Table Of ContentThree-configurational surface magneto-optical Kerr effect measurement system for an
ultrahigh vacuum in situ study of ultrathin magnetic films
J.-W. Lee, J.-R. Jeong, D.-H. Kim, J. S. Ahn, J. Kim, and S.-C. Shin
Citation: Review of Scientific Instruments 71, 3801 (2000); doi: 10.1063/1.1310346
View online: http://dx.doi.org/10.1063/1.1310346
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REVIEWOFSCIENTIFICINSTRUMENTS VOLUME71,NUMBER10 OCTOBER2000
Three-configurational surface magneto-optical Kerr effect
measurement system for an ultrahigh vacuum insitustudy
of ultrathin magnetic films
J.-W. Lee, J.-R. Jeong, D.-H. Kim, J. S. Ahn, J. Kim, and S.-C. Shina)
DepartmentofPhysicsandCenterforNanospinicsofSpintronicMaterials,KoreaAdvancedInstituteof
ScienceandTechnology,Taejon305-701,Korea
~Received 29 March 2000; accepted for publication 19 July 2000!
We have constructed a three-configurational surface magneto-optical Kerr effect system, which
provides the simultaneous measurements of the ‘‘polar,’’ ‘‘longitudinal,’’ and ‘‘transverse’’ Kerr
hysteresis loops at the position where deposition is carried out in an ultrahigh vacuum growth
chamber. The present system enables in situ three-dimensional vectorial studies of ultrathin film
magnetism with a submonolayer sensitivity. We present three-configurational hysteresis loops
measured during the growth of Co films on Pd~111!, glass, and Pd/glass substrates. © 2000
American Institute of Physics. @S0034-6748~00!05310-7#
I. INTRODUCTION lar pump ~Alcatel ATP400! backed by a 500 l/min mechani-
calpump~KODIVAC!.Withthesepumps,abasepressureof
Surface magneto-optical Kerr effect ~SMOKE! has be-
5310211Torr is typically obtained after a 48 h bakeout at
come an important tool in the study of ultrathin film magne-
150°C.
tism due to its easy implementation and power as a surface
sensitive in situ characterization under ultrahigh vacuum A. Sample manipulator
~UHV!.1,2 Especially, its usefulness is substantial in the un-
Inordertoalignasampleatthecenterofthechamber,a
derstanding of magnetic anisotropies3 and spin reorientation
sample manipulator was mounted on a rotary base with fine
transition4 in the ultrathin limit. To fully explore such mag-
XYZ motions. With an UHV compatible pyrolytic boron ni-
netic phenomena, a vectorial SMOKE system with three
trideheater,thesamplecanbeheatedupto1000°C.Forthe
probing axes is highly desired and has been developed.5–9
sample transport between the main chamber and scanning
Common difficulties come from electromagnets and optical
tunneling microscopy ~STM! chamber, Omicron STM
configurations, which are mainly restricted to an analysis
sample plate was modified to accommodate a rectangular
chamber separated from the main deposition and processing
window which permits radiation heating. A substrate with a
chamber, which may cause small systematic changes of ul-
maximum size of 15310 mm2 can be mounted. Tungsten or
trathin magnetism between measurements. To overcome
tantalum wires were used to fix the substrate on the plate.
such difficulties, we have constructed a more convenient
Itshouldbestressedthatmaterialselectionmustbecare-
SMOKE setup which is capable of three-configurational
ful for SMOKE measurement, because the optical align-
measurementsduringthedepositionwithoutperturbingopti-
mentsmaybeperturbedinaccordancewiththeappliedmag-
cal alignments of polarizing optical components. Compared
netic field if the sample holder is magnetic. Therefore, as a
with the conventional MOKE in air, in situ SMOKE experi-
nonmagnetic material, molybdenum, tantalum, and oxygen-
mentunderUHVismoreusefultoobtainagenuineproperty
free high-purity copper were mainly used for the sample
of ultrathin magnetic layer itself, without an overlayer,
holder block.
which may change the magnetic property through an addi-
tionalinterfaceanisotropyterm.1,10Therefore,oursetupwill
be useful to perform a systematic sequence of experiments
B. UHV evaporators
with thickness variation instead of preparing a wedge
sample. Two UHV evaporators ~Omicron EFM4 and EFM3T!
areusedforfilmdeposition.Asinglecellevaporator~EFM4!
