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KOTOPas OTKJIHKaeTC1l Ha npOXOll1lWHH tJepe3 KPHCTaJIJI TOK JI lIeHcTBHshy

TeJIhHO 3neKTpOMarHHTHaH BonHa npOXOll1l HanpHMep tJepe3 qeppoMarHHTshy

HhIH nH3neKTpHK MOiKeT B npHHUHne COBepwaTh B HeM nepeopHeHTaUHIO

IIOn1lpH3aUHH IIpeBpawa1l ero B cna6bIH qeppOMarBeTHK 06JIauaIOWHH TOshy

POHllHOH nOn1lpH3aUHeH KOHKpeTHO TaKHMH CBOHCTBaMH MoryT 06nanaTh

palnHtJHhIe nepOBCKHTbI MaHraHHTbI (CM Hanp [23]) H llPyrHe nOCTaTotJHO

cnOiKBbIe coenHHeHH1l

3KcnepHMeHTaTophI npH H3MepeHHH TOPOHllHOH nOn1lpH3aUHH KPHCTaJIshy

nOB eCTeCTBeHBO nocTynalOT npowe HanpHMep B [10] H3ytJaJIC1l OTKnHK

MOBOKpHCTaJIna F e-Ga-oKcHlla Ha MarHHTHoe none yhBeCTHo tJTO y TaKoro

MaTepHaJIa qeppoMarHHTHhIe CBOHCTBa cotJeTaIOTC1l C nhe303neKTpHtJeCKHMH

(BcnOMHHTe aHaJIOrHIO C yIIpyrHMH neTn1lMH) B 3KcnepHMeHTe H3Mep1lnaCh

senHtJHHa HHnyUHpoBaHHoH 3neKTpHtJecKoH nOn1lpH3auHH npH HanO)f(eHHH Ha

KpHCTann MarBHTBoro IIOn1l H

D _ (em)H LI - ij ) (9)

(em) rne TeH30p aij Ha3bIBaeTC1l TeH30pOM MarHHT03neKTpHtJeCKOH BocnpHHMshy

tJHBOCTH ABTHcHMMeTpHtJHaH tJaCTh TeB30pa a~jm) KaK pal H OIIpenen1leT

TOPOHllHbIH nHnonhHbIH MOMeBT cornacBo COOTBoweBHIO nyanhBOCTH

(em)amiddotmiddot (10)I)

rne eurooijk - aHTHCHMMeTpHtJBbIH ellHBHtJBbIH TeB30p JIeBH-tHBHTa TIon1lpHshy

3aUH1l npHxon1lWaHC1l Ba OllBY 3neMeBTapHYlO 1ltJeHKY KpHCTanna H3ytJaeshy

MOro OKCHlla IIpHBena K 3BatJeBHIO TOPOHllHOro nHIIonhHoro MOMeBTa PaBshy

BOro ITI24JLB A ABanorHtJBbIH 3ltpltpeKT 6bIn IIonytJeB nn1l MarBHT03neKTpHKa

Cr203 IIOMemeBBoro B cHnhBoe MarBHTBoe IIone IIpeBbIwalOwee IIone cnHBshy

qnOII IIepeXOlla

8

4 BKJIanbl IIOJIJIpu3yeMocTeu B BeKTopHble

IIOJIJIpU3auUu cpen U ux MYJIbTUIIOJIbHble

pa3JIOKeHUJI

B HaCTOJlIlleM naparpacpe MhI Pa30BbeM nOJIHhIH CPOPMaJIH3M BKJIanOB BhICWHX

( cMewaHHhIx) nOJIJlpH3yeMocTeH B lIeThIpe 6a3HCHhIe nJIOTHOCTH pacnpeneJIeshy

HHJI nOJIJlpH3aUHH npOH3BOJIbHOH CpenhI P M T(p) H Td) B npHHUHne

npOH3BOnJl naJIee MYJIbTHnOJIbHhIe pa3JIOEeHHJI 3THX nOJIHhIX BhIpaEeHHH nJIJI

3HeprHH HX B3aHMoneHCTBHH C BHeWHHMH nOJIJlpH3aUHJlMH MhI nOJIYlIHM 0606shyIlleHHe npenhInYIllHX CPOPMYJI Ha CJIyqaH HeJIHHeHHhIX cpen B COOTBeTCTBHH

