isom.yushuwu.org

DunlopandzdemirEarth,PlanetsandSpace(2018)70:164https://doi.
org/10.
1186/s40623-018-0928-zFULLPAPERRemanencecyclingof0.
6–135mmagnetitesacrosstheVerweytransitionDavidJ.
Dunlop*andzdenzdemirAbstractWereportzero-fieldlow-temperaturecyclingofsaturationremanence(SIRM)producedat300or10Kforcrushednaturalmagnetitesinninesizefractionsfrom0.
6to135m,onesetannealedtoreducestress,theotherunan-nealed.
Coercivitiesofisothermalremanenceincreasetenfoldbetween300and10K,possiblyexplaininganapparenttransitionnear50K.
300-KSIRMdecreasescontinuouslyoncooling,losing60–80%byTV=120K(Verweytransition),isconstantfrom120to10K,thenrecoversasmallmemoryinwarmingthroughTVto300K.
AdipandrecoveryofremanencenearTVforlarger(>15m)annealedgrainsisprobablyduetomemoryofcubicdomainstructuresbymonoclinicmagnetitebelowTV,permittingpartialrecoveryofinitialremanence.
Inwarming,10-KSIRMislittleaffecteduntillostcatastrophicallynearTV.
Asmallmemoryisrecoveredincoolingto10K.
Thecontrastingbehaviorsof300-Kand10-KSIRMsresultfromthecontrastinganisotropiesanddomainstructuresofcubicandmonoclinicmag-netite.
MemoriesofinitialremanencesafterfulltemperaturecyclesareattributedtomonoclinicmagnetiteprovidingatemplateforpartiallyregeneratinginitialcubicdomainstructuresonthesecondpassagethroughTV.
Memoryratiosasafunctionofgrainsizeforourmagnetitesaretooscatteredtobegranulometricallyuseful.
Keywords:Magnetite,Verweytransition,Saturationremanence,Low-temperaturecyclingTheAuthor(s)2018.
ThisarticleisdistributedunderthetermsoftheCreativeCommonsAttribution4.
0InternationalLicense(http://creativecommons.
org/licenses/by/4.
0/),whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedyougiveappropriatecredittotheoriginalauthor(s)andthesource,providealinktotheCreativeCommonslicense,andindicateifchangesweremade.
IntroductionMagnetite(Fe3O4)iscubicatroomtemperaturewithinversespinelstructure.
Itsfirstmagnetocrystallineani-sotropyconstantK1isnegativeandtheeasyaxesforspontaneousmagnetizationMsarethefour111bodydiagonals.
Belowroomtemperature,magnetiteunder-goesatleasttwotransitions.
Attheisotropicpointnear130K,K1changessignandtheeasyaxesswitchto001.
Domainstructuresmustchangeasaresultbutthereisusuallylittlesignofthisinthemeasuredsamplemagnetization.
TheVerweytransition(Verwey1939;Walz2002)near120Kisafirst-orderphasetransition.
Thecubiclatticedeformsonlyslightlyandexchangeinteractionisscarcelyaffected,asevidencedbythenear-continuityofMsacrossthetransition(e.
g.
,zdemir2000;Kosterov2001),butthemagnetocrystallineanisotropyconstantsofthenewmonocliniclatticeincreasemorethantenfold.
Msnowliesalonganeasyc-axiswhichisoneofthecubic001axes.
Lessreorganizationofdomainswouldseemtoberequiredthanattheisotropicpoint,buttherearetwocomplications.
Theanisotropyisnolongermultiaxial,withthepossibilityof90°wallsandclosurestructuresaswellas180°walls(zdemiretal.
1995),butuniaxial.
Inaddition,withineachgrainmonoclinictwinningtypicallyproducesamosaicoftwindomainswithdifferentc-axes,minimizingoverallcrystalstrain(Salje1993).
Avarietyoftechniqueshaveimagedeithermagneticdomainwalls(DWs)(Molonietal.
1996;Carter-Stiglitzetal.
2006)ortwinwalls(TWs,theboundariesbetweentwindomains)(Chikazumietal.
1971;OtsukaandSato1986;Medranoetal.
1999),butnotbothsimultaneously.
Inarecentbreakthrough,Kasamaetal.
(2010,2013)andBrysonetal.
(2013)haveimagedinteractingDWsandTWsusingtransmissionelectronmicroscopy(TEM).
MagneticstructurewasobtainedbothwithFresnelimag-inginLorentzTEMandbyoff-axiselectronholography(Harrisonetal.
2002).
TWsimpedeDWmotion.
Whena180°DWreachesaTW,itcannotpassintoaneighbor-ingtwindomainwhoseeasyc-axisisrotatedby90°.
InOpenAccess*Correspondence:dunlop@physics.
utoronto.
caDepartmentofPhysics,UniversityofToronto,Toronto,ONM5S1A7,CanadaPage2of14DunlopandzdemirEarth,PlanetsandSpace(2018)70:164addition,theTWisasiteofspontaneouslatticestrain;magnetoelasticinteractionmustaddtoDWpinning(XuandMerrill1989).
IndirectevidencefordomainreorganizationandDWpinningattheVerweytransitionisprovidedbyrema-nencecyclingandmagnetichysteresisexperimentsacrossthetransitionregion(e.
g.
,Hartstra1982,1983;Hodych1986,1991;HalgedahlandJarrard1995;zdemirandDunlop1998,1999;Muxworthy1999;KingandWil-liams2000;MuxworthyandMcClelland2000;zdemir2000;Kosterov2001,2003;zdemiretal.
2002;SmirnovandTarduno2002;Muxworthyetal.
2003;Yuetal.
2004;Smirnov2006,2009;KosterovandFabian2008).
Thepre-sentpaperaddstothisbodyofmeasurements,fillingadatagapbetweenthesubmicronandmm-sizemagnet-itesstudiedbyzdemiretal.
