the spin-flop transition in the nearly one-dimensional antiferromagnets rbnicl3 and csnicl3

Solid StateCommunications,Vol. 24,pp. 51—53,1977. PergamonPress, Printedin GreatBritain

THE SPIN—FLOPTRANSITION IN THE NEARLY ONE-DIMENSIONAL ANTIFERROMAGNETSRbNiCl3 AND CsNiC13

E. Cohen* andM.D. Sturge

Bell Laboratories,Murray Hill, New Jersey07974,U.S.A.

(Received30March 1977by A.G. Chynoweth)

A spin—floptransitionhasbeenobservedin theorderedphaseof thenearlyone-dimensionalantiferromagnetsRbNiC13and CsNiC13(H8~= 19.3±0.5and19.2±0.3kG at 1.65K, respectively).Thetran-sition involvesfloppingof thespinswithin the linearchainswhile theinter-chainorder(the “triangularconfiguration”)is preserved.ThelowvaluesofH31 imply a smallanisotropyparameter(D = —0.05cm

1).

RbNiC13 AND CsNiC13 aremagneticallyorderedbelow

11.1 K and4.85K respectively[1]. Extensiveneutronscatteringstudies[2] revealamagneticstructurein a. H 0

which nearestneighborNi2~ionsform antiferromagnetic

chainsparallelto thec-axis(Dh spacegroup).Compe-tition betweentheinterchainexchangeinteraction(.13) ___________________

andcrystalfield anisotropy(D), causesthe spinsto forma triangularconfigurationin thebasalplaneof the mag- I

netic unit cell, shownschematicallyin Fig. 1(a). Two I

thirdsof the spinsare canted,the cantingangle0 being C0

closeto 120°;onethird areuncanted. ——

Becausethe intrachainexchangeinteraction(Jr) is

dimensionalbehaviorin their magneticsusceptibility [1]muchgreaterthan.13, thesecrystalsexhibitnearlyone-

aoI~andquasi-elasticneutronscattering[21,for T> T0. Inthethree-dimensionallyorderedstate(T< T~)thecalculatedspinwavedispersioncurvesanddensityofmagnonstatesshowdistinct featuresof a nearlyone-dimensionalsystem[3]. TheextrapolatedT= 0 value b. H> Hsf

of thesublatticemagnetizationis reducedby some50%by thefluctuationscharacteristicof one-dimensionalantiferromagnets[1].

In this communicationwereportthe observationofa spin—floptransition,by antiferromagneticresonance I(AFMR) andby opticalabsorption141. l’his transitionaffectsonly the orientationof the spinswithin thechains,while preservingthetriangularantiferromagneticconfiguration.

Thespin—flopnatureof the transitionis demon- -•--.. --

stratedby theangulardependenceof theAFMR whichis almostexactlyas predictedfor aspin—flopmode[5].

TheAFMR spectraof singlecrystalsRbNiQ3 and Fig. 1(a). Theequilibrium configurationof thesix spinCsNiC13 wereobservedin Q-bandat T= 1.7K. Figure2 sublatticesin themagneticunit cell (a0 and c0 aretheshowstypical absorptionspectra(takenin the derivative dimensionsof thecrystallographicunit cell). Thespin

directionsall lie in asingleplaneperpendicularto themode)of CsNiC13 at 38.56GHzfor variousvaluesof °H~ basalplane,whoseazimuthalorientationis determined

by crystalimperfection.(b) The equilibriumconfigur-* On leave of absencefrom PhysicsDept.,Technion, ationin thespin—flopphase.All spinslie almostin the

Haifa,Israel (presentaddress). basalplane.

51

52 THE SPIN—FLOPTRANSITION IN RbNiC13 AND CsNiCI3 Vol. 24,No. 1

HI C ~ ~ (cm) -

~H o3~°~

25°

(Li0

3°w 6135-z0

RbNi Cl3 ,f ~a-

T = 1.8°K

HIIC °~

HIIC 00

I I I I • I I0 5 10 15 20 25 30 if

H, kG

Fig. 2. AFMR absorptionderivativespectraof CsNiC13 6125 — I I I I I I0 4 8 12 16 20 24at 1.7K and38.56GHz. The ordinateis in arbitrary

units.The resonancelinesfor0H = 0°and3°are in the H (kG)

spin flop phase.Fig. 4. Zeemaneffect of the3A2g -÷ 3T

2 (r3) excitonabsorptionlinesfor H II c.At the spin

4loptransitionthetwo upperlinescoalesce.

26

Weinterprettheseexperimentalresultsin termsof24 - two q = 0 spinwavemodes.Onegivesrise to thereson-

ancein the low field (cantedantiferromagnet)phase

22 ~ (observedfor OH1t> 5°).The otheris observedin the

spin—flopphaseonly (IOHI ~ 5°,shownas an elongated

20 . ~ . lobe in Fig. 3). Considerfirst the low field phase.Spin wavecalculations[3] indicatethat two of thesix modesare low-lying at theBrillouin zonecenter:at

