REVISTA ~1EXICANA DE FíSICA ~S SUI'LEMENTO 1. 112-11-l

Inductance spectroscopy: a statc-of-thc-art

R. Valenluela/lIstitwo de /m'(>.Higaciolles eH Mll1eria!es, Ullil'('rsidm/ NacioNal Autónoma de México,

P.O. box 70-360. 0-1510 .Iléxico. D.F. Me.•icoe-mai!: mOfljaras0.\w.I1.itiOl:W/{/f1I.IlIX

Recibido el 26 de fehrero de 199X: aceplíldo rl 2Xde mayo de 19l.JX

JUNIO 1999

Intillcl;lllCCSJ'l'Clrt1"COpy(InS), ¡.l'., Ihe Illeasuremenl and analysis nI' Ihe induCI<lnre response o\'er a wide frcquency range. has shown lohe a powerful ml'lhodology lo rcsolvc the magnetization proccsses of I1ltlnysoh rnaglll.'tic matcrials. In Ibis paper, the hasic aSpC'clsof 15:m: n:vÍL'wcd "" \\'l'11 as its applicatinll to a selection 01' soft magnclic malerials, SllCh as :lIllOrphous ribbons, polycryslílllinc ferriles ami

amorphou" win.'s.

KI',I'II'(m/s: Imllll'lalKC speclroSCt)py: amorphous ferromagnets: magncloimpedancc

La cspcclroscopía de indw.:t;lllrias (Eln), que consiste en la medición y :ln:ílisis de la re.•..puesta inductiva en un amplio intervalo de frecucn¡;ias,ha mostrado ser 1111;\poderosa metodología para resolver los procesos de magnclil.ilciúl1 dc 1111gran número dc maleriales magnéticos blanúos.En este arlírulo, se hace Ulla revisión de los aspectos hásicos de la El. así como de su aplicH.:ión a una selección de materiales magnélico,;lales como (:inta.; amorfas. ferritas policristalinas e hilos amorfos,

l)e~cril'((m'.\: i:sPC(:lrost.:'tlpíadc imluetancias; ferromagnetos amorfos: magnetoimpedancia

p,\es: 7S.50,kj; 75.60.ch: 75.60 ej.

J. Intrnductinn

Impcdancc Spcctmscopy (ImS). i.e., the measurel1lcnt andanalysis 01"lhe illlpedanee responsc 01' a large range of matc-rials \\'ith inleresling clt:etrical propcrlics (dielcctrics, fcrro-c1eclries, ionie rondllctors, rtc,) has shown lo he a powerflllcllaracleri/alion Illclhodogy. The hasic aspccls and applica-lions to 111.\11)'c¡¡ses nI' diclectrics can he found in [11.

Tllc prilH:iplcs 01" ImS llave heen eXlended lo lhc mag-nclic counlL'rparl uf fcrroelcctric malerials, I"crri- and ferro~magnclic lllillerials, by lIsing a coil (inslcad 01' eleclrodcs).ami w(lrkil1~ in CllITL'nt mode (inslead 01' vollage mode), Ac-cordingly. lhe llIain illlpedances are hascd 011inductances. in-slead of capacilances, In lhis paper, a shart accounl of sOllleimportan! cases is given.

2. Basics ,,1'inductancc spcctroscnpy

i\k¡¡surin~ Ihe indllclance response or :t magnctic materialohcll allo\\'s 10 rcsol\'e lhe several rnagnetization proeessesaClive in a gin.'11 malerial. This rcsolulion is possihle tille tothe faclthalc;lCh maglletization process possess its 0\\'11 limc-c01l'\la11l. and Ihercfore. a charaelcrislic fr('quelle)' wherc adel:rcase ("a dispersioll") in Ihe response lakcs place, Thernain SICps in this mcthodology, as in lmpcdanee Spcc-Irosropy are:

a. ~1casllrillg in lhe \Videst fn:quency rangc. in urder loellcornpass lbe highesl number nI' magnclizalion pro-ccsses;

h, idenlify Ihe dispersion frequcncies. including if possi-hle, their rclaxation/resonance character; in the case ofmagnetic matcrials, Ihe analysis l1f inductances is farmore re\'ealing Ihan that nf impcdances:

c. proposc an ClJui\' •.l1elll circuit which is ahlc io represenlIhe experimenlal dala:

ti. find ¡¡nd verify an association hCI\vecn the circuit clc-Illenls and physical p;¡ramcters nf Ihe salllple.

