Atomic ordering in nano-layered FePt

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Intermetallics 17 (2009) 907–913

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Intermetallics

journal homepage: www.elsevier .com/locate/ intermet

Atomic ordering in nano-layered FePt

M. Koz1owski a,*, R. Kozubski a, Ch. Goyhenex b, V. Pierron-Bohnes b, M. Rennhofer c, S. Malinov d

a Interdisciplinary Centre for Materials Modelling, M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Krakow, Polandb Institut de Physique et Chimie des Materiaux de Strasbourg, 23, rue du Loess, BP 43, F-67034 Strasbourg, Francec Faculty of Physics, University of Vienna, Strudlhofg. 4, A-1090 Vienna, Austriad School of Mechanical and Aerospace Engineering, Queen’s University Belfast, Stranmillis Road, Belfast BT9 5AH, UK

a r t i c l e i n f o

Article history:Received 7 August 2008Received in revised form26 February 2009Accepted 18 March 2009Available online 21 April 2009

Keywords:A. Magnetic intermetallicsD. Defects: antiphase domainsD. MicrostructureE. Simulations, atomisticE. Simulations, Monte Carlo

* Corresponding author. Tel.: þ48 12 663 57 16; faxE-mail address: [email protected] (M

0966-9795/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.intermet.2009.03.019

a b s t r a c t

Monte Carlo simulation of chemical ordering kinetics in nano-layered L10 AB binary intermetallics wasperformed. The study addressed FePt thin layers considered as a material for ultra-high-density magneticstorage media and revealed metastability of the L10 c-variant superstructure with monoatomic planesparallel to the surface and off-plane easy magnetization. The layers, originally perfectly ordered in ac-variant of the L10 superstructure, showed homogeneous disordering running in parallel with a spon-taneous re-orientation of the monoatomic planes leading to a mosaic microstructure composed of a- andb-L10-variant domains. The domains nucleated heterogeneously on the surface of the layer and grewdiscontinuously inwards its volume. Finally, the domains relaxed towards an equilibrium microstructureof the system. Two ‘‘atomistic-scale’’ processes: (i) homogeneous disordering and (ii) nucleation of thea- and b-L10-variant domains showed characteristic time scales. The same was observed for the domainmicrostructure relaxation. The discontinuous domain growth showed no definite driving force andproceeded due to thermal fluctuations. The above complex structural evolution has recently beenobserved experimentally in epitaxially deposited thin films of FePt.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Properties of L10-ordered FePt intermetallics

The L10-ordered FePt alloy (Fig. 1) due to its high magneto-crystalline anisotropy accompanied with high superstructurestability is perceived as a functional material for future magneticdata storage devices. Both above features provide excellent thermalstability of the magnetization direction [1,2]. There are several newtechnologies that involve L10 FePt: thin layers for improvedconventional hard disc drives [3], or monodisperse FePt nano-particles [4,5] deposited with variety of techniques for patterneddata storage media [6]. Despite the substantial development ofdeposition techniques effective application of the materials stillfaces a number of problems, one of which is that the monodisperseFePt particles show no atomic long-range order [7]. Although L10

ordering occurs on annealing, the treatment causes a parasiticeffect of particle sintering and coalescence [8].

Recent results of both experimental studies and computersimulations are consistent about the fact that in the ordered L10

: þ48 12 633 70 86.. Koz1owski).

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nano-particles or nano-layers free surface causes a decrease of thesuperstructure stability [9–11]. However, there is still an opendiscussion about the atomistic origin of the observed behaviour. Incase of FePt recent MC simulations suggested the explanationeither in terms of surface Pt precipitation [12] or in terms ofsurface-induced disorder [10].

1.2. Previous results of MC simulations of chemical ordering in FePt

Results of Monte Carlo simulations of ‘‘order–order’’ kinetics inthe L10 bulk FePt as well as the preliminary observations of theprocess occurring in the related layers have been presented in ourprevious papers [13–15].

