Study Of Superconductivity And Antiferromagnetism In Rare Earth Nickel Borocarbides (RNi 2 B 2 C)

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1 IOSR Journl o Applid Pysis IOSR-JAP -ISS: olum 9 Issu r. II y - Jun 7 PP Study O Suprondutivity And Antirromgntism In Rr Ert il ororids Ri C r. Slil s nd Prti Sumn s prtmnt o Pysis rmpur UnivrsityIndi. Astrt: W v rportd tortilly t oxistn o ntirromgntism nd suprondutivity in rr rt nil ororid ompounds. y using suitl modl miltonin w v drivd ritil tmprtur zro ordr prmtr gp to rtio. W v sown tt t ritil tmprtur is drsd s yridiztion oiint inrss. W v lso lultd t t o xtrnl mgnti ild on t oxisting stt o suprondutivity nd ntirromgntism. Our numril lultions sow n intrply twn t two ordr prmtrs nd r l to xplin som o t xprimntl rsults rportd or Ri C suprondutors. Kywords:Suprondutivity; Antirromgntism; ororid I. Introdution oxistn o ntirromgntism A nd suprondutingsc proprtis o rr rt nil ororid ompounds Ri C wr R YLu yoer nd m motivt t rsrrs to go dp into tir ltroni strutur s wll s dtil invstigtion o t intrply twn SC nd A stts. oxistn proprtis o ts ompounds v om grt intrst or t tortil nd xprimntl rsrrs [-]. It s n sn tt ts ompounds v lyrd strutur md up o rr-rt ron R-C sts wit t sting o i sls long -xis. nd strutur o ororid Ri C xiit our nds rossing t rmi lvl. On o t our nds is lt wi indits t strong orrltion o t systm. lt nd yridizs wit otr onduting nds. u to tis yridiztion t A o t sultti quirs t lolizd stt o t d-nd.r xists p dnsity o stts t t rmi-lvl wr d nd o i nd otr nds ron oron nd rr rt ompound ontriut[5]. lolizd ltrons o t rr rt r mostly rsponsil or t nisotropi mgnti proprtis. On t otr nd t itinrnt ltrons rsponsil or suprondutivity wi riss rom spin wv du to rmi sur instility lso ontriut to ntirromgntism. s ororid ompounds xiit wll-stlisd oxistn o suprondutivity nd mgntism [ ] wit numr o intrsting proprtis. owvr dtild undrstnding o ow mgntism ts suprondutivity still nds to omplisd. rr rt ororid sris is uniqu s its mmrs v ll t onivl omintions o or Eri C 6 nd nd mi C.5 nd.5k or oi C 8.5 nd or yi C.5 nd 6.5 [7]. Point ontt msurmnt o t supronduting nrgy gp in Y[] nd o[] provids /.6.5. point ontt tniqus sd on Andrv rltion rom norml supronduting oundry rportd t vlus o / or yi C s.6[]. Similrly / vlu or Eri C otind rom point ontt sptr o t Andrv rltion urvs is.6 []. In tis ppr our im is to lult t gp prmtr o nil ororid ompound in prsn o mgnti ild y pplying t two-nd modl. ot Amii t.l.[9] nd Su t. l[] invstigtd som o t proprtis o ts ompounds y ting CW on CS suprondutors witin mn ild pproximtion. In tis ppr w v modiid t miltonin o Su t. l. y ting yridiztion in prsn o xtrnl mgnti ild. Som pysil proprtis li ordr prmtr gp to rtio wr invstigtd wi grs quit wll wit t xprimntl rsults. C C OI:.979/ Pg

