Effect of horizontal magnetization reversal of the tips on magneticforce microscopy images

Alexander Alekseev a,b,n, Anatoliy Popkov c, Andrey Shubin b, Feodor Pudonin d,Nikolay Djuzhev c

a Materials and Condensed Matter Physics, School of Physics and Astronomy, University of Glasgow, Room 413, Kelvin Building, G12 8QQ Glasgow, UKb NT-MDT Co, Zelenograd, 124482 Moscow, Russiac Moscow Institute for Electronic Engineering, 124482 Moscow, Russiad Lebedev Physical Institute RAS, 119991 Moscow, RussiaLebedev Physical Institute RAS, 119991 Moscow, Russia

a r t i c l e i n f o

Article history:Received 21 May 2012Received in revised form4 July 2013Accepted 8 August 2013

Keywords:Magnetic force microscopyMagnetic probeMagnetization reversal

a b s t r a c t

The effect of magnetization reversal of magnetic force microscope (MFM) tips based on low coercivethin-films on MFM images has been studied both experimentally and theoretically. By analyzing theMFM images obtained on structures with high magnetic stray fields we show that during the imagingprocess the magnetic state of the probe is modified anisotropically: the horizontal component of themagnetization follows the external field, whereas the vertical component of the magnetization staysalmost constant. The observed complex magnetic behavior of the tip is explained theoretically based onthe shape anisotropy of the tip. The obtained results are important for interpretation of MFM images ofstructures with high magnetic moment. Moreover, these results can be used for characterization of bothlaboratory-made and commercially available MFM tips.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Magnetic force microscopy (MFM) has become in the last twodecades a versatile tool for high resolution magnetic imaging[1–4]. MFM images with a resolution down to 30 nm are routinelyobtained at ambient conditions with commercially available thin-film magnetic probing tips, whereas a resolution below 10 nmwith advanced tips has been reported [5]. Phase- and amplitude-detecting techniques are mostly used in practice for MFM imagingbecause of their high sensitivity and stability [2–9]. These techni-ques make use of either the phase or amplitude of the oscillationsof the MFM tip as a signal to characterize the magnetic field of thesample. Since these values also depend on the magnetic state ofthe tip, the simplest approach of MFM is to avoid any changes ofthe magnetic state of the tip during scanning by employing tipswith magnetically hard coatings. However, even such coatings donot guarantee the stability of the magnetization of the tip, ifsamples with high fields are studied. In this case a reconstructionof the distribution of the magnetization inside the studied sample

based on MFM images is not possible without knowledge of themagnetic properties of the tip [10]. It is extremely difficult tocharacterize independently the magnetic structure of the tipduring the scanning process. Therefore, attempts to quantify theproperties of the MFM tips are based on imaging a well definedcurrent-carrying micro-source of the magnetic field (micro-ringsor parallel micro-wires) [11–16] or standard samples with knownmagnetic structures such as pieces of a hard disk [7,16–21] and arewidely used for characterization of the magnetic structure of MFMtips. Using this approach hysteresis loops of the active magneticvolume for different tips were obtained experimentally [12,14–16].The material of the magnetic coating, its thickness, and the initialdomain structure inside the tips are the most important para-meters determining the magnetic properties of the tips duringimaging [5,14,16,17,22,23].

Standard analysis of MFM images is based on the simplifiedmodel of the magnetically hard tip considered as an effectivemagnetic dipole. Our results presented in this paper show that insome cases the simple dipole model of the probe has to besignificantly improved. By comparing the results of numericalcalculations with MFM images obtained on a piece of a hard diskwith a known magnetic structure we demonstrate that the twocomponents of the magnetization of the tip have different mag-netic behavior: the horizontal component of the magnetizationfollows the external field, whereas the vertical component of themagnetization stays almost constant. The obtained results explain

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0304-3991/$ - see front matter & 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.ultramic.2013.08.007

n Corresponding author at: Materials and Condensed Matter Physics, School ofPhysics and Astronomy, University of Glasgow, Room 413, Kelvin Building, G12 8QQGlasgow, UK. Tel.: þ44 141 330 4707; fax: þ44 141 330 4464.

