ebook img

Three-configurational surface magneto-optical Kerr effect measurement system for an ultrahigh vacuum in situ study of ultrathin magnetic films PDF

6 Pages·0.418 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Three-configurational surface magneto-optical Kerr effect measurement system for an ultrahigh vacuum in situ study of ultrathin magnetic films

Three-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 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/71/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Developments in surface magneto-optical Kerr effect setup for ultrahigh vacuum analysis of magnetic ultrathin films Rev. Sci. Instrum. 76, 046102 (2005); 10.1063/1.1878192 Bragg magneto-optical Kerr effect measurements at Co stripe arrays on Fe(001) J. Appl. Phys. 97, 073909 (2005); 10.1063/1.1868853 Growth and magnetic properties of ultrathin Co films on Pd(111) investigated by ultrahigh vacuum in situ surface magneto-optical Kerr effect and scanning tunneling microscope J. Appl. Phys. 89, 7147 (2001); 10.1063/1.1359471 Magnetic phase diagram of ultrathin Co/Si(111) film studied by surface magneto-optic Kerr effect Appl. Phys. Lett. 74, 1311 (1999); 10.1063/1.123534 Magnetic susceptibility measurements of ultrathin films using the surface magneto-optic Kerr effect: Optimization of the signal-to-noise ratio Rev. Sci. Instrum. 68, 4212 (1997); 10.1063/1.1148368 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 193.50.135.4 On: Wed, 31 Dec 2014 09:10:56 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 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 193.50.135.4 On: Wed, 31 Dec 2014 09:10:56 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. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 193.50.135.4 On: Wed, 31 Dec 2014 09:10:56 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- This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 193.50.135.4 On: Wed, 31 Dec 2014 09:10:56 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 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 193.50.135.4 On: Wed, 31 Dec 2014 09:10:56 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!. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 193.50.135.4 On: Wed, 31 Dec 2014 09:10:56

See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.