II. SYSTEM DESCRIPTION providesalargeuniformarea~f;40mm!onthesubstrateat
adistanceof100mmwithanaperturediameterof10mm.A
In order to realize a simultaneous measurement and triple cell evaporator ~EFM3T! consisted of three indepen-
deposition at the same position, a spherical main chamber
dent evaporators integrated on a single cooling stem, and
was fabricated with a diameter of 400 mm. Ultrahigh eachofthemgiveanenoughuniformarea~f;10mm!with
vacuum in the chamber is provided by a 240 l/s ion pump
a 5 mm aperture.
~POSCON!,twotitaniumsublimationpumpswithLN cool-
2 With the help of a water-cooled shroud and an e-beam
ingshroud~PhysicalElectronics!,anda400l/sturbomolecu-
heater,onlytheevaporantsareheatedandthechamberpres-
sure can be maintained under UHV conditions, typically be-
a!Electronicmail:[email protected] low 1310210Torr. During the deposition, atomic flux is
0034-6748/2000/71(10)/3801/5/$17.00 3801 ©2000AmericanInstituteofPhysics
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3802 Rev.Sci.Instrum.,Vol.71,No.10,October2000 Leeetal.
monitored and feedback regulated using an automatic con-
troller ~Omicron EVC300!.
For refractory metal sources, we use a bare rod ~f52
mm! of each metal elements with high purity ~99.99% or
higher!, which is directly connected to a high voltage stem
with a barrel connector made of Mo. These rod evaporants
are free from the contamination or alloying problem with a
crucible. Deposition rates for Co and Pd were typically 0.78
and 1.0 Å/min with 10 and 20 W of e-beam, respectively.
C. Surface cleaning
An ion gun ~VG EX03! is used to sputter-clean the sur-
face of single crystal substrates. As an inert gas for the
sample cleaning, 531026Torr of Ar was introduced using
1
an UHV leak valve. The substrate was bombarded with Ar
ions accelerated at 1 keV from a working distance of 100
mm, which gave a uniform cleaning area of 15 mmf. To
obtain a fresh surface before deposition, the sputter-cleaning
procedure was repeated with a subsequent annealing at
500°C.
The polar SMOKE was measured during the sputtering
cycle,whichwasfoundtobeusefulforaninsitumonitoring
oftheresiduesofthemagneticlayeronthesubstrate.Atomic FIG.1. Schematicdiagramofathree-configurationalSMOKEmeasurement
force microscopy ~AFM!/STM ~Omicron! was also used to system. The polar and longitudinal SMOKES are measured on the same
inspectthecleanedsurface,beforedeposition,orbetweenthe scatteringplanewhichisparalleltothemagnetwhilesharingthesamelaser
source. The side view shows the optical plane of the transverse SMOKE,
SMOKE measurements. The sample is easily transferred to
whichisperpendiculartothemagneticfielddirection.Incidentangleis45°
the AFM/STM with wobble sticks and one linear magnetic foralltheconfigurations.
drive.
lessthan;20Oe.Amaximumfieldof2.0kOewasobtained
D. Three-configurational SMOKE setups
with a pole gap of 29 mm, for all the measuring geometries.
As clearly seen in Fig. 1, the main chamber is specially As a light source and a detector, a He–Ne laser ~JDS
designedforthreesetsofSMOKEsetupswhicharemutually Uniphase!andalargearea~535mm2!Siphotodiodeassem-
orthogonal to each other, which enable three-dimensional bly ~Hinds DET90! were used, respectively. The laser light
vectorial studies of ultrathin film magnetism. Three setups was introduced to the main chamber through several fused
are called the ‘‘polar,’’ ‘‘longitudinal,’’ and ‘‘transverse’’ silica windows. Windows were chosen to minimize a stress-
configurations, respectively, considering the scattering plane inducedstaticbirefringenceinordernottoperturbthepolar-
and substrate normal direction with respect to the direction ization state.
of an applied field. Forthepolarizingelements,crystalpolarizers~Newport!