(2002)andcomplementingthehysteresisstudyofDunlopetal.
(2018)onthesamesetofsamplesusedhere.
Thefirstpurposeofourstudywastousewell-sizedmagnetitesfromacommonsource(see"Samplechar-acterizationandexperimentalmethods"section)totesthowlow-temperatureremanencecyclingvarieswithmagnetitegrainsize.
Asecondpurposewastoinvestigatetheeffectofinternalstress.
Theferroelasticpropertiesofmonoclinicmagnetite(Salje1993)implythatinternalstressshouldbeparticularlyinfluentialatandbelowtheVerweytransition.
SamplecharacterizationandexperimentalmethodsOursamplesusednaturalmagnetitesinglecrystalsfromthePrincessQuarryinBancroft,ON,Canada,asourceofmuseum-qualitymineralspecimens.
PurityofthesecrystalswastestedbyX-raydiffractionandtheCurietemperatureTC.
OnlytheX-raylinesofstoichiometricmagnetitewereobserved;therewerenorhombohedralorsecondaryspinelreflectionsofhematiteandmagh-emite.
TCwas580°C,theCuriepointofstoichiometricmagnetite.
IdenticalCuriepointswereobtainedforthecrushedsizedfractionsdescribedbelow(Dunlop2014).
Experimentswereperformedoncarefullysizedfrac-tionsofmagnetite.
Thecrystalswerefirstcrushedbymortarandpestle.
Twocoarsesizefractionswereobtainedbysieving,andsevenfinefractionswereseparatedfromthepost-sieveresidueusingaBahcocentrifugaldustanalyzer.
Themeansizesofthefinefractionsspanabroadrange,from20.
0±4.
6mto0.
615±0.
30m(arithmeticmeans),withrelativelysmalloverlapbetweenfractions(Table1).
Forconveni-ence,dustfractionsamplesarereferredtointherestofthepaperbytheirmeangrainsizesroundedofftothenearestwholenumber;forexample,the6msamplereferstothe5.
85mfinefraction.
Thecoarsefractionsarealsonamedaccordingtomeansize,135mforthe125–150mand110mforthe100–125msievefractions.
Scanningelectronmicrographsandsizedis-tributionsappearinDunlopetal.
(2018,Figs.
1,2).
SizedistributionsaresymmetricalaboutthemeanandapproximatelyGaussianforthe20m,14mand9msamples,somewhatskewedtosmallsizesforthe6msample,andapproximatelylognormalforthe3m,1mand0.
6msamples.
Despitesomeoverlapbetweensizedistributions,oursamplesareprobablyasnarrowlysizedasispos-sibleusingadustanalyzer.
Thisisanimportantpointbecauseamajorobjectiveofthisstudywastotestthevariationofmagneticpropertieswithgrainsize.
Maxi-mizingthenumberofsamplesobtainablefromtheavailablematerialrequiressometrade-offwithsizeoverlapbetweensamples.
Anotherpurposeofthestudywastotesttheeffectofinternalstressonmagneticproperties.
Tothisend,twosetsofsampleswereprepared.
Samplesinthefirstsetwereunannealed,whilesamplesinthesecondsetwereannealedinvacuumfor7hat700°C.
Samplesweremeasuredasundispersedpowders.
Previouswork(Yuetal.
2004,Fig.
7)hasshownverylittledifferenceinthehysteresispropertiesofbulkpowdersand0.
5%disper-sionsofsyntheticmagnetitesrangingfrom0.
24mto16.
9minsize,presumablybecauseinteractingparti-cleclumpsareverydifficulttobreakup.
Temperaturecyclingofsaturationisothermalrema-nentmagnetization(IRM),impartedateither300Kor10K,wasperformedusingQuantumDesignMagneticPropertiesMeasurementSystems(MPMS)withSQUID(superconductingquantuminterferencedevice)detec-torsattheInstituteforRockMagnetism,UniversityofMinnesotaandattheDepartmentofEarthSciences,Table1GrainsizeandshapedeterminationsforthemagnetitesamplesaStandardsettingsofplatespacingsinBahcodustanalyzerbGrainlength/widthratiocRangeofmeshsizesSettingaNominalgrainsize(m)Grainwidth(m)Dispersion(m)AxialratiobSieved135125–150cSieved110100–125c42020.
0±4.
61.
5281414.
1±3.
71.
391298.
95±2.
71.
451465.
85±2.
251.
461632.
95±1.
151.
491710.
955±0.
501.
43180.
60.
615±0.
301.
49Page3of14DunlopandzdemirEarth,PlanetsandSpace(2018)70:164KyotoUniversity.
ThedependenceofIRMintensityonmagneticfieldstrengthwasalsomeasuredusingtheMPMS.
ResultsIsothermalremanenceasafunctionoffieldstrengthThemagnetocrystallineanisotropyandmagnetostrictionconstantsofmonoclinicmagnetitebelowtheVerweytransition(TV≈120K)aremorethananorderofmag-nitudehigherthanthoseofcubicmagnetiteaboveTV(Bickfordetal.
1957;Syono1965;Abeetal.
1976;Tsuyaetal.
1977;Kakoletal.
1991,1994).
Theresultisthatiso-thermalremanencerequiresmuchhigherfieldstoreachsaturationbelowTVthanabove(Fig.
1).
Thespectrumofcoercivitiesmeasuredat10Kextendsatleastashighas5T,whileat300Kafieldof0.
2TwillsaturatetheIRM.
Inwhatfollows,saturationIRMwasproducedbya2Tfieldat300Kandbya5Tfieldat10K.
Temperaturecyclingof300KsaturationremanenceAsetofresultsforthe1m,6m,9mand14mannealedmagnetitesappearsinFig.
2.
Dataweremeas-uredduringcoolingat10Kintervalsfrom300to130Kandfrom80to10Kandat5Kintervalsfrom120to90K.
Duringwarming,thesamemeasurementintervalswereused.