2 Study O Suprondutivity And Antirromgntism In Rr Ert il ororids Ri C II. ortil odl o study t intrply o suprondutivity nd ntirromgntism w onsidr modl miltonin [6] in wi sids piring intrtion mong ondution ltrons tr xists tiv ntirromgnti oupling twn nrst nigour lolizd ltron nd t intrtion twn ondution nd lolizd ltrons. ntirromgnti xng lds to l ground stt wi is rtrizd y ntirromgnti ordr. dirnt intrtions tn in our modl miltonin is givn y s v miltonin o involving opping o ondution ltrons twn two nigouring sits is tn s wr o.. o r t rtion oprtors o ltrons t sits nd or ondution ltrons nd r t orrsponding nniiltion oprtors. disprsion nrgy o is givn y o tos x os y mn ild CS miltonin dsriing ponon mditd suprondutivity is givn y s.... r only intr sultti Coopr piring is ssumd nd t supronduting gp prmtr is dind s ~ ~ is t strngt o ttrtiv intrtion twn two ltrons vi ponon. Etiv yridiztion twn t -ltrons nd t ondution ltrons ontriuts to t miltonin v.. 5 v i. givn y wr is t yridiztion intrtion onstnt i nd i i r t rtion nd nniiltion oprtors rsptivly t sits i o ltrons. Strongly ntirromgnti orrltion nd ondution o i d-ltrons is stimultd y stggrd mgnti ild o strngt nd tis ontriuts to t miltonin is writtn s 6 intr -ltron miltonin or t ltron in t lolizd lvls orrsponding to t lt nd in t prsn o xtrnl mgnti ild is g g i i i i 7 wr is t rnormlizd -lvl nrgy. g nd r Lnd g tor nd or mgnton rsptivly. OI:.979/ Pg

3 Study O Suprondutivity And Antirromgntism In Rr Ert il ororids Ri C OI:.979/ Pg xtrnl mgnti ild ontriuts to t miltonin is writtn s g 8 r is t xtrnl mgnti ild. E nd is untion o stggrd mgnti ild t supronduting gp prmtr nd strngt o yridiztionv. r w v solvd t Grn s untion to lult t pproprit singl prtil orrltion untion wi in turn dtrmins t ordr prmtr orrsponding to supronduting nd ntirromgnti long-rng ordr. s r givn y ~ 9 nd g Atr lultion w v d nd g wr [ ] [ ] [ ] nd

4 Study O Suprondutivity And Antirromgntism In Rr Ert il ororids Ri C [ ] wr is t dnsity o stts o t ondution ltrons t t rmi lvl. All t prmtrs usd in t ov qutions r dividd y t to m tm dimnsionlss wr W8t is t widt o t ondution nd. W v ~ z t t t ~ W W t t x 5 t t g t t 6 supronduting nd stggrd mgnti ild gp qution in dimnsionlss orm r z nd w~ dx ~ w W x x 7 λ [ x θ x θ + x θ - x θ ] 8 W W v onsidrd t l-illd nd sitution t rmi lvl li in t middl o t ntirromgnti nd gp wr t rmi lvl is tn s zro. Our qn. nd r oupld qutions nd v to solvd sl-onsistntly in ordr to study t tmprtur vrition o ny o ts two quntitis wi r nssry to undrstnd t ntur o t o-xistn ps. III. isussions r w v solvd ntirromgnti ordr prmtr long wit t gp prmtr sl-onsistntly nd numrilly or t ompounds oi C yi C Eri C mi C. A stndrd st o dimnsionlss prmtrs[6] r usd in t lultions wit ndwidt W nd 8t wr t is t opping intgrl. ig- sows mn ild viour o supronduting nd ntirromgnti ordr prmtr or 9.5 yi C 8.98 Eri C 7.8 mi C 7.8 xtrnl mgnti ild. ig- sows supronduting ordr prmtr long wit ntirromgnti ordr prmtr or t ompound in prsn o xtrnl mgnti ild. ritil tmprtur prmtr grs wll wit t xprimntl rsults. vlu o supronduting gp K.5 is omprl to tt o CS vlu. oi C in t sn o n oi C 8.5 nd.5 OI:.979/ Pg

