diEraction. TbAso* undergoesa ~~~~~ phase transitionat Td = 27.7+O.SK and a magnetic phase transition at TN= 1.48f 0.04K. Both transitions were extensively studied by therma&& spectroscopic[9] ard magnetic measurements[IO]. The first transition has been attr&uted to a long range interactioncaused by a Jahn-Teller distortion along[lIOl reducingthe symmetry to orthorhombic F&d. This has been studied by X-rayflll and neutron diffraction[l2), where the sync as well as the crystal structures could be determined. The magnetic phase transition at 1.48K is caused by induced moments between the two singlet crystal geld ground states of the Tb3* [email protected] in~~n has been calculated using a dipole field and the exchange tietd. This led ta an ~~~u~~ 0~~~ with dominantlynearest neighbor interaction[l3), based on a simpletwo-s&la&e magneticstructure. In that paper it was ehtcidated, that the moments should point along the orthorhombic[ MO]direction.

TbAs04 crysta&es at room temperature in the tetragonal &on-type-structure, space group 14kmd - D$,, with four formula units in the unit cell. A crystallographic phase transition to F&&f-T)g is observed at 27.7Kfll,l2] with a in along theflfOI direction. The new unit cell is described by oath* ‘t’2 * awu, &a=q2*Ilt#@ and cm=ct(Rf (u@fr=7.090K c,= 6.320& with fractinnal changes af Ad =-A# equal to 12.4vBI-' A.TIEvohneof the unit ceil is therefore un&an@ within expnrimemalaccuracy. The magnetic Tb ions, as well as the As ions, stay in general positions in the new orthorhombicspace group F&f. The nearest nsighbm uses are not atkted by the lattice distortion: nnfn K) = 3.881it 0.002A; un(4.2K) = 3~79 rt0.001A. IIS evatrtption of the magnetic neutron d&&ion data will therefore be done with the original tetragonal unit cell. This also aRows fairIy easy a cornparisan of the TbAs04 magnetk stpucturewith those of related compoundsstudied previously.

The experiments were performed on powdered material. TbAsG* powder, which had been hindly provided by Dr. G. Miller-Vogt, Technische Universitit

~~~~~~~~ With four Tb ions per unit cell, four &near conRgurationsare possible: (+ + + +) (If-tic), (+-+-) and (+--t+) with the signs (+ + --),

239

240

W.tiCdFF.Rand G. WILL

SCRTTERING Fig. 1. Neutron

RNGLE

2

THETR

IN

DEGREES

diiraction

patterns of TbAsO, at 4.2 K (top) in tetragonal indexing and 1.1 K (bottom). The correspondingorthorhombicindexing due lo the crystallographic phase transition at 27.7 K is given between the patterns. In the lower pattern the satellite indexingis shown.

referring to the Tb positions 0 0 0, 0 l/2 l/4, l/2 l/2 l/2, l/20 3/4 in the tetragonal unit cell. Table 1 lists the tetragonal and orthorhombic indexing together with the calculated intensities for these four possible models, with the spins being parallel (cpC= 0”) and perpendicular (cp, = 90”) to the c-axis. It can easily be realized that the low temperature diffraction diagram is not in accordance with any co&ear, or even with a simple linear magnetic moment configuration. For exampk. we do not observe the (loO)- and (11l)-reikctions at 28 = 9.7 and 17.6”resp., which must be present for the contigurations (+ + --) +). The configuration (+ - + -), which has or (+ -been proposed by Kahle et al.[13] is not present either, since, e.g. this would require the reflection (110) at 20 = 13.8”. (+ + + +) refers to ferromagnetic ordering, which must be discarded on the grounds of the other physical measurements.

