IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 1, JANUARY 2004 337

A Parametric Study of Head–Disk Interface InstabilityDue to Intermolecular Forces

Brian H. Thornton and David B. Bogy, Fellow, IEEE

Abstract—This paper presents a nonlinear dynamic analysisof the head-disk interface by including intermolecular adhesionforces for sub-5-nm flying air-bearing sliders. Experimentalevidence shows that one of the major roadblocks in achievingultralow flying heights is the stability of the head–disk interface.It is found that the inclusion of intermolecular forces betweenthe slider and disk in modeling the head–disk interface leads todynamic instability of the slider. A parametric study is conductedshowing the dependence of stability/instability on the variables.By understanding the effect each parameter has on stability, wecan achieve air-bearing surface and disk morphology systemdesign guidelines. From this study, it is found that the head–diskinterface can become unstable due to intermolecular forces belowa flying height of about 6 nm. However, from the results of theparametric study, it is shown that a head–disk interface can bedesigned such that it maximizes stability, although the instabilitycannot be attenuated completely. By minimizing the intermolec-ular adhesion forces and the flying-height modulation, and bymaximizing the air-bearing stiffness and damping, we achievemaximum stability. Also, it is found that the stiffening effect ofthe air-bearing film increases the stability. The implications ofthis study are that the head-disk interface stability is dramaticallycompromised in the sub-6-nm flying-height regime and that theglide height of “super-smooth” disks will not only be a function ofthe disk’s morphology, but also the intermolecular adhesion forceinduced instability of the slider.

Index Terms—Air bearing, dynamics, head-disk interface, insta-bility, proximity.

I. INTRODUCTION

I N ORDER to achieve a magnetic recording areal density of1 Tb/in , it is expected that the physical spacing between

the media and transducer or flying height (FH) will have to be3.5 nm [1]. For a head–disk interface (HDI) to perform reliably,both tribologically and magnetically, the fluctuations in the FHmust be held to a minimum. One of the roadblocks thus far forrealizing a 3.5-nm FH is the dynamic stability of the HDI. It hasbeen seen experimentally that a slider can transition from stableto unstable proximity flying by decreasing the FH only slightly[2]. Also, it has been widely observed that a slider’s touchdownand takeoff FHs are not equal. This “snapping” effect betweenstability and instability and the difference in a slider’s touch-down and takeoff FHs are evidence of a complicated dynam-

Manuscript received July 1, 2003. This work was supported in part by theIndustry Information Storage Industry Consortium (INSIC) and in part by theComputer Mechanics.

B. H. Thornton was with the Computer Mechanics Laboratory, Universityof California, Berkeley, CA 94720 USA. He is now with Maxtor Corporation,Longmont, CO 80503 USA (e-mail: brian_thornton@maxtor.com).

D. B. Bogy is with the Computer Mechanics Laboratory, University of Cali-fornia, Berkeley, CA 94720 USA (e-mail: dbogy@cml.me.berkeley.edu).

Digital Object Identifier 10.1109/TMAG.2003.821156

ical system when operating in the sub-6-nm FH regime. As theFH is decreased, the interface surface interactions are evidentlyno longer negligible. Two adhesion models have been proposedto account for the interactions between the slider and the disk:one is based on lubricant interacting with the slider causing ameniscus force and the other is based on intermolecular forcesbetween the two intimate surfaces.

Previous publications have studied the effects of lubricant onHDI stability and flying characteristics [3], [4]. Kato et al. usedan equilibrium meniscus force model in simulations to accountfor the dynamic slider-lubricant interactions [4]. However, theiruse of this meniscus force model neglects some very impor-tant assumptions of the model: extremely thin liquid lubricantfilm thickness (less than 15 ) and the kinetic formation ofa meniscus. Generally, lubricant is highly bonded to the disksurface, thus only a fraction of the lubricant layer is availableto behave as a liquid in the formation of a meniscus makinga meniscus more energetically difficult to form. Also, on thetime scale of interest for “bouncing” or unstable proximity ofthe air-bearing slider, the liquid volume required to form themeniscus does not have time to be transported and is far fromthe equilibrium state according to a kinetic meniscus formationmodel [5].

