An interface-proximity model for switchable interfacial uncompensated antiferromagnetic spins and their role in exchange bias

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An interface-proximity model for switchable interfacial uncompensated antiferromagnetic spins and their role in exchange bias

Ki-Suk Lee, Young-Sang Yu, and Sang-Koog Kim

Citation: Applied Physics Letters 86, 192512 (2005); doi: 10.1063/1.1920412 View online: http://dx.doi.org/10.1063/1.1920412

View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/86/19?ver=pdfcov Published by the AIP Publishing

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An interface-proximity model for switchable interfacial uncompensated antiferromagnetic spins and their role in exchange bias

Ki-Suk Lee, Young-Sang Yu, and Sang-Koog Kim^a^兲

Nanospintronics Laboratory, School of Materials Science and Engineering, and Research Institute of Advanced Materials, College of Engineering, Seoul National University, Seoul 151-744, Korea

共

Received 12 July 2004; accepted 11 March 2005; published online 5 May 2005

兲

We propose an interface-proximity model that allows us to solve a longstanding puzzle regarding large discrepancies between the experimentally observed and theoretically estimated values of exchange-bias field H_ebin coupled ferromagnetic/antiferromagnetic

共

F/AF

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metallic films. In this proposed model, switchable uncompensated

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UC

兲

AF spins in contact with an F layer are taken into account as an additionally inserting layer that is chemically or magnetically distinguishable from each of the nominal AF and F layers. Reductions in H_eb, enhancements in coercivity, and other exchange-bias behaviors typically observed in experiments are very well reproduced from this model. The switchable interfacial UC region with a sizable thickness, heretofore ignored, plays a crucial role in the exchange bias phenomenon. © 2005 American Institute of Physics.

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DOI: 10.1063/1.1920412

兴

The exchange bias

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EB

兲

effect, a shift of magnetic hysteresis loops centered at zero magnetic field toward a nega- tive or positive field, was first discovered in 1956 by Meikle- john and Bean

共

MB

兲

.¹ Its underlying physics has been intensively studied to unravel a longstanding puzzle regarding the EB origin for the past two decades. A lot of experimental results and proposed models reported so far have of- fered plausible scenarios of the EB phenomenon in a variety of ferromagnetic/antiferromagnetic

共

F/AF

兲

coupled systems.

It is believed that uncompensated

共

UC

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AF spins in close proximity to a ferromagnet yield the EB through a short- range exchange coupling J between the AF and F layers by the resistance of those UC spins to an applied magnetic field H.²For a fully UC F/AF interface with a strong resistance of the UC spins, the strength of EB

共

represented by the magnitude of a field shift H_eb

兲

can thus be estimated by J / M_Ft_F with the magnetization M_Fand the thickness t_Fof an F layer, when the AF and F spins are collinear. However, H_ebvalues predicted by this simple model are two orders of magnitude greater than the experimental values in metallic F/AF systems. This discrepancy has been stimulated to develop various models that are able to explain the reduced values of H_eb. Some earlier models are likely to correctly estimate the reductions of H_eb,^3–7but their different underlying physics re- main controversial.

Furthermore, Ohldag et al.⁸ suggested that a possible origin about experimentally observed reductions in H_eb be related to a small amount of tightly pinned UC spins, based on the vertical offsets of UC AF reversal loops observed from an IrMn/ Co film. Also, other groups observed similar vertical shifts.^9,10 However, they ignored a large amount of switchable

共

unpinned

兲

UC spins at interfacial AF layers and their possible role in the EB effect. In this letter, we thus study the role of the relatively large amount of switchable UC spins in the reduction of H_ebby making elaborate model calculations on the basis of earlier experimental results,^8,11 which is clearly evidence for the existence of the switchable

UC region with a considerable thickness at buried interfaces.

This interfacial region chemically and/or magnetically differs from the interior of the nominal AF and F layers because the proximity effect can modify chemical or magnetic properties at interfacial local regions.^12–14 Nevertheless, this effect for F/AF interfaces has been ignored for the understanding of remarkable reductions in H_eb experimentally observed, al- though this distinctly different region can influence the size of H_eband coercivity H_cas well.

Accordingly, we propose an interface-proximity model that offers a better insight into the experimental observations of enhancements in H_cas well as reductions in H_eb. In this proposed model, experimentally found switchable UC region is inserted between nominal AF and F layers as depicted in Fig. 1

共

a

兲

. Thus, different J_Fand J_AFvalues can be implicated at each of the two different UC/F and AF/UC interfaces, as shown in Fig. 1

共

a

兲

. The physical parameters relevant to this model are also illustrated in Fig. 1

共

a

兲

. The magnetocrystalline anisotropy

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MCA

兲

constant K and the saturation magnetization M are defined for the individual F and UC layers. By assuming the Stoner–Wohlfarth

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i.e., coherent rotation

兲

reversal, the total energy E_tot divided by an interface area ␥

a兲Author to whom all correspondence should be addressed; electronic mail:[email protected].

