We have studied the magnetoresistance of electrodeposited Bi wires with diameters between 200 nm and 2 μm in magnetic fields up to B=55 T. In zero field, the resistance increases with decreasing temperature, indicating that the mean free path is strongly influenced by the nanowire geometry. The high-field magnetoresistance shows strong dependence on field orientation; typically 200% for B parallel to the wires, and 600%-800% for B perpendicular to the wires. The perpendicular magnetoresistance is well described by a modified two-current model which suggests that the high-field response of the arrays is fairly insensitive to the wire diameter, and is dominated by bulk properties of Bi

Balakirev, FF

Boebinger, GS

Chien, CL

Hong, KM

Liu, K

Reich, DH

Searson, PC

Yang, FY

We have studied the magnetoresistance of electrodeposited Bi wires with diameters between 200 nm and 2 μm in magnetic fields up to B=55 T. In zero field, the resistance increases with decreasing temperature, indicating that the mean free path is strongly influenced by the nanowire geometry. The high-field magnetoresistance shows strong dependence on field orientation; typically 200% for B parallel to the wires, and 600%–800% for B perpendicular to the wires. The perpendicular magnetoresistance is well described by a modified two-current model which suggests that the high-field response of the arrays is fairly insensitive to the wire diameter, and is dominated by bulk properties of Bi

