ЖЭТФ, 2020, том 158, вып. 1 (7), стр. 124-127

INTERLAYER EXCHANGE COUPLING, SPIN PUMPING AND

SPIN TRANSPORT IN METALLIC MAGNETIC SINGLE

AND BILAYER STRUCTURES

P. Omelchenkoa*, E. Montoya^a,b, E. Girt^a, B. Heinrich^a

^a Department of Physics, Simon Fraser University,

8888 University Dr, Burnaby, BC, V5A 1S6, Canada

^b Department of Physics and Astronomy, University of California

92697, Irvine, CA, USA

Received March 3, 2020,

revised version March 3, 2020

Accepted for publication March 17, 2020

Contribution for the JETP special issue in honor of A. S. Borovik-Pomanov’s 100th anniversary

DOI: 10.31857/S0044451020070111

spacer layer) dependents strongly on the electronic

structure of the SL. The coupling across majority of

Interlayer exchange coupling in thin films is one of

metallic spacer layers oscillates between antiferromag-

netic and ferromagnetic as a function of the spacer layer

the cornerstones of modern spintronics-based techno-

logy. This phenomena has been an active area of re-

thickness. These oscillations originate from the sharp

transition in momentum space between filled and un-

search for several decades. The focus of this paper is

filled states at the Fermi surface of the spacer layer

a few coupling mechanisms relevant in ulta-thin film

structures. We review static interlayer exchange cou-

[1]. The models show that the critical spanning vectors

of the Fermi surface of the spacer layer determine the

pling, providing a brief overview of various coupling

mechanism including a new mechanism of non-collinear

oscillation period [2].

coupling which is attractive to spintronics applications.

Interlayer coupling has been observed across a ma-

The next part discusses proximity polarization coupling

jority of 3d, 4d and 5d non-magnetic metallic spacer

which can appear as a dominating coupling mechanisms

layers [3-8]. For applications it is often desired to

in Stoner enhanced materials. The last part reviews

have FM/SL/FM structures with large antiferromag-

spin-pumping as a form of dynamic coupling. A de-

netic coupling. The largest reported antiferromag-

scription of spin-pumping is presented as an extension

netic coupling (39 erg/cm²) was observed in Co/Rh/Co

of static, RKKY coupling into dynamic coupling by

multilayers deposited with molecular beam epitaxy

allowing for a time-delayed response. This approach

(MBE) [9]. Unfortunately, the same structure de-

makes a natural connection between static and dy-

posited by magnetron sputtering, which is preferred de-

namic coupling. We also present a detailed derivation

position techniques for fabrication of devices, results in

of the conventional spin-pumping theory in a reparam-

an order of magnitude smaller coupling strength. This

eterized form. This model is only applicable for highly

reduction in coupling is attributed to inter-diffusion at

conductive materials but fails for materials with large

the FM/SL interfaces in sputter deposited films [9].

spin-orbit coupling. In view of this we review several

Recently, it was demonstrated that a few atomic

spin-pumping studied in Au, Ag, Pd and Pt which ex-

layers thick spacer layers can be used to control the

plore the adequacy of this model and its limits.

angle between the magnetic moments of two ferromag-

The nature of the interlayer exchange coupling

netic layers in FM/SL/FM [10,11]. The spacer consists

in FM/SL/FM (FMs are ferromagnetic layers, SL is

of a nonmagnetic material (NM) alloyed with ferromag-

netic materials. Changing the nonmagnetic to ferro-

^* E-mail: ppo@sfu.ca

magnetic concentration ratio in the spacer allows for

124

ЖЭТФ, том 158, вып. 1 (7), 2020

Interlayer exchange coupling...

J, erg/cm²

thermodynamic equilibrium in the presence of inter-

face spin dependent scattering of NM electrons at the

FM/NM interface. Quantitatively spin-pumping was

0.2

first introduced by using formal spin algebra treatment

0.1

of the spin dependent scattering of NM electrons at

0.5

1.0

1.5

2.0

2.5

the FM/NM interface [16] leading to the generation of

-0.1

spin current acting as a peristaltic spin-pump. Alter-

0.8 nm

-0.2

natively, it was shown that the origin of spin-pumping

arises from time retarded interlayer exchange coupling

[17]. The advantage of the first treatment is that it

introduces explicitly the spin-pumping parameters and

allows one to extend this concept to the spin trans-

0.5

1.0

1.5

2.0

2.5

3.0

port in NM by using spin diffusion theory. The second

Pt Thickness, nm

treatment shows that spin-pumping is just a direct ex-

tension of time retarded interlayer exchange coupling

Fig. 1. Interlayer exchange coupling strength vs. thickness

and allows one to extent this concept to systems with

of Pt spacer layer. The line is a fit using an exponential fit

strong electron spin correlation effects.

derived from free energy of the Landau theory of phase transi-

A very clear example of dynamic coupling by spin-

tions, yielding ξ = 0.31 ± 0.1 nm. Inset shows the residuals to

pumping through Au was presented in [18]. Performing

the fit, the dashed line is a guide for the eye. Reprinted with

angular dependent ferromagnetic resonance (FMR) on

permission from Omelchenko Appl. Phys. Lett. 113, 142401

GaAs/16Fe/16Au/40Fe films the authors were able to

study the line-width of the two magnetic layers, 16Fe

control of the relative angle between the magnetic mo-

and 40Fe. As the resonance fields of the magnetic lay-

ments of the ferromagnetic layers. The onset of the

ers cross, the spin-pumping contribution to line-width

non-collinear alignment between the magnetic layers

also drops, see Fig. 2. This is in perfect agreement

coincides with the advent of magnetic ordering in the

with spin-pumping theory since at the crossing point

spacer layer, which is induced by the surrounding fer-

the magnetic layers are compensating each others losses

romagnetic layers or is inherent to the spacer layer.

due to spin-pumping.

