DSpace at VNU: Out-of-plane exchange bias and magnetic anisotropy in MnPd Co multilayers

The origin of the out-of-plane magnetic anisotropy in the samples has been suggested to be due to the formation of CoPd interfacial alloys which have tensile in-plane strains, while the

Out-of-plane exchange bias and magnetic anisotropy in MnPd/Co multilayers N.H Dunga, , N.P Thuya,b, N.A Tuana, N.T Longb, N.N Phuocc

a

International Training Institute for Materials Science (ITIMS), Hanoi University of Technology, 1 Dai Co Viet road, Hanoi, Vietnam

b

Faculty of Electronics and Telecommunications, College of Technology, Vietnam National University, Hanoi, Vietnam

c Physics Department, National University of Singapore, Singapore

a r t i c l e i n f o

Article history:

Received 3 April 2008

Received in revised form

18 June 2008

Available online 15 July 2008

PACS:

75.70.Cn

75.70.i

75.25.+z

75.30.Gw

Keywords:

Out-of-plane exchange bias

Out-of-plane magnetic anisotropy

Magnetic thin film

Multilayer

a b s t r a c t

Magnetic and structural properties in [MnPd/Co]10multilayers deposited onto Si(111) substrates have been investigated The dependences of anisotropy and exchange bias on the thicknesses of both MnPd and Co layers have been studied In most of the samples, the out-of-plane magnetic anisotropy and both large out-of-plane and in-plane exchange biases have been observed at cryogenic temperature below the blocking temperature TBE240 K With appropriate MnPd and Co thicknesses, we have obtained samples with a large out-of-plane exchange bias along with a large out-of-plane magnetic anisotropy The origin of the out-of-plane magnetic anisotropy in the samples has been suggested to be due to the formation of CoPd interfacial alloys which have tensile in-plane strains, while the spin structure of the antiferromagnetic layer at the interface which is believed to be responsible for exchange bias may be the same as that of the bulk material Also, the present study shows that the interplay between the out-of-plane magnetic anisotropy and exchange bias is evident in our multilayers and plays an important role in the out-of-plane exchange-bias mechanism

&2008 Elsevier B.V All rights reserved

1 Introduction

The phenomenon of exchange bias between antiferromagnetic

(AF) and ferromagnetic (FM) materials has been studied

exten-sively, since its discovery in 1956 by Meiklejohn and Bean[1]

However, most of the studies concentrate on the in-plane

configuration (the so-called in-plane exchange bias) The

investi-gations on out-of-plane exchange bias have recently received

much attention because it is relevant in the quest for a better

understanding of the microscopic origin of the exchange bias

phenomenon and it might lead to wide applications in magnetic

sensors, perpendicular recording media, perpendicular magnetic

read heads and magnetic random access memories (MRAMs) So

far, several groups [2–13]have observed out-of-plane exchange

bias and magnetic anisotropy in multilayers but very few works

[8] have indicated the significant contribution for out-of-plane

magnetic anisotropy arising from the induced unidirectional

anisotropy For the out-of-plane exchange bias mechanism, all

the studies concentrate on the explanation for the difference in

the exchange bias field (HE) in various directions based on the

orientation of the uncompensated AF spins at the interface Some

authors[4,7]suggest that the spin structure at the interface is the same as that of AF bulk, while others [5,13] believe in some interfacial AF spin fluctuations

Recently, our group has discovered a huge unidirectional anisotropy in exchange-biased MnPd/Co bilayer systems in the in-plane configuration[14] From the fundamental viewpoint, it will be interesting to extend our work from bilayers to multilayers

to investigate the role of out-of-plane exchange bias and magnetic anisotropy for a better understanding of the physical origin of exchange bias and related phenomena In this paper, we therefore focus our study on exchange bias in both the out-of-plane and in-plane directions and out-of-in-plane magnetic anisotropy in [MnPd/Co]10 multilayers

2 Experimental Samples with the structure of Si(111)/[MnPd/Co]10 were deposited at ambient temperature using the RF sputtering system The deposition was carried out in pure Ar gas with the pressure of

5  103mbar No external field was applied during the deposi-tion The atomic composition analyses using both the energy dispersive X-ray spectrometer (EDS) and the wavelength disper-sive X-ray spectrometer (WDS) pointed out Mn:Pd ¼ 11:89 Crystal structure was determined by X-ray diffraction (XRD) with

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Journal of Magnetism and Magnetic Materials

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Corresponding author Tel.: +84 4 8680787; fax: +84 4 8692963.

