Journal of Magnetism and Magnetic Materials 241 (2002) 340–344

Probing planar arrays of magnetic nano-particles by theextraordinary Hall effect

A. Gerbera,*, A. Milnera, J. Tuaillon-Combesb, M. N!egrierb, O. Boisronb,P. M!elinonb, A. Perezb

aRaymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel Aviv University, Ramat Aviv,

69978 Tel Aviv, IsraelbD!epartement de Physique des Mat!eriaux, Universit!e Claude Bernard Lyon 1, F-69622 Villeurbanne, France

Received 16 August 2001; received in revised form 4 October 2001

Abstract

The extraordinary Hall effect has been used to determine the blocking temperature, magnetocrystalline anisotropy

and magnetic moment of far-separated Co nano-particles arranged in single-layer arrays. The total mass of 3 nm

diameter Co particles produced by the low energy clusters beam deposition (LECBD) technique corresponded to as

little as 0.01 nm thick layers. The results have been confirmed by magnetization measurements of similar but much

thicker samples. The technique is shown to be a simple and reliable information source in the limiting cases of diluted

planar arrays of magnetic nano-particles. r 2002 Published by Elsevier Science B.V.

PACS: 73.50.h; 75.75.+a; 75.70.i

Keywords: Extraordinary Hall effect; Magnetic nano-particles; Spin-dependent electronic transport; Cluster deposition

Experimental study of magnetic nano-scaleparticles is a challenging task by itself. In orderto avoid mutual interference and coagulation intolarge coupled clusters the spatial density ofparticles has to be kept low. The total amount ofmagnetic material is negligibly small, in particularwhen the entire array is planar. Sensitivity ofconventional magnetometric techniques, includingVSM and SQUID magnetometers is usually notsufficient in these cases. Several state of artapproaches have been developed, including elec-

tron holography [1], vibrating reed magnetometry[2], Lorentz microscopy [3,4] and magnetic forcemicroscopy [5,6]. Impressive recent studies ofindividual nano-particles have been obtained bythe micro-SQUID technique [7]. Application ofeach technique is limited within a certain range ofphysical conditions: temperature, field or particledimensions. It is desirable, therefore, to keeplooking for more handy and versatile tools. Inthe following, we wish to present an alternativeexperimental technique designed to study dilutemagnetic systems, including planar arrays of nano-scale magnetic particles. The technique, based onthe extraordinary Hall effect, is remarkable due toits extreme simplicity and is unlimited by tempera-ture or field constrains.

*Corresponding author. Tel.: +972-3-6408193; fax: +972-3-

6422979.

E-mail address: gerber@post.tau.ac.il (A. Gerber).

0304-8853/02/$ - see front matter r 2002 Published by Elsevier Science B.V.

PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 1 0 4 9 - 6

In bulk ferromagnets and normal metals dopedwith magnetic impurities the Hall resistivity can bephenomenologically described [8,9] as: rH ¼R0B þ RsM; where R0 is the ordinary Hallcoefficient, Rs is the spontaneous or extraordinaryHall coefficient and M is the magnetizationperpendicular to current and voltage. R0 originatesfrom Lorenz force acting on charge carriersmoving in magnetic field. The source of theextraordinary Hall term is in the break of theright–left symmetry during scattering of electronsin the presence of magnetization due to spin–orbitcoupling. Rs can be much larger than R0; in thesecases rH is effectively proportional to magnetiza-tion. The effect has been used to study the detailsof the magnetization processes [10] and magnetismof very thin films [11] already in 1950s. Recently,the extraordinary Hall effect has been observed inheterogeneous ferromagnets demonstrating thegiant magnetoresistance effect: multilayers [12],and granular ferromagnets with metallic [13],insulating [14] and point-contact [15] spacers.Observation of the effect in granular ferromagnetswith a content of magnetic component below thepercolation threshold is crucially important, sinceit indicates the sensitivity of the effect to the localmagnetic moments of individual nano-particles, incontrast with the macroscopic magnetization ofbulk magnets.

In this work, we have adapted the measurementof the extraordinary Hall effect to probe planararrays of dilute Co nano-particles embeddedwithin a thin Pt matrix.

Samples were produced by the low energyclusters beam deposition (LECBD) technique[16,17] by the following procedure. A pulsedTiSa—laser beam is focused onto an ultrahighpure cobalt target (99.95%). A high pressure burst(B3.5 bars) of He-gas synchronized with the laserpulse is injected in the nucleation chamber of thesource allowing a fast cooling of the plasmagenerated by the laser impact. The nucleation istotally achieved after the supersonic expansion inthe vacuum chamber through the exit nozzle. Themass distribution spectra of the nascent ionclusters are measured in a time-of-flight (TOF)mass spectrometer. The neutral clusters with avery low energy gained in the supersonic

