Studies on the Anisotropi Properties of MgB
2
O.F. de Lima
InstitutodeFsiaGlebWataghin,
UniversidadeEstadual deCampinas-UNICAMP
13083-970Campinas,SP,Brasil
Reeivedon28February,2002
Thispaperpresents a reviewon reported anisotropi properties of MgB
2
. The rstdiret
mea-surementofananisotropisuperondutingpropertyinMgB2wasahievedforthebulknuleation
eldH2,insamplesofalignedrystallites. Aratio H ab
2 =H
2
1:7wasfoundbetweentheritial
eldparalleltotheab planeandparalleltotheaxisdiretion. Further,detailedstudyoftheH2
angulardependeneonrmeditsbulkorigin,inontrastwithwhatwouldbeexpetedforthe
sur-faenuleationeldH
3
. AFermiveloityanisotropywasevaluatedtobeV ab
F
1:6V
F
,assuming
an isotropi orderparameter. Forananisotropi s-wave pairingsymmetry ithas beenestimated
that V ab
F
2:5V
F
. Dierent H
2
anisotropy hasbeen foundbydierentauthors, usingdierent
samples, measuredinvariedtemperatureranges. Other reportedanisotropi properties ofMgB2
inthesuperondutingstatearetheeldpenetrationdepth,oherenelength,andenergygap
; inthenormalstate arethemagnetoresistane,ompressibility,andthermalexpansion. Sofar,
mostofthereportedresultshavebeenobtainedusingalignedrystallites,-axisorientedthinlms
andsub-millimeterrystals.
I Introdution
Thedisoveryof superondutivityat 39Kin
Magne-siumDiboride(MgB
2
)[1℄hasbroughtnewexitement
to theareaofbasiandapplied researhon
superon-dutingmaterials.
SeveralstudieshavealreadypointedoutthatMgB
2
has a good potential for appliations [2-5℄ in view of
the relatively high values of ritial urrent density,
J
, and the suessful preparation of wires and lms.
However, intense magneti relaxation eets,
assoi-atedwiththermallyativateduxreepanduxjumps,
havebeenfoundtolimittheJ
valuesathighmagneti
elds[6℄. Thismeansthateetivepinningentershave
tobeadded[7℄intothematerialmirostruture,in
or-dertohaltdissipativeuxmovements.
The observation of an isotope eet [8,9℄, a
BCS-typeenergygap[10℄, aswellasband struturestudies
[11-13℄ suggest the ourrene of a phonon-mediated
superondutivityin MgB
2
. Manyother experimental
[14-18℄andtheoretial[19,20℄workshavepointedalso
to the relevane of a phonon-mediated interation, in
the framework of the BCS theory. However, the
pos-sibility of hole superondutivity, assoiated with the
nearly lled boron planar p
x;y
orbitals, has also been
suggested [21℄. Questions have been raisedaboutthe
relevant phonon modes, as well as about the gap
en-ergy and Fermi surfae anisotropies. A onsiderable
a broad rangeof values, between 2.5 and 5.0, for the
gap ratio 2
0 =kT
, where
0
is the gap energy at T
= 0and k is the Boltzmann onstant. As a
ompari-son,theBCStheoryintheweakouplinglimitpredits
[22℄ 2
0 =kT
3:5, foranisotropigapenergy. Inan
eorttointerpretthis puzzlingsituation,multiple gap
models [19℄ as well as a general model of anisotropi
s-waveorderparameter[18,20℄ havebeenproposed.
The strongly anisotropi rystalline struture of
MgB
2
hasbeenknownforalongtime. Itseemed
there-forereasonablewhenspeiheatstudiesdonein
poly-rystalline samples [15℄ as well as band struture
al-ulations [11℄, pointed to the possible anisotropi
na-tureoftheeletroniandmagnetipropertiesofMgB
2 .
The rst diret measurementof ananisotropi
super-onduting property was ahieved for the bulk
nule-ationeldH
2
,in samplesofalignedMgB
2
rystallites
[23℄. Itwasfound aratioH ab
2 =H
2
1:7, betweenthe
ritialeldparalleltotheab planeandparalleltothe
axisdiretion. Theanisotropibehaviorofsome
nor-mal state properties, like ompressibility [24, 25℄ and
magnetoresistane[26℄, havealsobeenreported.