In virlually ¡¡II lhe knowlI cascs 01' magnclic malcrials, Iheohscrvcd ltIagnelizalioll processcs are Ihree: a) spin rOlalion.h) domain wall hulging, ami e) domain wall tlisplaeement.Spin rolalion is the mllsl simple magnclil:alion rnechanism: ilcall be represenled by lile partial or 10lal rofalion 01"spíns lo.\\'ard lhe applied ¡¡cId dircclion. whilc maintaning Iheir pre~cession ITHlVL'l1ll~llt.Since the lime-constant JepcnJs essetl-lially of Ihis preccssion, t!lis proccs<.; is Ihe faslcst and Ihere-fon.:: ils dispersion frl'ljuelu.:y (which has a resonanl Characlcr,the ferromagllL'lic rCSOIl<lnce), is Ihe highcs! 01' all Ihe rn~\g.Iletizalion proCL'sscs. It is gcnerally found in the GHz range,wcll abo\"c Ihe usual freqllcnc)' rangc 01" impct!ancc analyz-ers. ami cannol be ohsL'rwd. Spin rOlation appears thcreforeas a small remalH.'nt (real) indllcl<tnce valuc in L,. \'S. f plols.

DOlllain \\'all bllll:!in~ l'OnSiSls in an c1astic wall dcforma-lion produL'ed by iln applicd lielJ which is smaller Ihan thecocreive licld 01"Ihe sample. Thcrcfore, the dlll11ain wall re-rnains pinned in ils original posilion. The dispcrsion freqllen-des can be found in lhc lO kH/.-IO MIV rangc, ami in moslof Ihe ohscrwd malcrials h.IVL:a rclaxalion character.

J)olllain wall disp\aCCIIlClll, responsihle for magnl'tic hys-lCll'sis, is lhe slowcsl prol'ess, sincc il invol\'es lhe collcctive

INDUCTANCE SPECfROSC()!'Y' A STATE.OF-TIlE-ART tt3

f (Hz)

H" ~ 0.28 Alm0.31.0

400

•300

~~200-.J-

100

o10' 10' 10'

•o

•

10' 10' 10'

continue to raise inlercst hecausc oí" lheir low price. but alsoheeausc 01' their exccllenl rrequency behavior. Sincc they pos-sess a very high rcsistivily, losses dlle lo cddy currenls arecxlremely low. and magnelic pcrllleahility relain a high vallleal high frequcncies nI' c:xci[ing field. This fcalufe has strongtcchnological val LIC.

InS in ferriles has shown that lhcir frcquency behaviorcan cffcclively he approximalcd [5] hy the simple equivalen!cin':lIil mcnlioncd ahove. Inll1os( cases. Ihe dornain wall dis-persion exhihits a relaxalion characler with sornc resonancel'onlrihution. The analysis of the thermal va ions in disper-sion frcqucncy hns also shown :l direct correlation with theIllagnclocrystallinc anisotropy [GI. This opens que possihil-il)' lo determinc hasic, inlrinsic properties fmm indllctani.'cmcaSllrellle nts.

Fj(;URI. l. Ikhavior of Ihe renl part of inductancc as a fUllctiollof frcqul'llCY. for an <llllorphous Co-rich ",ire. showing Ihe.3 Ill<linrna!!rlCII¡ali(lIl proccsscs ..

1ll0\'l'lIll'l1l 01 IIlnl1Y spins wilhin a domain wall: firsl, il ishulged undcr lIJe applicd ficld prcssurc until it is unpinncdfmm j[S resl posifion; ¡hen, it is displnced Ihrough thc malc-ri;ll [o a new pinning position; f1nally, as Ihe flcld is removed(inlhe tirsl sellliperiod), lhe hulging disappears and the w¡¡1I[ecovers ils plane shape. For lhe Ilcxl scmiperiod, this pro-eess is repealcd, hUI the blllging ami displacemcnt occurs inIhe opposite direction, since the applied tield is revcrsed. Thisproccss takes place nt low frcqueneics and al applicd ficlds 01"high amplitude (larger Ihan Ihe eoereive f1cld for Ihe corre-sponding malcrial). An cxamplc 01' thcse processes, as lheyarpeal in a speell"oscopic plot 01' lhe real part (Jf induclance isshown in Fig. l.