E-mail address: nhdzung@gmail.com (N.H Dung).

Cu Karadiation (l¼1.54056 A˚) and small incident angle (11) The

vibrating sample magnetometer (VSM) was used to characterize

the magnetic properties of the samples For the exchange bias

study, all samples had to undergo the so-called field cooling (FC)

process First, MnPd/Co multilayers deposited onto Si(111)

substrates were heated to 590 K and kept at that condition for

5 min, and then cooled down to room temperature in the presence

of a magnetic field of 5 kOe applied either in the film plane

(in-plane direction) or normal to the plane (out-of-plane

direc-tion) This process was realized in a vacuum chamber with the

pressure better than 105mbar The annealing at such high

temperature will stabilize the structure of the sample The

samples were then cooled in a field of 5 kOe between the two

poles of the VSM system from room temperature down to

measurement temperature In the present study, the hysteresis

loops were measured in a magnetic field up to 13.5 kOe at

cryogenic temperature in both the in-plane and out-of-plane

directions It should be noted that the applied field direction in the

magnetization measurements is in the same direction as the

cooling field, except for some cases of additional experiments that

will be described in a later section

3 Results

Fig 1shows XRD patterns for [MnPd/Co]10multilayers It is

observed that MnPd is polycrystalline with fcc phase Meanwhile,

almost no peak for Co is found It is likely caused by the less

crystallinity formation of Co layers As a result, the average

saturation magnetization of these samples is only 320 emu/cm3,

much lower than that of Co bulk (about 1400 emu/cm3) Another

possibility is that the thickness of Co layer is not thick enough for

the detection of the diffraction peaks by XRD

Hysteresis loops at 120 K for the sample series in which the Co

thickness (tCo) is varied from 2.5 to 10 nm while the MnPd

thickness (tMnPd) is fixed at 10 nm are shown in Fig 2 The

negative shifts of the hysteresis loops show that exchange bias

effect exists in [MnPd/Co]10multilayers in both the in-plane and

out-of-plane directions Also, one can see the out-of-plane

orientation of the Co layer magnetization in the samples with

tCoo10 nm However, the sample with tCo¼10 nm exhibits an

in-plane magnetic anisotropy (the last graph inFig 2) This behavior

unambiguously demonstrates that the easy axis of Co layer

changes from the out-of-plane direction to the in-plane one with

increasing the Co thickness

Shown inFig 3are the hysteresis loops at 120 K for the sample series in which tMnPdis varied from 3.5 to 30 nm while keeping tCo

at 3.5 nm The negative shifts of the hysteresis loops in both the in-plane and out-of-plane directions are also observable Con-cerning the preferential orientation of the Co layer magnetization,

it is interesting to note that the easy axis of Co layer switches from the in-plane direction (in the sample with the smallest tMnPd, 3.5 nm, as seen in the first graph inFig 3) to the out-of-plane one

as tMnPdincreases

In order to know better about the preferential orientation of the Co layer magnetization at temperature higher than TB, hysteresis loops were measured at room temperature for the as-deposited samples Besides, the samples annealed at 590 K for

5 min in vacuum were also used in these experiments The results indicated that the out-of-plane magnetic anisotropy is present in most of the cases Especially for the multilayer with tMnPd¼10 nm and tCo¼7.5 nm, the in-plane anisotropy in the as-deposited sample switched to the out-of-plane one after annealing (see

Fig 4)

We have also carried out some additional hysteresis loop measurements at cryogenic temperature in which the FC process

is similar to that described in a previous section but the measurement field is applied both perpendicular and parallel to the FC direction A representative result depicted inFig 5for the sample with tMnPd¼10 nm and tCo¼5.5 nm shows a double shift

of the out-of-plane hysteresis loop after the in-plane FC However,

no loop shift was observed in the case of the in-plane hysteresis loop after the out-of-plane FC

4 Discussion

It should be noted that the blocking temperature is quite narrow for our multilayers and its value is around 240 K for all the samples as can be seen inFig 6for some representatives where the temperature dependence of the HE is derived from the hysteresis loops measured at various temperatures Therefore, the effect of variation of blocking temperature leading to variation

in the exchange bias properties which is usually observed in the literature can be negligible in the present cases