Intermolecular adhesion forces can be extremely large whentwo very flat surfaces come within proximity. In fact, it has beenshown that intermolecular adhesion forces is the mechanism thatallows gecko lizards to “stick” on molecularly smooth surfaces[6]. Therefore, when flying an extremely smooth air-bearingslider over a “super-smooth” disk at ultralow FHs, intermolec-ular forces must be accounted for. Thus far, publications in-vestigating the effect of intermolecular forces on the HDI havebeen based on static analysis [7]–[9]. It has been shown that forair-bearing sliders flying in the sub-5-nm regime, intermolec-ular forces can become important and cause a significant de-crease in static FH [7]. The implications of the intermolecularforces on the dynamic stability of the HDI have recently beenpublished by the authors [10], [11].

In this paper, we present some experimental evidence of theabrupt stable to unstable flying transition and the FH hysteresis,which are measures of instability for the HDI. We also show thateven for nonlubricated disks HDI instability occurs, suggestingthis phenomenon is more likely to be caused by intermolecularforces than by meniscus forces.

By accounting for the intermolecular forces through aLennard–Jones potential and modeling the HDI as a lumpedparameter one-degree-of-freedom (1DOF) model, we haveshown previously that the system becomes highly nonlinear inthe proximity region. Also, it was shown that the dynamics of

0018-9464/04$20.00 © 2004 IEEE

338 IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 1, JANUARY 2004

Fig. 1. Typical experimental results showing the touchdown, takeoff, andhysteresis FH as a function of lubricant thickness.

this nonlinear system are extremely complicated and can evenbe chaotically unstable causing the experimentally observedinstability and FH hysteresis [10], [11]. From a nonlineardynamics analysis with nominal values and from a parametricstudy, the variables implicating the HDI stability/instability arediscussed in this paper including design guidelines to minimizeHDI instability due to intermolecular forces.

II. EXPERIMENTAL RESULTS

It has been observed that when the FH of a slider is graduallyreduced to within proximity of an extremely “super-smooth”disk, the slider can be easily set into unstable high amplitudeoscillations. This transition from stable to unstable proximitycan happen abruptly at FHs greater than the glide height of adisk. This “snapping” effect from stable to unstable flying sug-gests complex dynamics of the HDI system.

It has also been widely observed that as a slider is forcedinto and back out of contact by decreasing and increasing diskspeed or pressure, a FH hysteresis is present (i.e., touchdownFH takeoff FH) [12]. Experiments investigating HDI insta-bilities as a function of the FH were conducted on a TTi T1000spinstand for various sliders and disks while controlling the FHwith the spindle speed of the disk. The sliders’ instability andcontact was initially measured by both LDV and an acousticemission (AE) sensor, however, the LDV was found to be muchmore sensitive than the AE sensor. Therefore, the sliders’ ver-tical motion was measured by a LDV and highpass filtered at60 kHz to obtain air-bearing resonance vibration and slider bodyvibration modes to detect unsteady proximity and contact, re-spectively. This signal was then acquired through a RMS circuitsampled at 4 kHz. It has been observed that the touchdown RPMis lower than the takeoff RPM or the touchdown height (TDH)is less than the takeoff height (TOH). This difference in RPM orFH is what constitutes this hysteresis (TOH–TDH). Several setsof experiments were conducted using four different subambientpressure pico sliders and a set of disks with varying lubricantthickness. Two types of disks were used in this experiment: B2

Fig. 2. FH hysteresis as a function of lubricant thickness for four differentsubambient pico sliders.