Following, a brief review of some aspets
regard-ingsamplepreparationwillbepresentedin SetionII.
In Setion III, a detailed analysis of the bulk
anisotropipropertiesofMgB
2
willbebrieyreviewed.
Finally, in Setion V, a onlusion will be presented.
For a more omplete review on the superonduting
propertiesofMgB
2
seeRef. [27℄.
II Sample preparation
The ompound MgB
2
is known to our in
equilib-rium with an exess of Mg, for temperatures above
650 Æ
C [28℄. By 1953 its AlB
2
-type rystal
stru-ture was determined, using X-ray diration studies
[29, 30℄. This layered struture belongs to the spae
groupP6/mmm,andonsistsofalternatingtriangular
layersof Mg atoms and graphite-like hexagonallayers
of Batoms. The unit elllattieparameters typially
reported[29,30,31,32℄arearounda=3.085
Aand
=3.521
A.
A ommon route to prepare MgB
2
polyrystalline
samplesstartsbymixingthepureelements,MgandB,
in the atomi ratio B:Mg= 2:1. Beause of the
rela-tivelyhighvapourpressureofMgitisadvisedtoreat
themixturesealedinanevauatedtubeorontainerof
anappropriatematerial(e.g. Ta,Nb,Fe,Mo, BN).In
ordertoavoidoxidationofthetube/ontainerexternal
surfae, espeially in aseswhenopen-airfurnaes are
used,thesealedtube/ontainerissealedinsideaquartz
ampoule,in aresidual atmosphereof argongas.
Typ-ially,areationtimearound2hoursattemperatures
between700 Æ
Cand1000 Æ
Chavebeenused, followed
by ooling to room temperature. However, to obtain
smallsinglerystals,ahigherreationtemperature
be-tween1200 -1400 Æ
C andaddition of Mgin exessto
provideaninternalvapourpressureabove1bar,was
re-ported in1973 [31℄. This isessentiallythe sameroute
employedreentlybydierentgroups,toobtainMgB
2
rystallites having sub-millimeter sizes [23,33℄. A
dif-ferent approah onsists of reating the quasiternary
Mg-MgB
2
-BNsystem,at pressuresaround50barand
temperaturesrangingbetween1400-1700 Æ
C,fortime
periods between 5to 60 minutes. In this ase MgB
2
rystals reahing linear dimensionsup to 0.7 mm has
beenreported[32℄.
MgB
2
thin lms havealsobeengrownsuessfully,
using pulsedlaserdeposition [4,34℄ aswellasby
ele-tronbeamevaporationofBandMg[35℄. Insomeases
textured thin lms were obtained,onsisting ofgrains
that havetheirrystallographi axisaligned
perpen-diularly tothesubstrateplane. Anintriguingfeature
of thin lms is that their T
ranges typially between
25-37K,alwaysbelowthebulkvalueof39K.
II.1. Aligned MgB
2
rystallites
WhilepolyrystallineMgB
2
isveryeasytogrowand
is a readily available reagent, good-sized single
rys-tals of this material, with lineardimensionsabove0.7
promisesto keep being a real hallenge. However, by
themiddleofFebruary2001,intheearlydaysofintense
ativitiesonthenewMgB
2
superondutor,samplesof
alignedMgB
2
rystalliteswerepreparedatUNICAMP
[23℄. Firstly,aweaklysinteredsampleofMgB
2
was
syn-thesised,startingfromastoihiometrimixtureof99.5
at%pureBand99.8at%pureMg, bothinhipsform
(JohnsonMattheyEletronis). Theloosemixturewas
sealed in aTa tube under Ar atmosphere, whih was
then enapsulated in a quartz ampoule and put into
the furnae. The ompound formation was proessed
byinitiallyholdingthefurnaetemperatureat1200 Æ
C
for1hour,followedbyadereaseto700 Æ
C(10 Æ
C/h),
thento600 Æ
C(2 Æ
C/h),andnally toroom
temper-atureatarateof100 Æ
C/h. Theweaklysintered
prod-utwaseasilyrushedandmilledbyemployingmortar
andpestle. Usingastereomirosopeoneouldobserve
atthisstageaveryuniformpowder,onsistingmainly
of shiny rystalliteswith aspet ratiosranging from 2
to 5 and linear dimensions going up to 50 m. The
powder was then sieved into a range of partile sizes
between5-20m,whihallowedtherystallites
fra-tiontobemaximised to almost100%. Smallamounts
ofthepowderwerethenpatientlyspreadonbothsides
ofasmallpiee of paper,produinganalmost perfet
alignmentoftherystalliteslaiddownontopoftheat
surfae,as shown in theSEM pitureof Fig. 1. The
suess of this method relies on the rystallites
plate-likeshape,whihisindeedamarosopimanifestation
ofitsanisotropirystallinestruture. Fig. 2showsan
X-raydirationpattern(-2san)measuredonone
of the aligned sample, displaying only the (001) and
(002)reetions,omingfrom theMgB
2
phase. A
lat-tieparameter=3.5180.008
Awasevaluatedfrom
thesetwopeakpositions. Thetwosmallimpuritypeaks
markedwithasteriskswereindexedasSiO
2
. Theinset
ofFig. 2showsarokingurve(! san)for the(002)
peakthatrevealsanangularspread(FullWidthatHalf
Maximum)around4.6degrees,assoiatedwithasmall
misalignmentoftherystallites axis.