Hong, Kimin

Liu, Kai

eScholarship - University of California

UC DavisUC Davis Previously Published WorksTitleGiant positive magnetoresistance of Bi nanowire arrays in high magnetic fieldsPermalinkhttps://escholarship.org/uc/item/0f92n04kJournalJournal of Applied Physics, 85(8)ISSN0021-8979AuthorsHong, KiminYang, FYLiu, Kaiet al.Publication Date1999-04-15DOI10.1063/1.370215 Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaJOURNAL OF APPLIED PHYSICS VOLUME 85, NUMBER 8 15 APRIL 1999Giant positive magnetoresistance of Bi nanowire arraysin high magnetic fieldsKimin Hong,a) F. Y. Yang, Kai Liu, D. H. Reich, P. C. Searson, and C. L. ChienThe Johns Hopkins University, Baltimore, Maryland 21218F. F. Balakirev and G. S. BoebingerBell Laboratories, Lucent Technologies, 700 Mountain Avenue, Murray Hill, New Jersey 07974and Los Alamos National Laboratory, MS E534, Los Alamos, New Mexico 87545We have studied the magnetoresistance of electrodeposited Bi wires with diameters between 200 nmand 2mm in magnetic fields up toB555 T. In zero field, the resistance increases with decreasingtemperature, indicating that the mean free path is strongly influenced by the nanowire geometry. Thehigh-field magnetoresistance shows strong dependence on field orientation; typically 200% forBparallel to the wires, and 600%–800% forB perpendicular to the wires. The perpendicularmagnetoresistance is well described by a modified two-current model which suggests that thehigh-field response of the arrays is fairly insensitive to the wire diameter, and is dominated by bulkproperties of Bi. ©1999 American Institute of Physics.@S0021-8979~99!69908-X#icontibthcreilef Bal-sirinavnpotinlsitisndcem-thtratnesm-mea-stnce0de-y aion,sRecently, giant magnetoresistance~GMR! has attractedmuch interest because of its intricate physics and appltions in nonvolatile memory and field-sensing devices.1 InGMR, spin-dependent charge transport in heterogenemagnetic materials results in a large change of resistaupon the application of a magnetic field. In nonmagnematerials, the magnetoresistance of semimetals such asmuth ~Bi! has long been a subject of interest because ofunusual properties of their charge carriers.Crystalline Bi exhibits anisotropic magnetoresistanwhich depends on the direction of the applied field withspect to the crystal axes.2 This is due to its complex Fermsurface, which has elongated pockets of both holes and etrons with different effective masses. Since the carriers ohave a very long Fermi wavelengthlF'40 nm, it is particu-larly interesting to study thin films and wires with physicsizes approachinglF . In low-dimensional systems, phenomena such as quantum size effects have been observed.3 Usu-ally, thin films of Bi have been obtained by vacuum depotion techniques such as thermal evaporation and sputteOne of the drawbacks of these films is that they tend to hvery small grain sizes,4,5 and the magnetoresistance is in geeral very small. Recently, electrodeposition using nanorous templates has provided an enticing means of fabricaarrays of narrow wires composed of a variety of meta6This method has enabled us to obtain Bi nanowires wlarge grains.7 In this paper, we report the first magnetorestance measurements of electrodeposited Bi nanowires uvery high magnetic fields up toB555 T.Bi wires with diametersd5200 nm, 400 nm, 1mm, and2 mm were made by electrodeposition into pores produby nuclear particle track etching in polycarbonate mebranes. The membranes are approximately 10mm thick withpore density;107– 108 cm22. The pores are nominally parallel with some spread in angles as large as 15° fromnormal to the plane of the membranes. Transmission eleca!Electronic mail: kimin@pha.jhu.edu6180021-8979/99/85(8)/6184/3/$15.00a-uscecis-ee-c-i-g.e--g.h-erd-eonmicroscopy~TEM! and electron diffraction have shown ththe wires are polycrystalline, with grain sizes up to;2 – 4times the pore diameters with no preferred orientation.7 Elec-trical contacts were made on both sides of the membrawith vacuum-deposited Au layers and silver epoxy. The teperature dependence of the resistance at zero field wassured atT54.22290 K. High-field magnetoresistance wameasured in fields up toB555 T using a pulsed magnet avarious temperatures betweenT54.2 K and 290 K in bothlongitudinal (Biwires) and transverse (B'wires) orienta-tions.The temperature dependence of the resistaR(T)/R(290 K) for arrays of Bi wires with diameters 20nm, 400 nm, 1mm, and 2mm is shown in Fig. 1. In all thearrays,R(T) increases monotonically as the temperaturecreases, and there is generally a larger change inR(T) as thewire size is reduced. In Bi, the resistance is determined bfairly delicate balance between the carrier concentratn(T), which decreases with decreasingT, and the mobilitym(T), which generally increases with decreasingT as themean free pathl (T) grows. In bulk single crystal samplesl (T) grows from;0.2 to 0.3mm at room temperature to aFIG. 1. Temperature dependence of zero-field resistanceR(T)/R(290 K) ofBi nanowires withd5200 nm, 400 nm, 1mm, and 2mm. The lines areguides to the eye.4 © 1999 American Institute of Physicseath-narleetuetoanleoenplles.d,iogeininin isiledwee atibeaeheeldsleslf-eral-uese-woeesingh-leg-ays.eldulae-6185J. Appl. Phys., Vol. 85, No. 8, 15 April 1999 Hong et al.large as;100mm at T54.2 K, and the resistance decreaswith decreasingT. In thin films, however,l (T) has less tem-perature dependence so thatn(T) has a larger effect onR(T).8 In our nanowire arrays, the increase of resistancelow temperatures shown in Fig. 1 indicates thatl (T) is cutoff in the wires as well, thatn(T) also determinesR(T) inour samples.The high-field resistanceR(B) for a 200 