By comparison of the neutron diffraction diagrams above and below the magnetic transition temperature of TN = 1.48 K (Fig. 1) one finds however in the 1.1 K pittem one new peak around 26 = 14.69 and an enhancement of intensities of several other peaks. The 6rst peak at 28 = 14.65“coincides with the position of the (101) nuclear re&ction. All peaks observed are generally not forbidden, however they would require ferromagnetic ordering. The magnetic structure is not ferromagnetic. An indication for a more complicated, probably helical magnetic structure is found in the signilkantly enlarged halfwidth of some, but not all reflections. For example the halfwidth of the (101) magnetic peak is increased to 1.1” in 28 in comparison to about 0.5“ for the nuclear peak. We are therefore led to assume a splitting of the magnetic peak into two nonresolved satellite peaks as the consequence of a helical spin arrangement. Since the

9.14 10.92

110

ifi

9.74 10.92

-

-

110

f3.79

13.711 13.88 14.65

-

-

2862

36%

f7S6 17.691 19.54

2431

1217

101

t4.65

f !E (YLO Iif

111

f7.62 1954

f z; 22a

200 210 002 201 102

5452 1893 -

2749 216f

-

-

s27s

-

20623@6-

2129 -

-

-

5452 -

2636

-

2749 2161 -

I

iff93 -

2129 -

2t.88

310 130

21.78> 22.00

-

-

I869

936

-

-

1869

936

21.95 22.44 24.06

OK? 221 112

21.95

-

-

;:z

1

1

1342 2.50

1089 1368

-

936 -

1342 zso

1089 1368

separation of the two peaks is beyond experimental resolutionwe have employedfnathernatical analysisof the broadenedpeaksby a kast squarestit with overlap pang Gaussian peaks of normal halfwidths.For the (lOl)-; WW sate&es tke rem&is shownin Fa 2 Two Gaussiancurvesof n&y equalintensityare centredat 28 = 14.39Dand 14.919The indexingis (lOl)- and (lOit+ JPCSV&.#,t&?.fB

withrespectto the tetragonalnuclear(Ml) penkcentered at 28 = 14.659 Satellitepeaks are associatedwith reciprocallattice vectoraby[161 (d*)“=grklr 01 where a* is th propsgationVCCtO~

Of the sp*

in

242

W. .9c&w1 and 0. WILL

reciprocal space. Splitting of the (101) peak but not of the (BO) peak (the halfwidth is unaltered) requires d*(200)‘=d*(200)-, and this is satisfied only when the propagation vector T* is along c*. Figure 3 depicts the ensuing satellite orthogonal lattice, eqn (1) reduces for

Fig. 3. Reciprocal lattice of magnetic TbAsO, with the satellite points as producedby a propagationvector aiong[OOlI.

this case to (B*)2*= h2 . a*2+ k2 - bS2t (I . c* 2 T*)‘.

(For tetragonal symmetry II = 6). In Fig. 4 the splitting of (d*)* is calculated according to eqn (2) for the significant magnetic peaks as a function of )r*l. Good agreement between the observed and calculated positions of the peaks is found for (~*1=0.005+0.003A-‘. The experimental uncertainties are indicated in Fig. 4 by the shaded areas. The helical configuration is essentially deduced from the first magnetic peak (101)’ and then verified by analysis of the others. This first peak is purely magnetic in origin and its splitting is not aflected by the small crystallographic distortion as a consequence of the orthorhombic symmetry. The peaks at 28 = 24.5” and 26.0”, with the indices (21l)* and (112)” resp. experience splitting by the crystallographic distortion (at T, = 27.7 K) as well as by the helical spin conliguration. This is indicated in Fig. 4. The intensities of the magnetic peaks in the diffraction diagram are given by hkl

=

K ’ j ’ p2 . (q2) . (F,,k,12

0 380 0378 0376 10221 I202l

o 37L 0372

0 356 (‘3’1

122010

(2)

03%

282

Fig. 4. Dependenceof the splittingof the fumiamentslp&s into satellitesin dependenceof the propagationvector length. The crystailgnphic sp&ing from tetragonal to orthorhombii symmetry is kdkated: the kft part of the diagramshowsthe tetrqonal peaks at T > T,. The middle part showsthe orthorhombispiittingatTd>T>TN.At right the satellite splitting is shown.