Coupling through polarizable spacer layers (Pt or

Usually spin-pumping manifests itself as an effect on

Pd) is predominantly of ferromagnetic nature with

the FMR line-width or the measured magnetic damp-

exponentially decreasing strength by increasing the

ing. However, it can also lead to a driving toque which

spacer layer thickness. An oscillatory coupling is su-

can also generate precession. In [20] the authors used

perposed on top of the ferromagnetic coupling back-

a temporal and spacial resolved magneto-optical Kerr

ground, which does not affect the sign of the coupling

effect to study the response of 12Fe due to driving of

[12]. The results of [13] and [14] indicate that the in-

16Fe in 16Fe/nAu/12Fe structures. It was found that

terlayer exchange coupling through Pt is dominated by

the 12Fe response is out-of-phase with the 16Fe preces-

proximity induced magnetization as oppose to RKKY

sion which a consequence of the fact that spin-pumping

like oscillatory coupling behavior observed for weakly

toque is proportional to the time-derivative of the mag-

polarized materials (Au, Cu, Ag). This is not surpris-

netic moment and therefore is 180^◦ out-of-phase with

ing considering that Pt is a Stoner enhanced material

the source.

and therefore is able to mediate long range magnetic

Spin-pumping into materials such as Au, Ag and Cu

order. The ferromagnetic proximity coupling decays

is in good agreement with the conventional spin-pum-

exponentially with increasing Pt thickness on a length-

ping model [19]. However for Stoner enhancement ma-

scale of ξ = 0.31 nm, see Fig. 1. The coupling is rep-

terials such as Pd and Pt, the interpretation of the

resentative of the induced magnetization inside of Pt.

spin-pumping model leads to an unusual limit. Mag-

This length-scale is very similar to the length-scale of

netic damping studies on spin-pumping into Pd found

induced magnetic moment in Pt in the Co/Pt struc-

that the spin relaxation time (τPdsf = 1.70 · 10-14 s)

tures as studied by XMCD [15], ξ_XMCD = 0.41 nm.

is quite similar to the electron momentum relaxation

So far the discussion is focused on time-independent

time (τPdel = 1.91 · 10-14 s). It can be shown that in

coupling, however, the dynamics of the ferromagnet can

this limit the spin-pumping model would suggest that

also lead to coupling by spin-pumping. The concept of

Pd acts better then a perfect spin-sink (absorber of spin

spin-pumping comes from a general ideas of reaching

current).

125

P. Omelchenko, E. Montoya, E. Girt, B. Heinrich

ЖЭТФ, том 158, вып. 1 (7), 2020

For Pt the situation is even more unnatural since

τ^Pt

is estimated to be ∼ 10 larger than τPtel. Pt

therefore provides a good test for the conventional

spin-pumping model. However, the difficulty of testing

spin-pumping in Pt is that it mediates proximity

induced coupling, see Fig. 1, on similar length-scales

as the spin-pumping length scale. In [8] the effect of

proximity coupling was utilized in FMR measurements

to study the behaviour of spin-pumping through Pt.

Calculation

The proximity coupled structure resulted in two FMR

16 AL data

modes, in-phase and out-of-phase precession of the

40 AL data

two magnetic layers. The in-phase precession resulted

in a suppression of spin-pumping induced damping,

100

110

120

similar to the result of [18] for reduction of the

line-width during mode crossing in 16Fe/16Au/40Fe

Angle of DC-field, deg

structure. The out-of-phase precession led to en-

Fig. 2. Dependence of FMR linewidth in the 16Fe and 40Fe

hancement of the magnetic damping. This is inline

layers. Notice that the resonant field crossing the contribu-

with the spin-pumping model since for out-of-phase

tion of spin current is entirely removed [18]. The solid line is

precession the two magnetic layers are exchanging

calculation using the spin net flow Isp(16Fe)-Isp(40Fe) for the

spin current of opposite polarization and effectively

16Fe/Au interface and vice versa for the Au/40Fe interface.

enhancing each others damping, see Fig. 3. It was

Spin current was calculated using conventional spin-pumping

found that all the data could be consistently analyzed

theory [19] with the magnetic parameters for 16Fe and 40Fe.

with two spin-pumping parameters, spin diffusion

Notice that the thinner layer exhibits an increase in the spin-

length (δsd = 1.1 nm) and spin-mixing conductance

pumping damping before it drops down to zero. This clearly

(g↑↓ = 4.3 · 1015 cm-2). This result emphasize the

shows that the phase of precession plays an important role.

robustness of the spin-pumping/spin diffusion model.

Close to the crossing of resonance fields it can even enhance

the damping. The thicker layer just show a gradual drop to

the bulk damping. AL — atomic layer

Funding. We would like to express our thanks

to Natural Sciences and Engineering Research Council

^sp,

10^-3

of Canada (NSERC) for its generous financial support

without which this work would have not been possible

to carry out.

Acknowledgments. Authors would also like to

thank to our colleagues, G. Woltersdorf, B. Kardasz,

O. Mosendz, Z. Celinski, R. Urban, T. Monchesky,

Z. Nunn and A. S. Arrott (SFU), Kirschner (MPI

Halle), C. H. Back (University of Regensburg) and

M. Freeman (University of Edmonton) for their very

Py|Pt

valuable contributions to our SFU program in spin

Py|Pt|Py — Acoustic mode

dynamics.

Py|Pt|Py — Optical mode

The full text of this paper is published in the English

0.5

1.0

1.5

2.0

2.5

3.0

3.5

version of JETP.

Pt Thickness, nm

Fig. 3. Damping with increasing thickness of Pt for the

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