Etude des propriétés du couplage d'échange dans des nano-structures de type ferromagnétique/multiferroïque

HAL Id: tel-01486729

https://tel.archives-ouvertes.fr/tel-01486729v2

Submitted on 10 Mar 2017

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Jerôme Richy

To cite this version:

Jerôme Richy. Etude des propriétés du couplage d’échange dans des nano-structures de type ferromag- nétique/multiferroïque. Matière Condensée [cond-mat]. Université de Bretagne occidentale - Brest, 2016. Français. �NNT : 2016BRES0075�. �tel-01486729v2�

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1PVS VOF QBSUJDVMF EF GPSNF FMMJQTP¯EBMF JM FTU QPTTJCMF EF NPOUSFS RVF M۝©RVJMJCSF EF M۝BJNBOUBUJPO TF USPVWF EBOT MF QMBO GPSN© QBS MFT EJSFDUJPOT EV ॑BNQ FU EF M۝BYF E۝BOJTPUSPQJF EF MB QBSUJDVMF $FU BYF E۝BOJTPUSPQJF DPSSFTQPOE JDJ   VOF BOJTPUSPQJF EF GPSNF NBJT DF॒F DPOTJE©SBUJPO QFVU ªUSF H©O©SBMJT©T   UPVUFT GPSNFT E۝BOJTPUSP QJF -FT BOHMFT VUJMJT©T TPOU JOEJRV©T T॑©NBUJRVFNFOU ੗HVSF ৻ਁ P¹

φ

SFQS©TFOUF MB EJSFDUJPO EF M۝BYF E۝BOJTPUSPQJF BWFD MB EJSFDUJPO QPTJUJWF EF

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H

FU

θ

M۝BOHMF FOUSF

M_'

FU M۝BYF E۝BOJTPUSPQJF

-۝©OFSHJF WPMVNJRVF EF MB QBSUJDVMF

E

E©QFOE EF EFVY UFSNFT M۝©OFSHJF EV ॑BNQ E©NBHO©UJTBOU

E_E

BJOTJ RVF M۝©OFSHJF ;५५ॳ१ॴ

E₎

TPJU

E=E₎+E_E.

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*M FTU QPTTJCMF EF NPOUSFS RVF QPVS VO FMMJQTP¯EF VOJGPSN©NFOU BJNBOU© MF ॑BNQ E©NBHO©UJTBOU T۝©DSJU

H#»_E=−N · #»

M_',

৻৻ৼ

P¹

N

SFQS©TFOUF MF UFOTFVS EFT DPFਖ਼DJFOUT EF ॑BNQ E©NBHO©UJTBOU -B NBUSJDF SF QS©TFOUBUJWF EF DF UFOTFVS EBOT MF S©G©SFOUJFM EFT BYFT EF M۝FMMJQTP¯EF FTU EJBHPOBMF FU W©SJ੗F

N_YY+N_ZZ+N_[[= 1.

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%F QMVT M۝FMMJQTP¯EF BZBOU VOF TZN©USJF EF S©WPMVUJPO QBS FY BVUPVS EF M۝BYF

z

MFT DPFਖ਼DJFOUT TPOU UFMT RVF

N_YY=N_ZZ =N_⊥= (1−N_∥)/2.

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-۝©OFSHJF

E_E

EVF BV ॑BNQ E©NBHO©UJTBOU QFVU BMPST T۝©DSJSF

E_E=−1

2µ_৺#»

H_E·#»

M_'

৻৻৿

= 1 2µ_৺N#»

M²_'

৻৻਀

= 1

2µ_৺M²_'(N_∥

DPT

²θ +N_⊥

TJO

²θ)

৻৻ਁ

= 1 2µ_৺M²_'

&N_⊥+N_∥

2 − N_⊥−N_∥

2

DPT(2θ

) '

.

৻৻ਂ

৻৻ਃ

-۝©OFSHJF ;५५ॳ१ॴ B QPVS FYQSFTTJPO

E_E=−µ₀HM_'

DPT(θ

+φ)

৻ৼ৺

-۝©OFSHJF

E^′

QPVS MB QBSUJF WBSJBCMF EF

E

FTU BMPST

E^′=−1

4µ_৺M_'²(N_⊥−N_∥)

DPT

2θ −µ₀HM_'

DPT(θ

+φ).