Thereisacontinuouslossof70–80%ofthestart-ingremanenceincoolingfrom300Kto≈115K,accel-eratingbelow150KastheVerweytransitionapproaches.
Thereisnoindicationinthedataoftheisotropicpointaround130Kwherethecubiceasyaxesswitchfrom111to001.
Thepointofsteepestdescentinthecool-ingcurvesistakentoindicatetheVerweytransitiontem-peratureTV(Table2).
AsmalllossofremanencecontinuesbelowTVbutthecoolingcurvesleveloutbelow80K.
Inthewarminghalf-cyclefrom10K,theremanenceisalmostunchanginguntil100–110Kandthenrecoversasmallamount—theso-calledmemory—inpassingfromthemonoclinictothecubicphaseatTV.
Forthe14msample,thereisasmalldipandrecoveryofremanencearound115K,closetoTV=118Kmeasuredincooling.
Thisdipisnotseenforsmallergrainsizes.
Figure3zoomsinontheVerweytransitionregionforthe14mandlargerannealedmagnetites.
Nowitbecomesclearthatthewarmingremanencereachesapeakbetween100and105Kbeforebeginningtodecreasebetween105and120K.
TheminimumnearTVbecomesmoremarkedatlargergrainsizes.
Amatch-ing,althoughsmaller,diptoaminimumcanbeseeninthecoolingcurvesaswellforthe110mand135msamples.
Figure4comparesdatafortheunannealedandannealed135mmagnetites.
Ahigherlevelofinternalstressreducesthepeakanddipinthewarmingcurveoftheunannealed135mmagnetitecomparedtoitsannealedcounterpart,whilethedipandpeakinthecool-ingcurvearecompletelysuppressedintheunannealedsample.
Thestructuralchangesoccurringduringthemonoclinic→cubictransformationand,evenmoreso,thechangesinthecubic→monoclinictransformationduringcoolingevidentlyaresensitivetointernalstress.
Turningtoevenlargergrainsizes,Fig.
5demonstratesaratherstrikingsimilarityinthebehaviorofthe14mannealedsampleanda1.
5mmsinglecrystalofmag-netite.
Bothexhibitpeaksinremanenceat105–110KduringwarmingfollowedbyaplungetoaminimumatTV=115–120K.
The1.
5mmcrystalexhibitsidenticalbehaviorinitscoolingcurve,whereasthecoolingcurveofthe14msampleisequivocal.
Temperaturecyclingof10KsaturationremanenceFigure6illustrateswarmingcurvesofsaturationrema-nenceproducedat10Kinunannealedsamples.
Eachsat-urationIRMwasproducedafterzero-fieldcooling(ZFC)ofademagnetizedsamplefrom300K.
Coolinghalf-cycleswerenotmeasured,buttheultimateremanencesat10K(theindividualdotsattheleft)areverysimilartothe300Kvalues.
TheVerweytransitioninthewarm-ingcurvesismarkedbyasimplefeaturelessdecreaseinremanence,withoutanypeak,diporrecoverylikethoseseeninthewarmingcurvesof300-Ksaturation0.
40Magneticfield(T)Isothermalremanence(normalized)0.
50.
60.
70.
80.
91.
01.
11234510K50K150K300KFig.
1Acquisitionofisothermalremanentmagnetization(IRM)asafunctionofappliedmagneticfieldmeasuredatvarioustemperaturesforthe0.
6mannealedmagnetitesamplePage4of14DunlopandzdemirEarth,PlanetsandSpace(2018)70:164remanence.
TVisagaintakentobethepointofsteepestdescent(Table2).
AboveTV,thecurvesareflatandfea-tureless,whereasthecorrespondingwarmingcurvesofFig.
2tracedagentlearchbetween120and300K.
Rema-nenceimpartedtothemonoclinicphaseseemstolackthememorycapacitythatthecubicphaseremanenceretainsevenafterithasbeentransformedtothemono-clinicphaseandback.
Remanencewarmingcurvesfortheannealedsamples(Fig.
7)haveanumberoffeatureslackingintheunan-nealedsampleresults.
First,forthethreesmallestgrainsizesinparticular,thereisamarkedremanencedecreaseduringwarmingfrom10Kto50K,afterwhichthecurvesleveloutinapproachingtheVerweytransitionregion.
Second,thedecreaseinremanenceacrosstheVerweytransitionissharperthanfortheunannealedsamples.
Third,theremanenceaboveTVdecreasesnoticeablywithwarmingforthesmallergrainsizesbutafterrecoolingto10K,theremanencerecoversorincreasescomparedtovaluesatTVforallgrainsizes.
Thezoom-inviewsofFig.
8illustratethesharpnessofremanencechangesacrosstheVerweytransitionregioninannealedsamples.
70–80%ofthetotalchangeoccursinthe10Ktemperatureintervalfrom105to115K.
Inunannealedsamples,theremanencedropisbroaderandmoregradualandtheupperterminationofthechangeiscloseto130K.
Inannealedsamples,theelbowmark-ingtheterminationoftheremanencedropispreciselyatTV=115–120K.
Inanearlierstudy(Dunlopetal.
2018,Fig.
7),changesinhysteresisparametersweresharperforannealedthanforunannealeddustfractionseparates(althoughnotforsievedfractions).
1μm1μm6μm6μm9μμm9μm14m14μmM/Mo000.
20.
20.
40.
40.
60.
60.
80.
81.
01.
0005050100100150Temperature,T(K)150200200250250300300Fig.
2TemperaturedependenceofsaturationIRMproducedbyafieldof2Tat300K,cooledinzerofieldto10Kandwarmedinzerofieldbackto300Kforfourmagnetitesamples.
