Spintronics M1 Nano

Laurent

Description

Niveau: Supérieur, Master, Bac+4
Spintronics M1-Nano 1 Chapter V: spintronics • Magnetism and itinerant magnetism •Giant magnetoresistance •Hard disks magnetic heads •Spin valve effect •MRAM's

• spintronics m1-nano


• spin symmetries


• babags rrrrrrrr


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• atoms


• screens repulsion between


• magnetic exchange


• spatial spin

Sujets

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Informations

• Publié par: larec
• Nombre de lectures: 22
• Poids de l'ouvrage: 1 Mo

Extrait

ChapterV: spintronics • Magnetismanditinerantmagnetism •Giantmagnetoresistance •Hard disksmagneticheads •Spin valve effect •MRAM’s SpintronicsM1-Nano1

r ⊗ψχ )( ψψψψψ 1 2 1221 =−−−−− r r r r r r r r rRrRrRrR XEABAB snoineewteb noislupersneercs  egrahcnortcele SG nI , ψψ rr SGXE rr )()(  niygrene  bmoluoC yb tesygrenE »telpirt« 1,1,1,1 =↑↑−=↓↓ 1,0 1 2 =↑↓+↓↑ nips noitcnufevaW noitcnufevaw cirtemmysitna  :elpicnirp iluaP χ 0,0 1 2 ==↑↓−↓↑ ψψψψψ 1 2 1221 =−−+−− r r r r r r r r rRrRrRrR SGABAB palrevosmota :sdiloS Atomsfar away: nooverlap ψ ( r ) ⊗χ «singlet» spatial elpicnirp  iluaP+noitcaretni bmoluoC :egnahcxecitengaM 2onaN-1MscinortnipS

Exchange energy(twoions) antisymmetric(spin triplet→F) symmetric(spin singlet→AF) J (Coulomb) sets spin (magnetic) state SpintronicsM1-Nano J αoverlap 3

1s 7s 2 7 S p ip Exchange energyin atoms(Hund rule) 6 5 tnr d o 1 n 0 i 0=l 21x 2 s2 4 sc n f =l 1=l 3x2 n p2 ,32 7Xrra eaetr l=2, 2X5 4s 2 4p 6 3d n transition metals h M1-Nano4 1s 2

L L ↑↑↑↑ ↓↑↓↑ LL LL ψψψ ψψψ 1 1 () (1)() 1(1)() rrrr rrrr A atomiclevel N M1-Nano n Spintronics g Most commonspin symmetries isP P PPn SNPPn P =− = ∏ ∏ )( )()( orrefitna orref )dnab(snoitcnifevaw tnereffidhtiw elbissoppalrevotnereffiD ecittal a ni egnahcxE 5

dnab d3 )ecilsygrenerep setatsforebmun( setatsfoytisneD htdiwdnabdna etatsfoytisneD 3d level atomiclevels Non-magneticmetal spin ↑and↓bandscoincide Fermi surface isnotpolarized Magneticmetal(Fe, Ni, Co…) spin ↑and↓bandsshiftedby exchangeenergyJ 6M1-Nano Thelargerthebandwidth, thelowerthedensityofstates 3d bandnarrow, 4d and5d bandwide→3d transition metalsare magnetic 4 and5d are not ( S b o a li n d d l s e ) vels Spintronics

uCnadN Copper  iedsntiyfosatet Nickel s 3d bandfull 3d bandpartiallyfilled Fermi levelin wide4s band Fermi levelwhere n ( ε F ) small n ( ε F ) Islarge Condition to getferromagnetism n ( ε F ) J > 1 Spintronics Stonercriterion M1-Nano7

dnabworran→ SOD egraL ε EE nJ Kxe F Δ+Δ> > 0 0 )( ↑↓ Δ= − = 2 22 22 ε σ ε E NN n N n K FF )()( )( , m ↑↓ = ∫ K J J End ε εεε )( desaercnisiygrenecitenik TUB Δ=−++−−=− xe EJ N J N σσσ 4 112 2 2 22 2 2 )()( NNN =+ ↑↓ snortceleforebmuN ε F N ↑ = ∫ ε n ( ε ) d ε − J ε F N ↑ = ∫ ε n ( ε ) d ε J 8 polarization σ= N ↑ − N ↓ N potentialenergy(exchange) gained 22 Δ E ex =− J ⎛ ⎜ ⎜ N ↑ 2 − ⎛ ⎜ N ⎞ ⎟ ⎞ ⎟ ⎟ − J ⎛ ⎜ ⎜ N ↓ 2 − ⎛ ⎜ N ⎞ ⎟ ⎞ ⎟ ⎟ ⎝ ⎝2⎠ ⎠⎝ ⎝2⎠ ⎠ Shift 2J betweenspin ↑and↓band Spin upgainSpin down gain ytilibatsnirenotS onaN-1MscinortnipS

ps rof htapeerfnaemtnereffid→ , 0 , = ↑↓↑↓ σσε n F )( evoba 0 F εwoleb 1 noitcnuf imreF f eerf etats lanif deipucco etats laitini → ∫ =−σσεε dkff kkkk 1 3 '' )()()( htapeerf-naem seitirupmifo noitartnecnoc :c ecnatsiserotengamtnaiG n ↓ ( ε F ) > n ↑ ( ε F ) σ ↓ >σ ↑ ⇒ l ↓ < l ↑ oC M1-NanoSpintronics l ∝ 1 ,l ∝ 1 ↑ cn ↑ ( ε F ) ↓ cn ↓ ( ε F ) smalldiffusion large diffusion 9 ↓,↑ ni

aVel-teFtromedlp( MultilayersofCu-Cosandwidches assume nospin flip ( R ↑ + R ↓ ) 4 R ↑ R ↓ ( R ↑ + R ↓ ) 2 ( R ↑ + R ↓ ) 2 Spintronics R~ ↑ ciotira M1-Nano )l Resistanceratio ( R ↑ 4 + R R ↑ ↓ ) 01

rehtO Spintronics equivalentpicture M1-Nano (Landauer) 11