Fig. 3. Free body diagram of the forces acting on the slider body while inproximity or contact with the disk.

with nm and B4 with nm both with glideheights of 2 to 4 nm. The disks were all processed in exactly thesame manner with the only variation being the lubricant thick-ness: 0 (not lubricated), 8, 12, 16, and 20 . The lubricant isa perfluoropolyether (PFPE) with a high bonding ability to thedisk of approximately 80%. For every test, new samples wereused so as to not affect the experimental results by lubricantpickup on the slider, wear, and other factors. Fig. 1 shows an ex-ample of the experimentally measured touchdown, takeoff, andFH hysteresis ( FH) as a function of lubricant thickness. Fig. 2summarizes the experimental results for sliders 1–4. The graphshow the hysteresis RPMs (TO–TD) as a function of lubricantthickness. It is interesting to notice that for all of the lubricantthicknesses tested, there is no trend in the FH hysteresis as afunction of lubricant thickness. What is common among all thetests is that a FH hysteresis is present for all disks and sliderstested including the nonlubricated disks and that the TO RPMwas always higher than the TD RPM. This FH hysteresis can beused as a measure of instability of the HDI. For example, takethe case of slider 3 flying over the disk with 0 of lubricant. Ifthe slider is flying at any speed between 3500 RPM (TD) and8000 RPM (TO) the slider has the ability to become unstable andremain unstable until the RPM is increased beyond 8000 RPM(TO).

Both the “snapping” effect from steady to unsteady prox-imity flying and the presence of a FH hysteresis are new phe-nomena not well understood. By simulating a quasi-static FHand the touchdown-takeoff process, accounting for all of theforces shown in the free-body diagram in Fig. 3, we would notpredict this “snapping” effect from stable to unstable proximityor the FH hysteresis. Therefore, to explain the above experi-mental observations, it appears that additional forces at the HDIcan no longer be neglected for such low FHs.

THORNTON AND BOGY: PARAMETRIC STUDY OF HEAD–DISK INTERFACE INSTABILITY 339

III. ADHESION FORCES AT THE HDI

With FHs decreasing and the probability of contact in-creasing, a better understanding of the interface interactionsare becoming more important in developing a reliable HDI.Also, with the intimate surfaces of the slider and disk becomingextremely smooth (i.e., close to atomically smooth) and withthe presence of a thin layer of lubricant on the disk surface,the interface interactions become very complicated. Generallythe interface is a diamond-like carbon (DLC) coated slidersurface/air/lubricated disk surface during flying, and a DLCcoated slider surface/lubricated disk surface interface duringcontact. If the disk is not lubricated, the interface would includethe DLC coated disk instead of the lubricant layer. The sourceand nature of the interface forces acting between the slider andthe disk can be very complicated. Such forces can be generatedthrough electrostatic charging, tribocharging, and adhesion.In this paper, we will only consider adhesion forces actingat the interface. At least two types of adhesion forces can begenerated at the HDI: capillary (meniscus) and intermolecular.In order for meniscus forces to be generated, a liquid layermust be present at the interface. In the case of the HDI, theliquid layer would consist of primarily the mobile lubricantand possibly a very thin condensed water vapor layer. Also,the formation of a meniscus force is kinetic, hence, highlytime dependent [5]. It has been shown through experimentsand simulation that the meniscus force is negligible when theslider and lubricant are in contact over a short enough timeperiod and increases to a steady-state value over a time periodon the order of minutes [5], [13]. Under dynamic instability ofthe HDI, the slider oscillates at a frequency of 200–300 kHzallowing the slider to be in contact with the lubricant layer forless than 800 ns; far too short to form a measurable meniscusforce as predicted from a kinetic meniscus formation modeland previous experimental results. Also, for the high velocityvibration of the slider under unstable proximity, it is stillunknown if the lubricant behaves as a liquid or a solid whenthe slider impacts the lubricant. Our experimental results agreewith the above analysis. If meniscus forces were partiallythe cause of the additional interface forces, then we wouldexpect the FH hysteresis to increase as the lubricant thicknessincreases, and little or no FH hysteresis should exist for aninterface without lubricant. Our experimental results, shown inFig. 2, show no clear trend in the FH hysteresis with increasinglubricant thickness and that a FH hysteresis is present even foran interface without lubricant.