Onlythe14mmagnetiteshowsadipandrecoveryofremanenceatTV(≈115K)Table2TransitiontemperaturesTVestimatedfrompointsofsteepestdescentinfirstcrossingsoftheVerweytransition,whilecooling300-KSIRMsandwarming10-KSIRMsaUncertainbecauseofnoisydataGrainsize(m)AnnealingTV(K),coolingTV(K),warming135Annealed122112110Annealed12020Annealed11611414Annealed1181109Annealed1161106Annealed108a1103Annealed107a1Annealed112112135Unannealed12211520Unannealed11814Unannealed1209Unannealed1203Unannealed1201Unannealed120Page5of14DunlopandzdemirEarth,PlanetsandSpace(2018)70:164LowtemperaturememoryratiosIntheearlydaysofpaleomagnetism,low-temperaturedemagnetization(LTD)byzero-fieldcyclingthroughTVwaswidelyinvestigatedasanondestructivemeansofselectivelycleaninglow-stabilityremanencecar-riedbymagnetite(e.
g.
,Ozimaetal.
1964;CreerandLike1967;KobayashiandFuller1968;Merrill1970).
Theideaofcontinuoustrackingtodelineatethetem-peraturespectrumofdemagnetizationcamemuchlater(e.
g.
,Dunlop2003).
Inthe1990s,memoryratiosofremanenceintensitybeforeandafterLTDwerelinkedtomagnetitegrainsizesintwocarefulstudiesbyHei-deretal.
(1992)andHalgedahlandJarrard(1995)andproposedasapotentialgranulometrictool.
Althoughthissuggestionwasnotputtomuchpracticaluseintheyearsthatfollowed,itisinterestingtotesttheideausingthedatafromthepresentpaper.
KingandWilliams(2000)pointoutthattheorigi-nalnotionofamemoryratioinvolvedtherecovery,ormemory,ofremanencethathadbeenlostincrossingtheVerweytransition.
Forconvenience,wewillusealooserdefinition,asimpleratiooftheremanenceremainingattheendofatemperaturecycleorhalf-cycletothestartingremanence.
InFig.
9a,thehalf-cycleandfull-cycleratiosR1=M10/M300andR2=M′300/M300fortheannealedmag-netitesareseentodecreaseroughlyaslogd,wheredismeangrainsizebutthedispersionaboutthemeanlinesistoogreatforanypracticalapplication.
Furthermore,R1andR2forthe110and135mmagnetitesdonotfitthelinesdefinedbythe1–20mdata.
InFig.
9b,thehalf-cyclememoryratiosforsaturationremanencesproducedat10Kareplottedforbothannealedandunannealedmagnetites.
Theseratiosmoreorlessfollowsinglelines,exceptforthe0.
6mdata.
Magnetization,M/Mo8090100110120130140150Temperature,T(K)135μm110μm20μm14μmFig.
3Zero-fieldcoolingandwarmingcurvesof300-KsaturationIRMoverthe75–150Kinterval,centeredonTV,forfourlargergrainsizemagnetites.
AllshowadipandrecoveryofremanenceatTVtovaryingdegreesinthewarmingcurves;the110and135msamplesshowitalsointheircoolingcurvesannealedunannealed8090100110120130140150Temperature,T(K)135μmmagnetiteMagnetization,M/MoFig.
4Zero-fieldcoolingandwarmingcurvesof300-KsaturationIRMfortheunannealedandannealed135mmagnetites.
Intheunannealedsamples,theremanencedipandrecoveryatTVismuchreducedinthewarmingcurveandabsentfromthecoolingcurvePage6of14DunlopandzdemirEarth,PlanetsandSpace(2018)70:164DiscussionIsthereaphasetransitionat50KTheIRMacquisitioncurvesofFig.
1showthatmono-clinicmagnetiteatandbelow50Khasaspectrumofcoercivities10–20timesharderthanthatofroomtem-peraturecubicmagnetite.
Thisobservationfitswithmeasurementsofthetemperaturedependenceofcoer-civeforceHc(Dunlopetal.
2018,Figs.
5,6)inwhichHcincreasesbyafactorof≈5aftercoolingthesamplethroughtheVerweytransition,andbyafurthersmalleramountbelow50K.
Isthereatruephasetransitionat50Koristhisapointatwhichanisotropyand/ormag-netostrictionconstantsbegintoincreaseThereisnoindicationofasuddenchangeinanisotropyormagne-tostrictionaround50KinthedataofAbeetal.
(1976)orKakoletal.
(1994),butitisevidentinFig.
1thatindi-vidualcoercivitiesarealmosttwiceaslargeat10Kasat50K.
Magneticsusceptibilityundergoeschangesbelow40–50Kwhicharenotgenerallymanifestedinremanencedata(Muxworthy1999;Kosterov2003;zdemiretal.
2009).
Magneticviscosityisalsoaffected(MuxworthyandWilliams2006).
Theseeffectsareusu-allyattributedtodiffusionafter-effectanddisaccom-modationofsusceptibilityratherthantoanyphasetransition(Walz2002;WalzandKronmüller1991).
Inthewarmingcurvesof10-KsaturationIRMfortheannealedmagnetites(Fig.
7),thethreefinestgrainedsamples(1,6and9m)haveaclearinflectionat50Kbetweenasegmentofrapidremanencelossfrom10to50Kandamoreslowlydescendingportionfrom50to80K.
However,thisinflectionisdoubtfulfor14mandlargermagnetitesandiscompletelyabsentfromthecorrespondingunannealedmagnetitewarmingcurves.
Itisalsoabsentfromthecoolingorwarmingcurvesof300Ksaturationremanenceforthe1,6and9msam-ples(Fig.
2).
Thus,50Klikelydoesnotmarkastruc-turalchangeinmagnetite,whichshouldmanifestitselfinoriginallycubicmagnetitestransformedtomono-clinicbycoolingto10K,buttheendofarapiddeclineTemperature,T(K)1.
5mmsinglecrystal(unoriented)14μmcrushedmagnetiteMagneticmoment(emu)Magnetization(emu/g)001234563.
84.
0123.
23.
43.
63.
84.