Figure 1. Sanning Eletron Mirosopy (SEM) piture
ma-20
30
40
50
60
70
80
0.0
0.5
1.0
1.5
2.0
2
θ
(deg)
In
te
nsi
ty
(
a
rb
. uni
ts)
*
*
(001)
(002)
15
20
25
30
35
0
1
2
3
o
~ 4.6
ω
(deg)
Figure2. X-raydirationpatternshowing onlythe(001)
and(002)peaksofMgB
2
,plustwospuriouspeaksindexed
asSiO2. Inset: rokingurve(!-san)forthe(002)peak,
showing anangular spread of about4.6 degreesalong the
rystallitesaxis.
Eletronmiroprobeanalysisdoneonfourdierent
areasbetweenthe MgB
2
rystallites, revealed the
fol-lowing averageonentration (in at%) of elements: O
(62.9), C (22.2), Ca (9.48), Si (1.48), Mg (1.44), Al
(1.37), K (0.09), Fe (0.50), Cr(0.21), Ni (0.09). The
rst eight elementsin this list were found also in the
omposition analysis made on the same type of
pa-per used (Canson, ref. 4567-114). Miroprobe
anal-ysis donealso on theinitial Mg and B revealed afew
small preipitates,smallerthan 10m andontaining
upto8at%Fe,onlyintheMghips. Thisonrmsthe
expetationofFebeingaommonimpurity[36℄in
om-merialMg, andsets ageneralonernon itspossible
eets,althoughreentreports[5,37℄havesuggestedno
negativeeetstothesuperondutivityofMgB
2 from
Fe additions. The average omposition found on top
of several rystallites, normalised to the whole MgB
2
formulaunit,was: Mg(30.80),O (2.20),Ca (0.17), Si
(0.07), Fe (0.06). Although Boron ontributeswith a
fration of66.6at%it doesnotshow-up inthe
miro-probeanalysisbeauseitistoolight. Theontaminants
foundontopoftherystallitesmostpossiblyamefrom
asurfaeontaminationausedbythealignment
teh-nique, whih required vigorous rubbing on top of the
powder, using a steel tweezerstip to spreadthe
rys-tallites uniformly. This is orroborated by a further
analysis done on top of several as-grown rystallites,
whihdetetedonlyMgandasmallamountofO
(pos-siblyfromMgO).Thisresultisonsistentwiththevery
smallsolidsolubilitylimitofabout0.004at%FeinMg,
whihis known toour[38℄ atthe solidiation
tem-peratureof650 Æ
C.Theinter-rystallitetypeofrubbish
showninFig. 1isattributedmainlytothepaper
abra-sion, whih produesavarieddistribution ofirregular
grainsofpaperfragments. Inordertoharaterisethe
superondutingandmagnetipropertiesofthealigned
rystallites several samples were mounted, onsisting
2
rystallite-painted paperandgluedwithAralditeresin.