(3)

Neutronlotion

study of nragncticauy ordered ‘hAsO

where K contains the scale factor, the geometricalfactors and the temperature factor and i is the muftiphcity. If there is a cone spiral structure (which cannot be excluded at this stage) with halfcone angle upthe magnetic scatteringlength p is defined by[161

/

243 1

for the fundamental peaks due to a cohnear axial component of the ordered moments,and by p=p.f-siny,

<4b)

for the spiral component. p is the moment of the lb* ion and f the magnetic form factor[l7]. The magnitude (q*) is conveniently expressed by (q2)=

sin2y

for the axial component and by (q2)= 114* (1 + cos2y)

(54 (Sb)

for the satellite reflections; y represents the angle between the cone axis and the scatteringvector. Completeanalysis is achieved by a least squares fit of the observed intensities to the model. The c~cula~n does not result in a cohnear component, therefore p= = 90”.The final calculation resulted in a moment value of 6.220.1 pR per Tb” ion at 1.1K (flTN =0.75). A comparison of observed and calculated neutron intensities for the magnetic spiral structure of TbAsO, is given in Table 2.

As a result of this study we can describe the magnetic structure of TbAsO, by a planar spiral, where the moments are perpendicular to the c-axis rotating ~ound[~ll in the a-b-plane (Fig. 5). The ~op~tion vector is calculated from 7* . c = 0.032kO.OO2(Fig. 4). Withc = 6.320A we get r* = 0.0052 0.003hi-‘, yieldinga spiralpropagationperiod of 197k 12A, or 31-C2 unit cells. The rotationangleof the spiralin the horixontai(091)plane Bmountsto only about I 1.4”.In a distanceof about200Aor 31 originalunit cells the initialmomentorientationrecurs. This is one of the longest spirals found so far. This neutron diffraction measurement and this structure clearfy rejects the proposition of a simple cohnear antiferromagneticstructure, as derived by analysisof the macroscopic data[13]. In agreement with these rn~~rnen~ there is indeed no macroscopic magnetization in the boy ordered state, since there exists for each fe~om~tic~iy ordered microscopic crystallographicunit cell an antiparalleloriented cell in a distance of about 100A (Fig. 5). Since the rotation plane is the a-~-plane, we can just aa well assume the momentary orientation of the moments along(100).Also, since the present diffractiondata donot allow to determine the phase diflerence between parallel spirals in one unit cell, a two-sublatticemodel can beLassumedin one singleunit cell without contmdiction. The interaction is calculated Fii. 5. ‘l%efinalspiralstructureof TbAs04.The momeatsarc considering the nearest neighbors only, and there is perpendicutar to the c-axisret&g arouad0011in the o-bpkuIc.The spiralastir periodis 1971 or 31unitcells. therefore no ~on~diction.

244

W.tiandG.Wu.r Table 2.

Comparison of calculated and observed neutron intensities for the magnetic spiral structure of TbAsO4at 1.1K(m tetragonal and orthorbombic indexing; compare text)

hkt tetr.

28 tetr.

hkl

29

O&l.

orth.

101101+

14.39 14.91

Ill111+

200’

19.54

211211+

24.35 24.67

112112+

25.71 26.31

220”

27.77

301301103103+

31.43 31.68 34.31 35.00

321-

37.26

321+

37.48

312-

38.20

312+

38.62

220” 311I 13i311+ 131’ 202I 022+ I 202+ 022I 480’ 040” 331331+ 113113+ 511151I‘511+ 151’ ( 422242I 422’ 242’

q2

i

1cak

1EPlC

L

14.39 14.91

0.394 0.385

8 8

1922 1761

3683

3908

19.54 24.27 24.47 24.59 24.78 25.66 25.76 26.26 26.36 27.62 27.97 31.43 31.68 34.31 35.08 37.09 37.49 37.31 37.71 38.12 38.32 38.54 38.74

0.500

1224< 423I 413 409 403 520 512 491

1224

1380

0.300 0.299 0.434 0.432 0.425

4 8 8 8 8 4 4 4

1648

1600

2007

1900

0.424

4

484

0.500 0.500

2 2

243 2451

488

500

0.280 0.281

8 8

186 189I

375

200

0.475 0.484 0.272 0.272 0.272 0.272 0.335

8 8 8 8 8 8 8