C CPYHnaMeHTaJIbHhIMH B3a~MoneHCTBHJlMH KaEnoH H3 nOJIJlpH3anHH BBeneM

nOJIJlpH3yeMocTH YlIHThIBalOillHe Bce B03MOXltHhIe BapHaHThI HHnYUHpoBaHHJI

naHHOH nOJIJlpH3aUHH BHeWHHMH nOJIJlMH H TOKaMH 0603Hallag KOJIHlIeCTBO

CsepHYThIX HHneKCOB B Ka)KnOM lIJIeHe TOllKaMH BhInHweM CaMhIe 06mHe BhIshy

pa)KeHHJI nJIJI 3JIeKTpHlIeCKoi nOJIJlpH3anHH -C YlIeTOM Bcex BKJIanOB BnJIOTb no

lIeTBepToro nOpJlnKa

P =a~e) E+a~e) EE+a~e) EEE++a~em) EH+a~em) EEH+

+B~m)H+Bm)HH+Bm)HHH+ +Bme)HE+Bme)HHE+ bull (11)

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+5~r) Je+51r)jeJe+51r) JeJeJe+ +51er) EJe+51mr)HJe++51errmiddotmiddot)EHJe+

rne Jm = ~(i + b) == rotH Je = rotE lIHCJIa npH nOJIJlpH3yeMOCTJlX 060shy3HallaIOT HX TeH30pHhIH paHr H MO)KHO nepeHTH K HenpHBOnHMhIM TeH30PaM

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nJIJI MarHHTHoH nOJIJlpH3aUHH

M =amp~m)H+ampm)HH+amp~m)HHH+ +ampem)HE+amp~em)HEE+

+p~e) E+pie)EE+pe) EEE++p~me) EH+pme) EEH+ (12)

+i~r) Jm+i~r) JmJm+ir) JmJmJm+bull+i1er)HJm+i~mr) EJm++imer)HEjm+

+S~r) Je+S1r)JeJe+S~r) JeJe Je + +S~er) EJe+S1 mr) HJe+ +S~emr) EHJe+ j

nml TOP0HllHOi nOJIJlpH3ar(HH MarHHTHoro npOHCXO)KneHHJI

T M =atr)Jm+ar) JmJm+~r) Jm JmJm+ +a1re)JmE+~re) JmEE+

+~e) E+i31e) EE+7f4e)EEE+ +per) EJm+~er) EEJm+ (13)

+~m)H+Y1m)HH+~m)HHH+ +Y1rm)JmH+Y1re)JmE+ +~rme)JmHE+bull

+6~r) Je+6r) JeJe+~r) JeJeJe++~e) EJe+~m) HJe+bull+6~me) EHJe+bull j

9

nJISI TOPOHZJHOH nOJISIpH3anHH 3JIeKTpHqeCKoro npOHCXOJKneHHSI

T p =a~) Je+a~)JeJe+a~) JeJeJe++a~e)JeE+a~e) JeEE+

+8~e) E+8e) EE+8e) EEE++8e) EJe+8e) EEJe+ (14)

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+gir)Jm+I~)JmJm+g)JmJmJm+ +g~e)EJm+g~m)HJm+ +Sme)EHJm+

HeTpynHo YleCTb B 3THX BhlpaJKeHHSIX nJISI naHHOro paccMaTpHBaeMoro

KpHCTaJIJIa nYaJIbHhle CHMMeTPHH KOTOphIe npHBenYT K paBeHCTBaM THna (m) f3(e) -r(T) (T) B

f32 = 2 (12 = U2 H T n ce ~KJIaZJhIB nOJISIpH3anHH conepJKalJlHe

BeKTOphI Jm H Je Ha3hIBaJOT HeJIOKaJILHhIMH H B nOCJIenHeeBpeMSI 3KCneshy

pHMeHTaTOphI HayqHJIHCL HX H3MepSITb B HeKOTOphIX cnyqaJIX OTneJIbHO OT

JIOKaJIbHhIX 3laquoplaquopeKTOB [24J EcTeCTBeHHO ITO B npHBene~lHhIX BhIIlle laquoPOPMYshy