Other lubricant interactions could possibly cause new dy-namic HDI phenomena; however, the above experimental re-sults showed very little correlation between a meniscus force ef-fect and instability. For the following analysis, the contributionof adhesion due to meniscus formation under the unsteady prox-imity regime seems unlikely and adhesion due to intermolecularforces, which is time independent for unsteady proximity of theHDI, is considered to be the sole contributor to adhesion. To getan idea of the magnitude of the adhesion force generated by in-termolecular forces, we focus on a particular system. For a flatarea, m (approximate area of the alumina at thetrailing edge of a slider) placed parallel to a flat disk surface,

Fig. 4. Intermolecular adhesion force as a function of spacing.

Fig. 5. Schematic of the 1DOF nonlinear HDI model.

the van der Waals intermolecular adhesion force as a functionof separation distance is [14]

(1)

where is the Hamaker constant assumed to have a valuebetween 0.4–4 10 J for condensed phases across air orvacuum [14]. Fig. 4 shows the adhesion force as a functionof separation distance for the range of Hamaker constantsgiven above. It is seen that at a separation distance of 3 nm,the adhesion force can range from 0.12 to 1.2 g, which isquite significant at the HDI. This example does not take intoaccount the slider’s attitude, crown, camber, and twist orroughness effects. In the following analysis, we account for theslider geometry parameters and will comment on the effect ofslider/disk roughness in the discussion section.

IV. HDI MODEL

This HDI model is based on a nonlinear lumped parametersingle degree-of-freedom system as described in detail by theauthors in [10], [11]. The schematic of the model is shownin Fig. 5 where is the slider mass, is the disk forcing,

is the adhesion force modeled bya Lennard–Jones potential and and are the air-bearing stiffness and damping, respectively. Due to the depen-dency of the forces on spacing , the equation of motion be-comes highly nonlinear. The nominal values listed in Table Iwere obtained for a pico size slider [10], [11].

340 IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 1, JANUARY 2004

TABLE INOMINAL VALUES USED IN THE 1DOF MODEL OBTAINED FOR A PICO SLIDER

Fig. 6. Bifurcation plot showing equilibria FH, FH , as a function of thesteady-state FH, FH : (-) stable, (- -) unstable.

V. PARAMETRIC STUDY

The 1DOF system used to simulate the HDI is greatly simpli-fied to give an understanding of the effects of adding intermolec-ular forces in the system and to show how certain parametersaffect HDI dynamic stability. However, due to the assumptionsmade in reducing the HDI to a 1DOF system, the results mustbe viewed as merely qualitative. It is desired to make the HDIas stable as possible, and previously it was shown that stabilitycan be highly compromised when flying in the sub-6-nm regimedue to the presence of intermolecular forces [10], [11].

It was shown that the slider has the ability to become unstablewhen multiple equilibria exist according to the bifurcation plotshown in Fig. 6 [10], [11]. Therefore, if it were possible to ex-clude this regime of multiple equilibria, the slider system dy-namics would be much simplified, and not exhibit instabilityand a FH hysteresis due to intermolecular forces. However, theinclusion of the intermolecular forces in the modeling will al-ways predict this regime. The bifurcation plot in Fig. 6 is usefulin visualizing the regime where multiple equilibria exist, andthe model elements controlling the location and length of thisregime are both the intermolecular and the air-bearing forces.

A. Intermolecular Force

The cause of the complicated dynamics of this systemstems from the intermolecular force. By simply scaling theintermolecular force, we obtain the bifurcation plots as shownin Fig. 7, which clearly illustrates its effect on HDI stability.It is seen that by decreasing the intermolecular force toone-fourth and one-half its nominal value, the multiple equi-libria regime shrinks from FH nm (nominal) to

FH nm and FH nm, respectively.These decreases result in much smaller FH regimes wherethe system has the ability to become unstable. On the other

Fig. 7. Bifurcation plot showing equilibria FH as a function of the steady-stateFH as the intermolecular force amplitude is varied: (-) stable, (- -) unstable.

(a)

(b)

Fig. 8. Slider and disk displacement at a FH of 3 nm with (a) F =

half the nominal and (b) F = nominal.

hand, by increasing the intermolecular force by two timesits nominal value, the multiple equilibria regime increases to

FH nm. Fig. 8 presents plots of the slider’smotion flying over a measured disk topography at a FHof 3 nm for two different amplitudes of the intermolecularforce. It is seen that as the intermolecular force increases, sodoes the instability of the HDI. Fig. 9 shows the TD–TO FHhysteresis simulation results as a function of intermolecularforce amplitude. It is seen that as the intermolecular force isincreases, so does the FH hysteresis.