In the polar and longitudinal geometries, the field is ap- of the Glan–Taylor type were used, which provided enough
plied perpendicular and parallel to the film plane, respec- contrast with an extinction ratio better than 1025. For the
tively, with the field vector remaining on the optical scatter- fine alignment of a polarizing angle with respect to the
ing plane. However, in the transverse geometry, the optical sample surface with a null method, they were mounted on a
plane is perpendicular to the field, which is parallel to the precision rotator with a micrometer.
film plane. With these three-axis configurations, we can Asaprecisioncompensatortoprobemagneto-opticalac-
probebothperpendicularandin-planemagneticanisotropies. tivity, a photoelastic modulator ~Hinds PEM90D! with fre-
And also, with the transverse configuration, magnetism per- quency of 50 kHz was used. It provided dynamic phase re-
pendicular to the applied field can be explored, which may tardation of d(5a sinvt) on the elliptically polarized light
0
be related to domain-wall motion. from a sample with magneto-optical activity. Therefore, we
AsinglesetofelectromagnetswasusedfortheSMOKE can obtain the magneto-optical property through phase-
system. The magnets mount externally to the vacuum cham- sensitive detection with high accuracy down to ;0.001°, in-
berthroughthe6in.conflat~CF!flangeswithadeeppocket stead of rotating an analyzer to make a nulling. The peak
of 4 in. diameter. Water-cooled electromagnets were wound retardation amplitude, a , was tuned to be a 0.383 wave for
0
with 1.0 mm copper wire with a resistance of 3.5 V, which an optimal, where J (a)50, the reason is described in the
0 0
matched the output impedance of a bipolar current supply Appendix.
~EMI BOSS!. Additional pole tips were introduced in the As readout devices, one digital multimeter ~HP34401A!
vacuum chamber to intensify and guide the field to the and two digital lock-in amplifiers ~EG&G 7265! were used.
sampleposition.Poletipsweremadeofsoftmagneticmate- A manual multiplexing switch was used to select a signal
rial such as Permendur ~Goodfellow! with a remanence field from the polar, longitudinal, and transverse configurations.
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Rev.Sci.Instrum.,Vol.71,No.10,October2000 Surfacemagneto-optical 3803
FIG. 2. SMOKE hysteresis loops of 150 Å Co/200 Å Pd/glass measured
with~a!thepolar,~b!thelongitudinal,and~c!thetransverseconfigurations.
Arrowsindicatethedirectionsoftheloops.
In order to minimize a pickup of rf noise, silver braided
coaxial cables were used between the devices. Computer
control was performed on a Pentium personal computer
through GPIB and RS-232C interfaces. Data acquisition and
analysisprogramswerewritteninLABVIEW~NationalInstru-
ments!.
Light intensity, I , measured on the detector of the
f
present system can be described as follows:
S D
r
I 5ur u21ur u224J ~a!ur u2Im ps sinvt
f ss ps 1 0 ss r
ss
S D
r
24J ~a!ur u2Re ps cos2vt ~1!
2 0 ss r
ss
for s polarization (p5p/2, m50, and a5p/4), and
S D
r
I 5ur u21ur u214J ~a!ur u2Im sp sinvt
f pp sp 1 0 pp r
pp
S D FIG.3. Thicknessdependenciesofthree-configurationalSMOKEhysteresis
r loopsofCofilmgrownon~a!Pd~111!singlecrystal,~b!glass,and~c!200
24J ~a!ur u2Re sp cos2vt ~2! ÅPd/glasssubstrate.
2 0 pp r
pp
for p polarization (p50, m50, and a5p/4).