0x10x10x10x10-4-4-2-200505050100100100150150200200250250300300Fig.
5Zero-fieldcoolingandwarmingcurvesof300-KsaturationIRMforthe14mcrushedandannealedmagnetitesampleandfora1.
5mmnaturalmagnetitecrystal.
SimilardipsandrecoveriesofremanenceareseenatTVintheseverydifferentgrainsizesofmagnetitePage7of14DunlopandzdemirEarth,PlanetsandSpace(2018)70:164incoercivitythatunpinsabout20%oftheremanenceofmonoclinicgrainsmagnetizedat10K.
Whycoarserannealedgrainsandalltheunannealedmagnetitesareunaffectedisunclear.
CyclingroomtemperatureremanencethroughtheVerweytransitionTheVerweytransitioniswellexpressedinallremanencecyclingexperiments(althoughtheisotropicpointisinvisible,asinmostpreviousstudies).
Butitsexpressiondependsongrainsize,annealing,andthenatureofthephasegiventheinitialremanence—monoclinicorcubic.
Remanencegiventocubicmagnetiteat300Kisalreadyreducedby70–80%atTV=115–120K(Fig.
2)becauseofthesteadydeclineinanisotropyandmagne-tostrictionoverthistemperaturerange(Hodych1986;zdemir2000).
Inthenext≈20Kofcooling,therema-nencecontinuestochangeonasmallerscale,asdothemagnetichysteresisparametersofthesesamesamples(Dunlopetal.
2018,Fig.
7).
TheVerweytransitionhasasharponset,asmonoclinicphasenucleiappearandtheirboundariespropagaterapidly,butthedisappearanceofthecubicphasedoesnotmeantheendofallchange.
KosterovandFabian(2008)foundthatbelowTV,morefrequentandlargerjumpsoccurredinMvs.
TcurvesofindividualgrainscomparedtoaboveTV.
ThemainmechanismofchangeislikelythecontinuingevolutionofthemosaicofmonoclinictwinsandtheirTWs(Kasamaetal.
2010,2013).
DWstrappedwithintwindomainsandpinnedattwinboundariescanmovelimiteddistancesasthetwindomainsshifttheirpositionsandsizes.
Arraysofmobile180°DWsobservedbyKasamaetal.
(2013)inoccasionallargeuntwinnedmonoclinicregionsmayalsoplayarole.
MoreintriguingandnotexplainedinanyobviouswayaretheremanenceminimacenteredonTVin14mandlargerannealedmagnetites(Fig.
3).
Thesebecomequiteaccentuatedinthe110and135mannealedsamplesandina1.
5mmmagnetitecrystal(Fig.
5),wheretheyappearinbothcoolingandwarminghalf-cycles,evidencethattheunderlyingmagnetoelasticphenomenacausingthemarereversible.
Whatcouldbecausingtheremanencetospontaneouslyincreaseincoolingthroughthe15–20KintervalbelowTVandtodecreaseevenmoremarkedlyinthewarminghalf-cycleAlthoughnotremarkeduponinanydetailinmostcases,similarmagnetizationdipsandrecoverieshavebeenobservedpreviouslyincycling300-Kremanences(Hartstra1982,1983;HalgedahlandJarrard1995;zdemirandDunlop1999;MuxworthyandMcClelland0.
40.
40.
20.
2000050501001001501502002003003002502500.
60.
60.
80.
81.
01.
0M/MTemperature,T(K)Unannealedcrushedmagnetites120mmmm135mm39141392014135Fig.
6Zero-fieldwarmingcurvesofsaturationIRMproducedbyafieldof5Tat10Kforsixunannealedcrushedmagnetites.
ComparedtoFig.
2,thecurvesareratherfeatureless,particularlyaboveTV.
Coolingcurveswerenotmeasuredbuttheremanencesaftercoolingbackto10Kareshownasindividualpointsattheleft.
Inmostcasesthesearevirtuallyidenticaltothevaluesmeasuredat300K,indicatingzerorecoveryofremanenceinthesecondcrossingofTVPage8of14DunlopandzdemirEarth,PlanetsandSpace(2018)70:1642000;KingandWilliams2000;zdemiretal.
2002;Kos-terov2003).
Theyareusuallyassociatedwiththelargergrainsizes.
InHartstra'sstudiesofsizedcrushedmagnet-ites,dipandrecoverywaswelldevelopedin150–250m,100–150mand25–30mgrains,justdetectablein10–15mgrainsbutabsentfromthedatafor15masthetypicalnat-uralcandidatesforremanencereboundjustbelowTV.
Thus,stress,whichfavorsstrongerDWpinning,inhibitsthephenomenon,whilegrainsizesabovethenominalpseudo-single-domain(PSD)-multidomain(MD)bound-arypromoteit,presumablyforthesamereason:largernumbersofmoremobileDWs.
Smirnov(2006)andRob-ertsetal.
(2017)arguethatthePSDstateisaphysicallydistinctmagneticstateandnotamixofsingle-domain(SD)andMDstatesasmodeledbyDunlop(2002).
Ineithercase,mostofthegrainsizestypicallydisplayingdipandrecoveryarelargeenoughtocontainatleastafewwell-developedDWs.
ThereboundofremanenceincoolingbelowTVisreminiscentofthememoryphenomenon,inwhichacertainfractionoftheinitial300-Kremanenceisrecov-eredinthesecondpassagethroughTV.
Onedifferenceisthatmemorypersistsinwarmingtoroomtemperature,0.
40.
40.
20.
2000050501001001501502002003003002502500.
60.
60.
80.
81.
01.
0M/MTemperature,T(K)Annealedcrushedmagnetites6,9120201496113516mm20m13514m9m14m135Fig.
7Zero-fieldwarmingcurvesofsaturationIRMproducedbyafieldof5Tat10Kforsixannealedcrushedmagnetites.
Comparedtotheresultsforunannealedsamples(Fig.