A lot of simulations following the methodology developedpreviously for Ni3Al [16] and applied to the bulk and homogeneouslyL10-ordered FePt seemed to reveal two time scales in the ‘‘order–order’’ kinetics, with a very weak contribution of the short time scale[13]. The simulations recently repeated with averaging the resultsover 128 samples did not confirm the contribution of a fast relaxationcomponent and definitely indicated one single time scale of theprocess. This result corroborates with a Phase-Field analysis [17]showing that only one time scale in the ordering kinetics in FePtcorresponds to homogeneous ordering; the remaining two onesbeing related to phenomena connected with antiphase boundaries.

Fig. 1. L10 unit cell: C A-sublattice, B B-sublattice.

M. Kozłowski et al. / Intermetallics 17 (2009) 907–913908

Preliminary MC simulations [14] addressed chemical ordering inlayered FePt samples limited by (001) free surfaces and initiallyperfectly ordered in the c-variant of L10 (i.e. with (001)-orientedmonoatomic Fe- and Pt-planes, Fig. 1). The configurational energyof the system was evaluated within the Ising model with nearest-neighbour (nn) and next-nearest-neighbour (nnn) pair-interactionenergies (Table 1) calculated for FePt by means of a combination of‘‘ab initio’’ calculations with a ‘‘Cluster Expansion’’ procedure [18].MC simulations of bulk FePt parameterised with these pair-inter-action energies yield the ‘‘order–disorder’’ transition temperatureTt¼ 1580 K [13,14]. It was shown that the homogeneous disorder-ing (generation of dispersed antisite defects) was dominated bya heterogeneous and discontinuous nucleation and growth ofa- and b-variant L10 domains (i.e. the re-orientation of the mon-oatomic planes in perpendicular to the (001) free surface). Thedomains nucleated predominantly (almost exclusively) on the Fesurface and the sharp discontinuous reaction front – i.e. the anti-phase boundary, advanced inward the sample until the opposite Ptsurface of the layer was reached.

Recent analysis of the process in terms of its driving force [15]showed that the L10 c-variant / a(b)-variant transformationwithin the Fe-surface layer of the L10 unit cells (Fig. 2) decreases thesystem configuration energy by

DEConf ¼ s� 4�

V ð1ÞFeFe � V ð1ÞPtPt

�(1)

where s is the number of unit cells at the layer surface.

Table 1Pair-interaction energies for FePt [14]: Vik

(1) nn pair-interactions, Vik(2) nnn pair-

interactions.

i–k Vik(1) [meV] Vik

(2) [meV]

Fe–Fe 11.45 �1.145Fe–Pt �67.05 6.705Pt–Pt 85.63 �8.563

DEConf given by Eq. (1) contains both the energy gain broughtabout by the transformation and the energy loss following from thecreation of the flat c-variant-a(b)-variant antiphase boundary(APB). It is remarkable that it does not depend on the nnn pairinteractions, despite the fact that the nnn interactions were takeninto account during the analysis. According to Table 1 DEConf< 0which explains the selective nucleation of the process on thesurface initially occupied by Fe atoms.

Further advancement of the process by a steady movement ofthe flat APB does not change the configurational energy of thesystem, which drops again only after the APB has reached theopposite Pt free surface.

It is remarkable that the surface-induced L10 c-variant / a(b)-variant transformation predicted here by MC simulations imple-mented with a very simple Ising model of the system has recentlybeen experimentally observed in FePt multilayers by means ofconversion electron Mossbauer spectroscopy (CEMS) [19].

The present paper reports on a detailed analysis of the orderingphenomena in FePt layers revealed by MC simulations of an Isingmodel.

2. Methodology of new simulation studies

A cubic supercell built of 403 fcc unit cells was generated and its256,000 lattice sites were filled with equal numbers NA and NB of Aand B atoms in the way that c-variant L10 superstructure wasformed (Fig. 1). A single vacancy was introduced to the system byemptying one lattice site selected at random. 2-Dimensional peri-odic boundary conditions were then imposed upon the supercell in[100] and [010] directions, so that a 80-atomic-plane-thick layerlimited by two parallel free (001) surfaces was simulated. Possibletetragonal distortion occurring in real L10-ordered binary systemswas neglected.