From the hysteresis loops inFig 2, the HE, the unidirectional anisotropy energy or exchange bias coupling energy (JK), the coercive field (HC) and the remanence-to-saturation magnetiza-tion ratio (MR/MS) for both the in-plane and out-of-plane cases at

120 K have been derived and are shown inFig 7as a function of the Co thickness Here, JKwas calculated by JK¼1HEMStCo, where HE is the exchange bias field, and tCo and MS are the thickness and saturation magnetization of Co layer, respectively The factor of1in the above equation is because each Co layer has two interfaces It is worthwhile to note that from this figure the maximum values of the HEare huge, up to 1650 and 950 Oe for the out-of-plane and in-plane cases, respectively, and much higher than those reported in the previous studies for FePt/FeMn multilayers[10,11] Another behavior of this sample series is that the out-of-plane JKis larger than the in-plane one and JKreaches the maximum values of 0.17 and 0.15 erg/cm2for the out-of-plane and in-plane cases, respectively, at the largest tCo

Shown inFig 8is the variation of the HE, the JK, the HCand

MR/MS with the tMnPd for both the in-plane and out-of-plane cases at 120 K derived from the experimental curves in Fig 3

Of interest are the opposite trends of HEin these two configura-tions Specifically, the out-of-plane HEincreases with tMnPdfrom 3.5 to 7.5 nm, approaching a maximum value of 1650 Oe, and decreases gradually with increasing tMnPdlarger than 7.5 nm On the contrary, a decrease in HE for the in-plane case can be seen clearly with increasing t from 3.5 to 7.5 nm down to

x = 4.5 nm

x = 3.5 nm

x = 2.5 nm

2θ θ (deg.)

Fig 1 X-ray diffraction patterns for [MnPd(10 nm)/Co(x nm)] 10 (x ¼ 2.5, 3.5,

4.5 nm) multilayers with small incident angle (11).

a minimum value of 250 Oe, followed by an increase with tMnPd

over 7.5 nm These are very different from the results reported by

Phuoc and Suzuki for FePt/FeMn multilayer system[10,11]

We note here that by choosing appropriate tCo and tMnPd

we can obtain samples with the out-of-plane anisotropy

which have a nearly ‘‘pure’’ out-of-plane exchange bias, i.e the

in-plane exchange bias is almost suppressed in the sample with

the strong out-of-plane anisotropy The sample with tCo¼3.5 nm

and tMnPd¼7.5 nm as mentioned above is a good example (see

Figs 3 and 8) This behavior is again rather unusual comparing with

other works, e.g in [FeMn/FePt]10multilayers[10]where both

out-of-plane and in-plane exchange biases are always coexistent

As can be seen inFigs 7 and 8, HCfor the samples depends on

both tCoand tMnPd Especially for the multilayers with large tCoand

also small tMnPd, the opposite behavior of out-of-plane and

in-plane HCwith tCoand also tMnPdreflects the modification of the

anisotropy property in these samples Meanwhile, the values of

the MR/MSwhich are obtained after recentering the loops for the

HEalso vary with tCoand tMnPdin response to the change of the

anisotropy property The ratio of MR/MSobtained from the

out-of-plane hysteresis loops for the samples with the out-of-out-of-plane

anisotropy is rather high, up to 0.9 when the tMnPdis over 15 nm as

shown inFig 8

Regarding the origin of the out-of-plane magnetic anisotropy,

based on the fact that the out-of-plane magnetic anisotropy is

already existent at room temperature and can be obtained in the

case of the multilayer with tMnPd¼10 nm and tCo¼7.5 nm after annealing as mentioned above (Fig 4), we suggest that the out-of-plane magnetic anisotropy observed in most of our samples most likely comes from the formation of CoPd alloys at the interface between Co and MnPd layers This assumption is consistent with the previous studies on out-of-plane magnetic anisotropy in Co/Pd multilayers [15,16] These alloys are known to have extremely large negative magnetostriction constants and can experience significant tensile in-plane strains due to the lattice mismatch with MnPd layers in the multilayers leading to the out-of-plane orientation of the FM magnetization The existence of the in-plane anisotropy in the multilayer with the smallest tMnPdin the sample series with varying tMnPd (see Fig 3) may originate from the reduction of the tensile in-plane strains of CoPd alloys

