Features of incommensurate phases in crystals TlGaSe2 and TlInS2

Transcription

1 Fetues of iommesute phses i ystls TlGSe TlIS B.R. Gjiev Itetiol Uivesity of Ntue Soiety Ms Du 9 9 Uivesitetsky st. Du Mosow Regio Russi gjiev@ui-u.u Astt The theoy of sequee of phse tsitios of high-symmety-iommesute-ommesute phse otolle y ompetig oe pmetes is ivestigte. The tempetue epeee of ieleti ostt is eive. The ompiso of the otie esults with expeimetl t fo ystls TlGSe TlIS is isusse. Itoutio I isussio of the iommesute phses i iel ystls o the sis of the Lu theoy two ses e usully istiguishe. I the fist of them we hve the symmety of two o moe ompoet oe pmete whih is suppose y the Lifshit giet ivit whih les to sptilly moulte phse []. I the seo se it is set fo oe ompoet oe pmete []. These two ses e lle s iommesute phses of type II I espetively. As is kow the oe-imesiol moulte iommesute phses i pope feoeletis oespoig to type II whees i impope feoeletis to type I. Thee is seies of woks i whih the fetues of stti ymi popeties of iommesute phses of the types II I e the oml-iommesute the iommesute-ommesute phse tsitios e ivestigte [ 5]. I impope feoeletis ieleti ostt t the poit T i the tempetue of tsitio fom high-symmety i iommesute phse oes ot show y omlies whees i solito egime iommesute phse ehves s T T T is the tempetue of tsitio fom iommesute i ommesute phse the vlues of ieleti ostt oiie i high-symmety ommesute phses. I the iommesute phse the tempetue epeee of ieleti ostt of pope feoeletis is simil to tht of ieleti ostt of impope feoeletis [ 5]. Howeve i phse tsitios of pope feoeletis ieleti ostt i high-symmety ommesute phses shows the Cuie- Weiss type ivegee. To the peset time of physil popeties of ume of ystls with iommesute phse e eough eeply ivestigte. The esehes of themoymi optil eletil popeties of these phses s whole hve show the goo geemet of theoetil expeimetl esults [5]. Now thee is questio o hte of the phse tsitio i the lyee ystls TlGSe TlIS. The expeimets o X-y lysis the eutos stteig show tht i high-symmety phse these ystls hve the spe goup of symmety C h []. The TlGSe TlIS ystls e i the iommesute phse i tempetue itevl fom T i K ow to T K fom T i K ow to T K espetively [7 9 ]. A moultio wve veto i oth ystls is q i σ.5 whee σ. [ 9 ]. The elemety ell of these ystls is quuplite i ommesute phse tht is quite hteisti fo impope feoeletis []. The ommesute phse is pol. Howeve the symol of the goup of the ommesute phse i these ystls is ot etemie yet. O the sis of these t i [] the theoy of the impope feoeletis with iommesute phse is evelope. I ptiul the tempetue epeee of ieleti ostt is otie i the egio of sequee of phse tsitios high symmety