Three domains were distinguished in the layer:

� the inner (bulk) domain containing 40 inner atomic planes,� two outer (surface) domains built of the 20 first and 20 last

atomic planes.

Previous results [14,15] allowed to expect that the L10

c-variant / a(b)-variant re-orientation front would not reach theinner domain as defined above.

The evolution of atomic configuration in the system was simu-lated allowing the atoms to change their positions exclusively byjumping to nn vacancies. According to the applied Glauber algo-rithm the probability of such a jump was equal to

Pi/j ¼expð � DE=kBTÞ

1þ expð � DE=kBTÞ (2)

where: DE denotes the difference between the configurationalenergies of the system after and before the jump, kB and T areBoltzmann constant and absolute temperature, respectively [21].

An Ising model of the system similar as in the previous work [14]was implemented. A conventional single MC step regarded as a unitMC time consisted of:

- random selection of an atom in the 1st co-ordination shell ofthe vacancy

- execution or suppression of its jump to the vacancy accordingto the probability (2).

Isothermal relaxations of the system configuration alwaysstarting from the state of a perfect c-variant L10 long-range order(LRO) – i.e. the superstructure with monoatomic planes parallel to

Fig. 2. Scheme of an initial stage of L10 c-variant / a(b)-variant transformation in a FePt layer [15] (atoms residing on two nn crystallographic planes are represented bysmall and big circles).

M. Kozłowski et al. / Intermetallics 17 (2009) 907–913 909

the (001)-oriented free surfaces of the layer, were simulated at fourtemperatures below Tt: 800 K, 1000 K, 1200 K and 1400 K.

Monitored was time (MC steps) dependence of the followingparameters:

1. Total configurational energy of the system:

EConf ¼Xi;j;r

NðrÞij VijðrÞ; (3)

where: Nij(r) and Vij

(r) denote the number of i–j atom pairs and i–jpair-interaction energy at a distance r, respectively.

2. Bragg–Williams LRO parameters for particular L10 variants a:

hðtot=bulkÞa ¼ 2

Nðtot=bulkÞPtPta

Nðtot=bulkÞPta

� 1; (4)

where: Nðtot=bulkÞPtPta

denotes the number of Pt atoms on the‘‘right’’ positions in the L10 a-variant: in the entire layer (tot)and in the bulk domain defined above (bulk); Nðtot=bulkÞ

Ptadenotes

the number of the right Pt positions related to the L10 a-variant:in the entire layer (tot) and in the bulk domain (bulk)

hðsurfÞa ¼

�hðtotÞ

a � hðbulkÞa

�þ 1 (5)

0.96

0.98

1.00

c

In view of the equal volumes of the bulk and surface domains ofthe layer the parameter ha

(surf) defined by Eq. (5) accounts forLRO features in the surface domains of the layer without anycontribution of the processes occurring in the ‘‘bulk’’.

3. Pair-correlations of nn Fe- and Pt-atoms (short-range order(SRO) parameters):

CFeFe ¼1

NFe

XNFe

i¼1

NFeFei and CPtPt ¼

1NPt

XNPt

i¼1

NPtPti (6)

where NiFeFe denotes the number of Fe atoms in the 1st co-

ordination shell of the i-th Fe-atom, and NiPtPt respectively the

same for Pt atoms.

The MC-time evolutions of the parameters were averaged over32 identical parallel simulation runs.

0.0 8.0x106 1.6x107 2.4x107

0.94

t [MC steps]

Fig. 3. MC time dependence of simulated hc for the bulk and hc(bulk) for layered FePt at:

800 K (- bulk, , layer); 1000 K (C bulk, B layer); 1200 K (: bulk, 6 layer) and1400 K (; bulk, 7 layer).

3. Results

The MC simulations revealed four processes occurring in theFePt layers:

1. homogeneous disordering (generation of antisite defects).2. nucleation of a- and b-variant L10 domains within the surface

layer of the L10 unit cells.

3. growth of the nucleated a- and b-variant L10 domains inwardthe layer.