Even though the intermolecular force cannot be attenuatedcompletely, there are ways to reduce its effect. Decreasing theeffective slider area within proximity of the disk is the most ef-fective method [recall (1)]. This reduction in area can come fromtexturing the ABS, through design of the ABS rails, form factor

THORNTON AND BOGY: PARAMETRIC STUDY OF HEAD–DISK INTERFACE INSTABILITY 341

Fig. 9. FH hysteresis (�FH) as a function of varying the intermolecular force,air-bearing stiffness, and air-bearing damping by a constant multiplier.

Fig. 10. Intermolecular adhesion force as a function of ABS design and formfactor.

(nano, pico, femto, etc.), and by slider attitude. An example ofthis is shown in Fig. 10, where the adhesion force is shown fortwo different ABS designs in two form factors at two differentpitch angles. It is seen, as the pitch increases and the rear-padarea decreases, the intermolecular force decreases. By simplydecreasing the rear ABS pad area and increasing the pitch angle,the adhesion force decreases; however, for manufacturability,flyability, stability, and other design criteria, the rear ABS padhas to have certain minimum dimensions and pitch cannot betoo large. Also, the intermolecular force scales proportionallywith the Hamaker constant. In this analysis, a nominal value of

J was used, however, this value is only approximate.A more accurate value of the Hamaker constant needs to be ob-tained for the HDI. Also, surface chemistry could also changethe Hamaker constant between various lubricants and DLC coat-ings. Some recently published values of the HDI Hamaker con-stant are J with lubricant on the disk surfaceand J without lubricant at the interface [9].These values are close to what has been used in this analysis;therefore, it is expected that the adhesion force for this range ofHamaker constants will always be present below 3.5-nm FHscausing possible HDI instabilities.

B. Air-Bearing Stiffness: Nonlinear

The air-bearing stiffness is another variable affecting the na-ture of multiple equilibria. The air-bearing stiffness is a functionof the ABS design, suspension preload, slider attitude, relative

(a)

(b)

Fig. 11. Slider and disk displacement at a FH of 3 nm with a linearizedair-bearing stiffness of (a) k = quarter the nominal and (b) k = four times thenominal.

disk velocity, and other design parameters. Generally, the lin-earized “vertical” resonant mode of vibration of an air-bearingslider system is between 150 and 400 kHz. A change in the stiff-ness by factors in the range of 0.25–4 changes the linearized res-onant frequency half to twice the nominal value: 108.6–434.4kHz. The bifurcation plots change when the air-bearing stiff-ness is varied similar to the previous section. For 0.25 and 4times the nominal stiffness, the FH regime of possible insta-bility changes from FH to FHand FH nm, respectively. A series of simulationswas performed at a FH of 3 nm showing how the stiffnessaffects the HDI stability. It is seen from the results shown inFig. 11 that stability increases as the air-bearing stiffness in-creases. Also, the TD–TO FH hysteresis was simulated as afunction of air-bearing stiffness, and the results are shown inFig. 9. The trend between the FH hysteresis and air-bearingstiffness does not appear to be monotonic. This is due to thecomplex disk forcing function and the varying air-bearing res-onant frequency as the stiffness changes. The disk topographyfrequency spectra is not uniform across the frequency spectrum,and at different resonant frequencies, the disk affects resonancedifferently. However, there is an overall decreasing trend of theFH hysteresis as the stiffness is increased.

C. Air-Bearing Stiffness: Linear

If the air-bearing stiffness were linear and not a power-hard-ening nonlinear spring, the bifurcation plot would be affected aswould be the stability. For a linear air-bearing stiffness equal tothe linearized stiffness of the nonlinear air bearing the unstableregime extends from FH nm to FH

nm. By increasing the extent of the unstable regime, weknow that the stability of the HDI would be less. We concludethat the power-stiffening air film of an actual air bearing is ex-tremely beneficial in increasing the stability of the HDI.