JIax qaCTL BeKTOpOB HanpSIJK~HHOCTeH MOJKHO 3aMeHHTL Ha HX npOH3BOnHhIe

PaHr nOJISIpH3yeMocTeH UpH 3TOM B03p~CTeT H 3TH BKJIanhI B COOTBeTCTBYshy

IOlJlHe nOJISIpH3anHH TaKJKe 6yneM Ha3hIBaTb HeJIOKaJILHhIMH B03MOJKHhI H

npyrHe HeJIHHeHHhIe KPOCC-qJIeHhI KpOMe MarHHT03JIeKTpHqeCKHX MexaHQ-

MarHHTHhIe TepM03JIeKTpHqeCKHe H np

Tenepb npOH3BeneM MYJILTHnOJILHhIe pa3JIOJKeHHJI BeKTOPHhlX nOJISIpH3ashy

nHH cpen C yqeTOM CBOHCTB HX nOJISIpH3yeMoCTH llJISI 3TOro BOCnOJIL3yeMCSI

laquopopMYJIaMH nJISI 3HeprHH B3aHMoneHCTBHSI 3THX nOJISIpH3aUHH C BHeIllHHMH

nOJISIMH (1) H (2) HaqHeM C aHaJIH3a 3JIeKTpHqeCKOH nOJISIpH3aUHH TIPHCYTshy

CTBHe B BhIpaJKeHHH nJISI n9JISIpH3anHH BeKTopa 3JIeKTpHIeCKOH HanpSIJKeHshy

HOCTH MonHlaquopHnHpyeT onpeneJIeHHe MYJIbTHnOJILHhIX MOMeHTOB HanpHMep

3JIeKTpHqeCKHH nHnOJILHhIH MOMeHT Q = J P(r )cfr nOJIyqHT n06aBKH 3a CqeT w (e) (e) (emT) TI

nOJISIpH3yeMocTeH 02 03 bull 4 bull bull bull pHBeneM nJISI npHMepa BKJIan OT (eL

O 3

(15)

TaKOH BKJIaZJ MOJKeT 6hITL nOCTaTOqHO BeJIHK eCJIH Cpena 06JIanaeT CHJILshy

HhIMH HeJIHHeHHhIMH CBOHCTBaMH H BeJIHqHHa o~e) cymecTBeHHa KpOMe TOrO

3TOT BKJIaZJ MOJKeT YCHJIHBaTLCSI H 3a CqeT HHTerpaJIa TIepexonSI B ClaquopepHqeshy

CKYlO CHCTeMY KOOpnHHaT MhI MOJKeM nepenHCaTL ero B BHne

2f Ei E kd3r = f E2r dr f ninkdfl (16)

rne n TaKHe HHTerpaJIhI qaCTO BCTpeqalOTCSI B 3JIeKTponHHaMHKe= E lEI H CTaTHCTHqeCKOH MexaHHKe H HX 3HaqeHHSI HaxonSITCSI COrJIaCHO 06meH laquoPopshy

MYJIhI

f linjn nl = ~ aijak 0 1 - aikaj 0 1+ (17) L

10

5

IlPH HaJIHqHH nOnOJIHHTeJIhHhIX YCJIOBHH THna divE = 0 HJIH divH = 0 B3J1THe TaKHX HHTerpaJIOB YCJIOJKHJleTCJI B QgtH3HqeCKOM 3KcnepHMeHTe HaJIashy