4. relaxation of the microstructure of a- and b-variant L10

domains.

3.1. Homogeneous disordering

The process was extracted from the entire transformation bymonitoring the MC time dependence of hc

(bulk) (Fig. 3).As follows from Fig. 3, the hc

(bulk)(t) isothermal relaxationsshowed exactly the same time scale as the ones observed in the bulksamples – i.e. with 3-dimensional periodic boundary conditionsimposed upon the simulated supercell. The hc

(bulk) (t) curves fittedsingle exponentials:

hðbulkÞc ðtÞ � h

ðbulkÞc;eq

hðbulkÞc ðt ¼ 0Þ � hðbulkÞ

c;eq

¼ exp��t

s

�(7)

The resulting values of the relaxation times s and the equilib-rium values hc,eq

(bulk) of the LRO parameters at particular temperaturesare displayed in Table 2.

3.2. Nucleation and growth of L10 a- and b-variant domains

The simulated hc(surf) (t) curves are shown in Fig. 4. The well

visible complex time-scale structure of the curves has been eluci-dated by Laplace-transformations (Fig. 4b) clearly revealing the

Table 2Parameters of the hc

(bulk), hc(surf), CFeFe, CFeFe and the configurational energy EConf relaxations simulated in the FePt layer.

Temperature [K] LRO SRO EConf

hc(bulk) hc

(surf) CFeFe CPtPt

s hc,eq(bulk) s1 s2 hc,eq

(surf) sFe–Fe sPt–Pt s3

1000 5.42� 106 0.994 2.80� 107 1.13� 109 0.899 Too slow process 2.80� 109

1200 2.53� 106 0.980 9.92� 106 1.12� 109 0.881 1.7� 109 5.8� 108 9.93� 108

1400 2.09� 106 0.994 8.04� 106 1.24� 109 0.834 4.2� 108 2.0� 108 3.42� 108

M. Kozłowski et al. / Intermetallics 17 (2009) 907–913910

parallel operation of two relaxation processes. The curves fitted,therefore, weighted sums of two exponentials:

hðsurfÞc ðtÞ � hðsurfÞ

c;eq

hðsurfÞc ðt ¼ 0Þ � h

ðsurfÞc;eq

¼ A� exp�� t

s1

�þ ð1� AÞ � exp

�� t

s2

�

(8)

The results are displayed in Table 2 and indicate that althoughbeing of the same order of magnitude, the rates of the homoge-neous disordering (s) and of the fast component of hc

(surf) (t)relaxation (s1) definitely differ one from each other.

In order to interpret the above result the evolution of the sampleatomic configuration was directly imaged (Fig. 5) in a (010) cross-section and in the Fe-monoatomic (00-1) free surface. After thenumber of MC steps corresponding to s1 the mosaic of a- and b-L10

variant domains covered the entire (00-1) surface (Fig. 5b and c)indicating the completion of the domain nucleation and suggestingthat the fast component of hc

(surf) (t) should be assigned to the L10 a-and b-variant domain nucleation.

Among the two remaining processes observed in the system: (i)L10 a- and b-variant domain growth inward the layer (Fig. 5d–f) and(ii) relaxation of the L10 a- and b-variant microstructure (visible inFig. 5c–e) only the former process may affect the value of hc

(surf).Therefore, the slow component of hc

(surf) (t) should be assigned tothe kinetics of that process and, moreover, the equilibrium value ofhc

(surf) may be rescaled into an average depth of the L10 c-variant /

a(b)-variant re-orientation. As follows from Table 2, the rate of theprocess showed, however, no clear temperature dependence.

The reason of the above curiosity was elucidated by watching MCtime evolution of hc

(surf) and ha(surf) following from a single simulation

run (i.e. without averaging over independent simulation runs)(Fig. 6). The fluctuating ‘‘saturation’’ levels of the parameters reflectthe irregular fluctuating movement of the re-orientation front

0.0 2.0x109 4.0x109

0.85

0.90

0.95

1.00

t [MC steps]

a b

c

(surf)

Fig. 4. (a) MC time dependence of hc(surf) simulated at 800 K (B); 1000 K (,); 1200

(the L10 c-variant-a(b)-variant APB) directly visible in Fig. 5e and f.Specific character of the process is the reason why the analysis of thehc

(surf) (t) curves averaged over independent simulation runs (and,therefore, showing no fluctuations of the ‘‘saturation’’ level) yieldsthe temperature-independent rate of the slow relaxation component(Table 2).