In lIl<lny cases, a simple equivalenl circuil can he usedto represenl lhe ra\\' frcquency data: a u.~L:< series ann inseries with ¡¡ l?flLp parnllcl arrangelllelll. An association 01'the~e circuit elclllcnls \••..ith physical paralllclcrs can he madeas follnws 13]: Hs is lhe (copper) l'oit rcsislance, Ls is due[o spin rolalion. I.fI dcpends 011dOlllain wall magnctilalion,and HI' ís related wilh the iJlversc of the domain \vall damp-jl1~ coefficicnl. Reversible prncesses. ¡.e., spin rolalíon anddOlllain waH bulging can he wcJl reprcscntcd hy Ls anL! L]Hrl'speclivcly; howcver, hystercsis is Illore complcx ami hast1L'en allemptcd lo he takcn into accolllll hy a Warhurg-typeiJllpcdance. showing a good agreement only rOl" small fields<lh(lVClhe proragation ¡¡cid valuc I.tl. T!lis remains as <Innpenqucslion.

J. Applicatioll of rlls lo son magllctic malcrials

InS has neclI aprlied ro fcrriles. alllorphous ribhons and morerecently, to Ihe giant magnetoimpedancc ellecl.

.1,1. Ft'rritcs

Ferrilllagnclic oxides hnve been inves[igalcd ror lhe Iast 40ye;1!"s (l"or ;¡ recenl revic\\'. see ReL 2). Thc:sc son magnets

J.2, AIIl(lrphous rihhnns

The applicalion 01"InS to :lmorrhous ferromagnetic rihhonshas lel! lo a \\'ide variel)' of results: lhe effects oí" agcingand .mnealings (decrease 01' permcahility by an association01"pair-ordcring on dOlllain \valls, inercase hy rclicving fmmin-qllenchcd stresscs) [i"J, Ihe clfects ofmacro- (dornain wal!pilltling) 18.9) ami nano-cryslallizalion (randomizalion andslrong delTe~ISC in indul'ed anisotropy) 110], and effecls oflensile stress 011rnagncliwlion proccsscs [11].

J.J. (;iant ma~n('tnilllpt'danct.

As-casI. alllorphous ferromagnclic wires of 10\\', nega-(ive magnctoslriclion have cxhihiled a slrong decreasc inil1lpedance (with ¿¡ AC l'urrcnt of smal! amplitudc tlowingIhrough (he samplc) whcn lhey are suhmitted to a DC mag.IiL'[ic lield. This cllect, known as gianl magncloimpcdancc((lMI) [121, has raiscd tcehnologie:ll inleresl sinee il can helJ"l'd in lIl:Jny lIlagnelic licld and elcctrie currenl sensors.As in Ihe pn."violls cases, swilc!ling fmm impedancc to ill-duclallce forrnalislll has Jed [o a clear insight into the in-':nlved l11agnetic phl'nolllena. Induclance spcctroscopy hasshown thal il can he r\."prcscnlcd hy simple equivalenl cir-cuits II;~1,allowing a separalion oi" thc :.1lllain magnelil.ationproccsscs. A Iso. Ih\." elfects 01' De licld [14] and slrcss 115 J

can he clcarly expbincd wilhin InS Illelhodology. A questionrelllaining in l/lis representatioll of GMI is Ihe role played bylhe eddy cUlTents. which js invokcd as a basic assumplion bylhe ,Iassic Irealmcnt; in InSI, macroscopic skin elTcel doesllol seclll lo llave a signilicanl importancc.

Acknnwlcdgmenls

This rese;¡rch program has hcen panially supponed hyDGAPA-UNAl'v1 (granl IN 10(996). The aulhor lhanks IH",l-UNArvl rol' SUpporl lo :lllcnd "Reuniones de Invierno: NcwHorilons in ~1atcrials SCiCllCC", Juriquilla, México, Janllary26-JO, 1l)l)X. \vhere Ihis work was prcsenlcJ.

Rel'. Mex. Fú . .JS SI (1999) 112-11-1-

114 R. VALENZUELA

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Prcss. 1994)

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3652.

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1162.

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Re\'. Afex. F/.\'. 45 S 1 (1999) 112-114