The complex Kerr rotation angle, Q ([u 1ie ) is III. EXPERIMENTAL RESULTS
K K K
givenfromtheKerrangle,u , andtheellipticityangle,e ,
K K
Using the present system, we have carried out in situ
from the light intensity as follows:
three-configurational SMOKE measurements of ultrathin Co
If/Idc2152J1~a0!eKsinvt12J2~a0!uKcos2vt. ~3! films grown on various substrates. Figure 3~a! shows three-
axis SMOKE data of ultrathin cobalt layers grown on a
In Fig. 2, three-configurational SMOKE measurements
are demonstrated for a cobalt film ~150 Å! grown on a glass Pd~111!singlecrystalsurface.Consideringthe2.04Åheight
of the Co monolayer, our data clearly display the submono-
substrate with a Pd buffer layer of 200 Å. The hysteresis
layersensitivityofthepresentsystem.Below3.9Å,nohys-
loopsareclearlyidentifiedfromalltheconfigurationswitha
sensitivity of 0.001° as seen in Fig. 2. To obtain a polar teresis loop is observed in all of the three configurations,
signal, magnetic field, H, was swept at 110 Oe/s. Because whichcanbeascribedtothelossofferromagnetism,consis-
in-plane coercivity was small ~;20 Oe!, the sweep speed of tent with the Co/Au~111! case.11 Polar coercivity increases
6.7 Oe/s was used for the longitudinal and transverse con- andshowsamaximumaround6Å,thendecreases.Also,the
figurations. From the loops, one can obtain saturation, rema- longitudinal loop has a large coercivity up to ;10 Å, then it
nence,andcoercivityvalues,whichproviderichinformation demonstrates an in-plane easy-axis behavior with further
about thin film magnetism with vectorial analysis, which is deposition. The loop could be not obtained at 5.9 Å because
beyond the scope of this article. the coercivity is beyond our available maximum field. Simi-
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3804 Rev.Sci.Instrum.,Vol.71,No.10,October2000 Leeetal.
S D
lar results are found from the transverse case. Spin reorien- 1 0
tation is probably under progress from polar to in-plane, of M5 0 eid , ~A3!
which the trajectory is not clear yet.
S D
Figure3~b!showsCogrownonaglasssubstratewithout
r r
a buffer layer. In this case, data of the bare substrate show a S5 pp ps , ~A4!
r r
substantial linear signal in the polar and the longitudinal ge- sp ss
S D
ometries, which is attributable to the Faraday effect of a
cosu 2sinu
transparentglasssubstrateduetothereflectionfromtheback R~u!5 . ~A5!
side. Large noise in the early stage is originated from the sinu cosu
scattered light from the substrate holder. The longitudinal
d(5asinvt) is the retardation value of a phase modulator.
data have smaller coercivities than those of the polar ones.
Sample matrix S is represented by the Fresnel complex re-
Polarcoercivityincreasesbeyondthelimitofourfieldabove
flection coefficients r , r , r , and r . R(u) is the ro-
34 Å. At 45 Å, the sample shows the hard- and easy-axis pp ss ps sp
tationmatrixwithangleubetweencomponents,sop,m,and
behaviors in the polar and in-plane directions, respectively.
a represent the angle of polarizer, modulator, and analyzer,
Smallfeaturesfoundinthetransversecasearebelievedtobe
respectively.InthisJonesmatrixrepresentation,E-fieldvec-
an existence of the Ne´el wall during the domain reversal
tor is spanned with $p,s%-polarization bases.
process. If one accepts such a domain-motion scenario, the
With E5(1) one obtains
thickness of the Ne´el wall12 can be roughly estimated to be i 1
about 10 Å from the ratio of remanences of the longitudinal E 5~r cosp2r sinp!@cos~a2m!
f pp ps
and transverse case.
In order to minimize the Faraday effect of a glass sub- 3cosm2exp~id!sin~a2m!sinm#
strate, a Pd buffer layer was deposited on a glass substrate.
2~r cosp2r sinp!