raeMhIe Ha KPHCTaJIJI nOJIJI MorYT HMeTh pa3Hoe npOHCXOJKneHHe B qaCTHoshy

CTH MorYT HMeTh palHYIO qaCTOTY TaK 3JIeKTpOOnTHqecKHH 3QgtQgteKT Iloshy

KeJIhCa 06hIqHO Ha3hIBaeMhIH JIHHeHHhIM eCTh 3QgtQgteKT BTOpOro nOpJlnKa TK

JlBJIJleTCJI pe3YJIhTaTOM onHOBpeMeHHoro B03neHCTBHJI 3JIeKTpHqeCKoro nOJIJI

HH3KOH qaCTOThI H CBeTOBOH BOJIHhI B KOTOPOH CYlUecTBeHHOH 06hIqHO JlBJIJIshy

eTCJI 3JIeKTpHqeCKaJI COCTaBJIJllOlUaJI 3HaMeHHThIH 3QgtQgteKT Keppa 06hIqHO

HalhIBalOT KBanpaTHqHhIM nOCKOJIhKY nOKalaTeJIb npeJIOMJIeHHJI KpHCTaJIJIa

npOnOplIHOHaJIeH KBanpaTY CMelUalOlUero HH3KOqaCToTHoro nOJIJI OnHaKO no

qHCJIY nOJIeH CTOJllUHX B BhIpaJKeHHH nJIJI 3HeprHH B3aHMoneHCTBHJI 3TOT

3QgtQgteKT Boo6me roBOPJl TpeThero nOpJlnKa CJIenyeT TaKJKe pa3JIHqaTh CTashy

THqeCKHH H nHHaMHqeCKHH 3QgtctgteKThI IlPH H3yqeHHH MexaHH3MOB nHHaMHshy

QeCKHX 3ltlgtltlgteKToB YQHThIBalOT CYMMOBhIe H PalHOCTHhIeqaCTOThI H OT HX

HanJIeJKalUero BhI60pa MOJKeT CHJIhHO 3aBHceTh BeJIHqHHa 3QgtQgteKTa

HeTPynHo BhInHcaTh Qgt0PMYJIY nJIJI Q yqHThIBalOlUYIO Bce HeJIHHeHHhIe

JIOKaJIhHhIe BKJIa]lhI HCnOJIh3YJI BhIpaJKeHHe (11) B nomIpH3aUHJlX (11) (12) (13) H (14) HeJIOKaJIhHhIe nOJIJlpH3yeMocTH 6yneM 0603HaqaTh TeMH JKe 6yshy

KBaMH qTO U npeJKne HO 3arJIaBHhIMH Torna HanpHMep BKJIan 3a CqeT

HeJIOKaJIhHOH nOJIJlpH3yeMocTH BToporo paHra B nHnOJIhHhIH MOMeHT 6yneT

BhIrJIJlneTh TaK

(18)