235 250I 109 1071

485

*Al

l39f

1280

0.334 0.333 0.332

8

243 239 236

The structure determined by this neutron diffraction experiment allows one to understand the metamagnetic Asian from the ~~~o~e~ to the ferromagnetic state in an apphed field proposed by Wtichnerand Laugsch[l3] on the basis of a socalled “Schlauchmodel”. This Schlauchmodel is in fact a structure of needle shaped fe~om~tic domains. Neutron d&action on a singIecrystal in an outer magneticfield should reveal this rotation of the spirals into the field direction. Experiments of this kind are under way. Outer magneticfields or stress appliedon crystals with induced moment magnetism of cooperative Jahn-Teller systems result in scent variations of the m~tic exchange interaction as was studied by McPherson and Wang for TbAsO, and TbVO,[lSJ. With this in mind differences between the results of magnetization and spectroscopic measurements, which are carried out in outer magnetic fietds, and the results of this neutron diffractiou me~urement without an outside influenceare not surprising. Without outside magnetic fields we have to assume isotropic magnetic behaviour without any preferred diition in the basis plane (compare Fig. S).Thisagrees with the observed ~~~~ i~~n&nt rn~e~on in small external gelds just above the Neel temperature at T = 1.6K[lOI. The stated prediction on the isotropic spinbehaviourwithinthe plane perpendicularto the crysu&graphically preferred c-axis does not contradict the general ambiguitiesof determining spin orientations in uniqueaxial crystal systems arisingfrom powder neutron ~~tion~l9J. It is the nonfat rotational spin structure of TbAsO+which produces an additionaltrans-

0.301 0.300

lational symmetry causing the splittingof the tetragonal (101)reflection and which permits in this way additional info~ation, Acknowledgeme&s-We wish to thank R. Skowronek for his technical assistance in performing the neutron diffraction measurements. Financial support of this work by the Bundesrni~st~~ ftir Forschung und Technologie is gratefully acknowledged.

1. Wii G., Agnew. Chemie 81,984 (1969). 2. Forsyth J. B. and Sampson C. F., P/tyr. UC. XA, 223 (1971); Will G. and Sohfifer W., J. Pkys. C: So&f Srute Physics 4, 811 (1971); G&l H. and Will 6.. Phys. St&s Solidi(b)SO,147(1972). 3. SchHfer W. and Will G., J. Phys. C: Solid State Phys. 4,3224 (1971). 4. Spooner S., Lee J. N. and Moos H. W., S&d State Commun. 9, 1143(1971); B&i W., Herb R., Ke H. G., Kasten A., Laugsch J. and Wtlchner W., Phys. Status S&i (b) 54,527 (1972). 5. Scharenberg W. and Will G., Jut. 1. Magactism 1,277 (1971). wriebt J. G., MoosH. W., Cotwell J_ H., Mangum R. W. and Thornton D. D.. Phvs. Reu. 83,843 (1971). 6. Met&e hf. J. and Rosenberg H. hf., S. Pi& C: Solid Stare Phys. 5.459 (1972). 7. Cdwelt J. H., Mangum 8. W., aad Thornton D. D., Phys. Rco. B3,3855 (1971). 8. Rerkhabn W., Kabie H. G., Klein L. and Scbopper H. C., Phys. srohls solidi tb) SJ, 265 (1973). 9. WtichnerW.,L&nW.,KahkH.G.,KaatenA.andLaugschJ., Phvs. statnr sofilff ib) 51.273 (11972). 10.Kl& L., KahleH. G.;Schopper H. ?. and Walter H., Int. J. Ma@l&nr 3, 17 (1972). 11. G&be1H., h%Rer-Vogt G., Grliih R. and Kkii L., Phys. tiffs. IlA, 409 (1972).

Neutrondihction study of magneticallyorderedTbA.sOd 12. S&tier W., Will G. and Mllller-VogtG., Acta Ctyst. Uo be

published). 13. Wkhner W., LaugschJ., ht. J. Magnetism 5, I81 (1973). 14. Hiatzma~ W. end Miller-VogtG., J. Cryst. Growth 5, 274 (1969). 15. SchpferW., Will G., Grih@n K., Pofahl E. and Zwoll K., Nucl. Instr. Methods 143,489 (1977).

245

16. Will G., Frazer B. C., Shiiane G., Cox D. E. end BrownP. 1.. Phys. Reu. 142139 (1%5). 17. Brun T. 0. end Lander G. H., Phys. Reu. 119,31X13 (1974). 18. McPhersonJ. W. and Wan8 Y. L., J. Phys. Chem. Solids 37, 143(1976). 19. ShiraneG., Acta @wt. 12, 282 (1959).