342 IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 1, JANUARY 2004

(a)

(b)

Fig. 12. Slider and disk displacement at a FH of 3.4 nm with an air-bearingdamping of (a) c = half the nominal, (b) c = nominal, and (c) c = twice thenominal.

D. Air-Bearing Damping

As with the air-bearing stiffness, air-bearing damping isalso a function of many parameters. Generally, the linearized“vertical” mode damping is between 1% to 5% of criticaldamping. In the previous two sections the bifurcation plotswere used to show the degree of instability. On the other hand,air-bearing damping does not change the bifurcation plots. Innonlinear systems, generally, more damping enhances stability.Indeed, we find similar results here. Fig. 12 presents the effectof damping on slider instability at a FH of 3.4 nm as thedamping is varied from 0.46% to 3.64%. It clearly shows thatthe higher the damping, the more stable the HDI becomes. Also,the dependence of the FH hysteresis on damping as determinedby TD–TO simulations is summarized in Fig. 9, which showsthat the FH hysteresis decreases as the damping is increased.

E. Disk Topography

Disk topographies can vary substantially depending onsubstrate material, texturing, and other process conditions. Theforcing and initial conditions of nonlinear systems of the typedescribed here are the most sensitive variables to their chaoticnature that leads to the unstable oscillations. When the HDImodel exhibits a double-well potential, chaotic oscillations canarise even when it is forced by a single harmonic excitation.Fig. 13 shows a plot of single-frequency disk forcing amplitude,

, where the slider steady-state motion becomes unstableversus disk forcing frequency, , whereat initial conditions of (FH, velocity) nm mm/sat a FH nm. Above the curve shown in Fig. 13, theslider’s response is unstable and below it, the response in stablefor a single-frequency excitation. It is observed that the mostsensitive forcing frequency is around the systems linearizedresonant frequency of approximately 175 kHz. Unfortunately atechnique such as superposition cannot be used to extend theresults in Fig. 13 to the complicated disk forcing by an actualdisk. Fig. 14 compares the TD–TO FH hysteresis simulationresults for two measured disk topographies. It is observed that

Fig. 13. Stable-to-unstable boundary for single harmonic disk forcing.

(a)

(b)

Fig. 14. TD–TO simulations flying over disks (a) A and (b) B.

as the FH transitions from 12.65 to 4.65 to 12.65 nm, disk Bforces the HDI to transition into unstable slider oscillationswhile the forcing of disk A is too small at these FH to tran-sition the slider into unstable oscillations. This result suggeststhat the greater disk topography induced flying-height modula-tion (FHM), the higher FH values induce HDI instability. Byjust varying the amplitude of disk A, another parametric studyis performed, and the results are presented in Fig. 15, whichshows the TD–TO FH hysteresis simulations for amplitudemultiples of 0.25 to 1.75 times its original topography. It isobserved that as the disk topography amplitude is increased,the FH hysteresis remains relatively constant at FH 1 nm,but the unstable response amplitude increases.

VI. DISCUSSION

Experimental evidence of low FH slider instabilities is ev-ident from two effects: 1) the “snapping” effect from stable tointermittently unstable and further to indefinitely unstable prox-imity and 2) the presence of the FH hysteresis. Adhesion forcesdue to capillary (meniscus) effects appear to unlikely be thecause of these instabilities due the short time duration the slideris in contact with the lubricant film. Also, the experimental FHhysteresis results showed no dependence on lubricant thickness,

THORNTON AND BOGY: PARAMETRIC STUDY OF HEAD–DISK INTERFACE INSTABILITY 343

(a) (b)

(c) (d)

Fig. 15. TD–TO simulations flying over disk A with the amplitude multipliedby (a) 0.25, and (b) 0.5, (c) 1, and (d) 1.75.