TeH30p non HHTerpaJIOM MOJKHO eCTeCTBeHHO Pal6HTh Ha HenpHBOnHMhIe qashy

CTH Torna CJIen ero paBHhIH divE CBeneTCJI K pacnpeneJIeHHIO nJIOTHOCTI1

BHelliHero 3apJlna CHMMeTpHqHaJi qaCTh QgtHKcHPyeT KBa]lpynOJIhHhIe CBOHshy

CTBa neHcTBYlOlUero Ha CHCTeMY 3JIeKTpHqeCKoro nOJIJI a aHTHCHMMeTpHqHaJi

- aKCHaJIhHhIe CBOHCTBa 3TOro nOJIJI

3aKJIIOQeHHe

He npenCTaBJIJleT 60JIhIlIOro Tpyna palBHTh nOJIHhIH QgtOPMaJIH3M non06HhIx

MYJIhTHnOJIhHhIX palJIOJKeHHH IlOJIHaJI napaMeTpH3alIHJI JII060ro QgtYHnaMeHshy

TaJIhHOro B3aHMoneHCTBHJI OKaJKeTCJI Ky6HqeCKOH pellieTKoH 3anOJIHJllOlUeH

npOCTpaHCTBO Boo6lUe roBOPJl HeOrpaHHqeHHO HanpHMep B nOJIOJKHTeJIhshy

HhIX HanpaBJIeHHJlX oceH X Y H Z Ha OCH X KOTOPYIO 6yneM CqHTaTh

rJIaBHOH 6y~eM pacnOJIaraTh aHaJIH3HpYJl KaKYlO-JIH60 CJIOJKHYIO 3JIeKTposhy

MarHHTHYIO CHCTeMY 3HaqeHHJI onHChIBalOlUHX ee MOMeHTOB B nOpJlnKe B03shy

paCTaHHJI l-nOJIhHOCTH B HanpaBJIeHHH OCH Y 6yneM QgtHKCHpOBaTh 3Haqeshy

HHJI BKJIanOB 2n-CTeneHHhIX panHYCOB pacnpeneJIeHHJI KalKnoro MOMeHTa B

nOpJlnKe B03paCTaHHJI CTeneHH n HanOMHHM qTO MYJIhTHnOJIhHhIH aHaJIH3 B

11

ero MaTeMaTHqeCKOH nOllOnJIeKe OCHOBhIBaeTClI Ha TeopHH 0606meHHhIx ltPYHKshy

IlHH H HeCMOTpll Ha 06menpHHlIThIe 3a6JIYJKlleHHlI 0 llOMHHHpOBaHHH MOMeHshy

TOB BeJIHqHHhI pallHYCOB MorYT OKalaTbClI ropa3110 60JIee cymecTBeHHhIMH

npH onHcaHHH KaKoH-JIH60 KOHKpeTHOH CHCTeMhI TaK HanpHMep 3JIl1HnCoshy

Hll8JIbHhIH llBOHHOH CJIOH C He60JIbIllHM 3KcIleHTpHCHTeTOM npeJKlle Bcero 6yshy

lleT OnHChIBaTbClI cpellHeKBallpaTHqHhIM 3apmOBhIM PallHYCOM a nOTOM YJKe

3JIeKTpHqeCKHM KBallPynOJIbHhIM MOMeHTOM C reoMeTpHqeCKoHmiddot JKe TOqKH

3peHHlI pallHYChI onHChIBalOT Mepy OTKJIOHeHHlIKaJKlloro l-noJIbHoro MOMeHTa

OT 3allaHHSI ero B TOqKe C aKTYal1bHO HYJIeBhIMH palMepaMH [25] lial1ee

H MOMeHThI H pallHYCbI KaK MhI BHllHM H3 MaTepHal1a3TOH pa60ThI MorYT

HMeTb nonpaBKH 3a CqeT HeJIHHeHHOcTH B3aHMOlleHCTBHlI H3yqaeMOH CHCTeMhI

C BHemHHM nOJleM 8TH nonpaBKH MOJKHO paCnOJIOJKHTb BepTHKal1bHO napal1shy

JIeJIbHO OCH Z B nopmKe B03paCTaHHSI qHCJIa HHlleKCOB Y TeH30POB nOJISIpH3Yshy

eMOCTH Hall KaJKAOH n03HIlHeH MaTpHIlhI ltPHKCHpYlOmeH 3HaqeHHlI MOMeHTOB

HJIH pallHYCOB

OTMeTHM qTO B 60JIbIllHHCTBe 3KcnepHMeHTOB npH H3yqeHHH CBOHCTB CHshy

CTeMhI 06h1qHO HCnOJIb3YIOTClI JIH60 CTaTHqeCKHe JIH60 H3MeHj[IOmHeClI co

BpeMeHeM rapMOHHqeCKHe nomr MhI06pamaeM BHHMaHHe Ha TO qTO llJIlI

BhIsJBJIeHHj[ BHxpeBhIX CTPYKTYP nepBOro nopmKa - TOP0HllHhIX llHnOJIeH shy

qHCTYIO ltPYHKIlHIO OTKJIHKa (6e3 npHMeCH llPyrHx MYJIbTHnOJIbHhIX B3ashy

HMOlleHCTBHH) MhI 6YlleM nOJIyqaTb HaKJIallhIBaK Ha H3yqaeMYIO CHCTeMY

nOJIlI pacTymHe JIHHeHHO BO BpeMeHH liJIlI BhIlIBJIeHHlI BKJIallOB nOJIOHllal1bshy

HhIX llHnOJIeH HalOBeM HX BHxpeBhIMH CTpyKTypaMH BTOpOro nopauKa HJIH

2-TopaMH [26] Ha110 HaKJIallhIBaTb Ha CHCTeMY nOJIlI pacTymHe BO BpeMeHH

KBallpaTHqHO (H Tll COOTBeTCTBeHHO nOpllllKY n-TOpa) ECTecTBeHHo qTO

BeJIHqHHa OTKJIHKa 6YlleT CTpeMHTeJIbHO nallaTb C B03paCTaHHeM nopauKa n H3-3a Hal1HqHlI peJIlITHBHCTCKOro 4gtaKTopa (lc)n B 3HeprHH B3aHMOlleHCTBHlI