TherequiredthicknessisdeterminedfromthepolarSMOKE sp ss
measurement between the deposition sequence. With 200 Å 3@cos~a2m!sinm1exp~id!sin~a2m!cosm#.
of Pd, which is close to the penetration depth of light, the
~A6!
Faraday effect is reduced less than 0.01°.
The SMOKE data of the Co film grown on the 200 Å And the measured intensity is given by I 5E*E . Because
f f f
Pd/glass substrate are depicted in Fig. 3~c!. The longitudinal d5asinvt, one obtains harmonic expansion with the fol-
data show small coercivities similar to the Co/glass case. lowing relations:
Polar coercivities are larger than the longitudinal ones, how-
‘
everinthiscase,theyremainwithinthefieldlimit,withtheir (
cosd5J ~a!1 J ~a!cos2nvt, ~A7!
maximum around 14 Å. The SMOKE signals show a satu- 0 2n
n51
rated behavior over 162 Å, which is also related to the skin
depth of Co. ‘
(
These mixed anisotropy behaviors of cobalt grown on sind5 J2n11~a!sin~2n11!vt, ~A8!
Pd~111!, glass, and 200 Å Pd/glass substrates may have n50
some relation with the coexistent phase proposed by Millev where the J ’s are Bessel function of nth order. With d
etal.13Arelationwithsuchamodelneedsfurtherinvestiga- 5a sinvt, nwhere a is determined from J (a)50, dc
0 0 0 0
tion.
value has minimum elliptic components.
Therefore, for case I: s-polarized incident light with p
5p/2, m50, and a5p/4, it reduces to E 52r
ACKNOWLEDGMENTS f ps
1r exp(id) and
ss
ThisworkwassupportedbytheKoreanMinistryofSci- S D
ence and Technology through the Creative Research Initia- I 5ur u21ur u224J ~a!ur u2Im rps sinvt
tives project. The authors are grateful to T. W. Kim and B. f ps ss 1 0 ss r
ss
S D
C. Choi for their invaluable efforts.
r
24J ~a!ur u2Re ps cos2vt. ~A9!
2 0 ss r
ss
APPENDIX: SIGNAL ANALYSIS FOR VECTORIAL
SMOKE For case II: p-polarized incidence, with p50, m50,
a5p/4, E 5r 2r exp(id), and
f pp sp
When a light beam arrives detector through polarizer S D
~P!,sample~S!,modulator~M!,andanalyzer~A!,theEfield r
I 5ur u21ur u214J ~a!ur u2Im sp sinvt
at the detector is given as f sp pp 1 0 pp r
pp
S D
E 5A R~a2m! M R~m! S R~2p! P"E , ~A1!
f (cid:149) (cid:149) (cid:149) (cid:149) (cid:149) (cid:149) i r
24J ~a!ur u2Re sp cos2vt. ~A10!
where 2 0 pp r
S D pp
1 0 For case III: p5p/4, m50, a5p/4, E 5@(r 2r )
P5A5 , ~A2! f pp ps
0 0 2(r 2r )exp(id)#/&, and
sp ss
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Rev.Sci.Instrum.,Vol.71,No.10,October2000 Surfacemagneto-optical 3805
ur 2r u21ur 2r u2 n cosu2n cosu
I 5 ps pp ss sp r 5 1 1 3 3
f 2 ss n cosu1n cosu
1 1 3 3
12J ~a!Im$~r*2r* !~r 2r !%sinvt 4pin d cosu~n2cos2u2n2cos2u!
1 0 ps pp ss sp 1 1 2 1 2 2 3 3 ,
22J ~a!Re$~r*2r* !~r 2r !%cos2vt. ~A11! l~n1cosu11n3cosu3!2
2 0 ps pp ss sp
For case IV: p5p/2 ~s polarization!, m5p/2, a5p/4,
4pin n d Qcosu~n m cosu2n m sinu!
