The time variation of magnetostatic fields generated by space and time varying magnetization configurations in small perpendicular pole tips is studied. The magnetization configurations are a response to external fields driving the pole tip and soft under layer (SUL). When the system damping is sufficiently small the magnetization excitations persist for a long time after reversal. The effects of damping parameter, position in the media, and discretization cell size on the magnitude of the time varying magnetostatic fields will be given. Decreasing the damping parameter increases the magnitude of the magnetostatic field variation

Boerner, E.D.

Chantrell, R.W.

Gao, K.Z.

English

E.D. Boerner

K.-Z. Gao

R.W. Chantrell

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Effect of Damping on the Time Variation of Fields Produced by a Small Pole Tip With a Soft Under Layer

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This is a repository copy of Effect of damping on the time variation of fields produced by a small pole tip with a soft under layer.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/1837/Article:Gao, K.Z., Chantrell, R.W. orcid.org/0000-0001-5410-5615 and Boerner, E.D. (2004) Effectof damping on the time variation of fields produced by a small pole tip with a soft under layer. IEEE Transactions on Magnetics. pp. 2371-2373. ISSN 1941-0069 https://doi.org/10.1109/TMAG.2004.832238eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 4, JULY 2004 2371Effect of Damping on the Time Variation ofFields Produced by a Small Pole TipWith a Soft Under LayerEric D. Boerner, Kai-Zhong Gao, and Roy W. ChantrellAbstract—The time variation of magnetostatic fields generatedby space and time varying magnetization configurations in smallperpendicular pole tips is studied. The magnetization configura-tions are a response to external fields driving the pole tip and softunder layer (SUL). When the system damping is sufficiently smallthe magnetization excitations persist for a long time after reversal.The effects of damping parameter, position in the media, and dis-cretization cell size on the magnitude of the time varying magne-tostatic fields will be given. Decreasing the damping parameter in-creases the magnitude of the magnetostatic field variation.Index Terms—Damping parameter, head field, micromagnetic,perpendicular recording.I. INTRODUCTIONWHEN a magnetic system is subjected to a rapid reversalof the applied field, dynamic magnetization excitationsmay be generated due to a transfer of Zeeman energy to magne-tostatic and exchange modes [1], [2]. When the damping of thesystem is small and energy dissipation to the lattice occurs overa long time, these excitations allow the average magnetization toreverse in shorter times as compared to the coherent case, pro-vided the field amplitude is sufficient [3]–[5]. As the dampingparameter is decreased we observe an increase in the ampli-tude of the variation of the magnetostatic field about its equi-librium. Under conditions of smaller dissipation, this variationpersists for longer times. These time scales are approximatelyinversely proportional to the damping parameter. In small mag-netic writers, this results in fields in the media that have highfrequency modes.II. MODELOur three dimensional micromagnetic model is very similarto that described in [6]. The in-plane directions are discretizeduniformly, and the out of plane (perpendicular) direction is dis-cretized nonuniformly. In plane magnetostatic fields are calcu-lated more rapidly using fast Fourier transforms [7]. The outof plane direction is treated by direct pairwise summation. Theparallel model uses the Message Passing Interface (MPI), witheach layer handled by a seperate process. Earlier simulations onManuscript received October 15, 2003.E. D. Boerner and R. W. Chantrell are with Seagate Technology, Pittsburgh,PA 15222 USA (e-mail: eric.d.boerner@seagate.com; roy.w.chantrell@seagate.com).K.-Z. Gao is with Seagate Technology, Bloomington, MN 55435 USA(e-mail: kaizhong.gao@seagate.com).Digital Object Identifier 10.1109/TMAG.2004.832238Fig. 1. Field in the medium at track center near the trailing edge due to a poletip with  = 0:01.lower memory machines with a faster interconnect required aseperate CPU for each layer. For a cluster of workstations withmore memory per node but a slower interconnect, it becomesmore favorable to run several MPI processes per node. This isbecause the magnetostatic field calculation requires communi-cating the information contained in the spin directions betweenall nodes. The pole tip and leading edge side of the soft underlayer (SUL) are driven by long bar magnets with exponentialrise times. We have made this simplification in the SUL to avoidrequiring a large enough region to include the return pole. Weare primarily interested in correctly modeling the magnetizationvariation in the pole tip and SUL near the pole tip, and we ex-pect this will be a reasonable approximation for our purposes.The pole tip is driven by both magnetostatic and exchange fieldsfrom the long bar magnets. The SUL, hard layer (medium), andpole tip can all be discretized, but in this paper we will includeonly the SUL and write pole tip, and look at the fields from thepole tip and the SUL (not including the driving fields) where thehard layer would be. For the results presented, we have a nom-inal pole tip size at the ABS of 50 nm by 100 nm, total headto SUL spacing of 25 nm, driving field rise time of 200 ps, andpole tip and SUL saturation magnetization of 1600 emu/cm .III. RESULTSFig. 