FIG. 1.共Color online兲共a兲Illustrations of the interface-proximity model and the relationships of␾F,␾UC, and␾H;共b兲conceptual illustration of the microscopic origin of the magnetocrystalline anisotropy. Spin and orbital magnetic moments are coupled through a spin-orbital coupling.

APPLIED PHYSICS LETTERS 86, 192512

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2005

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can be given as

E_tot/␥^{= − J}AFcos␾UC− J_Fcos

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␾UC−␾F

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− M_UCt_UCH cos

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␾UC−␾H

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− M_Ft_FH cos

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␾F−␾H

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− K_UCt_UCcos²␾UC− K_Ft_Fcos²␾F,

where the first and second terms represent the exchange in- teraction energies, the third and fourth terms the Zeeman energies, and the fifth and sixth terms the in-plane MCA energies for the F and UC layers.

In the typical behaviors of the EB effect, the field shifts of hysteresis loops are followed by enhancements in H_c, but many previous models could not predict well the enhancements of H_c simply by using the energy equation. This is because the intrinsic bulk values of K_Ftypically used for an isolated F layer

共

or decoupled to an AF layer

兲

is also used for the coupled cases of F/AF systems, thus leading to an incor- rect estimation of the value of H_cin coupled F/AF systems.

To correctly calculate the enhanced H_cjust by using E_tot, one should consider an induced K_F. To derive the induced term K_Ft_F␥, we adopt a concept of the microscopic origin of MCA, as illustrated in Fig. 1

共

b

兲

. As a matter of fact, the MCA of a spin moment M_spinoriginates from the anisotropic nature of an orbital moment M_orbthrough their spin-orbital coupling

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s.o.c

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.¹⁵ Thus, K_Ft_F␥ for the coupled case can be given by the product of K_UCt_UC␥ ^{and J}F␥^{, if K}UCt_UC is greater than K_Ft_Fin its decoupled case, hence yielding K_Ft_F

=␩

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K_UCt_UC· J_F

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^1/2 with a proportional constant␩. Here, the K_UCt_UC␥ ^{and J}F␥ terms correspond to the strength of the orbital anisotropy and the spin-orbital coupling, respectively, in the light of the MCA origin. The square root is taken to satisfy the units of both sides. Similarly, for the UC layer coupled to the AF layer, K_UCt_UC equals ␩

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K_AFt_AF· J_AF

兲

^1/2. Consequently, H_c values for F and UC layers in coupled systems are determined by above relations, which are able to estimate enhanced H_c as well as reduced H_eb in coupled F/AF systems just by the use of E_totwithout any other model reported earlier.^16–18

Minimizing E_totwith respect to both␾Fand␾UCyields their equilibrium values. For a simple case of J_F

⬎

J_AF and

␾H= 0°, ␾UC equals ␾F, thus H_eb and H_c are analytically given as H_eb= −J_AF/

共

M_UCt_UC+ M_Ft_F

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and H_c= 2

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K_UCt_UC + K_Ft_F

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/

共

M_UCt_UC+ M_Ft_F

兲

. When t_UCapproaches zero, the MB model is recovered. For arbitrary J_Fand J_AFvalues,␾UCand

␾Fin equilibrium can be evaluated as a function of␾Hand H by finding local minima of E_tot. The representative M reversal curves of both F and UC layers at␾H= 0° are shown in Fig. 2

共

a

兲

for the case of J_F/ J_AF= 3

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i.e.,

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␣F,␣AF

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=

共

3 , 1

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, where J_F=␣FJ₀ and J_AF=␣AFJ₀ with J₀= 0.08 erg/ cm².¹⁹ In this case, the sizable values of H_eband H_cfor the individual F and UC layers are clearly found and both values are com- parable to those experimental ones obtained from element- and interface-resolved hysteresis loops for a Co/ FeMn interface, as shown in the inset.¹¹In the element-resolved loops, F Co and UC Fe reversals occurs simultaneously due to their strong coupling, as in our model case of J_F/ J_AF= 3. The␾H

dependence of H_eband H_cfor the F and UC layers are also calculated as shown in Fig. 2

共

b

兲

, which are in general agree- ments with the trend of experimental results reported earlier.²⁰For the case of

共

␣F,␣AF

兲

=

共

2 , 4

兲

, the␾Hdependen- cies of H_eb and H_c are also plotted in Fig. 2

共

b

兲

for their comparison between the different strengths of J_F/ J_AF.

