Uniform magnetic susceptibilities
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1 Uform magetc susceptbltes Typcal behavors ad measuremet techques SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 1 - M ICFP- lectroc propertes of solds (Fabrce ert
2 Varous behavors of M(H magetzato M Lear respose Paramagetsm No lear respose ferromagetsm M M saturato M remaet Appled feld H H magetzato M Lear respose Damagetsm Appled feld H No lear respose type II supercoductor M H SUSCPTIILIT UNIFORM & MAGNTOMTRIS page - M ICFP- lectroc propertes of solds (Fabrce ert
3 Uform susceptbltes some smple solds SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 3 - M ICFP- lectroc propertes of solds (Fabrce ert
4 Uform susceptblty Calculato of the uform magetc susceptblty M M N V N V D N V D where D s the eergy perturbato due to the effect of F the free eergy -> the effect of the Hamltoa (D eeds to be calculated at the d order perturbato to get fally M frst order of. SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 4 - M ICFP- lectroc propertes of solds (Fabrce ert
5 SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 5 - M ICFP- lectroc propertes of solds (Fabrce ert Calculato for sulators (wth solated ad localsed sps S g V m r A e p Z electros el. ( 1 H / r A Z electros Z electros el r m e r p m e m p m r A e p ( L p r r p. (..( m el e / Z r m e S g L 1 8.( H H gauge -> I the d term, oe recogzes the orbtal mometum ad the ohr mageto Hamltoa of a atom a magetc feld Uform susceptblty sulators
6 SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 6 - M ICFP- lectroc propertes of solds (Fabrce ert D ' ' ' H H H H (,, y x x y r Takg //Oz ad keepg oly the quadratc cotrbutos : Z r m e S g L 1 8.( H H Z S g L r m e S g L ' ' 1 '.( 8 ( Z S g L y x m e S g L ' ' 1 '.( ( 8 ( Uform susceptblty sulators
7 SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 7 - M ICFP- lectroc propertes of solds (Fabrce ert Larmor damagetsm D Z S g L y x m e S g L ' ' 1 '.( ( 8 ( 1 3 ( r Z y x Z D 3 8 r Z m e V N V N da 6 r Z m e V N da Cotrbuto of ths term to the magetc susceptblty: We use: where r s the oc radus We assume that temperature s low eough so that oly the groud state cotrbutes sgfcatvely Uform susceptblty sulators
8 Uform susceptblty sulators Larmor damagetsm da N V e 6 m Z r T - egatve, weak, T depedet - xsts all solds - mportat cotrbuto for sulators wth full shells (L=S= SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 8 - M ICFP- lectroc propertes of solds (Fabrce ert
9 Uform susceptblty sulators Strogly damagetc materals ca levtate strog magetc feld gradet graphte SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 9 - M ICFP- lectroc propertes of solds (Fabrce ert
10 Uform susceptblty sulators frog Strogly damagetc materals ca levtate strog magetc feld gradet graphte Hgh Tc supercoductors (cuprates SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 1 - M ICFP- lectroc propertes of solds (Fabrce ert
11 SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 11 - M ICFP- lectroc propertes of solds (Fabrce ert Va Vleck Paramagetsm D Z S g L y x m e S g L ' ' 1 '.( ( 8 ( We keep oly the effect of the mxg of the exted states to the groud state D.( S g L V N V N ( S g L a Uform susceptblty sulators
12 Uform susceptblty sulators Va Vleck paramagetsm a ( L g S T - postve, weak, T depedet - Detectable solds wth oly full shells (J= groud state SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 1 - M ICFP- lectroc propertes of solds (Fabrce ert
13 SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 13 - M ICFP- lectroc propertes of solds (Fabrce ert D Z S g L y x m e S g L ' ' 1 '.( ( 8 ( Cotrbuto for atoms wth partally flled shells (J<> All the states wth dfferet J z (J=L+S must be take to accout because temperature s comparable wth the dfferece eergy of these dfferet states. Statstcal physcs calculato (see Kttel or Ashcroft ( T k JH g J g V N M J coth( 1 1 coth( 1 ( J x J x J J J J x J Uform susceptblty sulators
14 Uform susceptblty sulators M N V g J J ( g k JH T x g JH / k T Is ot small s ot well defed lear respose y g JH / k T 1 => M N ( g V 3k Lear respose ok C Cure T C N J ( J T 1 H Cure costat V ( g 3k Cure Paramagetsm J ( J 1 SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 14 - M ICFP- lectroc propertes of solds (Fabrce ert
15 Uform susceptblty sulators Cure Paramagetsm Cure C T T - postve, vares as 1/T, domates all other terms at low T - exsts oly solds wth partally flled shells (upared sps SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 15 - M ICFP- lectroc propertes of solds (Fabrce ert
16 Uform susceptblty sulators Uform susceptblty a sold wth partally flled shells da VaVleck Cure Cure paramagetsm Va Vleck paramagetsm Total susceptblty Larmor damagetsm Temperature SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 16 - M ICFP- lectroc propertes of solds (Fabrce ert
17 Uform susceptblty o correlated metals Metals Dfferet calculato volvg sp ad orbtal mometum of the coducto electros (see tutoral. Two cotrbutos : -Sp susceptblty «Paul» Paul ( F -Orbtal susceptblty «Ladau» Ladau 1 3 Paul (Larmor ad Va Vleck cotrbutos are stll there SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 17 - M ICFP- lectroc propertes of solds (Fabrce ert
18 Uform susceptblty o correlated metals Uform susceptblty a «stadard» metal da VaVleck Paul Ladau Paul para. Global susceptblty Va Vleck para. Larmor da. Ladau da. Temperature SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 18 - M ICFP- lectroc propertes of solds (Fabrce ert