E-mail addresses: alalrus@gmail.com (A. Alekseev),afpopkov@inbox.ru (A. Popkov), shubin@ntmdt.ru (A. Shubin),pudonin@sci.lebedev.ru (F. Pudonin), djuzhev@unicm.ru (N. Djuzhev).

Ultramicroscopy ∎ (∎∎∎∎) ∎∎∎–∎∎∎

several features of the MFM images, often observed with bothlaboratory-made and commercially available thin-film MFM tipswith relatively low coercivity. Our results can therefore be usefulfor preliminary characterization of the prepared tips and properinterpretation of data obtained on samples with high magneticstray field.

2. Materials and methods

The MFM measurements were carried out with SPM NTEGRAAura (NT-MDT Co, Russia). Silicon cantilevers NSG11 (NT-MDT Co,Russia) with a conical tip covered by 50 nm thick Co90Ni10 filmwere used for imaging. The films were deposited using the RF-sputtering system Sputron-2 (Balzers) at Ar-plasma pressure10�3 mbar and RF-power of 700 W, resulting in a deposition rateof 0.07 nm/s. The direction of deposition was parallel to the tipaxis. Magneto-optic Kerr effect (MOKE) analysis of the magneticproperties of the CoNi film (see Fig. 1) on the lever has shown thatthe film is in-plane magnetized, having a coercivity of 4 kA/m.A samarium–cobalt magnet used for tip magnetization produces amagnetic field of 40 kA/m. A two-pass scanning technique wasemployed with a peak-to-peak amplitude of free cantilever vibra-tions of around 20 nm during the first pass and 10 nm during thesecond pass. The set-point amplitude during the first pass was10 nm. The total tip-sample distance Δz during the second pass isequal to sum of the pre-set lift height and set-point amplitude ofthe first pass.

The magnetic properties of the probing tip were studied on atest sample, which was a piece of a hard disk with the in-planemagnetization (Fireball SE, 3.2 GB, Quantum, Singapore) having amaximum data density of 50 kfci. Details of the magnetic structureof such disks can be found elsewhere [2,3,7,16]. In the followingdiscussion, the x-axis defines the direction along the track of thehard disk, and the z-axis is perpendicular to the sample surface asshown in Fig. 2. The phase-detecting MFM used in the presentwork is based on measurements of the phase shift of cantileveroscillations in the vicinity of the sample surface. With our setup,regions of the phase image with phase values below 901 corre-spond to attractive forces between the tip and the sample, whileregions with phase values above 901 correspond to repulsiveforces. In real measurements the phase of the freely oscillatingcantilever may be slightly different than 901. We assume that thetip axis coincides with the z-axis (i.e. oscillations of the cantileverare vertical).

3. Results and discussion

The magnetic tip was initially magnetized by the externalmagnet along the z-axis and the results of phase shift measure-ments with such a tip are shown in Fig. 3(a). The cross-sections inFig. 3 are average MFM profiles along the track direction (i.e. thex-axis) and the observed contrast in the phase-shift, Δφ is relatedto changes in the second derivative of the sample field, which for atip magnetized along z is

Δφ¼�ðQ=kÞμ0mz∂2Hz=∂z2 ð1Þwhere Q and k are the cantilever quality factor and the forceconstant, respectively, μ0 is the magnetic constant and m is the tipmagnetic moment [2,7,9]. The negative sign in (1) implies a phasechange from 1801 to 01 when the frequency crosses the resonance.The obtained MFM phase contrast then looks inverted in compar-ison to that of a real oscillator. Images similar to that shown inFig. 3(a) can be found in a variety of papers related to character-ization of both magnetic media and tip. Only bit transition regions

Fig. 1. Hysteresis loop of Co90Ni10 alloy recorded using the Magneto-OpticalKerr-Effect technique on the lever of magnetic probe.