for the thickness range tested. On the other hand, the time in-dependent intermolecular adhesion force was shown to be sig-nificant when a slider and disk come within proximity of eachother. The Lennard–Jones model was used to incorporate addi-tional adhesion and repulsion forces into the CML Static AirBearing Simulation Code solutions and into a simple lumpedparameter 1DOF model. The 1DOF model was used for inves-tigating the experimentally observed nonlinear dynamics asso-ciated with the HDI. It was shown from bifurcation plots of thesystem, that as the FH approaches sub-6-nm, multiple equilibriaexist. Also, for lower FH, the intermolecular force overcomesthe air-bearing load capacity and the slider “snaps” down ontothe disk. From a static analysis, one would expect that the onlyeffect caused by intermolecular forces are at low FHs wouldbe a static spacing loss, and by further decreasing the FH, theintermolecular forces would overcome the air-bearing load ca-pacity. However, a much greater implication arises when in-cluding the intermolecular force that has not been previouslyaddressed—that of dynamic instability. It was shown that thepossibility of the HDI becoming dynamically unstable is re-stricted to a regime where multiple equilibria exist, which ex-tends into FHs much higher than those resulting from static anal-ysis. The dynamics associated with this double-well potentialsystem can be quite complicated when the system is forced. Thechaotic characteristic of the system with a double-well potentialis what causes the HDI instability due to intermolecular forces.

These results imply that the HDI has a fundamental lowerlimit of FH at which the slider remains stable. This lower limitis a function of not only the disk morphology but also the ABSdesign and slider attitude. It was shown by a parametric studythat the FH at which instability occurs as well as the severityof the oscillations change with the parameters. The effect of

the parameters discussed must be understood to obtain a stableHDI design when flying extremely low. Also, it was shownthat the power-stiffening feature of an air bearing increases theHDI stability. In order of importance, we found that the fol-lowing parameters can be adjusted to obtain maximum HDI sta-bility: 1) the intermolecular force should be reduced; 2) the diskmorphology and slider should be optimized to produce min-imum FHM; 3) air-bearing stiffness should be increased; and4) air-bearing damping should be increased. It was shown for allthe parameter values studied, HDI stability can always be com-promised, however, by considering the findings in this paper,the instability due to intermolecular forces can be minimized.Practically achieving the above requirements will not be trivialand also, they may not be necessarily achievable by a tradi-tional-style air-bearing design.

VII. CONCLUSION

Experimentally, it is observed that as a slider flies withinproximity of the disk HDI dynamic stability is lost. Additionalforces due to capillary and intermolecular adhesion were con-sidered. Due to the kinetic formation of a meniscus and the ex-perimental results presented, we concluded that meniscus forcesneed not be considered in the dynamic modeling of the HDI. Anonlinear dynamic analysis of a modeled HDI incorporating in-termolecular forces revealed a new kind of dynamics that cannotbe captured by static analysis. By analyzing the system’s equi-libria and stability, it was found that multiple equilibria existin the sub-6-nm FH regime associated with a double-well po-tential. Within this regime, the slider’s motion can be stable orchaotically unstable when it is externally forced by a disk to-pography. From the analytical and numerical analysis presentedpreviously, the experimentally measured FH hysteresis, the in-termittent slider instability, and the abrupt transition betweenstable and unstable proximity could be explained. A parametricstudy was used here to show how the variables affect HDI sta-bility. Also, the effect of the power-hardening air-bearing stiff-ness was shown to be beneficial in increasing HDI stability. Byoptimizing the parameters such as the air-bearing design andthe disk morphology, the stability of the HDI can be improved.However, for practical values of the parameters, it is found thatinstability is likely to occur when flying below 6 nm. Fromthese results, we are forced to conclude that there maybe a fun-damental lower FH limit for a given slider–disk combination,below which the slider would not be able to fly due to HDI dy-namic instability caused by intermolecular adhesion forces.

ACKNOWLEDGMENT

The authors would like to thank R. Mai for aiding in some ofthe experiments.

REFERENCES

[1] R. Wood, “The feasibility of magnetic recording at 1 terabit per squareinch,” IEEE Trans. Magn., vol. 36, pp. 36–42, Jan. 2000.

[2] B. H. Thornton and D. B. Bogy, “Nonlinear aspects of air-bearing mod-eling and dynamic spacing modulation in sub-5-nm air bearings for harddisk drives,” IEEE Trans. Magn, vol. 39, pp. 722–728, Mar. 2003.