nm wire sampleat several fixed temperatures betweenT54.2 K and 290 K isshown in Fig. 2 for both the perpendicular~solid lines! andparallel ~dashed lines! field orientations. There is clearlydramatic difference between the two orientations, withparallel resistanceRi saturating nearB520 T as the temperature is reduced, and the perpendicular resistanceR' continu-ing to rise at the highest field measured. In both orientatiothere is a strong temperature dependence inR(B) down toT'100 K, but little temperature dependence belowT'50 K. The small spikes visible on some of the tracesdue to electronic noise, and are not intrinsic to the sampThese data are representative of the behavior ofR' in allthe samples measured, as will be discussed in more dbelow. There is somewhat more variability inRi . In all thesamplesRi shows most of its change with field belowB520 T at low temperatures, but in some samples it continto rise slowly at higher fields. This may be attributablesmall misalignments of the samples, which would mix incontribution fromR' . In the perpendicular orientation, othe other hand, the effects of misalignment are muchpronounced. In the remainder of this paper, we will focusanalyses ofR' .To illustrate the magnetoresistance~MR! we show, inFig. 3~a!, DR5R(B)2R(0) derived from the data on thd5200 nm sample atT54.2 K and 290 K. In this plot, onlyevery tenth data point from the traces in Fig. 2 is showFigure 3~b! shows the corresponding data for ad5400 nmsample. At each temperature, the curves for the two samlook very similar, and in fact they differ only by a scafactor. At T54.2 K, MR rises more steeply at lower fieldThis is characteristic of all the samples we have measurewill be demonstrated below.The largeDR leads to large magnetoresistance ratDR/R, typically 600%–800%. These values are very larbut small compared to that reported for single-crystal BiFIG. 2. Field dependence of resistance forB'wires ~solid lines! andBiwires ~dashed lines! at fixedT for d5200 nm.sates,es.ailsssn.esas,,high fields. The general shape of the perpendicular MRour samples is similar to that of single-crystal Bi up toB530 T,9,10 but the large decrease around 40 T seen therenot observed in our samples. In the absence of a detatheoretical framework based on the microscopics of Bi,resort to the standard description of magnetoresistanchigh fields using the Frank’s formula,11,12 DR}B2/@11(mB)2#, where the constantm is related to the carriermobility. This formula alone does not adequately descrour data. Very good fits may be obtained, however, bytwo-term generalization of the Frank’s formula, which wwrite asDR5R1~m1B!211~m1B!2 1R2~m2B!211~m2B!2 .The solid lines in Fig. 3 are examples of these fits. Tagreement with the data is excellent even at the lowest fiwhere the agreement is still very good.The parameters derived from fitting data of five sampwith varying wire diameter are shown in Fig. 4. The seconsistency of all parameters lend credence to the genized Frank’s formula. The two ‘‘mobilities’’ are effectivelyindependent of both temperature and wire size, with valm1'0.12 m2/V s andm2'0.03 m2/V s. This lack of variationwith T is consistent with the picture of a temperaturindependent mobility~or mean free path! restricted by thewire geometry and/or grain size. The two values ofm1 andm2 differing by about a factor of 4 suggests that there are tdifferent species of carriers.The ratioR1 /R2 indicates the relative importance of thtwo species of carriers. As shown in Fig. 4~c!, the ratioR1 /R2 displays a remarkable similarity for all the samplmeasured, increasing from roughly 0.2 to 0.5 with decreasT. This reflects the growth in importance of the higmobility term,m1 , at low temperatures which is responsibfor the faster rise of the MR in the low-T data.In summary, we have reported the first high-field manetoresistance measurements of bismuth nanowire arrThe dependence of MR on temperature and magnetic fican be well described by the generalized Frank’s formwith two mobilities which are essentially temperature indFIG. 3. ~a! Transverse magnetoresistanceDR of ~a! 200 nm Bi wires and~b!400 nm Bi wires atT54.2 and 290 K.therarelec-o.tt.u-40e6186 J. Appl. Phys., Vol. 85, No. 8, 15 April 1999 Hong et al.FIG. 4. The best-fit results of~a! m1 , ~b! m2 , and ~c! R1 /R2 obtained byusing the generalized Frank’s formula for Bi wires of diameters 200 nm,nm, 1mm, and 2mm. ~The twod5200 nm samples were cut from the sammembrane.!pendent due to constraints imposed by the wires. Furexperiments, including measurements on thin films,clearly necessary to elucidate the high-field behavior of etrodeposited bismuth.This work was supported by NSF MRSEC Program N96-32526.1M. N. Baibich et al., Phys. Rev. Lett.61, 2472~1988!.2L. S. Lerner, Phys. Rev.127, 1480~1962!.3Yu. F. Komnik, E. I. Bukhshtab, Yu. V. Nikitin, and V. V. Andrievskii,Sov. Phys. JETP33, 364 ~1971!.4D. E. Beutler, T. L. Meisenheimer, and N. Giordano, Phys. Rev. Lett.58,1240 ~1987!.5N. O. Birge, B. Golding, and W. H. Haemmerle, Phys. Rev. Lett.62, 195~1989!.6T. M. Whitney, J. S. Jiang, P. C. Searson, and C. L. Chien, Science261,1316 ~1993!.7K. Liu, C. L. Chien, P. C. Searson, and Kui Yu-Zhang, Appl. Phys. Le~to be published!.8N. Garcia, Y. H. Kao and M. Strongin, Phys. Rev. B5, 2029~1972!.9N. Miura, R. G. Clark, R. Newbury, R. P. Starret, and A. V. Skogarevsky, Physica B194-196, 1191~1992!.10K. Hiruma and N. Miura, J. Phys. Soc. Jpn.52, 2118~1983!.11A. Sommerfeld and N. H. Frank, Rev. Mod. Phys.3, 1 ~1931!.12J.-P. Jan, Solid State Phys.5, 1 ~1957!.0

Giant positive magnetoresistance of Bi nanowire arrays in high magnetic fields

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