Fig. 2. Sketch of the stray fields of the sample and magnetization reversal of theprobing tip magnetized under some angle with respect to the z axis.

Fig. 3. Evolution of the MFM images recorded using tips pre-magnetized by anexternal field applied at different angles with respect to the tip axis as indicated byarrows: (a) 01, (b) 201, (c) 451, (d) 701 and (e) 901. Left panels: MFM imagesthemselves. Right panels: corresponding average cross-sections taken along track.The dashed lines indicate the level of a zero force gradient (Δφ¼ 01), Δz¼20 nm.

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are visible in Fig. 3a, as ∂2Hz=∂z2 has its strong maximum near thedomain edges (see Fig. 2). The amplitudes of the repulsive andattractive forces (considered as the differences of the maximumand minimum values in Fig. 3(a) with respect to the meanbackground value, respectively) are approximately the same,which should be if almost no magnetic reversal occurs duringscanning, since the vectors of magnetic fields at two adjacent bittransitions are antiparallel to each other.

As the next step, the cantilever was magnetized at an angleabout 201 with respect to its axis. The results of the measurementswith the tip magnetized at such a way are presented in Fig. 3(b),clearly illustrating a strong asymmetry between attraction andrepulsion regions; the amplitude of repulsion being much smallerthan that of attraction. Further increase of the magnetization angle(up to �451) results in a practically undetectable repulsion (seeFig. 3(c)), whereas only an attraction is observed in the image.Larger angles (�701) result in images with regions correspondingto attraction only. Moreover, bit transitions demonstrating repul-sive forces for tips with almost vertical magnetization, show inthis case attractive, albeit weaker forces in Fig. 3(d). The horizontalmagnetization of the tip leads to an image with attractive forces ofsimilar strength for all bit transition regions (see Fig. 3(e)). It isimportant to note that all of the above described images arecompletely reproducible for a given tip. Thus, one can concludethat a particular domain structure created by the magnetization inthe field of the external magnet is stable [7,20,23,24]. The exactdomain structure of MFM probes is still unknown and requiresadditional investigations. In particular, in [23] the closure domainstructure in the tip has been proposed and discussed. We canassume the presence of similar structures inside the probes usedin our experiments.

Let us now discuss the symmetry of the images with respect tomagnetization reversal of the tip. Fig. 4 demonstrates that reversalof the magnetizing field from the direction parallel to the z-axis todirection antiparallel to it leads to inversion of the contrast of theimage. On the contrary, reversal of the magnetizing field along thex-axis or even rotation of the field in the xy-plane does not changethe image at all. To understand qualitatively this behavior let usgeneralize Eq. (1) in the case of an arbitrary orientation of the tipmagnetization [2,7]:

Δφ¼�ðQ=kÞμ0 ∑i ¼ x;y;z

mi∂2Hi=∂z2 ð2Þ

As discussed above, the vectors of magnetic fields at two adjacentbit transitions are antiparallel to each other, resulting in alternat-ing patterns for the regions with repulsive and attractive forces,provided the z-component of the magnetization is not changingwhen the tip moves from one bit transition to another. Thestability of mz is also corroborated by the inversion of the contrastseen in Fig. 4 when the magnetization direction is reversed. Theattractive forces detected in Fig. 3(e) (i.e., for horizontal orienta-tion of the magnetization) for all bit transitions clearly indicate

that the horizontal component of the magnetization undergoes itsreversal while the tip is scanned from one bit to another. A strongasymmetry between regions of repulsive and attractive forces seenin Fig. 3(b–d) apparently corresponds to the situation, when thez-component of the magnetization is stable during the scan whilethe x-component oscillates, when the tip moves from one bit toanother. Such a behavior is only possible, if tip has a low coercivityin the xy-plane and a high coercivity in the z-direction. Suchanisotropic coercivity can be connected with the shape of the tipresulting in a shape anisotropy with the easy axis along thez-direction. In fact, it is well known [24] that magnetization of athin film along a hard axis takes place softly almost withoutcoercivity, whereas for remagnetization along the easy axis a givencoercive field has to be overcome. Experimentally observedreduced coercitive field of MFM tips for the lateral directions[16] confirms the above consideration.