Eahoneofthesesamplesontainsanumberof
rystal-lites estimated to bearound 6.510 5
, ending upwith
aneetivevolumeof0.065mm 3
. Thisvalueis
reason-ably lose to 0.060 mm 3
that wasevaluated from the
expetedslopeM/H =-1/4,whenthemagnetization
M ismeasuredataveryloweld H.
III H
2
anisotropy
H
2
anisotropyisoneofthemarosopimanifestations
of an anisotropi gap energy or an anisotropi Fermi
surfae, as well as a possible ombination of both
ef-fets[39,40℄. Therefore,itsstudyis ofparamount
im-portane to help understanding thebasi mehanisms
involvedin thepairinginteration. Samples ofaligned
MgB
2
rystallites, as desribed above, have been
em-ployed in detailed studies of the H
2
angular
depen-dene,providingalearidentiationofitsanisotropy
fatoranditsbulkorigin[23,41℄.
Figure3showstheanisotropisignatureoftheH
2
line in theeld interval0H 40 kOe. The
exper-imental points weretakenfrom thetransition onsetof
therealomponent(')ofACsuseptibility,measured
usingaPPMS-9Tmahine(QuantumDesign),withan
exitationeldofamplitude1Oeandfrequeny5kHz.
The insetshows anenlargedview ofthe '(T) urves
for H // ab (open symbols) and H // (solid
sym-bols),theeld orientationparalleltotheab planeand
parallel to the axis, respetively. The '(T) as well
astheM(T)(inset ofFig. 4) measurements,for H =
10Oe,showsharptransitionsatthesameritial
tem-peratureT
39K. Typially, someof the published
data on the tempera ture dependene of H
2
[42, 43℄
agree with the result displayed in Fig. 3 for H
2 //
ab. As an example, the data from Ref.[43℄ is plotted
in Fig. 3as stars. This mean that in polyrystalline
samplesthetransitionsarebroadened,showingthe
on-set atthehighesttemperaturethatorrespondsto the
highestritialeldavailable,whihisH
2 //ab.
TheratioH ab
2 =H
2
,betweentheupperritialeld
when H is applied parallel to the ab plane and when
it is along the diretion, was evaluated at dierent
temperatures,produingavaluearound1.7. From[22℄
H ab
2 =H
2 =
ab =
, H
ab
2
(T)=
0 =(2
ab
)H
2 (T)=
0 =(2
2
ab
), and using the Ginzburg-Landau (G-L)
meaneld expressionfortheoherenelength,(T)=
0
(1 T=T
)
0:5
,onends
0;ab 70
Aand
0; 40
A,
theoherenelengthatT=0intheabplanesandalong
the axis, respetively. Thequantum ofux,in CGS
units, is
0
= 2:0710 7
G m
2
. A mass anisotropy
" 2
= (H
2 =H
ab
2 )
2
0:3 is then found for MgB
2 ,
whihouldbeonsideredamildanisotropywhen
om-pared to thehighly anisotropi high-T uprates [44℄,
likeYBa
2 Cu
3 O
7 Æ ("
2
0.04)and Bi
2 Sr
2 CaCu
2 O
8+x
20
22
24
26
28
30
32
34
36
38
40
0
10
20
30
40
50
60
H
c2
(k
O
e
)
T (K)
H // ab
H // c
Müller
et al.
10
20
30
-0.20
-0.15
-0.10
-0.05
0.00
H (kOe)
0.01
1.00
10.00
20.00
30.00
40.00
χ
' (
a
rb
. u
n
its)
T (K)
Figure 3. Upperritial eld H2 vs. Temperature phase
diagram,for bothsampleorientations. Thestarsrepresent
the H2 vs. T line from Ref. [43 ℄. The inset shows the
realomponent' oftheasuseptibilityvs. temperature,
measured atseveralDCeldsfor bothorientations. Open
symbolsare for the H // ab urvesand solidsymbolsfor
H==.
Inorderto studytheH
2
angulardependene,
un-der axial applied elds, a speial sample rotator was
built[41℄withallpartsmahinedfromalowmagneti
teon rod. Magnetization measurements were
per-formedwithaSQUIDmagnetometer(modelMPMS-5,
made by Quantum Design). Fig. 4 shows the
mag-neti dependene of the magnetization in T = 25 K,
for afewrepresentativeangles, , betweenthe sample
axisandthemagnetielddiretion. TheZFC(Zero
FieldCooling)measurementsshowninthemainframe
look noisypossibly due to the eet of intense vortex
reep[6℄,ombinedwithaomplexregimeofux
pen-etration in thegranularsample of alignedrystallites.