5 Study O Suprondutivity And Antirromgntism In Rr Ert il ororids Ri C ig- sows t plot o supronduting nd ntirromgnti ordr prmtr or sows grtr tn lis in t rng. to.8 orrsponding to yi C. grp wi mts wit xprimntl rsults. vlu o ritil tmprtur prmtr ~ 6.5 to nd. orrsponding to nd ~.78 rsptivly.similrly t vlu o supronduting gp prmtr otind is in t rng o 5.8 wi is igr tn CS vlu. On t otr nd ntirromgnti ordr prmtr otind is vry smll. In t oxisting rgion t lrg lutution is osrvd. ~ 6.5 to 7.5 nd Eri ig- rprsnts t plot o supronduting nd ntirromgnti ordr prmtr or wit tmprtur y vrying xtrnl mgnti ild tn y vrying yridiztion potntil. ritil tmprtur prmtr nd l tmprtur prmtr rmin in t rng.-.6orrsponding to in t rng o.-. orrsponding to ~ 5.7 to 7. vlu o. K nd..5. vlu drss wit inrsing mgnti ild nd lso wit v. ntirromgnti gp rdusy lrg mount y inrsing yridiztion nd lso wit xtrnl mgnti ild. ompound mi C. grps sow similr trnds nd or tis. ritil tmprtur nd l tmprtur rmins in t rng o 7.5 nd 7. ig-5 sows t plot o ordr prmtrs or C rsptivly. vlu o.7 K nd.65. vlu drss wit inrsing mgnti ild nd lso wit v. ntirromgnti gp rdus y lrg mount y inrsing yridiztion nd lso wit xtrnl mgnti ild. rsults sown ov suggsts t oxistn o supronduting nd ntirromgnti stts.it is osrvd tt wn yridiztion inrss ot supronduting nd ntirromgnti gp rdus or ll t ompounds. n w onlud tt yridiztion plys n importnt rol in nging t supronduting trnsition tmprtur nd gp prmtr. rg rrirs ppr to oupl vry strongly to t spin systm.similrlyy inrsing mgnti ild ot trnsition nd l tmprtur rdus trougout t rng. OI:.979/ Pg

6 Study O Suprondutivity And Antirromgntism In Rr Ert il ororids Ri C igur. In ig- t tmprtur dpndn o SC gp z nd A gp in t o-xisting ps in sn o mgnti ild or smll vlu o yridiztion v is onsidrd. Grp or dirnt vlus o yridiztion Grp or dirnt vlus o xtrnl mgnti ild p igur. In ig- t tmprtur dpndn o SC gp z nd A gp in t o-xisting ps in prsn o mgnti ild or oi C is onsidrd. Grp or dirnt vlus o yridiztion Grp or dirnt vlus o xtrnl mgnti ild p igur. In ig- t tmprtur dpndn o SC gp z nd A gp in t o-xisting ps in prsn o mgnti ild or yi C is onsidrd. p Grp or dirnt vlus o yridiztion Grp or dirnt vlus o xtrnl mgnti ild igur. In ig- t tmprtur dpndn o SC gp z nd A gp in t o-xisting ps in prsn o mgnti ild or Eri C is onsidrd. OI:.979/ Pg

