©2002 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.The magnetization spectrum from an erased (ac demagnetized or dc saturated) particulate medium was derived analytically using the autocorrelation function of a long line of separate and contiguous particles. The derived expressions indicated a strong dependence on the percentage of chains and their length inside the magnetic medium. Using the values of these quantities as fitting parameters, good agreement to measured noise spectra from a digital tape system was obtained

Aziz, Mustafa M.

Middleton, Barry K.

Miles, J. J.

IEEE Transactions on Magnetics

M.M. Aziz

B.K. Middleton

J.J. Miles

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Particle distributions and noise in metal particle tapes

Open Research Exeter

IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 5, SEPTEMBER 2002 1901Particle Distributions and Noise inMetal Particle TapesMustafa M. Aziz, Barry K. Middleton, and Jim J. MilesAbstract—The magnetization spectrum from an erased (ac de-magnetized or dc saturated) particulate medium was derived an-alytically using the autocorrelation function of a long line of sep-arate and contiguous particles. The derived expressions indicateda strong dependence on the percentage of chains and their lengthinside the magnetic medium. Using the values of these quantitiesas fitting parameters, good agreement to measured noise spectrafrom a digital tape system was obtained.Index Terms—Metal particle, noise, tape.I. INTRODUCTIONADVANCED tape media consist of needle shaped iron par-ticles of approximately 100-nm lengths, axial ratios ofaround 8 and coated with a protective oxide layer of thicknessbetween 2 and 4 nm [1], [2]. These particles are aligned duringmanufacture by an external magnetic field in the direction of thetape motion to increase the magnitude of the replay signal. How-ever, the alignment process is not perfect and leads to a distribu-tion of particle axes throughout the tape. Furthermore, particlesalso exhibit variation in their sizes throughout the volume of thetape. These variations constitute noise and conspire to contam-inate the replay output signal and limit the recording resolutionof magnetic tapes. This paper is concerned with the noise pro-duced by such media.By treating the individual particles as independent voltagesources the replay power spectral density of a tape medium haspreviously been predicted as the sum of these individual volt-ages [3]–[5]. The effects of the variations in particle attributeswere included subject to their statistical distributions. Simpli-fied models of clustering in particulate media were also pro-duced and yielded good agreement with measured noise spectra[6], [7]. These models used size distributions that did not allowclosed form expressions for the noise spectra to be derived, andtreated size variations and particle chaining independently to ex-plain the measurements.This paper utilizes the autocorrelation method to derive ananalytical expression for the magnetization power spectral den-sity of an erased (ac demagnetized or dc saturated) particu-late medium [8] taking into account particle size variations andchaining to explain measurements on ac-demagnetized tapes.Manuscript received February 11, 2002; revised May 23, 2002. This work wassupported by the Engineering and Physical Sciences Research Council underGrant GR/M46648/01.M. M. Aziz is with the School of Engineering and Computer Science, Uni-versity of Exeter, Exeter EX4 4QF, U.K. (e-mail: M.M.Aziz@exeter.ac.uk).B. K. Middleton and J. J. Miles are with the Department of ComputerScience, University of Manchester, Manchester M13 9PL, U.K. (e-mail:B.Middleton@cs.man.ac.uk, J.Miles@man.ac.uk).Digital Object Identifier 10.1109/TMAG.2002.802828.Fig. 1. Line of particles.II. THEORYFig. 1 illustrates a line of particles of length containingindividual particles. Each particle has a length , orientation ,width , and thickness and, hence a volume .A. Uncorrelated ParticlesWith no correlations between the particles, it was shown thatfor small uniform distributions of particle orientations of theorder of where , the magnetiationpower spectral density is given by [8]:(1)where is the uniform magnetization vector inside each par-ticle, is the particle density, and are the average particlewidth and thickness respectively, and the overbar indicates en-semble averages. is the wavenumber and is thewavelength.Assuming that the particle lengths follow the Gamma distri-bution [8]:(2)where is the standard deviation of the particle length, is theaverage particle length, and is the Gamma function, thenthe averages in (1) can be evaluated analytically to yield(3)B. Chains of ParticlesObservations of arrangements of carbon steel wires in a vinylchloride binder in a large scale model of a tape coating have0018-9464/02$17.00 © 2002 IEEE1902 IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 5, SEPTEMBER 2002Fig. 2. Chain of particles.indicated the presence of strong interactions between particlesand the formation of long chains of particles during alignmentfor packing fractions greater than 0.01 [9]. The formation ofchains was also observed in computer simulations of elongatedFe particles in a strong applied field [10]. Hence, correlationsin a particulate medium will be simulated using chains of con-tiguous particles as demonstrated in Fig. 2, with uniform mag-netization throughout each chain.To simplify the modeling and the fitting process, it is assumedthat each chain will contain identical particles and the lengthof each chain is therefore equal to .The power spectral density of a line of particles containingindividual and contigous particles, both assumed uncorrelated,is given by [8](4)whereis the proportion of chains inside the medium and is thenumber of chains in the medium. For a uniform distribution ofparticle numbers inside each chain between 1 and a maximumof , inclusive, the magnetization power spectral density wasfound to be(5)III. EXPERIMENTAL MEASUREMENTS AND INTERPRETATIONThe noise measurements were performed on a helical scandigital tape system using ac-demagnetized, 4-mm metal par-ticle tapes. The properties of the tapes are given in Table I. Avibrating-sample magnetometer was used to measure the hys-teresis loop (shown in Fig. 3) of a tape sample to obtain themagnetic properties of the tapes. The magnetic layer thicknessand particle packing fraction values of the tapes were providedby the tape manufacturer.TABLE IMETAL PARTICLE TAPE PROPERTIESFig. 