19 Uform susceptblty o correlated metals Temperature depedece of Paul susceptblty some trasto metals SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 19 - M ICFP- lectroc propertes of solds (Fabrce ert
20 Uform susceptblty smple solds Susceptbltes some smple solds Ferromagetc metals metals closed shell sulators SUSCPTIILIT UNIFORM & MAGNTOMTRIS page - M ICFP- lectroc propertes of solds (Fabrce ert
21 More «exotc» behavors of magetc uform susceptbltes SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 1 - M ICFP- lectroc propertes of solds (Fabrce ert
22 Uform susceptbltes exotc systems Sp 1 cha wth atferromagetc teractos (o log rage order Y ano 5 N O exp D T cste Gap the magetc exctatos Shmzu et al., PR (1995 SUSCPTIILIT UNIFORM & MAGNTOMTRIS page - M ICFP- lectroc propertes of solds (Fabrce ert
23 Uform susceptbltes exotc systems Hgh T C supercoductg cuprates as a fucto of dopg for T>T C Ya Cu 3 O 6+x Cu O ~ Paul lke, T-depedet Strog T depedece: pseudogap T supercoductvty Johso et al At Ferro Atferro Supracoducteur dopage x T C SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 3 - M ICFP- lectroc propertes of solds (Fabrce ert
24 Uform susceptbltes exotc systems Cobaltates Na x CoO Very good oc coductors (batteres No covetoal supercoductors Large thermoelectrc power.1 supra atferro magétsme 3 Kc (%.5 x=.6 x=.58 x=.66 x= x Co 3d 7 4s. x=.44 x=.3 x= T (K Lag et al., PR SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 4 - M ICFP- lectroc propertes of solds (Fabrce ert
25 Magetometres : dfferet techques to measure uform susceptbles SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 5 - M ICFP- lectroc propertes of solds (Fabrce ert
26 xpermetal measuremet of uform susceptblty Measuremet based o a force Faraday balace Sample s a magetc feld gradet desged so that: H z z cste Oe measures the force o the balace F z M. H M z H z z from whch oe gets M z the magetzato alog z SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 6 - M ICFP- lectroc propertes of solds (Fabrce ert
27 xpermetal measuremet of uform susceptblty Faraday balace SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 7 - M ICFP- lectroc propertes of solds (Fabrce ert
28 xpermetal measuremet of uform susceptblty Iductve techques xtracto of the sample: bobe Sample s moved sde a pck-up col: U ( t d dt echatllo M U(t H a Varato of flux whe sample s serted: ( H M A H A colwthsa mple emptycol a a Leadg to a voltage at the col: U ( t dt D M MA SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 8 - M ICFP- lectroc propertes of solds (Fabrce ert
29 xpermetal measuremet of uform susceptblty Iductve techques U xtracto of the sample: col sample M U(t Area uder the curve s proportoal to the magetzato t U ( t dt D M SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 9 - M ICFP- lectroc propertes of solds (Fabrce ert
30 xpermetal measuremet of uform susceptblty Iductve techques U vbrato : VSM vbratg Sample Magetometer Sample s moved perodcally wth a frequecy t The perodc voltage s measured wth a lock- detecto SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 3 - M ICFP- lectroc propertes of solds (Fabrce ert
31 xpermetal measuremet of uform susceptblty VSM : vbrato frequeces about 1Hz SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 31 - M ICFP- lectroc propertes of solds (Fabrce ert
32 xpermetal measuremet of uform susceptblty SQUID magetometer SQUID : Supercoductg Quatum Iterferece Devce squd DC squd AC (rf supra sulator supra SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 3 - M ICFP- lectroc propertes of solds (Fabrce ert
33 xpermetal measuremet of uform susceptblty supra solat supra AC SQUID (rf: I s Josephso jucto: Cooper pars tuel through the sulator. A dc curret I S appears due to the phase jump accross the jucto I s Flux quatzato the rg: Wthout jucto: Wth oe jucto: I s( s 1 I h / e rg rg / Oe apples a exteral flux (L : rg ductace : rg ext LI s ext ext ext LI LI LI s s s rg rg SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 33 - M ICFP- lectroc propertes of solds (Fabrce ert
34 xpermetal measuremet of uform susceptblty t e LI s t The flux the rg vares perodcally wth the exteral flux, wth the perod example : LI 1. 5 y measurg the umber of passg through the squd rg, oe ca measure very precsely the exteral flux, therefore the magetzato of the sample wth a accuracy (much better tha : very good sestvty because =.1-15 Wb s small. SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 34 - M ICFP- lectroc propertes of solds (Fabrce ert
35 xpermetal measuremet of uform susceptblty Ac squd setup : ductve detecto Mutual ductace Mutual ductace 4.K below the supercoductg T C Rf curret M U H a t The magetzed sample duces a flux the pckup col the flux s trasfered to the squd by ductve couplg Measured a resoat crcut used at resoace : flux chage duces L chage ad voltage chage SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 35 - M ICFP- lectroc propertes of solds (Fabrce ert
36 SQUID SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 36 - M ICFP- lectroc propertes of solds (Fabrce ert
37 xpermetal measuremet of uform susceptblty DC squd DC : alteratve setup SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 37 - M ICFP- lectroc propertes of solds (Fabrce ert
38 xpermetal measuremet of uform susceptblty Advatages ad drawbacks of SQUID Strog sestvty + o eed of (fast extracto UT Max magetc feld 7T (commercal ad expesve SUSCPTIILIT UNIFORM & MAGNTOMTRIS page 38 - M ICFP- lectroc propertes of solds (Fabrce ert
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