3.3. Relaxation of the microstructure of L10 a- and b-variantdomains

The process was analysed by monitoring the MC-time depen-dence of two parameters:

� System configurational energy EConf

� SRO parameters C (CFeFe and CPtPt (Eq. (6))

all determined for the entire layer without extracting the bulkand surface effects. The results are presented in Fig. 7.

Both EConf(t) and C(t) isotherms show an initial fast increasefollowed by a slow decreasing relaxation. Comparing the EConf(t)and C(t) curves simulated in bulk and layered FePt it is concludedthat the initial increase results from two effects: (i) homogeneousdisordering (generation of antisites) and (ii) nucleation of the L10

a- and b-variant domains (see Fig. 7 in Ref. [14]). The same reference(Fig. 7 in Ref. [14]) indicates that the domain growth itself does notaffect SRO, which remains almost constant during the process andrapidly decreases only once the layer is percolated (which does notoccur in the process analysed in the present paper). It is, therefore,concluded that the slow decrease of EConf(t) and C(t) reflects therelaxation of the microstructure of the L10 a- and b-variantdomains leading to the minimisation of the APB density within there-oriented volume of the FePt layer. The process shows its owntime scale different from the other ones related to L10 ordering.

0 1x109 2x109 3x109 4x109 5x109

0.85

0.90

0.95

1.00

100 102 104 106 108 1010

t [MC time]

cont

ribut

ion

c

(surf)

K (7) and 1400 K (6); (b) Laplace transform of hc(surf) (t) simulated at 1400 K.

Fig. 5. MC-time evolution of initially Fe-monoatomic free surface of the FePt layer at 1200 K, (010) the cross-section view and from (00-1) direction (Fe surface) (C Fe, Pt).

M. Kozłowski et al. / Intermetallics 17 (2009) 907–913 911

4. Discussion

The (001) free-surface-induced destabilisation of the L10

c-variant in a layer of FePt was revealed by atomistic MC simulationof the Ising system. The phenomenon may be of substantialimportance for the technology of high-density magnetic storagedevices based on this material as just the chemical ordering in theL10 c-variant yields the off-plane easy magnetization, crucial forsome of the technologies. As remarked in Ref. [14], the simulationsdid not account for the possible effect of the substrate and alsoneglect the tetragonal distortion, both factors being able to effec-tively stabilise the desired superstructure or give rise to particularphase microstructure [20]. Nevertheless, as mentioned earlier in

this paper, the L10 c-variant re-orientation into a mosaic of a- and b-variant domains predicted by our simple model has recently beenexperimentally observed in FePt by means of CEMS [19].

As follows from the presented simulation results, the phenom-enon is multiscale both in size and in time. The nanoscale vacancy-mediated atomic jumps are the mechanism for the generation ofantisite defects and antiphase boundaries, the motion of the latterleads then to the mesoscale APB microstructure relaxation.

Very interesting is the energetic characteristics of the processindicating no definite change of the configurational energy of thesystem while the L10 a- and b-variant domains discontinuouslygrow inward the layer (there is strictly no energy change in the caseof a flat APB). This means that possible driving force for the process

0.0 2.5x109 5.0x109 7.5x109 1.0x1010

0.0

0.2

0.8

1.0

t [MC steps]

d) e) f)

Fig. 6. Particular LRO parameters evolutions: 7hc(bulk) (t), , hc

(surf) (t), B ha(surf) (t),

following from a single simulation at 1200 K (without averaging over independentsimulation runs).

M. Kozłowski et al. / Intermetallics 17 (2009) 907–913912

may result mainly from an increase of configurational entropy dueto chemical disordering in the APB range.