6),theremanencedemagnetizesmorebetween10and100K,withaninflectionpointat50K;theremanencelossatTVislargerandmoresudden;andtheremanencedecreasesfurtheraboveTVformostgrainsizes.
Thereissubstantialrecoveryofremanenceafterrecoolingto10KforthelargergrainsizesPage9of14DunlopandzdemirEarth,PlanetsandSpace(2018)70:164whereasthereboundgainofremanenceislargelytransi-toryanddisappearswithfurthercooling.
MuxworthyandMcClelland's(2000)explanationfortherebound,whichtheycallapositiveanomaly,istheremovalofscreeningsoftDWs,revealingaharddomainstructurecarryinganetmomentinthedirectionoftheinitialremanence.
WhilethismightbereasonableforthePSD-sizehydro-thermalgrainsthatdisplaytheanomalyintheirsampleset,itisdoubtfulforthelargerMD-sizenaturalmagnet-itesthatmoretypicallyshowreboundinotherstudies,includingours.
AlsoifscreeningwallsinthecubicphaseareremovedatTV,whyshouldthepositiveanomalyper-sistasthemonoclinictwinanddomainstructuresevolveduringafurther15–20KofcoolingCyclinglowtemperatureremanencethroughtheVerweytransitionCubicmagnetitemagnetizedat300Khasalreadyirre-versiblylost70–80%ofitssaturationremanencewhenitreachesTV.
LittleremanenceislostincrossingTV;indeedmoretypicallyremanenceisgained.
Incontrast,monoclinicmagnetitemagnetizedat10Klosesonly10–25%ofitssaturationremanenceinwarmingto100K,butafurther50–80%disappearsbetween100and120K(Figs.
6,7).
TheplungeisparticularlyprecipitousforannealedsampleswithmoreeasilyunpinnedDWswhereupto70%oftheremanencedisappearsintheinterval105–115K(Fig.
8).
Thereisnosignofanydipandrecov-eryatornearTV.
Domainstateschangewithtemperatureinbothcubicandmonoclinicmagnetiteasaresultofchangesinani-sotropy.
Forexample,our6mannealedmagnetiteannealedunannealed80000.
10.
10.
20.
20.
30.
30.
40.
40.
50.
50.
60.
60.
70.
70.
80.
890100110120130140150Temperature,T(K)1μmmagnetiteMagnetization,M/Moannealedunannealed80000.
10.
10.
20.
20.
30.
30.
40.
40.
50.
50.
60.
60.
70.
70.
80.
90.
80.
990100110120130140150Temperature,T(K)20μmmagnetiteMagnetization,M/MoabFig.
8Anillustrationofthesharpnessofremanencelossinwarming10-KsaturationIRMacrosstheVerweytransitionfortheannealedcomparedtotheunannealedmagnetites.
60–80%oftheremanenceislostbetween105and115Kfortheannealedsamples.
Grainsizes:a1m;b20mPage10of14DunlopandzdemirEarth,PlanetsandSpace(2018)70:1640.
40.
40.
3R=M/MR=M/M1210300/300300Meangraindiameter,d(μm)Memoryratios,RandR120.
30.
20.
20.
10.
1000.
50.
711.
523457101520304050701001500.
40.
40.
3unannealedannealedMeangraindiameter,d(μm)Memoryratio,M/M300100.
30.
20.
20.
10.
1000.
50.
711.
52345710152030405070100150abFig.
9Memoryorremanencerecoveryratiosasafunctionofgrainsizefora300-KsaturationIRMcycledto10Kandbackto300K,andb10-KsaturationIRMcycledto300Kandbackto10K.
Inathefull-cycleratioR2=M′300/M300ismoreeasilymeasuredandmorepracticalbutshowsmorescatterthanthehalf-cycleratioR1=M10/M300.
Neitherdatatrendincorporatestheresultsforthe110and135mmagnetites,whoseroomtemperaturememoriesareanomalouslyhigh.
Inb,thehalf-cyclememoryratiosM300/M10comeclosertolyingonasingletrend.
Full-cycleratios(notplotted)aresimilartothehalf-cycleratiosPage11of14DunlopandzdemirEarth,PlanetsandSpace(2018)70:164samplehasPSDhysteresispropertieswhenmagnetizedinthecubicphaseatroomtemperature,butitshyster-esispropertiesareMDasitapproachesTV(Dunlopetal.
2018,Fig.
9).
Inthemonoclinicphase,itrapidlyhardensandwhenitreaches10KithasthehysteresispropertiesofasmallPSDgrain,approachingSDsize.
Thus,alloursampleswhenmagnetizedasmonoclinicmagnetiteat10KhavemorePSD-orSD-likebehavior—fewerand/orlessmobileDWs—thantheyhavewhenmagnetizedascubicmagnetiteat300K.
ThishelpsexplainwhysomuchmoreofthecubicphaseremanenceisdemagnetizedwhencooledtoTVthanthecorrespondingmonoclinicphaseremanencewhenwarmedfrom10K.
Inturn,thecontrastingsignaturesincrossingTVaredeterminedbytheamountofremanenceremainingtobedemagnet-izedonreachingtheVerweytransitionregion—mostofthe10-Kremanencebutvirtuallynoneofthe300-Kremanence.
Unfortunately,themassivedemagnetiza-tionofthemonoclinicphaseremanencemasksanysub-tledetailslikethoseweseeinthecubic→monoclinictransformation.
TheVerweytransitiontemperatureTVatwhichthestructuraltransformationoccurshassomevariability(Table2).
Forannealedsamples,apartfromtworatheruncertaindeterminations,TVmeasuredincooling300-Ksaturationremanencedecreasessteadilywithdecreas-inggrainsizefrom120to122Kforthe110and135msamplesto112Kforthe1msample.
Onthefaceofit,thismightbetakenasevidenceforsomedegreeofoxida-tionofthefinergrainsizesbutthereisnocorrespondingtrendintheTVvaluesdeterminedfromwarmingcurvesof10-Kremanence,whichareuniformly110–114K.