344 IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 1, JANUARY 2004

[3] X. Ma, D. Kuo, J. Chen, H. Tang, and J. Gui, “Effect of lubricant onflyability and read-write performance in the ultra-low flying regime,”in Proceedings of the Symposium on Interface Tribology Toward 100Gb/in , vol. 10, ASME Tribology, C. S. Bhatia, A. A. Polycarpou, andA. Menon, Eds., Seattle, WA, Oct. 2000, pp. 27–34.

[4] T. Kato, S. Watanabe, and H. Matsuoka, “Dynamic characteristics of anin-contact headslider considering meniscus force: Part 1—formulationand application to the disk with sinusoidal undulation,” Trans. ASME J.Tribol., vol. 122, pp. 633–638, July 2000.

[5] C. Gao and B. Bhushan, “Tribological performance of magneticthin-film glass disks: Its relation to surface roughness and lubricantstructure and its thickness,” Wear, vol. 90, pp. 60–75, 1995.

[6] K. Autumn, M. Sitti, A. M. Peattie, W. Hansen, S. Sponberg, Y. A. Liang,T. Kenny, R. Fearing, J. N. Israelachvili, and R. J. Full, “Evidence forvan der Waals adhesion in gecko setae,” Proc. Nat. Acad. Sci., vol. 99,no. 19, pp. 12 252–12 256, 2002.

[7] L. Wu and D. B. Bogy, “Effect of the intermolecular forces on the flyingattitude of sub-5-nm flying height air bearing sliders in hard disk drives,”Trans. ASME J. Tribol., vol. 124, pp. 562–567, July 2002.

[8] J. H. Li, B. Liu, W. Hua, and Y. S. Ma, “Effects of intermolecular forceson deep sub-10-nm spaced sliders,” IEEE Trans. Magn, vol. 38, pp.2141–2143, Sept. 2002.

[9] B. Zhang and A. Nakajima, “Possibility of surface force effect inslider air bearings of 100 Gbit/in hard disks,” Tribol. Int., vol. 36, pp.291–296, 2003.

[10] B. H. Thornton and D. B. Bogy, “Head–disk interface dynamic insta-bility due to intermolecular forces,” IEEE Trans. Magn., to be published.

[11] B. H. Thornton, “Head-disk interface dynamics of ultra-low flying airbearing sliders for hard-disk drive application,” Ph.D. dissertation, Univ.California, Berkeley, 2003.

[12] R. H. Wang, V. Raman, and U. V. Nayak, “Head-disk interface issues fornear contact recording,” in Proceedings of the Symposium on Nanotri-bology and Nanotechnology for 1 Tbit/in , vol. 11, ASME Tribilogy, A.A. Polycarpou and C. Singh Bhatia, Eds., San Francisco, CA, 2001, pp.37–43.

[13] N. V. Gitis and L. Volpe, “Nature of static friction time dependence,” J.Phys. D, Appl. Phys., vol. 25, pp. 605–612, 1992.

[14] J. N. Israelachvili, Intermolecular and Surface Forces, 2nd ed. SanDeigo, CA: Academic, 1992.

[15] S. H. Strogatz, Nonlinear Dynamics and Chaos. Cambridge, U.K.:Perseus, 1994.

[16] L. N. Virgin, Introduction to Experimental Nonlinear Dynamics: A caseStudy in Mechanical Vibration. Cambridge, U.K.: Cambridge Univ.Press, 2000.

[17] F. C. Moon and P. J. Holmes, “Magnetoelastic strange attractor,” J.Sound Vib., vol. 65, pp. 275–296, 1979.

[18] P. J. Holmes and F. C. Moon, “Strange attractors and chaos in nonlinearmechanics,” ASME J. Appl. Mech., vol. 50, pp. 1021–1032, 1983.

[19] S. I. Lee, W. Howell, A. Raman, and R. Reiferberger, “Nonlinear dy-namics of mircocantilevers in tapping mode atomic force microscopy:a comparison between theory and experiment,” Phys. Rev. B, Condens.Matter, vol. 66, p. 115 409, 2002.