Consequently, the growth occurs due to specific fluctuatingmotion of the c-variant/a(b)-variant APB (Figs. 5b and 6). The

0 1x107 2x107 3x107 4x107 5x1071.0x105

1.3x105

1.5x105

1.8x105

2.0x105

EC

on

f=

E(t)-

E(0) [eV

]

t [MC steps]

t [MC steps]

a

0 1x107 2x107 3x107 4x107 5x107

4.0

4.1

4.2

c

C

Fig. 7. Energy and SRO parameters evolutions. (a) System energy evolution at the beginningenergy relaxation at 1400 K in the layer. (c) Evolution of the SRO C parameters at the beginComplete C relaxations with insets showing zoomed decreasing parts (- CFeFe, CPtPt).

amplitude of the fluctuations increases with temperature, whichcauses temperature effect on the averaged depth of the re-orien-tation (Table 3). This specific character of the L10 a- and b-variantdomain growth suggests that the possible effect of the substrate(neglected in the present study) in sufficiently thick layers may beweak. However, the authors are aware that additional strain due tothe presence of substrate may in some cases cause even phasemosaic structure [20]. It is remarkable that the fluctuating motionof the ‘‘re-orientation’’ front was also observed experimentally [19]in the FePt multilayer epitaxially deposited on the MgO substrate.The effect was not observed when FePt sample was covered withNiPt capping layer [22].

Another effect revealed by the simulations and especially bydirect imaging of the evolution of atomic configuration in the FePtlayer (Fig. 5) is the strip-like microstructure of antisites generatedin the bulk domain of the sample, the strips being parallel to the(001) planes. This is a result of vacancy migration being the easiest(the most probable) along the monoatomic planes (withoutaffecting the degree of LRO). Only from time to time the vacancyjumps away from the plane generating an antisite.

A detailed analysis of the configurational energy during atomicjumps provides explanation of the simulated slowing-down of thehomogeneous disordering when thinning a layer initially orderedin the L10 a-variant (see Fig. 3a in Ref. [14]). In such a case it isenergetically more favourable for the vacancy to stay at the surface,according to the previous remark at the Fe sublattice. Therefore,

t [MC steps]

t [MC time]

0.0 5.0x108 1.0x109 1.5x1093.8x104

3.9x104

4.0x104

4.1x104

b

E [eV

]

0 1x109 2x109 3x109 4x109 5x109

4.00

4.05

4.10

4.15

4.20

4.25

4.230

4.235

4.240

4.245

5.0x108 1.0x109 1.5x109 2.0x109

4.170

4.175

C

τFeFe= 4.2x108

d

τPtPt= 2.0x108

= 3.42e8

of relaxation at 1200 K (- bulk, , layer), and at 1400 K (C bulk, B layer). (b) Completening of relaxation at 1400 K in bulk (- CFeFe, C CPtPt), and layer (, CFeFe, B CPtPt). (d)

Table 3Estimated depth of the L10 c-variant / a(b)-variant re-orientation in the FePt layer.

Temperature [K] Estimated re-orientedsurface domain depth [nm]

1400 2.481200 1.801000 1.52

M. Kozłowski et al. / Intermetallics 17 (2009) 907–913 913

penetration of the sample’s interior by the vacancy is slower whatadditionally affects the relaxation time. The more atoms at thesurface (thinner layer) the slower is the relaxation.

The phenomenon reported in the present paper is currentlymodelled by means of ab initio calculations, as well as by MCsimulations implemented with many-body potentials grounded inthe electron theory of FePt. The effects of tetragonal distortion andthe substrate affected epitaxy are studied.

Acknowledgment

Work pursued within the European Action COST P19 and sup-ported by the Polish Ministry of Science and Higher Education(Grant no. COST/202/2006). Financial support granted by thegovernments of France and Poland within the POLONIUM pro-gramme is greatly acknowledged. Two of the authors (R.K. andS.M.) collaborated within the International Fellowship granted toR.K. by Queen’s University, Belfast, UK. Calculations were carried onat PW ICM Warsaw, computational grant G31-5.

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