Ontheotherhand,unannealedsampleshavehigherTVval-uesthantheannealedsamples,almostallcloseto120K.
MemoryandmemoryratiosMemoryisthespontaneousrecoveryonasecondcross-ingthroughTVofsomefractionoftheremanencethatwaslostonthefirstcrossing.
InFig.
2,the1,6and9msampleshavesmallmemoriesafterwarming:Theirrema-nencesaboveTVandatroomtemperaturearehigherthantheywerebelowTV.
The14msamplehasadipinremanenceatTV,thenamodestrecoverywithfurtherwarming,buttheremanenceat300Kisscarcelylargerthanitwasat100K:thememoryisnegligible.
Memoryoflow-temperatureremanenceisnotpaleo-magneticallyusefulbutisinterestingnonetheless.
InFig.
6,theunannealedmagnetiteswithoutexceptionhavenomemory:Theremanencesat10Kafterafullwarm-ing–coolingcycle(theindividualpointsneartheleftaxis)areidenticaltothehalf-cycleremanencesmeasuredat300K.
Theannealedmagnetitesdohavesignificantmemories(Fig.
7);thefractionalremanencesrecoveredbetween300Kand10Kbeingsmallestforthe1msam-pleandlargestforthe135msample.
Thus,low-temper-atureremanenceofmonoclinicmagnetitedoespreservesomememoryofitsoriginaldomainconfigurationsafterconversiontothecubicphaseandback.
Toourknowl-edge,thisbehaviorhasnotbeennotedbefore.
Themechanismofconventionalmemory—thatofroomtemperatureremanenceofthecubicphase—hasbeenclarifiedbytheTEMobservationsofKasamaetal.
(2013).
TheirinitialLorentzimagesat143Kshowedlargemagneticdomainsseparatedby90°or180°DWs.
At103Kafterzero-fieldcooling,thedomainsweresmallerandwereseparatedby180°DWs.
Inspiteofthechangeofphaseandanisotropy,therewasagoodcorrespond-encebetweenmagnetizationdirectionsobserved(fromelectronholograms)aboveandbelowTV,particularlynearthespecimenedgewhereself-demagnetizingeffectscomeintoplay.
Inthefinalremanentstatesrecordedafterzero-fieldwarmingbackto143K,largedomainsredevel-oped.
DespitesomedifferencesinpositionsofspecificDWs,theoverallpatternofdomainsandmagnetizationdirectionsroughlymatchedthatseeninitiallyat143K.
ItseemsclearthattheuniaxialdomainstructureinthemonoclinicphasebelowTVpreservesatemplatesufficienttorenucleateapartialreplicaoftheinitialmultiaxialdomainpatternonrewarmingaboveTV,ashaslongbeenspeculatedintheliterature(e.
g.
,Kob-ayashiandFuller1968).
ThedirectionalstabilityofsaturationremanenceincyclingthroughtheVerweytransition(SmirnovandTarduno2011)lendsfurthersupporttothismodel.
Ifthemonoclinicphasecanactasabridgepreservingoverallmemoryofcubicphaseremanence,itseemslikelythatthedipandrecoveryofremanence(or"positiveanomaly")atandimmediatelybelowTVisalsoaresultoflinkagebetweendomainstructuresoneithersideofthetransition.
Detailedobservationsofdomainstructureswithin10–15KofTVareneededtotestthisidea.
ConclusionsWehavemadeasystematicstudyofremanencecyclingasafunctionofgrainsizeinmagnetitesrangingfromsmallPSD(≈1m)tomoderateMD(100–150m)sizesandalessthoroughinvestigationoftheeffectofinter-nalstress,throughtheuseofmatchingunannealedandannealedsamplesets.
Themagnetitesalloriginatedfromnaturalpurecrystals.
Internalstrainresultedfromvary-ingamountsofcrushingandmillingbeforeseparationintosizefractions.
Ourresultsarecompatiblewiththoseofpreviousstudiesofcrushednaturalmagnetite(Hart-stra1982,1983;Kosterov2003)butdiffersignificantlyfromobservationsonhighinternalstressglassceramicmagnetites(HalgedahlandJarrard1995)andlow-stressPage12of14DunlopandzdemirEarth,PlanetsandSpace(2018)70:164hydrothermalmagnetites(MuxworthyandMcClelland2000;zdemiretal.
2002).
Apossiblephasetransitionfrommonoclinictoanotherphaseofmagnetitearound50Kseemsmorelikelytobeatemperatureatwhichtheanisotropyand/ormag-netostrictionconstantsbegintoincrease.
Theevidenceagainstatransitionisthatonlythefinestannealedgrains(<9m)haveaconvincinginflectionintheir10-Krema-nencewarmingcurvesatthistemperature,thatunan-nealedgrainsofallsizeshavenoindicationofsuchatransition,andthatcoolingandwarmingcurvesof300-Kremanencesforallsamplesalsolackthetransition.
Coerciveforcesofthefinergrainedmagnetitesincreasearound50K(Dunlopetal.
2018,Figs.
5,6),althoughtheydonotcontinuetoincreaseatlowertemperatures.
However,IRMacquisitioncurvesshowthattheentirespectrumofcoercivitiesismultipliedalmosttwo-foldbetween50and10K(Fig.
1).
OneofthestrikingfeaturesofourcyclingexperimentsistheverydifferentbehaviorofmonoclinicmagnetitewhenitismagnetizedatlowtemperatureandwarmedinzerofieldthroughTVasopposedtobeingmagnetizedascubicmagnetiteatroomtemperatureandconvertedtomonoclinicmagnetitebyzero-fieldcoolingthroughTV.
Previousauthorshaveremarkedonthiscontrast(e.
g.
,MuxworthyandMcClelland2000),butitislesssurpris-ingwhenthecontrastingdomainstructuresandanisotro-piesat10Kand300Karetakenintoaccount.