S8 • H= 0, ~ = 0 and w

2 -~ lcm’, dependingon the

exactvaluesof J1,J3 andD. Theremainingfour modes

16 are severalcm1 higher. Theresonancewe seeisthe ~

modewhich correspondsto free precessionof the basalS

14 • planecomponentsof thecantedspins.For large0H theenergyof this modeis givenapproximatelyby hw1 =

geffpBHl,whereger,= 2.0 andH1 H sin °H is the2 ~ Ii I LIII’’’ 1! I componentofthefieldinthebasalplane.Atsmaller-5 0 5 30 60 909H 0H the behaviorismorecomplex,becausethebasal

planeanisotropyis notzero in a realcrystal [6]. TheFig. 3. Angulardependenceof the field for resonancein w

2 modeis belowour resonancefrequency.It decreasesCsNIC13.Note theshiftedorigin forH, andthe changeof in energyfor H II v andreachesthevaluew2 = 0 (corre-scalefor

0H at 5°.Thefull line isthe theoreticalpre-diction for the spin—flopphase. spondingto spin—flop) for H H

3~= (8J1D)”2.

Thecalculatedspin floppedconfigurationforthe anglebetweentheappliedmagneticfield andthe H>HØ, is shownschematicallyin Fig. 1(b), in eachcrystallinec-axis.The full angulardependenceof the chain thespinsremainantiparallel,but now lie in theAFMR absorptionline is shownin Fig. 3. Similar results basalplane.Within the basalplane,theweakinterchainare obtainedfor RbNiCl

3. exchange(J3) maintainsthetriangularconfigurationwith

Vol. 24, No. 1 THESPIN—FLOPTRANSITION IN RbNiCl3 AND CsNiC13 53

120°betweenthe spins.Theangulardependenceand while the othertwo haveonly monoclinicsymmetry.Anrelativeintensitiesof thetwo resonancelinesin thespin— externalmagneticfield perpendicularto thec-axisflop phasecorrespondcloselyto thosepredictedby producesno changein the spectrum.However,for H IIFonerfor a uniaxialantiferromagnet[51,andobserved thehighertwo linesmergeoverthe range18—22kG, asby him in Cr2O3 [7]. We canfit hiscurvesto our dataat shownin Fig.4. As canbe seenfrom Fig. 1(b)the sub-frequenciesbetween36.5 and39 GHz,withH51 = 19.2 ± latticesarephysicallyequivalentin thespin—flopped0.3kG for CsNiC13 and 193 ±0.5kG for RbNiC13, phase,sothatonly two excitonlinesarepossible. Intaking g = 2.25 [8] for both.The resonancelobeextends CsNiCI3 thesplittingof the excitonsistoo small to beto larger

0H thanpredicted. This could be due to crystal resolved.lineageor to inhomogeneityof field direction.With the The AFMR datashowconclusivelythat thetran-knownvalueofJ~ 10 cm~we obtainD ‘-‘ —0.05 cm’ sition near 20kG observed optically andacousticallyis(for bothcrystals). dueto spin flop. In the low field phasethe AFMR is

It shouldbenotedthat IDI is considerably lower quite different, in its dependenceon orientationandthanthat reportedfor the isomorphouscrystal frequency,from thatnormally encountered[51.This isNi: CsMgCl

3,for whichD = — 2.0cm~[8]. Thedis- becausethe quasi-one-dimensionalexchangeleadsto ancrepancy,muchtoo largeto be attributableonly to unusualspinconfiguration(Fig. 1(a))whichhasdipolar interaction,indicatesthat, asin otherantiferro- rotationaldegeneracyin thebasalplane.In thespin—magnets,anisotropicexchangemakesanimportantcon- floppedphase,this degeneracyis removed,andthe Q-tribution. bandAFMR is almostindistinguishablefromwhat

Thespin—flop transitionof RbNiC13 wasalso would be expectedin a three-dimensionalantiferro-observedin the Zeemaneffect of the

3A2g * 3T2g tran- magnetsuchasCr2O3.

sition of Ni2~,in thenearinfrared. Thelowestlying

exciton,which originatesfrom the doubly-degenerateI’~substateof 3T2g, issplit for T< T~into threelines, Acknowledgements — We aregratefulto J.Makovskyas shownin Fig. 4. Thisextrasplittingmustbe due to andD.E. Cox for providingsamples,to S. Geschwindthe inequivalenceof the threetypesof antiferromagnetic andR.C.Miller for commentson themanuscript,and tochains,in oneof which trigonal symmetryis preserved, E.A. Sadowskifor technicalassistance.

REFERENCES

I. ACHIWAN., J. Phys. Soc. Japan 27,561 (1969).

2. YELONW.B. & COXD.E.,Phys.Rev.B6, 204 (l972);Phys.Rev.B7, 2024 (1973).

3. SORGENA., COHENE. & MAKOVSKYJ.,Phys.Rev. BlO, 4643 (1974).

4. ALMOND D.P. & RAYNE J.A.,Phys.Lett. 55A, 137 (1975),haveobservedthis transitionat 4K by ultra-sonicattenuation,butcouldnot identify it unambiguously.

5. FONERS.,inMagnetism,Vol. I, (EditorsRADO G.T.-& SUHL H.),p. 383. AcademicPress,N.Y., (1963).

6. A similarbehavioris also observedin land K bands.A full report will be published elsewhere.

7. FONERS.,Phys.Rev. 130, 183 (1963).

8. McPHERSONG.L.,KISTENMACHER T.J.& STUCKYG.D.,J.Chem.Phys. 52,815(1970).