soft bilayers

ARTICLE IN PRESS

Physica B 403 (2008) 320–323 www.elsevier.com/locate/physb

A study on the macroscopic properties of hard/soft bilayers A. Ktenaa,, V. Alexandrakisb, I. Panagiotopoulosc, D. Fotiadisd, D. Niarchosb a

Department of Electrical Engineering, TEI of Chalkida, GR 34400, Greece Institute of Materials Science of NCSR ‘‘Demokritos’’, GR 15310, Greece c Department of Materials Technology, University of Ioannina, GR 45110, Greece d Department of Computer Science, University of Ioannina, GR 45110, Greece b

Abstract The dependence of the macroscopic properties of the soft layer on the hard-layer magnetization and microstructure in exchange spring bilayers is studied. The exchange bias field experienced by the soft layer varies proportionally with magnetization as well as magnetic hardness of the hard layer. On the other hand, there is an inverse relationship between the coercivity of the soft layer and the hard layer magnetization, as well as between the coercivities of the two layers. Domain wall and interface processes offer a qualitative explanation of the results. A vector Preisach-type model for exchange spring bilayers is used to investigate the above. r 2007 Elsevier B.V. All rights reserved. Keywords: Exchange spring bilayers; Magnetic recording; Preisach modeling

1. Introduction Exchange spring media [1,2] have recently been proposed as a means to satisfy the conflicting media design constraints of writability and thermal stability required for the development of ultra-high density recording media. These media consist of a soft spring layer ferromagnetically coupled to a hard layer. Similarly, to antiferromagnetically coupled (AFC) bilayers [3–6], they may have a two-phase hysteresis characteristic (Fig. 1). The soft layer switches first, at a field Hex–H1c, followed by the switching of the hard layer at a much higher field H2c. Hex is the exchange bias field responsible for the shifting of the soft layer loop; it is negative for exchange spring media and positive for AFC media. H1c is the coercivity of the soft layer or the half-width of the soft layer (minor) loop, and H2c is the coercivity of the bilayer, which is considerably less than the coercivity of the hard layer alone. These structures allow for a lower Mrt product with respect to conventional thin films and tip the balance between thermal stability and higher density towards the latter [5,6]. The magnetic behavior of these structures is a function of the soft and Corresponding author. Fax: +30 22280 99603.

E-mail address: [email protected] (A. Ktena). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.08.039

hard layer magnetic properties and depends sensitively on the interlayer coupling. The coupling length, defined as the soft layer thickness beyond which a two-phase behavior is observed, the roughness of the interface and the existence or not of a non-magnetic spacer between the hard and the soft layer, all, affect the macroscopic magnetic properties of the bilayers. The assumption that the onset of nucleation in the soft phase occurs when the Zeeman energy of the applied field overcomes the domain wall energy of the p soft phase [7] ffiffiffiffiffiffiffiffiffiffiffi ffi yields a rough estimate of H ex ’ H 1N ¼ 2 A1 K 1 =M 1s t1 but cannot explain its dependence on the hard-layer properties observed experimentally. If the domain wall nucleated in the soft phase at H1N is allowed to propagate in the hard phase through the interface, the field required to overcome the pinning of the wall against the interface [8–10] Hdw can be obtained. If H1N4Hdw, the two layers switch together and the twophase characteristic is not observed. The one-dimensional atomic model used in Ref. [11] corroborated the above results and showed that magnetic moments in the soft layer rotate more further away from the interface because the pinning by the hard layer is less. As the applied field increases, the spins at the interface start rotating and the domain wall is introduced in the hard

ARTICLE IN PRESS A. Ktena et al. / Physica B 403 (2008) 320–323 Table 1 Sample properties

1.5 1.0 M (memu/cm2)

321

0.5 0.0 H2c (kOe) Mr (memu/cm2) H1c,max (kOe) Hex,max (kOe)

-0.5 -1.0

Sample 1 (Tanneal ¼ 710 1C)

Sample 2 (Tanneal ¼ 600 1C)

Hard layer

Bilayer

Hard layer

Bilayer

13.15 0.96

10.85 1.45 0.32 0.97

8.15 0.80

4.90 1.14 0.53 1.33

-1.5 -24 -20 -16 -12 -8

-4 0 4 H (kOe)

8

12 16

20

24

Fig. 1. Major loops of hard layer and bilayer with minor loops.

layer. A rough estimate of the switching field for the hard layer is obtained; H sw ¼ A2 K 2 =A1 M 1s , which is in agreement with the experimental observation that the coercivity of the bilayer is less than the coercivity of the hard phase alone. The above treatments assume negligible anisotropy in the soft layer which is governed solely by reversible processes while all the irreversible processes are taking place in the hard phase due to its multidomain structure. Measurements, however, have shown that soft-layer minor loops exhibit coercivities of a few hundred Oersteds and that both the exchange bias, Hex, and the coercivity, H1c, depend on the hard-layer properties. 2. Experimental results and discussion Co–Pt hard–soft bilayers with (1 1 1) texture have been prepared through sputtering. The hard layer has been heat treated at various temperatures in order to investigate the effect of the hard-layer microstrusture on the soft-layer properties. Table 1 summarizes the properties of two typical samples (1 and 2) whose hard-layers were previously annealed at 710 and 600 1C, respectively. Fig. 1 shows minor loops of the soft layer measured at different levels of the hard-layer magnetization. The sample was initially brought to positive saturation. Then the field was decreased to a certain negative value and removed to obtain the respective DC demagnetized state. A loop of the soft layer was measured at that state and the process was repeated for a larger negative field until negative saturation was reached. The half-width, H1c, of each minor loop and the offset from zero, Hex, have been determined for each DC demagnetized state. The dependence of H1c and Hex on the hard-layer magnetization, M2, for the two samples of Table 1 are shown in Fig. 2. In both cases, Hex increases and H1c decreases with M2. A similar behavior has been observed in AFC media [3]. As far as the dependence of Hex on M2 is concerned, only the exchange bias was positive. This direct relationship between Hex and M2 is expected since it is an interface