Hysteresisresults(Muxworthy1999;zdemiretal.
2002;Dunlopetal.
2018)showthatdomainstructurebecomesmoreMD-likeasmagnetite'sanisotropyandmagnetostrictiondecreaseenroutetoTV,thenabruptlyreverttoPSD-likeinthemuchhigheranisotropymonoclinicphasebelowTV,ultimatelyapproachingSD-likebehaviorat10K.
Inthesimplestterms,DWsaboundandmovereadilywhencubicmagnetiteiscooledfrom300K;atTVthereislit-tleornoremanenceremainingtobedemagnetized.
Butwhenmonoclinicmagnetiteiswarmedfrom10KthefewDWsavailablearestronglypinnedattwinboundariesorcrystaldefects;massivedemagnetizationcanonlyoccurwiththemassivedropinanisotropyandinfusionofnewmobileDWsnearTV.
Althoughsimplistic,webelievethisisthebasicreasonforthecontrastingcyclingcurvesofFigs.
2,6and7.
AninterestingandunexplaineddetailofsomecyclingcurvesofroomtemperatureremanenceisasmalltopronouncedminimumatTV,particularlyinwarm-ingcurves(Figs.
3,4,5).
Wheretheminimumiswelldevelopedthereisanaccompanyingpeakinbothwarmingandcoolingcurvescenteredon100–105K.
Incooling,thisrepresentsaspontaneousrecoveryofremanencelostincrossingtheVerweytransition.
Thisdip-and-recoveryphenomenonhasbeenwidelyobservedbutnotconvincinglyexplained.
Itisabsentfromsampleswithsignificantinternalstressandfromnaturalmagnetitesbelowabout15minsize.
Butarti-ficialmagnetitesproducedinalow-stresshydrothermalenvironmentexhibitdipsandpeaksnearTVinsmallgrainsandlackthemin≈100mgrains(MuxworthyandMcClelland2000;zdemiretal.
2002).
ThekeymaylieintheratherunexpectedsimilaritybetweenuniaxialmonoclinicmagnetizationdirectionsbelowTVandthecorrespondingcubicmultiaxialpatternsandMsvectorsaboveTV,asdemonstratedbyKasamaetal.
(2013).
Whatisrecoveredonasmallscaleoverafewtensofdegreescanevidentlyberetainedasremanencememoryoverthebroadtemperaturerangeoftheentirecyclingexperiment.
Remanencememoriesarerathersmallforoursam-plesifmemoryistakentobestrictlytherecoveryofremanencebetweenthemonoclinicandcubicphaseonthesecondpassageofTV.
AmoreutilitariandefinitionwouldbesimplythefractionofinitialremanencethatsurvivesthedoublepassagethroughTV,andisavailableforpaleomagneticmeasurement.
Fromthisviewpoint,oursamplesretainrespectableworkingmemories,rang-ingfrom20to40%forthe1–14mannealedsamples.
Itisinterestingthatthesamesamplesalsohavemeasurablealthoughsmallermemories,byeitherdefinition,whengivenasaturationremanenceat10Kandcycledto300Kandback(Fig.
7).
Unfortunately,thevariousmemoryratiosaretooscatteredasafunctionofgrainsizetohavepotentialasgranulometricindicators(Fig.
9).
Authors'contributionsDDastheseniorauthorgatheredthemajorityofthedataanddidmostofthewritingofthemanuscript.
participatedinthedatagatheringandongoingdiscussionsofthemeaningandinterpretationofresults.
Bothauthorsreadandapprovedthefinalmanuscript.
AcknowledgementsResearchsupportedbytheNaturalSciencesandEngineeringResearchCoun-cilofCanada.
ThankstoMikeJackson,BruceMoskowitzandPeatSlheidfortheirdiscussionsandhelpduringourvisitstotheInstituteforRockMagnet-ism,whichisoperatedwithsupportfromtheNationalScienceFoundation,EarthSciencesDivisionandtheUniversityofMinnesota.
MeasurementsatKyotoUniversityweretakenduringavisitfundedbytheJapanSocietyforthePromotionofScience.
WethankProf.
MasayukiToriiforhostingourvisitandparticipatingactivelyinthemeasurements.
ConstructivereviewsbyAlekseySmirnov,AndreiKosterovandAdrianMuxworthyimprovedthepaper.
AsstatedintheAcknowledgments,MikeJackson,BruceMoskowitzandPeatSl-heidofthestaffoftheInstituteforRockMagnetism,UniversityofMinnesota,helpedinsettingupexperimentsandinformaldiscussionsofthedatabutdidnotparticipateactivelyinthedatagatheringandfinalinterpretation.
Prof.
MasayukiToriitookamoreactiveroleinthemeasurementsatKyotoUniversitybecauseofhisgreaterexperiencewiththeinstrumentsused.
Hehas,however,specificallydeclinedtobeincludedasanauthoronthepaper.
Allthesecol-leaguesareagreeabletobeingacknowledged.
CompetinginterestsTheauthorsdeclarethattheyhavenocompetinginterests.
Page13of14DunlopandzdemirEarth,PlanetsandSpace(2018)70:164AvailabilityofdataandmaterialsThedatasetsusedand/oranalyzedduringthecurrentstudyareavailablefromthecorrespondingauthoronreasonablerequest.
FundingThesourcesoffundingfortheresearchreportedweretheNaturalSciencesandEngineeringResearchCouncilofCanada(GrantNo.
A7709)andtheJapanSocietyforthePromotionofScience,asdeclaredintheAcknowledgments.
Neitherfundingbodyhadanydirectinfluenceonthedesignofthestudyorthecollection,analysisandinterpretationofdataoronthewritingofthemanuscript.
Publisher'sNoteSpringerNatureremainsneutralwithregardtojurisdictionalclaimsinpub-lishedmapsandinstitutionalaffiliations.
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