Thus,theourreneofrandomweaklinksandthe
var-iedouplingbetweengrainsontributealsoto produe
a utuating behavior in the sample overall response.
However,inallasesitwaspossibletodeneH
2 (),at
therossingpointbetweenthehorizontal baselineand
the straightline drawnarosstheexperimental points
in theregion near the onset of transition. This linear
behaviorof themagnetizationlose to theonset is
in-deed expeted from the G-L theory [22℄. A onstant
paramagnetibakgroundwassubtratedfrom allsets
ofdata. InfatoneofthereasonsformeasuringatT=
25 Kis beauseat thistemperatureH
2
()ranges
be-tween28-36kOe,wheretheparamagnetibakground
isalreadysaturated[23℄.
Figure5displaysH
2
()for between-20degand
120deg. Thevertialerrorbarswereestimated to be
around1kOewhilethehorizontalerrorbars,of2.5
deg, almost oinide with the symbol size. The solid
agoodtoftheangulardependene,preditedbythe
3DanisotropiG-Ltheorytobe[22,39℄
H
2
()=H
2
os 2
()+" 2
sin 2
()
1=2
; (1)
where" 2
,isthemassanisotropyratio. Thebesttting
isobtained with " 2
0:39, implyingthat H ab
2 =H
2
1:62,whihisloseto thevalue1.7 antiipatedbyAC
suseptibility measurementsdonefor the two extreme
positions,at0and90degrees(seeFig. 3). InFig. 5
weseealsovedatapoints( =0,25, 65,85,90 deg)
markedwithstars,whihwereobtainedattheonsetof
transitionoftherealpartoftheomplexsuseptibility,
measured with an exitation eld of amplitude 1 Oe
andfrequeny5kHz.
-0.8
-0.6
-0.4
-0.2
0.0
20
40
H = 10 Oe
ZFC
FCC
T (K)
M (G
)
25
30
35
40
45
50
-6.0
-4.0
-2.0
0.0
T = 25 K
0 deg
65 deg
80 deg
90 deg
M (
G
)
H (kOe)
Figure4. ZeroField Coolingmagnetization measurements
asafuntionoftheappliedeld, for =0,65, 80, 90
de-grees. The bulk nuleation eld H2() is dened at the
rossing of the auxiliary straight lines and the horizontal
baseline(M=0). TheinsetshowsZFCandFCC
magneti-zationmeasurementsasafuntionoftemperatureforH=
10Oe,givingT39K.
TheratioH ab
2 =H
2
1:62remindstherelationship
predited for the surfae nuleation eld [45℄ H
3
1:7H
2
. However, this is learly not the ase for the
presented data, as one an see from the dash-dotted
urvein Fig. 5, whih is aplotof theexpeted
angu-lardependene ofthesurfaenuleation eldforthik
samples,givenby[46℄:
H()
H
3 sin
2
[1+ot (1 os)℄+ H()
H
2
where H
3
= H( = 90 Æ
) and H
2
= H( = 0 Æ
).
Thedashedurveinbetweenrepresentsthewell-known
Thinkham'sformula[22,47℄
H()
H ab
sin
2
+
H()
H
os
=1; (3)
whih is valid for the surfae nuleation eld in very
thin lms. Fromboth plotsoneseesthat a
harater-istifeatureofthesurfaenuleationeldisausplike
urve shape near = 90 degrees. This behavior
on-trastswiththesinusoidalshapefollowedbytheMgB
2
data displayed in Fig. 5. Thus, a strong support is
giventointerprettheobservedupperritialeldasa
genuinebulknuleationeld.
-30
0
30
60
90
120
30
35
40
45
c
H
θ
c
c
ab
H
c2
/ H
c2
~ 1.6
ab
H
c2
H
c2
aligned MgB
2
crystallites
T = 25 K
H
c2
(k
O
e
)
θ
(deg)
Figure5.Bulknuleationeld(orupperritialeld),H2,
asafuntionoftheangle,,betweenthesampleaxisand
themagnetielddiretion. Plotsoftheexpetedangular
dependene for the surfae nuleation eld, H3, in thik
samples (dash-dotted urve) and very thin lms (dashed
urve)are also shown. The stars at =0, 25, 65, 85, 90
degreesrepresentH
2
()obtainedattheonsetoftransition
oftherealpartofa suseptibilitymeasurements.