In other words, the spin switching between the in-plane and out-of-plane directions in this sample series can be reversibly controlled by strain modulation through the inverse magnetos-trictive effect[17]

From the area enclosed between the in-plane and out-of-plane magnetization curves, the effective magnetic anisotropy (Keff) can be readily obtained A positive (or negative) Keff describes the case of a preferential direction of the FM magnetization along the out-of-plane (or in-plane) direction It is well estab-lished that the Keff could be phenomenologically separated into a volume contribution (KV) and a contribution from the interfaces (K), and approximately described by K ¼K +2K/t

-1.0 -0.5 0.0 0.5 1.0

-1.0 -0.5 0.0 0.5 1.0

-1.0 -0.5 0.0 0.5 1.0

Out-of-plane In-plane

tCo = 2.5 nm

Out-of-plane In-plane

tCo = 3.5 nm

Out-of-plane In-plane

tCo = 4.5 nm

H (kOe)

Out-of-plane In-plane

tCo = 5.5 nm Out-of-plane

In-plane

tCo = 7.5 nm Out-of-plane

In-plane

tCo = 10 nm

H (kOe)

Fig 2 Out-of-plane and in-plane hysteresis loops at 120 K for [MnPd(10 nm)/Co(x nm)] 10 (x ¼ 2.5, 3.5, 4.5, 5.5, 7.5, 10 nm) multilayers The out-of-plane loops were measured with the field applied along the film normal, while the in-plane loops were measured with the field applied in the film plane The applied field direction is in the same direction as the cooling field.

or KefftCo¼KVtCo+2KS[18] By combining this equation with the

linear fit of the plot of the product Keff tCoversus tCo, one can

readily deduce KVfrom the slope of the fit line and 2KSfrom the

vertical axis intercept (seeFig 9) The value of KSobtained by this

way for the sample series with varying tCois about 0.6 erg/cm2,

which is close to that reported by Engel et al [19] for

Co/Pd multilayers (0.63 erg/cm3), while |KV| is in the order of

106erg/cm3, which is much lower than that found in the literature

[18] It should be noted that in the above calculations we have

ignored the influence of the induced unidirectional anisotropy on

the FM anisotropy, which is not simply the loop shifts

The plot inFig 9also indicates that the easy axis of Co layer

transforms from the out-of-plane direction into the in-plane one

as tCopasses a critical value of about 9 nm Of interest is that this

value is much larger than that in previous studies[18]as a result

of the reduction of the Co layer magnetization which leads to a

decrease in demagnetizing field, an opponent of the out-of-plane

anisotropy Since MSis slightly different over the tCorange from

2.5 to 10 nm, the low saturation magnetization is not directly

related to the low magnetization of CoPd interfacial alloys It is

likely because the large entropy for these interfacial layers would

disorder the Co layers, thus lowering its magnetization This

magnetization disordering mechanism is similar to that observed

in Co/Re multilayers[20] Another possibility is that the strains

may give rise to the less crystallinity for Co layers

Since MnPd layers are polycrystalline and not textured as

determined from XRD, we assume that isotropic crystallographic

orientation is present for these AF layers Upon the FC process, the interfacial AF spins are presumed to be frozen into the preferential bulk spin anisotropy axes which are closest to the orientation of the interfacial FM spins due to the bilinear exchange interaction between the FM spins and AF spins at the interface The reorientation of the interfacial AF spins or repopulation of the

AF domains with the magnetic easy axes leading to uncompen-sated spins or net moments at the interface and forming AF regions locally oriented in various directions can induce a unidirectional anisotropy at the interface and give rise to exchange bias These AF regions are not necessarily AF domains

in the strict thermodynamic sense, but rather are areas where the properties of the AF, most likely the orientation of the uncom-pensated AF spins at the interface, are modified due to the presence of the FM[21] Here, the FM domains are expected to be much larger than the AF regions so that each FM domain will feel the average effect of several of these AF regions and can be essentially treated as a separate sample[22] Then the uncom-pensated spins of various AF regions are distributed in a cone with

a limited half-apex angle and the averaged direction of the uncompensated AF spins is along the direction of the FM spins Naturally, one may expect that the FM spins at the interface favor to align in the FC direction However in some cases, they are canted with the FC direction because our cooling field is not enough to entirely saturate the magnetization along the hard axis

of the FM layer, especially for the samples with the strong out-of-plane magnetic anisotropy field cooled in the in-out-of-plane direction