n-Topa C BHeIllHHM nOJIeM

IIollqepKHeM TO qTO BhIlleJIeHHe BeKTOPHhIX BKJIallOB HaH60JIee yll06HO llJIj[

3KcnepHMeHTaTopOB npH aHal1H3e KPHCTal1JIHqeCKHX 06beKToB Mal1hIX palMeshy

pOB Eme 60JIee HarJIj[llHO npHMeHeHHe 3TOH MeTOllHKH npH HCCJIellOBaHHH

3JIeKTpOMarHHTHhIX OTKJIHKOB HH3KOpalMepHhlX CTPYKTYP npHMeHlIeMhIX B

HaHO~eXHOJIOrHlIX

ABTOPhI 6 JIarona PHhI MHTII ltIgtYHllaMeHTal1bHaK MeTpOJIOrHlI 3a nOllshy

llepJKKy 3TOH TeMaTHKH no corJIaIIIeHHIO 251

12

[1] BeHeBueB IOH rarYJIHH BB nI06HMOB BH CezHemoMazHemunu M HaYKa 1982 224 c

[2] lly60BHK BM lJelliKoB AAMyJlbmUnOJlbHble pa3J10HCeHUJI 6 nJlaCCU14eshy

cnOfl U 6 n6aum060fl meopuu nOJlJI U U34Y14eUue ltlgtH3 3JIeM llaCTHU H aT anpa (3lJASI) 1974 5 B3 c791-837

[3] lly60BHK BM TOCYHJlH nA TOpououble MOMeHmbl 6 ffiu3une 3J1enmpOshy

MazuumHblX U CJla6bX 63auMooeflcm6uiJ ltlgtH3 3JIeM llaCTHU H aT JIltpa (3lJA5I) 1983 14 B5 c1193-1228

[4] lly60BHK BM TOpouoHble MOMeHmbl nan o6UCeffiu3UleCnUe napaMempb

B KH TeopeTHKo-rpYlIlIoBbIe MeTOltbI B qH3HKe TpYltbI TpeTlero ceshyMHHapa IOpMaJIa 22-24 Mag 1985 r T2 M HaYKa 1986 c356-362

[5] BJIaTT llJIlt BaicKolIq B TeopemulecnaJI JIOepHaJI ffiu3una M 1960

[6] )l(eJIYlteB HC 06 OOHOiJ ffiOpMaJlbHoiJ 603MOHCHOCmU c030aHUJI cnOHshy

maHHoiJ nOJlJIpU3aijUU 3a C14em ynopJIOOleHHOZO 06UHCeHUJI 3J1enmpOH06

H3B AH cep ltlgtH3HlleCKU 1969 XXXIII N2 c204-206

[7] Schmid H Int J Magnetism 4 1973 p337

[8] Ascher E in Magnetoelectric interaction phenomena in crystals Eds A Freeman and H Schmid New York 1975 p69

[9J lly60BHK BM KPOTOB CC TyrYllieB BB Manpocnonu14ecnaJI CUMMeshy

mpUJI U MunpOCnonU14ecnaJI npupooa napaMemp06 nopJIona npu monoshy

60M U cnUH-mon060M ynopJIOOleHUU 6 npucmaJlJlax KPHCTaJIJIOrpaqHg 1987 32 N3 c540-549

[10] llOIIOB 10lt1gt 3Be3ltHH AK KanoMueBa AM H ltp MazHumoMenshy

mpu14ecnuiJ 3ffiffienm U mopOUOaJlbHOe ynopJIOO14eHUe 6 npucmaJlJlax

Ga2-xFex03 )l(3TltIgt 1998 114 BbIlI1(7) c263-272

[11] llOIIOB 10lt1gt KaltOMueBa AM 3Be3ltHH AK BenoB 1lB Boposhy6beB rll HHoyijUp06aHue MaZHumHbM nOJleM mopOUOaJlbHOZO MOMeHma

6 MaZHumOMenmpune Cr203 TIHcLMa B )l(3TltIgt 1999 69 BbIlI4 c302shy306

[12] lly60BHK BM TOCYHJlR nA TyrYllieB BB AnCUaJlbHble mopouoHble

MOMeHmbl 6 3J1enmpOOUHaMune U ffiU3une m6epoozo meJla )l(3TltIgt 1986 63 T 90 BbIlI 2 c590-605

13

[13] MapueHlOK MA MapueHlOK HM 0 npoucxoJICae1tuu apOMaZ1temU3Ma IIHcbMa B )K3TltIgt 1991 53 B 5 c229-232