Several other studies have already onrmed the
H
2
anisotropy in MgB
2
. Measurements of resistive
transitions on three -axis oriented thin lms [48℄
showedanisotropyratios(H ab
2 =H
2
)of1.8,1.9and2.0,
the ratio inreasing with higher resistivity, orrelated
withamoreimpureoralloyedsample. Resistivity
mea-surementsdoneonsinglerystals,havingthemajor
lin-earsizearound0.5mm[32,33℄,showedanisotropy
ra-tiosloseto2.6. InRef.[33℄theauthorshavealsoshown
anisotropiH
1
linespointingtoH ab
1 =H
1
1:4,where
H
1
isthe lowerritialeld. However,oneshould be
aware about the large unertainty usually assoiated
with H
1
evaluations, mainly due to twofators: the
very slow departure from linearity, when leaving the
Meissnerregime,andthestrongdependeneon
demag-onveryleanepitaxialthin lms[26℄,gavearelatively
smalleranisotropyratioaround1.3in alarge
tempera-tureregionbetween2-32K.Amuhsmalleranisotropy
ratiovaluearound1.1 wasalsoreportedonapartially
textured, hotdeformed, bulkmaterial[49℄.
More reently the eet of temperature on H
2
anisotropyhasbeenreported byseveral groups.
Mea-surementsoftorquemagnetometryinMgB
2
single
rys-tals haveshownavariationfromH ab
2 =H
2
2.8at35
Kto 6at 15K [50℄. Resistivetransitions measured
insinglerystals[51℄,aswellasin-orientedthinlms
[52℄ havealso shown the same trend, although in the
rstaseH ab
2 =H
2
variedbetween2.2 and3.0when T
dereasedfrom39Kto30K,whilefortheseondase
it varied between 1.5 and 2.0 when Tdereased from
33Kto20K.Contrastingtheseexperimentalresultsa
theorybasedonatwo-gapmodelpreditsthatH ab
2 =H
2
shouldinreasefrom 1.5do2.4,whenTinreasesfrom
18Kto 39K[53℄.
TherelativelylargesatteringofvaluesfortheH
2
anisotropy ratio, going from 1.3 to approximately 6,
ould possibly be asribed to at least three fators.
One is the sample purity, sine it aets diretly the
energygapanisotropyatthemirosopilevel[39,40℄.
Theseondistheexperimentalriterionusedtodene
H
2 or T
2
, suh that a reliable bulk transition point
is atually guaranteed. The third fator is a possible
temperature dependene of the anisotropy ratio that
ouldbeoriginatedfromatemperaturedependentgap
anisotropy [20, 54℄. Therefore, results obtained with
samplesof dierent puritylevelsandmeasured at
dif-ferent temperatures should not be diretly ompared
withoutadetailed analysis.
Themarosopi H
2
anisotropyanbeaused by
an anisotropi gap energy orby an anisotropi Fermi
surfae, as well as by a ombination of both eets.
Assuminganisotropigap,onegets
ab =
=V
ab
F =V
F ,
sine[22℄ /V
F =
0
. Therefore, the datafor aligned
MgB
2
rystallites [23, 41℄ implies V ab
F
1:6 V
F , for
theFermiveloities withintheab planeandalong the
diretion. However,several experimental[15, 17,18℄
and theoretial [11, 12, 20℄ works have suggested an
anisotropi gap energy for MgB
2
. In partiular, two
works [18, 20℄ based on the analysis of spetrosopi
andthermodynamidataproposeananisotropis-wave
pairing symmetry, suh that the minimum gap value,
0
1:2 kT
, ours within the ab plane. Using
this result and assuming an isotropi Fermi surfae
theexpeted H
2
anisotropywouldbeH ab
2 =H
2 0:8.