Next, we calculate the dependence of H_eband H_cas well as the shape of M reversal loops upon both J_Fand J_AF for individual F and UC layers. In Fig. 3

共

a

兲

, the resultant M reversal loops are plotted versus both ␣F and␣AF,²¹ which manifest that the relative strength of J_Fand J_AF determines the characteristic shapes of F and UC reversals. For the case of J_Fand J_AFwhose values are within the gray-colored area

FIG. 2.共Color online兲共a兲normalized M reversal curves of individual F and UC layers, calculated for tAF= 20, tUC= 1.2, and tF= 3.5 nm. The inset shows the normalized Kerr rotation␪Kloops of element-resolved and interface- sensitive M reversals for an interfacial Co and UC FeMn layers;共b兲angular

␾Hvariations of H_eband H_cfor共␣F,␣AF兲=共3 , 1兲and共2, 4兲. The physical parameters relevant to the model are used as follows: MF= 1500, MUC

= 800 emu/ cm³, KAF= 30 000 erg/ cm³, KFtF=␩共KUCtUC· JF兲^1/2, KUCtUC

=␩共KAFtAF· JAF兲^1/2 with a proportional constant ␩= 0.16, and JAF= J0␣AF, JF= J0␣F, with J0= 0.08 erg/ cm².

FIG. 3. 共Color online兲共a兲normalized M reversal curves at ␣Fand ␣AF

values as noted. The physical parameters used in this calculation are the same as those in Fig. 2共a兲. The gray-colored area indicates共␣F,␣AF兲values at which the F and UC layers switch simultaneously;共b兲calculations of Heb

and Hcfor the F layer as a function of␣Ffor different␣AFvalues.

192512-2 Lee, Yu, and Kim Appl. Phys. Lett. 86, 192512共2005兲

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in Fig. 3

共

a

兲

, the F and UC layers switch simultaneously because their coupling is stronger than that between the UC and nominal AF layers. This model thus reproduces well experimentally observed coupling behaviors of interfacial UC AF and F layers, as shown in the insets of Fig. 2

共

a

兲

.^11,14 According to our interface-proximity model, the UC spins do not pin directly an F layer during its exchange biasing because the former follows the switching of the latter. How- ever, the F layer is still exchange-biased through the switchable UC region by the resistance of the AF layer. This is because the UC spins are still coupled to the nominal AF layer. For the other case where J_Fand J_AFvalues are outside the gray-colored area, the reversals of the UC and F layers do not occur simultaneously, i.e., are partially or nearly decoupled.

To clarify the origin of the reductions of experimentally observed values of H_eb, we calculate H_eband H_cversus J_Fup to␣F= 10³ for various␣AF

共

from 0 to 10

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, as shown in Fig.

3

共

b

兲

. For␣AF

艋

1, H_ebremains almost constant, i.e., is inde- pendent of ␣F even up to 10³. For the larger value of

␣AF, H_eb monotonically increases with ␣F up to its certain value and then saturate above the value. These results indicate that such significantly reduced␣AF values can lead to the reduction of H_eb even for the largest value of ␣F= 10³. Until now, the reductions of H_ebtypically observed in experiments cannot be explained by using the MB model when one considers the large value of theoretical J_F in metallic F/AF systems, but our interfacial-proximity model can do that. In addition, the enhancements of H_c observed in experiments are well predicted just by solving E_tot for the sufficiently sizable values of ␣F, as shown in Fig. 3

共

b

兲

. Figure 4

共

a

兲

shows the dependencies of H_eband H_cupon t_Fand t_UC. The t_Fdependencies of H_eband H_care compared with those experimental data for various samples containing a NiFe/ FeMn system, as shown in Fig. 4

共

b

兲

. Those experimental and calculation values agree well to some extent. Here, we do not intend to fit the calculation data to the experimental ones.

In conclusion, the simulation results based on the interface-proximity model reveal that switchable UC regions

with a sizable thickness in conjunction with J_AFweaker than J_Fcan give rise to remarkable reductions in H_eb. It is worth noting that experimental estimations of J through the mea- sured values of H_ebin exchange-coupled F/AF metallic films would be the determination of J_AFinstead of J_Ffor the case of J_F

⬎

J_AF. The conditions of sample preparations as well as EB setting would influence not only the relative strength of J_F and J_AF but also t_UC. These parameters can govern the values of H_eband H_cin real samples, and their M reversal characteristics as well. The most important parameter to govern H_eb is likely to be J_AF that can be modified at an F/AF interface through the proximity effect during sample preparations as well as by a certain field-cooling procedure. The density of interfacial UC regions and degree of the rigidity of an AF layer in real samples can be implemented into an effective value of J_AFin our model case.

This work was supported by the KOSEF through the q-Psi at Hanyang University.

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21The Hcand Hebvalues were estimated by finding H at zero M.

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23S. M. Zhou, K. Liu, and C. L. Chien, Phys. Rev. B 58, R14717共1998兲. FIG. 4.共Color online兲共a兲the dependencies of Heband Hcon tF共and tUCin

the inset兲for simultaneous F and UC switching at 共␣F,␣AF兲=共3 , 1兲; 共b兲 Comparisons of those calculation results with experimental data. The different types of circle共Ref. 3兲triangle共Ref. 22兲, and square共Ref. 23兲symbols represent different samples for a NiFe/ FeMn bilayer system. The solid and open symbols indicate Heband Hc, respectively.

192512-3 Lee, Yu, and Kim Appl. Phys. Lett. 86, 192512共2005兲