To confirm further the above scenario, numerical simulationsbased on the profiles of the stray fields of the studied samplesuggested by Rugar et al. [2]. Magnetic properties of the sample inthe y direction were assumed to be uniform, restricting thesimulations by the xz-plane only. This assumption is reasonableas the typical tip size is much smaller than the width of the harddisk track (�3 μm). Following the above model, the magneticproperties of the tip were modeled by an assumption that thevertical component of the magnetization is not changed duringscanning, while the horizontal component of the tip magnetiza-tion is always directed along the corresponding component of thesample stray field, as illustrated in Fig. 2. The MFM response wascalculated as follows:

ΔφpZtip

∑i ¼ x;z

Vimiðxþx′Þ∂2Hiðxþx′Þ=∂z2 !

dx′ ð3Þ

where x determines the position of the tip center, and x′ is theintegration variable over the tip size of 150 nm. Weight coeffi-cients Vx and Vz in (3) are used to take into account the direction ofmagnetization; Vx/Vz can be interpreted as a ratio of volumes withx and z directions of magnetization. Since experimental MFMresults are highly reproducible with respect to prior magnetizationangle, we assume that ratio Vx/Vz is not changing during scanning.It is also assumed that the x-component of the tip magnetizationfollows the field: mx(x)¼χHx(x) with saturation magnetization atMt¼1000 kA/m, where χ is the magnetic susceptibility of the tipin the horizontal direction. At the same time the z-componentstays unchanged: mz(x)¼Mt, as indicated by the arrows in Fig. 2.In terms of [25] it means that in our model, the horizontal tipmagnetization gives susceptibility MFM contrast, while a fixedz-component produces charge MFM contrast. For calculations weused χ¼4, which was estimated from horizontal hysteresis mea-surements for cobalt-coated probe with similar behavior in [16]and a remanent sample magnetization Ms¼500 kA/m. The resultsof simulations for different ratios of Vx/Vz atΔz¼20 nm are shown

Fig. 4. Inversion of MFM contrast caused by the reversal of the vertical magnetization of the tip. Left panels: MFM images. Right panels: average cross-sections. The circles onthe images indicate the same feature of the sample. Δz¼20 nm.

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in Fig. 5. The arrows in Fig. 5 illustrate the orientation of theaverage magnetization in the tip, corresponding to a given ratioVx/Vz. Comparing Figs. 3 and 5 one can conclude that the proposedmodel provides a good agreement with the experimental findings.

Note here that the fine structures observed in MFM which are seenclose to the main maxima are probably due to simplifications usedin the model, for example lack of integration over the tip volume.The Hx and Hz at a tip-sample distance of 20 nm are shown inFig. 6a. One can see from these images that Hx has a minimum inthe center of bit when Hz is approximately zero, and a maximumvalue of Hx is larger than the maximum Hz. The proposed scenarioimplies that maximal Hz does not exceed the axial coercivity of tip,which is realistic if values of Hz in Fig. 6 are compared with axialcoercivity of tips measured in [14,16]. Fig. 6b shows mx changesduring scanning within model described above. Larger values of χlead to a saturation of horizontal magnetization at Mt and then mx

can be approximated by mx(x)¼ Mt sign(Hx(x)). The results ofcalculations in this case will be similar to that shown in Fig. 5.

To demonstrate experimentally the role of reversal of thelateral component of the magnetization during the scanningprocess we have performed additional experiments where theexternal vertical magnetic field, which suppresses the reversal, hasbeen applied during the scan. The results of this study are shownin Fig. 7. It is clearly seen that with increasing field the imagesshow a gradual evolution similar to that observed in Fig. 3(c) and(d), indicating the decreasing role of the reversal. This can beexplained by a decreased ratio of Vx/Vz when an relatively strongexternal field is applied. A similar result has been observed in [16]for cobalt-coated probes when external vertical magnetic field hasnullified the z-component of tip magnetization and a nearlysymmetrical MFM signal becomes highly asymmetric with onlyattraction regions.