-1.0 -0.5 0.0 0.5 1.0

-1.0 -0.5 0.0 0.5 1.0

-1.0 -0.5 0.0 0.5 1.0

Out-of-plane In-plane

Out-of-plane In-plane

Out-of-plane In-plane

Out-of-plane In-plane

Out-of-plane In-plane

Out-of-plane In-plane

H (kOe)

H (kOe)

Fig 3 Out-of-plane and in-plane hysteresis loops at 120 K for [MnPd(y nm)/Co(3.5 nm)] 10 (y ¼ 3.5, 5.5, 7.5, 10, 15.5, 30 nm) multilayers The applied field direction is in the same direction as the cooling field.

(seeFig 10) In these cases, with the out-of-plane FM easy axis,

larger net moment components can be induced along the

out-of-plane cooling field than those along the in-out-of-plane cooling field,

leading to the higher out-of-plane HEthan the in-plane one, and

vice versa These arguments explain why the in-plane H seems to

be suppressed in the sample with the strong out-of-plane magnetic anisotropy as mentioned above They are also in good agreement with the experimental results in most of the present cases, except for the case of [MnPd(30 nm)/Co(3.5 nm)]10 multi-layer In this exception, the sample with the out-of-plane magnetic anisotropy, however, exhibits the smaller out-of-plane

HEthan the in-plane one (seeFigs 3 and 8) The orientation of the interfacial AF spins may not be strongly influenced by the orientation of the FM anisotropy as a result of the strong anisotropy of the thick AF layer[7] Moreover, some demagnetiz-ing effects will tend to keep them in the film plane givdemagnetiz-ing rise to smaller net moment components induced along the out-of-plane

FC direction than those along the in-plane FC direction Based on the above reasons, the opposite trends of HEin the in-plane and out-of-plane configurations in the sample series with changing

tMnPdas shown inFig 8can be clarified

As for [MnPd(10 nm)/Co(10 nm)]10 multilayer, since the FM anisotropy is expected to be very small, the cooling field is sufficient to completely saturate the FM magnetization in both the in-plane and out-of-plane directions leading to that the interfacial

FM spins is along the FC direction Therefore, the fact that the in-plane HEis nearly equal to the out-of-plane one as seen inFigs 2 and 6b again confirms the bulk spin structure of the AF layers

In order to explain the behavior of exchange bias in the sample series with varying tCo(seeFig 7), it should be noticed that the interfacial FM spins align in the FC direction when the cooling field is applied along the film normal The HEis usually expected

to be inversely proportional to tCoabove a certain Co thickness Thus, with tColarger than 5.5 nm the out-of-plane HEdecreases, indicating that this is an interfacial effect This is confirmed by the fact that J for the out-of-plane case is only slightly different over

-1.0

-0.5

0.0

0.5

1.0

-1.0

-0.5

0.0

0.5

1.0

H (kOe)

As-deposited

Out-of-plane In-plane

Out-of-plane In-plane

After annealing

Fig 4 Out-of-plane and in-plane hysteresis loops at room temperature for

[MnPd(10 nm)/Co(7.5 nm)] 10 as-deposited and after-annealing multilayers.

-1.0

-0.5

0.0

0.5

1.0

HFC ⊥ Plane

HFC // Plane

H (kOe)

Out-of-plane

Fig 5 Out-of-plane hysteresis loops at 120 K for [MnPd(10 nm)/Co(5.5 nm)] 10

multilayers field cooled in the out-of-plane and in-plane directions.

0.0 0.3 0.6 0.9 1.2 0.0 0.3 0.6 0.9 1.2

Out-of-plane

In-plane

HE

T (K)

Out-of-plane

In-plane

HE

Fig 6 Temperature dependence of in-plane and out-of-plane exchange bias fields (H E ) for (a) [MnPd(10 nm)/Co(4.5 nm)] 10 and (b) [MnPd(10 nm)/Co(10 nm)] 10

multilayers.

this tCorange An increase in the out-of-plane HEwith tCobelow

5.5 nm may be related to the formation of CoPd interfacial alloys

depending on the FM thickness in this range Meanwhile, an

increase in the in-plane J with t is obviously affected by the

strong out-of-plane FM anisotropy and a tendency toward the in-plane FM anisotropy with increasing tCo