[14] ToncToH HA CnapTaKoB AA H06blU 6Ua MaZ1temU3Ma apOMaZ1teshymU3M IIHcbMa B )K3TltIgt 1990 52 B3 c796-798

[15] AqaHacbeB r H Cmapble U 1t06ble npo6AeMbl6 meopuu 3(fi(fie~ma Aap01t06a- EOMa ltlgtH3HKa 3l1A5I 1990 TOM 21 Bhln 1 c172-240

[16] He XG and McKellar BHJ Topological Phase due to Electric Dishypole Moment and Magnetic Monopole Interaction Phys Rev 1993 A47 p3424-3429 AqaHaCbeB rH CPu3UleC~Ue npUAOJICeHUJl COAe1tOshyUa06 ltlgtH3HKa 3l1A5I 1993 24 Bhln2 c512-593

[17] nYOOBHK BM MapueHlOK MA MapueHlOK HM Topoua1taJl nOAJlpU-3aqUJl azpeZUp06aHHbIX MaZ1tUm1tbIX cycneH3UU U ~OMn03um06 ltlgtH3HKa 3neM qacTHU HaT lInpa (3l1A5I) 1993 24 BhlnA cl056-1132

[18] ltlgtHnHnnoB EH KOP3YHHH JIr Hnp HeAU1teUHaJl aUHaMU~a 6uxpe6blX aOMeHHbIX cme1ton 6 MaZHUmHbIX nAe1tnaX 6 tltuponOU o6Aacmu mOAtLtU1t ltlgtH3MeTH MeTaTIJ1oBen 1999 87 No6 c17-23

[19] Usov NA Magnetization curling in soft type ferromagnetic particles with large aspect ratios JMagand MagMat 1999 203 p277-279

[20] Dubovik VM and Kuznetsov VE The Toroid Dipole Moment of the Neutrino IntJModPhysA 1998 13 N30 p5257-5277

[21] Bukina KN Dubovik VM Kuznetsov VE Transition radiation of the neutrino toroid dipole moment PhysLettB 1998 435 N 1-2 p134-138

[22] KOplOKHH BM 3gJgJeICm f(a3uMupa zpa6umaqUJl U peAunm06ble HeUshympU1to JhBecTHlI BY30B ltlgtH3HKa 1996 N 10 c119-120

[23] Sandratskii LM and Kiibler J Role of Orbital Polarization in Weak Ferromagnetism PhysRevLett 1996 76 pA963-4966

[24] npaqeB Bll llepMHHoB CB PaYTHaH cr CaqOHOB Bll IIHcbMa B )K3TltIgt TOM 68 Bhln8 c618-622

[25] Dubovik VM and Tugushev VV Toroid Moments in Electrodynamics and Solid-state Physics Phys Reports 1990 187 NA p145-202

[26] Afanasiev GN Dubovik VM Some Remarkable Charge-Current Conshyfigurations PhysElem Partand AtNucL(Particles amp Nuclei) 1998 29 NA p891-945

PyKonHcb nocTYIIHna B H3laTenbCKHH OTlen bull 18 OKT1I6pll 1999 rola

14

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P17-99-276EYKI1Ha EH Jly60Bl1K BM BKJIaubI nOnap3yeMocTeH B qeTblpe 6a3I1CHble nOn5Ip3aull 3neKTpOMarHl1THbIX cpen

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npenpHHT 060enHHeHHoro HHcTHTyra $IllepHblX HccnenOBaHHH lIy6Ha 1999

Bukina EN Dubovik VM P17-99-276 Contributions of Polarizabilities to Four Basis Polarizations of Electromagnetic Media

All contributions to four basis polarizations of an arbitrary electromagnetic medium at the expense of mixed polarizabilities up to fourth rank tensors are preshysented Some concrete examples are considered

The investigation has been performed at the Bogoliubov Laboratory of Theoshyretical Physics lINR

Preprint of the Joint Institute for Nuclear Research Dubna 1999

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1999lss.fnal.gov/archive/other1/jinr-p17-99-276.pdf2 TeopHH 3q,q,eKTa BOMa-AapoHoBa [15] H...

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Transcript of 1999lss.fnal.gov/archive/other1/jinr-p17-99-276.pdf2 TeopHH 3q,q,eKTa BOMa-AapoHoBa [15] H...