2 iommesute ommesute phse fo ystls of type TlGSe. Howeve i [9] is show tht it is ot possile to expli the expeimetl tempetue epeee of ieleti ostt of ompous TlGSe TlIS y use the esults of wok []. Thus elly i ystls TlGSe TlIS tempetue epeee of ieleti ostt i the egio of sequee of phse tsitios high symmety iommesute ommesute phse shows popeties i the eti sese hteisti fo pope feoeletis with iommesute phse []. I ptiul the mesuemets hve show tht oth the highe T i the lowe T the low-fequey ieleti suseptiility sumits to the lw Cuie- Weiss whih is hteisti fo pope feoeletis with iommesute phse []. Howeve i iommesute phse of oth ompous ieleti ostt the wekly epes o tempetue tht is ot hteisti eithe fo pope o fo impope feoeletis [9]. I futhe ws show tht s oppose to stutul esehes the Rm optil expeimets i ompous TlGSe iite o pesee of soft moe with tempetue epeee eig hteisti fo pope feoeletis []. I this se thee is ot le eso quuple of volume of elemety ell log xis. Thus o the oe h the stutul expeimets show tht the ystls TlGSe i tempetue itevl fom T i K ow to T K TlIS fom T i K ow to T K e i iommesute phse [7 9]. A moultio wve veto i oth ystls is whee q i σ.5 whee σ. [ 9 ]. Hee the phse tsitio hs the hte of impope feoeletis. O the othe h the Rm optil expeimets show tht i spet thee is oly soft moe thee e o some ppeile ttiutes of phse tsitios with quuple of volume of elemety ell []. Lst o see is use vey smll ispesio of flututios o ietio. oeeig fom ove-stte it is possile to olue tht elly i these ystls the phse tsitios e ompie y two soft moes oespoig to wve vetos Γ q of the spe goup C h. I the peset wok the theoy of sequee of phse tsitios with iommesute phse otolle y ompetig oe pmetes is ivestigte. Theoy Let us osie stutue uegoig sequee of phse tsitios of type highsymmety iommesute ommesute phse otolle y two mjo oe pmetes. Let oe-imesiol oe pmete mely the y ompoet of veto politio e tsfome y ieuile epesettio A u of the spe goup. The two-imesiol q oe pmete is tsfome y ieuile epesettio D of the spe goup C h oespoig to the poit q.5. The symmety opetios ieuile epesettio oespoig to the wve veto q.5 e give i Tle. Tle. Two imesiol ieuile epesettio of the spe goup Ch oespoig to the wve veto q.5 whee ε exp iπ/ τ / C {e/} { σ h / τ } {I/} { C / τ } h D *q ε * ε q D C h ε * ε

3 Thus the phse tsitio i system is esie y euile epesettio Ξ whih q my e epesete s iet sum of ieuile epesettios A u D tht is q Ξ A u D. q The fee eegy of the system is otie fom ivie of epesettio Ξ A u D. Aoig to the oitio of ivie the fee eegy futiol is expesse y Φ f x x α β ϕ k ϕ f x γ osϕ x x ξ / os / ϕ x x x E. Hee α α T T T T ϕ mplitue phse of the oe pmete espetively. is the politio log the xis E is the extel eletil fiel is the peio of fee eegy esity f x. Results of expeimetl esehes of ifluee of extel fiels o itil tempetue of phse tsitio i ystls TlGSe TlIS llows to ssume tht T T. O see it is oete with stog itetio of the oe pmete optil soft moe with politio [ ]. The equiliium phses of the system e etemie fom the oitio of miimum fee eegy. Thus fo the iitil high-symmety phse with the spe goup of symmety C h we oti tht ϕ e uetemie. I high-symmety phse the tempetue epeee of ieleti ostt is χ C T Ti. ϕ I the ommesute phse we hve. x x x oitio we oti:. C N fom the miimitio. si ϕ C N. osϕ S N. osϕ C N V Hee N V V e volumes of elemety ell i ommesute highsymmety phses espetively. V The tempetue epeee fo the ieleti ostt i ommesute phse is χ C T T. Miimitio of the futiol fee eegy with espet to ϕ les to followig Eule equtios: ϕ si k γ ϕ ξ si ϕ x ξ os ϕ E. x x x

4 These lst equtios my hve peioi solutios with iffeet peios. The equiliium peio is etemie y the oitio whih tkes the fom / F Ф E x k x x x x ϕ ξ ϕ γ β α ϕ os os 5 Let us otie tht the left pt of the equtio 5 oes ot epe o x epesets itegl of eegy. The equtios 5 e use togethe with equtios i fiig the futios ϕx x. By mkig the sustitutio x usig the equtio 5 e witte i the followig fom:. Ф s g k g g E ξ ξ γ Hee γ β α Ф Ф ] [ v E g 7 ]] [ [ v s We fi the solutio i the fom e Z. To etemie e we sustitute ito oti the followig expessios: α e α Φ 9 If solutio of equtio is kow the futio x e fou fom the eltio x [] theefoe we get Z x / ] [ Afte itegtio we fi:

5 x ηs px κ whee κ η κ κ p e κ. e Hee > the equtio Z hs fou el oots fo wht it is ptiully eessy tht <. Equtio hs el solutio oly fo Z >. The itevl of vlues fo whih Z > must e oue sie othewise woul eh ifiite vlues. Thus the peio of fee eegy esity is etemie s follows: K κ p whee κ [] Kκ is the omplete ellipti itegls of the fist kis. Coitio 5 tke iffeet fom if it is itegte ove x fom eo to the expessio fo Φ is sustitute fom : ϕ [ k ] x. x x x The expessio efies tempetue epeee of pmete κ i iommesute phse. Ф The tempetue epeee of ieleti ostt χ lim E i the iommesute E phse is expesse s whee γ k p s ξ w χ T x K ξ κ ξ w w g E. As it follows fom the expessio i the poit of the tsitio γ χ T i i iommesute phse the ieleti ostt χ χ T wekly epes o ξ tempetue. Summy A lge ume of woks is evote to expeimetl stuyig of tempetue epeee of the ieleti ostt i ystls TlGSe TlIS [5]. As well s it ws eessy to expet the esults give i these woks i essee o ot iffe. The hteisti expeimetl tempetue epeee of the ieleti ostt fo the TlGSe TlIS ystls is tke fom [] show i Fig. Fig. Compisos of the otie i peset eseh the tempetue epeee of ieleti ostt with expeimet i high-symmety ommesute phses show tht the vlue of the Cuie-Weiss ostt is C K. Tht is hteisti fo phse tsitios with mixe mehism of phse tsitios. Desiig the expeimetl tempetue epeee of ieleti ostt i γ iommesute phse y the fomul we oti ξ α k. 5. At ompiso β of theoetil esults with expeimet it is eessy to me tht ε πχ. Besies the expeimetl esehes show tht χ χt wekly epes o tempetue i this phse. Thus s oppose to tsitios of type II I i systems with ompetig itetio i iommesute phse ieleti ostt wekly epes o tempetue.

6 I ommesute phse the lttie quuple spe goup of symmety of stutue is C. Besies the ommesute phse is pol. Thus the ompiso of theoetil esults with expeimetl llows to esie the si fetues of phse tsitios i ystls TlGSe TlIS. Refeees. V. A. Golovko Sov. hys. Soli Stte 9.. V. A. Golovko Sov. JETF B. R. Gjiev Sov. Low Temp. hys B. R. Gjiev Sov. hys. Soli Stte T. Jsse A. Je Av. hys W. Heke H. D. Hohheime C. Cloe A. Wee S. Ves H. G. v. Sheig hys. Rev. B S. B. Vhushev V. V. Zov B. E. Kvytkovskii N. M. Okuev K. R. Allkhveiev R. A. Aliev R. M. Sly JET Lett S. Kshi Y. Koyshi J. Koe hys. So. S S. Kshi Y. Koyshi J. hys.: Coes. Mtte S. Kshi K. Nkmu Y. Koyshi J. hys.: Coes.Mtte D. F. MMoow R. A. Cowley. D. Htto J. Bys J.hys.: Coes.Mtte F. M. Gshime B. R. Gjiev K. R. Allkhveiev R. M. Sly V. Y. Shteishie Sov. hys. Soli Stte R. A. Aliev K. R. Allkhveiev A. I. Bov N. R. Ivov R. M. Sly Sov.hys. Soli Stte Е. А. Vigov V. М. Bulkov М. R. Ykhev А.. Ryov N. N. Melik B. S. Umov А. А. Aikev Sov. hys.-soli Stte F. A. Mikilov E. Bs E. Setuk J. hys.: Coes. Mtte 77.

7 Fig. Tempetue epeees ε x ε of the ystl TlGSe o fequey kh [] Fig. Tempetue epeees ε x ε x of the ystl TlIS o fequey kh []