The discrepant behavior of the hysteresis loops as shown in

Fig 5 affirms that the FM anisotropy is clearly affected by the induced unidirectional anisotropy, i.e the competition between the FM and unidirectional anisotropies in the case of the in-plane

FC and/or the enhanced out-of-plane magnetic anisotropy in the case of the out-of-plane FC These features may originate from the strong J in our samples and they are rather unique compared

0.00

0.05

0.10

0.15

0

1

2

3

4

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.5

1.0

1.5

2.0

Out-of-plane

In-plane

JK

In-plane Out-of-plane

MR

HC

In-plane Out-of-plane

In-plane

HE

Out-of-plane

Fig 7 Co thickness dependence of exchange bias field (H E ), exchange bias

coupling energy (J K ), coercive field (H C ) and remanence-to-saturation

magnetiza-tion ratio (M R /M S ) at 120 K for [MnPd/Co] 10 multilayers.

0.0 0.5 1.0 1.5 2.0

0.00 0.03 0.06 0.09 0.12

0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 4 5

In-plane

HE

Out-of-plane

In-plane

Out-of-plane

JK

2 )

In-plane

Out-of-plane

MR

In-plane

Out-of-plane

HC

Fig 8 MnPd thickness dependence of exchange bias field (H E ), exchange bias coupling energy (J K ), coercive field (H C ) and remanence-to-saturation magnetiza-tion ratio (M R /M S ) at 120 K for [MnPd/Co] 10 multilayers.

with previously published studies on out-of-plane anisotropy and

exchange bias The existence of the double-shifted loop as seen in

Fig 5, which rather looks like a symmetric double-shifted loop

reported by Bru¨ck et al [21], is a further proof of the FM spin

canting After the out-of-plane FC, the projection of the

uncom-pensated AF spins to the out-of-plane direction is along the ‘up’

direction, leading to a single-shifted loop (seeFig 10a,c), while the

small projection of the uncompensated AF spins to the

out-of-plane direction is equally spread along the ‘up’ and ‘down’

directions due to the FM spin canting after the in-plane FC, giving

rise to both the negative and positive HE(seeFig 10b,d) In other

words, since each FM domain can be regarded as a separate

sample and the sign for the net exchange bias for each of these domains is set by the direction of the magnetization of the FM domain, the FM spin canting results in both the negative and positive HEforming the double-shifted loop In a similar way, this argument also indicates why no shifted loop could be seen in the in-plane measurements after the out-of-plane FC

5 Conclusions

In summary, we have systematically examined both in-plane and out-of-plane exchange biases of the multilayers of [MnPd/Co]10as a function of the thicknesses of MnPd and Co layers The results show

a strong out-of-plane magnetic anisotropy originating from the interface anisotropy of MnPd/Co multilayers and also from the induced unidirectional anisotropy, and exchange bias coming from the spin structure at the interface which may be similar to that of the AF bulk In return, this strong out-of-plane anisotropy plays a vital role in the behavior of in-plane and out-of-plane exchange biases, and vice versa, suggesting that one must take into account the interplay between out-of-plane magnetic anisotropy and exchange bias when studying out-of-plane exchange biased systems

Acknowledgement This work was supported by the State Program on Funda-mental Research of Vietnam in the periods 2006–2007 (Grants 4.049.06 and 4.105.06) and 2008–2009

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-0.5

0.0

0.5

1.0

1.5

0 1 2 3

Keff

tCo

tCo (nm)

T = 120 K

2KS

Keff

6 erg/cm

3 )

tCo (nm)

Fig 9 The plot of the product K eff t Co versus t Co at 120 K for [MnPd(10 nm)/

Co(x nm)] 10 (x ¼ 2.5, 3.5, 4.5, 5.5, 7.5, 10 nm) multilayers The sketches are taken

from Johnson et al [18] The inset indicates the dependence of K eff on the Co

thickness.

FM AF

AF region

FM domain

Direction of uncompensatedAF spins

Averaged direction of uncompensated AF spins

Fig 10 Sketch of the magnetic configurations at the interface in the multilayers

with the out-of-plane anisotropy field cooled along the out-of-plane (a) and

in-plane (b) directions, and the corresponding configurations (c) and (d) simplified

for explanation of exchange bias.