Fig. 2. Coercivity and exchange bias field of the soft layer vs the hardlayer magnetization: (a) sample1 and (b) sample2.

effect and the interface changes with the hard-layer magnetization state facilitating the coupling between the two layers as more domains are magnetized in one direction. Contrary to AFC media, the soft-layer coercivity, H1c, decreases with M2. A possible explanation is that at lower M2 levels, the misaligned hard layer spins near the interface introduce a ‘‘magnetic roughness’’ across the interface increasing the pinning of the domain wall in the soft phase. The decrease of H1c along with the decrease in the softlayer loops’ squareness as a function of M2 may also suggest the existence of exchange anisotropy [12] proportional to the exchange bias field Hex which introduces an effective field at an angle to the applied field resulting in loops that are not ‘‘easy axis’’ loops anymore. Hex and H1c also decrease with the increasing anisotropy of the hard layer. Coupling between the two phases is

ARTICLE IN PRESS A. Ktena et al. / Physica B 403 (2008) 320–323

facilitated when the hard layer is softer and can support wider domain walls and therefore Hex is stronger. For samples with hard layers annealed below 600 1C, Hex was too large to be measured as the two layers seemed to reverse in union. Taking into account that the magnetization is not homogeneous across the interface and that in a hard layer of smaller magnetic hardness the rotation is easier, the enhanced H1c in samples with softer hard layers can be attributed again to the ‘‘magnetic roughness’’ of the interface.

1.5 1 0.5 M/Ms

322

-25

-15

-5

0

5

15

25

-0.5 -1

3. Preisach modeling and discussion

-1.5 H (kOe) Fig. 4. Calculated major loops of two bilayers with an identical soft layer and different hard layers.

1.5 1 0.5 M/Ms

A Preisach-type model has been developed to investigate the above observations. A previously presented model developed to model major and minor loops on AFC media [13] is adjusted to model the behavior of ferromagnetically coupled exchange spring media. In the case of exchange-coupled media, the characteristic density, r(a, b), is constructed as the weighted sum of two normal bivariate pdfs, one for each layer: rða; bÞ ¼ w1 r1 ða; bÞ þ w2 r2 ða; bÞ; w1 ¼ 1  w2 , where r1, w1 and r2, w2 are the probability density functions and weights of the soft and hard layer densities, respectively. Since Hex is the averaged-out effect of exchange interactions between the two layers, its effect can be modeled [13] by allowing r1 to be shifted along the Hi-axis of the Preisach plane by an amount proportional to M2 (Fig. 3). Similarly, the dependence of H1c on M2 can be modeled by allowing r1 to shift along the Hc-axis. Alternatively, following the discussion in Section 2, an effective field H1(t) acting on the soft layer only can be introduced. This field would be the sum of the applied field and the exchange bias field at a given level of the hard-layer

-20

-10

0

0

10

20

-0.5 -1 -1.5 H (kOe) Fig. 5. Calculated major loop with minor loops at various hard-layer magnetization levels.

b

ρ1(a,b)

Hex > 0 M< 0

Hex=0 M2=0

a

Hex < 0 M>0 ρ2(a,b)

Hi

Hc

magnetization: H 1 ðtÞ ¼ HðtÞ þ H ex ðM 2 Þ: In order to model hard layers with lower coercivity (sample2), r2 is shifted along the Hc-axis toward zero. The major loops of two bilayers with different hard layer properties but identical soft layer properties have been calculated by a Preisach-type model like the one described above (Fig. 4). The assumption that there is an exchange anisotropy increasing with M2 and lying in plane but at an angle to the applied field was used to generate the minor loops calculated at various levels of M2 (Fig. 5). However, in order to reproduce the increased H1c for lower K2, r1 had to be shifted along the Hc-axis as well, which is in agreement with the argument stated above that the ‘‘magnetic roughness’’ of the interface affects the switching field distribution of the soft layer. 4. Conclusions

Fig. 3. The Preisach plane and the soft and hard phase characteristic densities, r1 and r2; r1 shifts along the interactions axis, Hi, by an amount proportional to Hex(M2).

The dependence of the macroscopic properties of the soft layer on those of the hard layer in exchange spring bilayers

ARTICLE IN PRESS A. Ktena et al. / Physica B 403 (2008) 320–323

has been investigated and modeled using a Preisach-type two-dimensional model. The exchange bias field is negative and directly related to the magnetization of the hard layer. It is also stronger when the hard layer is softer because the coupling between the two layers is facilitated by the lower hard layer’s anisotropy. The coercivity of the soft layer is higher for softer hard layers and at lower magnetization levels because of stronger pinning introduced by the increased ‘‘magnetic roughness’’ of the interface and the lower exchange anisotropy. The Preisach-type model, using a mixture of two pdfs, one for each layer, reproduced the two-phase hysteresis loops of exchange spring media. Allowing a vector effective field, the sum of the applied field and the exchange bias field at a given hard layer magnetization level, to act on the soft layer characteristic density only, the dependence of the soft layer loop parameters on the hard layer magnetization was reproduced. Acknowledgments This work has been jointly funded by the European Community Fund and the Hellenic Ministry of Education.

323

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