৻ৼ৻

1PVS TJNQMJ੗FS M۝FYQSFTTJPO JM FTU QPTTJCMF EF MB S©EVJSF QBS MF GBDUFVS

µ_৺M_'²(N_⊥− N_∥) TPJU

η =−1

4

DPT

2θ−h

DPT(θ

+φ)

৻ৼৼ

BWFD

h = H/[M_'²(N_⊥−N_∥)] -B ੗HVSF ৻ਂ SFQS©TFOUF BJOTJ M۝©WPMVUJPO EF M۝©OFSHJF

QPVS EJ੖©SFOUFT WBMFVST EF ॑BNQ

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'࢕࢓ आऍ ‰WPMVUJPO EF Mڣ©OFSHJF EV NPNFOU NBHO©UJRVF EڣVOF QBSUJDVMF TPVNJTF   VO DIBNQ NBHO©UJRVF FO GPODUJPO EF MB EJSFDUJPO EF MڣBJNBOUBUJPO FU QPVS EFT WBMFVST EF DIBNQ E©

DSPJTTBOUFT -FT DFSDMFT WJPMFUT SFQS©TFOUFOU Mڣ©RVJMJCSF EF MڣBJNBOUBUJPO

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1PVS E©UFSNJOFS MB QPTJUJPO E۝©RVJMJCSF EF M۝BJNBOUBUJPO JM FTU O©DFTTBJSF EF DBM DVMFS MFT E©SJW©T QSFNJ¨SFT FU TFDPOEFT EF

η FO DPOTJE©SBOU MFT QBSBN¨USFTh

FU

φ

DPOTUBOUT -FT DPOEJUJPOT E۝©RVJMJCSF TPOU BJOTJ

∂η

∂θ = 1

2

TJO

2θ +h

TJO(θ

+φ) = 0,

৻ৼ৽

FU

∂²η

∂θ² =

DPT

2θ +h

DPT(θ

+φ)>0,

৻ৼ৾

-B S©TPMVUJPO EF DFT ©RVBUJPOT QFSNFU BJOTJ E۝PCUFOJS M۝©WPMVUJPO EF MB EJSFDUJPO EF M۝BJNBOUBUJPO FO GPODUJPO EF M۝BNQMJUVEF FU EF MB EJSFDUJPO EV ॑BNQ DPNNF SF QS©TFOU© ੗HVSF ৻ਂ SPOET WJPMFUT "੗O EF QPVWPJS DPNQBSFS DF॒F ©WPMVUJPO BWFD MFT NFTVSFT EF SFOWFSTFNFOU M۝BJNBOUBUJPO FTU H©O©SBMFNFOU QSPKFU©F TVJWBOU MB EJSFD UJPO EV ॑BNQ FU ©WFOUVFMMFNFOU QFSQFOEJDVMBJSFNFOU   DF॒F EJSFDUJPO -۝BJNBOUB UJPO QSPKFU©F TFMPO MB EJSFDUJPO EV ॑BNQ FTU BQQFM©F BJNBOUBUJPO MPOHJUVEJOBMF PV USBOTWFSTF EBOT MF DBT QFSQFOEJDVMBJSF -FT ©WPMVUJPOT TFMPO MF NPE¨MF EF 4ॆ EF M۝BJNBOUBUJPO MPOHJUVEJOBMF QPVS EJ੖©SFOUFT EJSFDUJPOT EV ॑BNQ TPOU SFQS©TFOU©FT

੗HVSF ৻ਃ

60 40 20 0 20 40 60 H/mT

1.0 0.5 0.0 0.5 1.0

<µF>/(MFVF)

'= 0°

'= 30°

'= 60°

'= 90°

'࢕࢓ आऎ 1SPKFDUJPO EV NPNFOU NBHO©UJRVF S©EVJU TFMPO MB EJSFDUJPO EV DIBNQ QPVS EJञ©

SFOUFT PSJFOUBUJPOTφEF MB QBSUJDVMF EBOT MF DBESF EV NPE¨MF EF 4ࡥࡠ࡟ࡖࡣ FU 8ࡠ࡙࡝ࡗࡒࡣࡥ࡙

ষঘঢঘUFT ঠধ ঢPঠ¨ঝF

.ªNF TJ MF SFOWFSTFNFOU FTU DPI©SFOU EBOT VO TZTU¨NF EPO O© JM TFSB UPVKPVST BDDPNQBHO© EF QSPDFTTVT JODMVBOU MF NPVWFNFOU EF QBSPJT EF

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