This onits with all experimental results that show
learlyH ab
2 >H
2
. However,by allowingaFermi
sur-fae anisotropy in their model, Haas and Maki have
found that [54℄ V ab
F
2:5 V
F
in order to math the
ratio H ab
2 =H
2
1:6, at T = 25 K. Therefore, it
seemsthatthetwofundamental souresofmirosopi
anisotropyis aeting the H
2
anisotropy of MgB
2 in
opposite ways. As a onsequene of ombining both
eets to explaintheH
2
velo-paredwith theisotropigaphypothesis. Interestingly,
aalulationbasedonatwo-bandmodelhasalsofound
[55℄ V ab
F
2:5 V
F
, while a muh smaller value of
V ab
F
1:03 V
F
was found in a band struture
alu-lation usingageneralpotentialmethod[11℄.
IV Other anisotropi properties
Another anisotropi property already assessed in the
superonduting state of MgB
2
is the eld
penetra-tion depth [56℄. Using a radio frequeny tehnique
(T) wasmeasured in polyrystalline samples and its
anisotropi values were evaluated, from a theoretial
analysis,tobearound
ab 1200
Aand
2450
A.
Besides the strongly anisotropi rystalline
stru-ture of MgB
2
, three other normal state anisotropi
propertieshavebeenidentied,themagnetoresistane,
the ompressibility and the thermal expansion. The
magnetoresistane measuredat T =45K,in epitaxial
thin lms,wasfound[26℄toinreasemonotoniallyup
to 8%forH // and upto 13%forH //ab,whenH
goesupto 60T. Conerningtheompressibility
stud-ies,similarresultswereobtainedbytwogroups,one[24℄
usingsynhrotronX-raydirationandapplyingupto
6 GPa of pressure on the sample and the other [25℄
using neutron powder diration and applying up to
0.6 GPaofpressure. Theyfollowedtherelativelattie
parametersvariationasafuntionof appliedpressure,
at roomtemperature, andfound thatthe ompression
along the axisis about64% largerthanalong the a
axis. Ref.[25℄reportsalso that the thermalexpansion
(between11K-297K) alongtheaxisisabouttwie
that alongtheaaxis.
Althoughno experimentalresultson J
anisotropy
wasreported yet, it ould be antiipated that the
in-plane ritial urrent density values are expeted to
be at least about 60% higher than the values along
the axis diretion (H// ab). This result is
ex-peted beauseJ
is proportional to 2
, therefore[44℄
J
(H==)=J
(H==ab)
ab =
H
ab
2 =H
2
. Thismeans
that inordertooptimiseJ
inwiresorother
polyrys-tallineomponentssometexturizationtehniquewillbe
useful.
V Conlusion
Starting at the beginning of 2001 an intense ativity
hasbeendevotedtothestudyofthebinaryompound
MgB
2
, sine it wasfound to be a superondutor for
temperatures below 39 K. The anisotropi rystalline
strutureofMgB
2
onsistsoftriangularlayersof
Mag-nesiumatoms sandwihedbetweenhexagonallayersof
Boronatoms. Therefore,itshould indeed beexpeted
someanisotropyinitsphysialandhemialproperties.
Thispaperpresentedabriefreviewon thealready
reportedanisotropipropertiesof MgB
2
,in the
super-onduting state (e.g. upper ritial eld H
2 , eld
gap ) as well as in the normal state (e.g.,
magne-toresistane, ompressibility, thermal expansion). So
far, the reported results have been arried out using
alignedrystallites,-axis orientedthin lmsand
sub-millimiter rystals. However, good-sized single
rys-talswithlineardimensionsabove1mmarestillhighly
desirable. This will open the possibility of new
ad-vanes,makingeasierto probediretlyotherexpeted
anisotropiproperties, likethe ritialurrentdensity
and the normalstate resistivity, among others. Sine
impurity satteringaets diretly the gap anisotropy
it will be also of interest to know the eets of
rys-talpurityontheanisotropyfators. Mostpossiblythis
ouldbeoneofthemainreasonsforthesatteredvalues
observed inthe H
2
anisotropyratio, rangingbetween
1.3and6.
Aknowledgements
I wouldlike to thankmy loseollaborators C.A.
Cardoso,R.A.Ribeiro,M.A.AvilaandA.A.Coelho,
fortheirhelpintheanisotropystudiesontheMgB
2
su-perondutor. Iaknowledgethenanialsupportfrom
theBrazilianSieneAgeniesFAPESPandCNPq.
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