Ef5rss2rpsexp(id), and S D rps5 l~n 1co2su2 1n co1su2!~zn cos3u13n ycosu2! ,
1 1 3 3 1 3 3 1
r
I 5ur u21ur u214J ~a!ur u2Im ps sinvt
f ps ss 1 S 0 Dss rss r 54pin1n2d2Qcosu1~n3mysinu21n2mzcosu3!,
r sp l~n cosu1n cosu!~n cosu1n cosu!
24J ~a!ur u2Re ps cos2vt. ~A12! 1 1 3 3 1 3 3 1
2 0 ss r
ss
For case V: p50 ~p polarization!, m5p/2, a5p/4, E where Q is the value of the magneto-optical activity, and
f
52r 1r exp(id), and (mx,my,mz) is the unit vector representing the direction of
sp pp S D magnetization.
I 5ur u21ur u224J ~a!ur u2Im rsp sinvt Note: from D5n2(E1iQmˆˆE), complex dielectric
f sp pp 1 0 pp r constants of magnetic material is
pp
S D S D
r
24J ~a!ur u2Re sp cos2vt. ~A13! 1 2im Q im Q
2 0 pp r z y
pp ˜e5n2 im Q 1 2im Q .
z x
TheFresnelcomplexreflectioncoefficientsincludingthe
magneto-optical Kerr effect are given as follows.14 2imyQ imxQ 1
For bulk,
rpp5nn2ccoossuu112nn1ccoossuu212inn1nc2omsuxQ1cnosuco1ssiunu2, 1SJ..AD..CB.adBelranadndanJ.dLB..EHrsekininreic,hU~lStrpartihnigneMr,aBgenrelitnic,1S9tr9u4c!t.uresII,editedby
2 1 1 2 2 1 1 2 2S.D.Bader,J.Magn.Magn.Mater.100,440~1991!.
n cosu2n cosu 3B.HeinrichandJ.F.Cochran,Adv.Phys.42,523~1993!.
r 5 1 1 2 2, 4Z.Q.Qiu,J.Pearson,andS.D.Bader,Phys.Rev.Lett.70,1006~1993!.
ss n1cosu11n2cosu2 5J.-P.QianandG.-C.Wang,J.Vac.Sci.Technol.A8,4117~1990!.
6M.T.Kief,Ph.D.thesis,PennsylvaniaStateUniversity,1991.
rps5i~nn1nc2oQs~uco1sun1/ccoossuu2!!~~nmycsoisnuu211nmzccoossuu2!!, 78ZC..JS..YAarnngoladn,dMM..DRu.nSlacvhye,inafneidn,DJ..AVpenpul.s,PhRyesv..7S4c,i6.8I1n0str~u1m99.36!.8, 4212
2 1 1 2 1 1 2 2 ~1997!.
in n Q~cosu /cosu!~m sinu2m cosu! 9H.S.Bergh,B.Gergen,H.Nienhaus,A.Majumdar,W.H.Weinberg,and
r 5 1 2 1 2 y 2 z 2 . E.W.McFarland,Rev.Sci.Instrum.70,2087~1999!.
sp ~n cosu1n cosu!~n cosu1n cosu! 10L.Zhong,M.Kim,X.Wang,andA.J.Freeman,Phys.Rev.B53,9770
2 1 1 2 1 1 2 2
~1996!.
For ultrathin film (d/l!1), 11InCo/Au~111!,nomagnetizationisobservedatroomtemperaturebelow2
ML because its T ,300K. See R. Allenspach, M. Stampanoni, and A.
n cosu2n cosu C
r 5 3 1 1 3 Bishof,Phys.Rev.Lett.65,3344~1990!.
pp n cosu1n cosu 12A.HubertandR.Scha¨fer,MagneticDomains~Springer,Berlin,1998!.
3 1 1 3
13Y. T. Millev, H. P. Oepen, and J. Kirschner, Phys. Rev. B 57, 5848
4pin d cosu~n2cos2u2n2cos2u! ~1998!.
1 1 2 1 3 2 2 3 , 14J. Zak, E. R. Moog, C. Liu, and S. D. Bader, J. Appl. Phys. 68, 4203
l~n1cosu31n3cosu1!2 ~1990!.
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