1 shows the time variation of the field in the mediaat track center near the trailing edge of the write pole. Thedamping constant is chosen to be . The results show0018-9464/04$20.00 © 2004 IEEE2372 IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 4, JULY 2004Fig. 2. Field in the medium at track center near the trailing edge due to a poletip with  = 0:01.Fig. 3. Standard deviation of the field versus damping parameter.a relatively smooth field variation with oscillations, due tolarger scale nonuniform dynamic reversal processes. Higherfrequency modes that may be initially excited are damped outwithin 0.5 ns.In Fig. 2, the time variation of the field for the same case asshown in Fig. 1, but smaller damping, , is plotted. Theresults show that the high frequency excitations are large com-pared to the case and persist for a longer time com-pared to our reversal period. For both cases, the magnetostaticfield may exceed the mean (saturation) field before the equilib-rium state is reached.To get an estimate of the magnitude of the field variation,first we define a window of certain length ending at the endof a bit period. We then compute the standard deviation of theabsolute value of the magnetostatic field in this window andaverage over each bit (the windows ending at 2 ns, 3 ns, 4ns, and 5 ns). In Fig. 3 the standard deviation of the field isplotted versus damping parameter. The results show that themagnitude of the field variation decreases monotonically withincreasing damping parameter. The results also show the effectof window length: longer windows capture more of the fieldvariation present at earlier times when there was more energyin the spin system, and hence have a larger standard deviation.Fig. 4. Time variation of field further downtrack with  = 0:01.Fig. 5. Standard deviation of field versus downtrack position.Different discretizations are compared. There is a weaker de-pendence on damping parameter for the smaller discretizationcells. For larger discretization cells, the normalized exchangefields are weak [8], allowing larger excursions of the spins afterexcitation for small damping.Fig. 4 shows the time variation of the field in the hard layerfor a position further downtrack (away from the pole tip). Theresults clearly show that further downtrack, a larger percentageof the field is composed of high frequency modes as comparedto the case near the trailing edge.Fig. 5 plots the standard deviation versus downtrack position.The result under the pole tip is complicated and depends on thewindow size. Beyond the pole tip the standard deviation then de-creases, but still more slowly than the decrease in the absolutefield magnitude generated from the pole tip as will be shownlater. Fig. 5 also shows the 10 nm discretization case with andwithout an SUL. The absence of the SUL decreases the standarddeviation because a smaller percentage of the solid angle con-tains pole tip or SUL excited spins.Fig. 6 plots the standard deviation relative to the mean fieldversus the downtrack position. We see that without an SUL theamplitude of the field variation scales with the field. With anSUL, however, the field variation increases relative to the fieldBOERNER et al.: EFFECT OF DAMPING ON THE TIME VARIATION OF FIELDS PRODUCED BY A SMALL POLE TIP 2373Fig. 6. Normalized standard deviation of field.further from the pole tip. This is believed to be due to excitationsin the SUL which are not localized directly underneath the pole.One would expect significant ringing in the SUL due to fast re-versal, and this would give a significant contribution to the fluc-tuations in the field. Including a larger region of the SUL may re-sult in a reduction of the field variation because the excitationsin the SUL would no longer be confined to a fairly small region.We will not discuss results of parameter variations with a10 nm discretization in any detail but point out several observa-tions obtained using this discretization. A relatively small effectwas observed due to crystalline anisotropy in a soft material overa fairly large range. This would appear reasonable since magne-tostatic fields generated near the edges and corners would dom-inate crystalline anistropy. Also with a 10 nm discretization