7 Study O Suprondutivity And Antirromgntism In Rr Ert il ororids Ri C Grp or dirnt vlus o yridiztion Grp or dirnt vlus o xtrnl mgnti ild p igur 5. In ig-5 t tmprtur dpndn o SC gp z nd A gp in t o-xisting ps in prsn o mgnti ild or mi C is onsidrd. I. Conlusion In our modl w study t oxistn o supronduting nd ntirromgnti stt or vrious rr rt ompounds witin t mn ild pproximtion. W v tn st o suitl rlisti modl prmtrs. In our lultion w v inludd t yridiztion y ting dirnt vlus o t xtrnl mgnti ild. Our rsult sows t omintion o θ nd θ or dirnt rr rt nil ororid ompounds. vlus o nd otind or dirnt ompounds is in drsing ordr wit inrsing mgnti ild nd yridiztion. u to lrg lutution w ould not gt good rsults or mi C ompound. Our lultd dt grs wll wit t xprimntl rsults. yi C nd Anowldgmnts W grtully nowldg Pro. S. y or usul disussions nd vlul suggstion to omplt t wor. Rrns []. uld Znui Zuringl G. Z.Pys 9 ; 99. uld. J Low mp Pys 95 5; 99. []. zumdr C grjn R Godrt G Gupt LC Ltro r SK Lvy Clmnt C Pdli ijyrgvn R. Solid Stt Communitions 87 ; 99. []. grjn R. t l Py Rv. Ltt 7 7; 99. []. Crild PC Gmml PL isip J. Pysis ody 5 ; Otor 998. [5]. r S Pnd Rout GC Entl P. Intrntionl Journl o odrn Pysis 5 59;. [6]. Co K Crild PC onston C. Pys Rv Ltt 77 6; 996. [7]. Rmrisnn rm C. Py Rv 7; 98. [8]. Pit W Sing J. Py Rv Ltt 7 7; 99. [9]. ttws L. Py Rv 9 79; 99. []. Stssis C ullo Zrsty J Crild PC Goldmn AI Sirn G Spir S. Py Rv 55 R 8678; 997. []. R JY Wng rmn. Py Rv ; I. []. Goldmn Stssis C Crild PC Zrsty J rvngs P Co K. Py Rv ; 99. []. Rout GC Pnd r S. Pysis C ;. []. Zurr. Son Pys Usp 95 7; 96. [5]. r S Pnd Rout GC Entl P. Int. J. od. Pys. 5 59;. Su K Pnd od. Pys. Ltt. 879;. [6]. s Slil Pdi PC. Intrnl Journl o odrn Pysis ol. o.8 65; 6. [7]. Andrson PW sul G. gntismvol..admi Prss w Yor; 96. [8]. urd. J.Pro.R. So. Lond. Sr. A. t. Pys. Si. 76.8; 96. [9]. Amii A lmir P. Journl o Low-mprtur Pysis ol. 7. os. 56; 999. []. idyu YUG r G orov L Crnoy rslr SL us G Kvitnitsy OE ugl G Rtny K Ynson IK. Journl o Pysis:Conrn Sris 5 578; 9. OI:.979/ Pg

8 Study O Suprondutivity And Antirromgntism In Rr Ert il ororids Ri C []. Rytn L. Pysi 8 89; 996. []. Ynson IK orov L omy C Pul K Pysi C 5;. []. Ryltno L. t l Europysis Ltt 8; 996. []. Su K Pnd Prmn 77 75;5 Su Pnd Pysi C ; 5. Appndix Grns untion o Zur [] typ is usd in t lultion. r w v usd A C nd i i A ω ; A ω ; A ω ; A ω ; A 5 ω ; A 6 ω i i ω ω ω ω ω ; ω ω A 7 ω ; A 8 ω ; ω 9 i wi r givn s ω ; ω ω ; ω C ω ; ω ω ; ω qution o motion nd ommuttion rltions o t rmion oprtors vlut t ov Grn s untion A i i-6 wi r g A A A5 A g A A A6 A g A A A7 A g A A A8 A g A7 A g A8 A g A5 A σ r usd to OI:.979/ Pg

9 Study O Suprondutivity And Antirromgntism In Rr Ert il ororids Ri C OI:.979/ Pg 6 A A g Similrly w n writ or C rmi lvl is tn in t middl o t ntirromgnti nd gp nd t rmi lvl is tn s zro. r t lolizd nrgy lvl oinids wit t rmi lvl. W v onsidrd t l-illd nd. symols tn in t qution r Atr solving t oupld qutions otind rom ov qutions w ind out t grn s untions. A C nd ω s A A C 5 6 ; ; E E 7

10 Study O Suprondutivity And Antirromgntism In Rr Ert il ororids Ri C wr g nd g g qusi prtil nrgy nds n otind rom t pols o t Grn s untion i i to nd 8 OI:.979/ Pg