Fig. 8 demonstrates the dependence of the MFM signal,obtained by a tip magnetized under an oblique angle with respectto the tip axis, on a tip-sample distance Δz. It is clearly seen that athigher tip-sample distances, the symmetry of the initially asym-metric magnetic signal recovers. Numerical calculations within ourmodel show a similar result (Fig. 9). One can see from Fig. 6a thatthe minimal value of Hx above bit centers is changed only insignif-icantly when Δz increased from 20 to 300 nm, which means thatminimal value of mx above bit center is almost same at bothdistances Δz (Fig. 6b). The observed behavior of magnetic probesis a result of a low coercivity of magnetic coating and high horizontalfield of the sample. In our case the in-plane coercivity of themagnetic coating measured by MOKE (Fig. 1) is significantly smallerthan the minimum value of the horizontal stray field above bit(Fig. 6), which is additional support for the proposed model.

Concluding this paragraph, let us note that tips coated bymagnetically hard alloy such as Co80Cr20 magnetized horizontallyresult in MFM images with alternating contrast, where amplitude ofattractive and repulsive forces is approximately equal [7,16,17,20]

This fact also confirms the importance of magnetization rever-sal during the scanning process of the used small-coercivity CoNitips. We found that not only CoNi alloy, but also some other

Fig. 5. Results of numerical simulation of MFM response for different tip magne-tization directions as indicated and Δz¼20 nm. (a) Vx¼0, Vz¼1 (b) Vx/Vz¼1;(c) Vx/Vz¼5 and (d) Vx¼1, Vz¼0.

Fig. 6. a) Vertical and horizontal components of hard disk stray fields: 1, 2 – Hx

and Hy at Δz¼20 nm; 3, 4 – Hx and Hy at Δz¼300 nm; (b) mx at 1 – Δz¼20 nmand 2 – Δz¼300 nm.

Fig. 7. MFM images recorded using horizontally magnetized tips under influence of the applied vertical field of different strengths as indicated. Left panels: MFM imagesthemselves. Right panels: corresponding cross-sections along the A–A′-line.

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widespread magnetic coatings such as neat Co and sometimesCoCr alloy often lead to similar magnetic tip behavior. Some of thetested tips do not produce symmetrical MFM contrast even aftermagnetization along the tip axis, which means the effectivemagnetic moment of such tips is always tilted with respect tothe tip axis during measurements.

4. Conclusions

Summarizing, the experimental and theoretical results pre-sented here show that samples with strong magnetic stray fieldscause magnetization reversal of the lateral component of themagnetization in MFM tips coated with magnetic alloys withrelatively low coercive fields, while the vertical component ofthe magnetization remains unchanged. This reversal, taking placecontinuously during the scanning heavily modifies the measuredcontrast of the MFM images, resulting in a strong asymmetrybetween the signals corresponding to the attractive and repulsiveforces. The ability of the tip to undergo such an anisotropicreversal strongly depends on the direction of the external fieldused for preliminary magnetization. The obtained results shouldbe used for interpretation of MFM images recorded using bothlaboratory-made and commercial thin-film tips.

Acknowledgments

This work was supported by the EC through the NANOSPIN project(Contract NMP4-CT-2004–013545) and the Ministry of Education andScience of Russian Federation, Projects 14.A18.21.0887, 14.A18.21.1955,

14.B37.21.1090. A. P. acknowledges RFBR grant 13-07-12405. Theauthors would like to thank Prof. S. Demokritov (University ofMunster, Germany) for his help with manuscript preparation,Dr. A. Goryachev (MIET, Russia) for the MOKE measurements.

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Fig. 8. Recovery of MFM signal symmetry at higher Δz. All curves are shifted to 01.The dotted lines approximately correspond to zero force.

Fig. 9. Calculated MFM signal at different Δz.

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