3. Hysteresis loop of metal particle tape sample measured in the directionof the longitudinal tape motion and at room temperature.Fig. 4. Particle length counts of 191 particles from a metal power samplecompared with the calculated Gamma distribution. Particles have an averagelength of 88 nm, standard deviation 23 nm, and an axial ratio of 7.For comparison with spectral measurements, information isrequired about the distribution of particle sizes inside a typ-ical metal particle tape. This is provided by the data in Fig. 4,which shows a particle length distribution obtained from an ex-perimental metal powder sample with coercivity 197 kA/m andsaturation magnetization 143 Am kg [1]. The Gamma distri-bution is also plotted in Fig. 4 using (2) for comparison usingthe measured average particle length of 88 nm and standard de-viation of 23 nm.In the following fittings, the values of the average particlelength and axial ratio of the particles will be those shown inFig. 4, as they represent values of an advanced metal particletape medium similar to the tape medium used in the measure-ments.AZIZ et al.: PARTICLE DISTRIBUTIONS AND NOISE IN METAL PARTICLE TAPES 1903Fig. 5. Measured replay noise spectra from an ac-demagnetized tape.Fig. 6. Measured medium noise spectrum normalized by the replay losses andthe fitted magnetisaton power spectral density given in (5).Replay was achieved using an inductive head with gap length0.2 m. The rotating head was moving at a speed of 18 m/sand the tape was moving at 0.023 m/s, with a flying height ofapproximately 40 nm. A spectrum analyzer was used to captureand analyze the replay signals with the following settings: band-width 50 MHz, resolution bandwidth 10 kHz, and video band-width 10 kHz, giving a sweep time of 1.272 s. The capturedreplay spectra were the average of 64 accumulated sweeps.Initially, the voltage from the replay head was measured inthe absence of the tape to give the system noise spectrum (elec-tronics plus drum noise) as is shown by curve (a) in Fig. 5.The spectrum was then measured in the presence of the movingvirgin tape to yield the total noise spectrum of curve (b). Sub-tracting, as powers, the electronics noise in (a) from the totalmeasured noise spectrum in (b) yields the medium noise powerspectral density of curve (c).The medium noise spectrum was then normalized by thereplay loss factors (gap-, spacing-, and thickness-loss factors)using the Lindholm head field transforms given in [11]. Theresulting spectrum, shown in Fig. 6, represents the particlemagnetization’s power spectral density.Using a least-squares algorithm, (5) was fitted to the mea-sured magnetization spectrum with the constant of proportion-ality, the chain percentage , and maximum chain lengthas the fitting parameters. Fig. 6 shows the results of the fittingwhere it can be seen that a chain percentage of 0.3% and a max-imum chain length of 200 particles yielded good agreement be-tween the measured and calculated spectra over a wide range ofwavelengths.IV. CONCLUSIONClosed form expressions for the medium noise spectra in par-ticulate media have been derived which include particle chains.The comparison of (5) with measurement has indicated the de-pendence of the shape of the medium magnetization spectrumon the chain length and proportion inside the medium es-pecially at long wavelengths.ACKNOWLEDGMENTThe authors wish to thank M. del Puerto Morales Herreroof the Materials Science Institute of Madrid for providing thedata of the particle length counts. The authors would also liketo thank the referees of this paper for their helpful comments.REFERENCES[1] M. P. Morales, S. A. Walton, L. S. Prichard, C. J. Serna, D. P. E. Dickson,and K. O’Grady, “Characterization of advanced metal particle recordingmedia pigments,” J. Magn. Magn. Mater., vol. 190, pp. 357–370, 1998.[2] M. P. Sharrock, “Recent advances in metal particulate recordingmedia, toward the ultimate particle,” IEEE Trans. Magn., vol. 36, pp.2420–2425, 2000.[3] I. Stein, “Analysis of noise from magnetic storage media,” J. Appl. Phys.,vol. 34, no. 7, pp. 1976–1990, 1963.[4] L. Thurlings, “Statistical analysis of signal and noise in magneticrecording,” IEEE Trans. Magn., vol. MAG-16, pp. 507–513, 1980.[5] H. N. Bertram, Theory of Magnetic Recording. Cambridge, UK: Cam-bridge Unive. Press, 1994.[6] P. Luo and H. N. Bertram, “Tape medium noise measurements and anal-ysis,” IEEE Trans. Magn., vol. 37, pp. 1620–1623, 2002.[7] L. L. Nunnelley, D. E. Heim, and T. C. Arnoldussen, “Flux noise in par-ticulate media: Measurement and interpretation,” IEEE Trans. Magn.,vol. MAG-23, pp. 1767–1775, 1987.[8] M. M. Aziz, B. K. Middleton, and J. J. Miles, “Autocorrelation analysisof the particle magnetization in erased particulate media,” IEEE Trans.Magn., vol. 38, pp. 279–287, 2002.[9] M. Matsumoto, “A study of particle arrangement in magnetic tapes,”IEEE Trans. Magn., vol. MAG-15, pp. 1312–1314, 1979.[10] G. N. Coverdale, R. W. Chantrell, G. A. R. Martin, A. Bradbury, A. Hart,and D. A. Parker, “Cluster analysis of the microstructure of colloidaldispersions using the maximum entropy technique,” J. Magn. Magn.Mater., vol. 188, pp. 41–51, 1998.[11] D. A. Lindholm, “Dependence of reproducing gap null on head geom-etry,” IEEE Trans. Magn., vol. MAG-11, pp. 1692–1696, 1975.

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