asmall change in the standard deviation relative to the mean wasobserved over a fairly limited range of head to media spacings.IV. DISCUSSIONWe have studied the fluctuations in the field from a pole tip pro-duced by high frequency magnetization fluctuations. The charac-teristic time for damping is inversely proportional to the dampingparameter. For our case this characteristic time is longer than thedriving field rise time and we are able to excite high frequencymodes. It was found that the results were strongly dependent onthe discretization. From an exchange length argument one wouldexpect a 5 nm discretization to be small enough to describe the re-versal process fairly accurately, however, smaller discretizationallows higher frequency modes to be excited [9], but it is not yetclear how significant this will be for the time variation of the field.Parallel models which scale better due to how they calculate themagnetostatic interaction will allow more accurate examinationof the effects of smaller discretization and larger head structures[10]. In the long term, multilength scale models which allow oneto study the effect of very small discretization cells [11] may be-come necessary.But how important is the field variation on noise due to play-back of recorded transitions? Simple slope models might sug-gest the possibility of a nontrivial contribution from this fieldvariation. But because the spins are not responding instanta-neously to the recording field, the effect on noise is expectedto be much smaller. The model used is capable of including thehard layer, but for simplicity of examining the effects shown inthis paper it was not included. To accurately model the effectof the hard layer, the hard layer needs to be included self-con-sistently and if performing micromagnetic simulations one willprobably need to run enough cases to understand the statisticsdue to variation in the media conditions present at each recordedtransition.V. CONCLUSIONThe amplitude of higher frequency oscillations in the fieldfrom a pole tip and SUL was characterized in terms of effec-tive damping parameters. A similar study can be done for otherstructures. This suggests a way to estimate effective dampingparameters through measurements of variation in the magneto-static field near test structures after reversal.Higher frequency modes imposed on the typically assumedsmooth time varying field from modeled pole tips was observed.The amplitude of the higher frequency modes increased with de-creased damping parameter. It was seen that an appropriate dis-cretization was necessary to avoid overestimating the amplitudeof the field variation. The field variation relative to the meanfield increases further downtrack, while the absolute variationdecreases further downtrack.REFERENCES[1] V. L. Safonov and H. N. Bertram, “Magnetization reversal as a nonlinearmultimode process,” J. Appl. Phys., vol. 85, pp. 5072–5074, 1999.[2] E. D. Boerner, H. N. Bertram, and H. Suhl, “Dynamic relaxation in thinfilms,” J. Appl. Phys., vol. 87, pp. 5389–5391, 2000.[3] K. Z. Gao and H. N. Bertram, “Write field analysis in perpendicularrecording using three-dimensional micromagnetic simulation,” J. Appl.Phys., vol. 91, pp. 8369–8371, 2002.[4] J. G. Zhu and D. Z. Bai, “Understanding field rise time and magneticdamping in thin film recording heads,” J. Appl. Phys., vol. 93, pp.6447–6449, 2003.[5] A. Y. Dobin and R. H. Victora, “Intrinsic nonlinear ferromagnetic relax-ation in thin metallic films,” Phys. Rev. Lett., vol. 90, pp. 167–203, 2003.[6] K. Z. Gao and H. N. Bertram, “3D micromagnetic simulation of writefield rise time in perpendicular recording,” IEEE Trans. Magn., vol. 38,pp. 2063–2065, 2002.[7] J. G. Zhu and H. N. Bertram, “Micromagnetic studies of thin metallicfilms,” J. Appl. Phys., vol. 63, pp. 3248–3252, 1988.[8] D. Goll, G. Schutz, and H. Kronmuller, “Critical thickness for high-re-manent single-domain configurations in square ferromagnetic thinplatelets,” Phys. Rev. B, vol. 67, p. 094414, 2003.[9] D. Berkov, “Fast switching of magnetic nanoparticles: Simulation ofthermal noise effects using the Langevin dynamics,” IEEE Trans. Magn.,vol. 38, pp. 2489–2495, 2002.[10] W. Scholz, J. Fidler, T. Schrefl, D. Suess, R. Dittrich, H. Forster, and V.Tsiantos, “Scalable parallel micromagnetic solvers for magnetic nanos-tructures,” Comp. Mat. Sci., vol. 28, pp. 366–383, 2003.[11] V. V. Dobrovitski, M. I. Katsnelson, and B. N. Harmon, “Statisticalcoarse graining as an approach to multilength scale problems in micro-magnetics,” J. Appl. Phys., vol. 93, pp. 6432–6437, 2003.

Effect of damping on the time variation of fields produced by a small pole tip with a soft under layer

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Effect of damping on the time variation of fields produced by a small pole tip with a soft under layer

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