expansion at the source exit are deposited on aroom temperature substrate without any damage.Vacuum during the deposition was about8 109 Torr. The detected oxygen pollution waslow enough (o5 at%) to be considered as accep-table in the framework of our study. In general, X-ray absorption (EXAFS), X-ray grazing incidencescattering (GIS), photoelectron spectroscopy(XPS), transmission electrons microscopy (TEM)and micro-SQUID technique [18,19] were used forstructural and magnetic characterization of 0D,2D and 3D films of Co-clusters embedded indifferent matrices: Pt, Ag, Nb, SiO2. Morphologyof Co particles was found to be the same for all thetested matrices and thickness: Co clusters arecrystalline in FCC-phase with a narrow distribu-tion of diameters about 3 nm [20–24]. Under- andover-layers Pt films of 5 and 15 nm, respectively,were deposited from an electron gun evaporatormounted in the same deposition chamber. Themean thickness of Co clusters, defined as a totaldeposited mass divided by Co density, variedbetween 0.01 and 1.1 nm. An average distancebetween centers of neighbor spherical Co clusterswith diameter a can be estimated as abouta3=2=ð2tÞ1=2 where t is a mean thickness of thedeposited magnetic material. For a ¼ 3 nm andt ¼ 1:1 nm (sample 1), 0.4 nm (sample 2), 0.1 nm(sample 3) and 0.01 nm (sample 4) the intergra-nular distances are about 3.5, 6, 12, and 37 nm,respectively.

The Hall voltage was measured between theroom and liquid helium temperatures in fieldsperpendicular to the plane of films. All fielddependence measurements included upward anddownward sweeps in both field polarities. A set oftypical curves measured at different temperaturesis shown in Fig. 1 for sample 2 (0.4 nm meanthickness of Co). The curve is reversible at 60Kwith no visible hysteresis. For each samplehysteresis develops below a well-defined tempera-ture. The width of hysteresis, defined as a doublecoercive field, increases as temperature is reduced.Fig. 2 presents the width of hysteresis as a functionof temperature for samples 1, 2 and 3. For sample3 the width of hysteresis approaches zero at about30K, whereas for sample 1 it occurs at muchhigher temperature of the order of 100K. The

A. Gerber et al. / Journal of Magnetism and Magnetic Materials 241 (2002) 340–344 341

onset of hysteresis can be identified as the effectiveblocking temperature Tb of Co clusters. Signifi-cantly higher blocking temperature of sample 1can be explained by a relative proximity andtherefore, either physical or magnetic couplingbetween some of the deposited Co clusters. Insample 3 the average distance between neighboringgrains is about four times the granular size and theprobability of intergranular correlation is low.

More precise determination of the blockingtemperature can be obtained by monitoring theremnant Hall signal as a function of temperature,as plotted in Fig. 3 for sample 2. The sample hasbeen magnetized at 4.2K and gradually heated upat zero external field. The remnant Hall signaldecreases monotonically and approaches zero atabout 25K, which indicates the blocking tempera-ture of Co clusters in this sample. Determinationof the blocking temperature in this experiment isequivalent to the zero-field versus field cooledmagnetization measurement. The latter has beendone using much thicker (600 nm thick) samplesprepared by a simultaneous co-deposition of Coclusters and Pt matrix. Fig. 4 presents the field—cooled versus zero field—cooled magnetization oftwo such samples with Co volume concentrationsof 4% and 14%. Tb is about 30K in the samplewith low Co concentration (4%) and far separatedclusters in agreement with the Hall techniqueresult of diluted planar samples 2 and 3. In samplewith higher Co volume concentration (14%) andhigher probability of larger cluster formation, theblocking temperature is much higher, as well inagreement with the Hall technique results ofsample 1.

Magnetic anisotropy energy density C can beestimated as CVE25kBTb; where V is the particlevolume, and kB is Boltzmann constant. For

-1.0 -0.5 0.0 0.5 1.0

-0.05

0.00

0.05

4.2K10K20K60K

RH

(Ω

B0 (T)

(

Fig. 1. Hall resistance of sample 2 (mean thickness of Co

clusters is 0.4 nm) as a function of applied magnetic field

measured at different temperatures. Arrows indicate the

direction of field sweep.

0 20 40 60 80 100 120 1400.0

0.2

0.4

0.6

0.1nm Co0.4nm Co1.1nm Co

∆ B(T

)

T (K)

Fig. 2. Temperature dependence of the width of hysteresis

loops (double coercive field) of three samples with mean

thickness of Co clusters corresponding to 0.1, 0.4 and 1.1 nm.

10 20 30 40

0

5

10

15

20

RH

(0)

(mΩ

T (K)

(

Fig. 3. Remnant Hall resistance of sample 2 as a function of

temperature.

A. Gerber et al. / Journal of Magnetism and Magnetic Materials 241 (2002) 340–344342

Tb ¼ 30K we calculate CE7 106 erg/cm3 whichis close to the value found in 3D films [25].

Magnetic moment of far-separated superpara-magnetic particles can be estimated by fitting themeasured Hall signal by the Langevin function.Fig. 5 presents the Hall resistance measured insample 4 (a mean thickness of Co is 0.01 nm, anintergranular spacing is about 37 nm) at 77K(above the blocking temperature). Perfect fit (solidline) is found for M ¼ 4:6 1017 emu, which

corresponds to about 3 103 atoms of Co with abulk value of atomic magnetic moment (1.7 mB). Itshould be noted that a straightforward fitting ofthe measured Hall signal by Langevin function iscurrently applicable for materials with a narrowdistribution of particle sizes, as in the present case.Correlation between the particle size and theextraordinary Hall coefficient has not been studiedso far. Knowledge of this correlation is needed formaterials with wide size distributions.

To conclude, we have demonstrated that scat-tering by a single layer of far-separated super-paramagnetic particles embedded in a thinconducting matrix generates the extraordinaryHall voltage. The measured signal is proportionalto magnetic moment of magnetic clusters averagedover the volume of the sample. Hysteresis isdeveloped in the Hall voltage versus applied fieldcurve below the blocking temperature of magneticparticles. The blocking temperature can be deter-mined either by extrapolating the width of thehysteresis or via the temperature dependence ofthe remnant Hall signal. The absolute value ofmagnetic moment of individual nano-particles canbe found by fitting the signal measured in thesuperparamagnetic state by the Langevin function.The technique is simple in application, free of fieldand temperature constrains and is well adapted forthe study of ultrathin magnetic films and two-dimensional arrays of diluted magnetic nano-particles.

This research has been supported in part byAFIRST, Franco–Israeli research program onnano-technology, grant No. 9841.

References

[1] A. Tonomura, T. Matsuda, J. Endo, T. Arii, K. Mihama,

Phys. Rev. B 34 (1986) 3397.

[2] H.J. Richter, J. Appl. Phys. 65 (1989) 9.

[3] S.J. Hefferman, J.N. Chapman, S. McVitie, J. Magn.

Magn. Mater. 95 (1991) 76.

[4] C. Salling, S. Schultz, I. McFadyen, M. Ozaki, IEEE

Trans. Magn. 27 (1991) 5185.

[5] T. Chang, J.G. Chu, J. Appl. Phys. 75 (1994) 5553.

[6] M. Ledermann, S. Schultz, M. Ozaki, Phys. Rev. Lett 73

(1994) 1986.

0 50 100 1500.0

0.2

0.4

0.6

0.8

1.0

1.2

ZFC

FC

ZFC

FC Co/Pt 14%Co/Pt 4%

Mag

netiz

atio

n (a

.u.)

T (K)

Fig. 4. Field cooled and zero-field cooled magnetization of two

600nm thick samples prepared by co-deposition of Co clusters

and Pt matrix. Volume concentrations of Co clusters are 4%

(open circles) and 14% (crosses).

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Mfit=4.6×10-20Am2

Pt(11nm)/Co(0.01nm)/Pt(5nm)

T=77 K

RH

(a.u

.)

B0 (T)

Fig. 5. Hall resistance of sample 4 (mean thickness of Co is

0.01 nm) as a function of the applied magnetic field measured at

77K (symbols). Solid line is the Langevin function calculated

with M ¼ 4:6 1017 emu.

A. Gerber et al. / Journal of Magnetism and Magnetic Materials 241 (2002) 340–344 343

[7] W. Wernsdorfer, D. Mailly, A. Benoit, J. Appl. Phys. 87

(2000) 5094.

[8] L. Berger, G. Bergmann, in: C.L. Chien, C.R. Westgate

(Eds.), The Hall Effect and its Applications, Plenum Press,

New York, 1980, p. 55.

[9] A. Fert, A. Hamzic, in: C.L. Chien, C.R. Westgate (Eds.),

The Hall Effect and its Applications, Plenum Press, New

York, 1980, p. 77, and references therein.

[10] S. Foner, Phys. Rev. 95 (1954) 652.

[11] R. Coren, H.J. Juretschke, J. Appl. Phys. 28 (1957) 806.

[12] S.N. Song et al, Appl. Phys. Lett. 59 (1991) 479.

[13] P. Xiong, G. Xiao, J.Q. Wang, J.Q. Xiao, J.S. Jiang, C.L.

Chien, Phys. Rev. Lett. 69 (1992) 3220.

[14] A.B. Pakhomov, X. Yan, B. Zhao, Appl. Phys. Lett. 67

(1995) 3497.

[15] A. Gerber, B. Groisman, A. Milner, M. Karpovsky,

Europhys. Lett. 49 (2000) 383.

[16] P. M!elinon, et al., Int. J. Modern Phys. B 9 (4 & 5) (1995)

339.

[17] A. Perez, et al., J. Phys. D 30 (1997) 1.

[18] W. Wernsdorfer, et al., J. Appl. Phys 78 (1995) 7192.

[19] M. Jamet, et al., Phys. Rev. Lett. 86 (2001) 4676.

[20] V. Dupuis, et al., J. Magn. Magn. Mater. 165 (1997) 42.

[21] J. Tuaillon, et al., Phil. Mag. A 76 (1997) 493.

[22] F. Parent, et al., Phys. Rev. B 55 (1997) 3683.

[23] M. Jamet, et al., Phys. Rev. B 62 (2000) 493.

[24] M. Negrier, et al., Phil. Mag. A 81 (2001) 2855.

[25] M. Jamet, et al., J. Magn. Magn. Mater. 226–230 (2001)

1833.

A. Gerber et al. / Journal of Magnetism and Magnetic Materials 241 (2002) 340–344344