Journal of Magnetism and Magnetic Materials

Increase of the blocking temperature of Fe – Ag granular multilayers with increasing number of the layers

Judit Balogh

^a

, Dénes Kaptás

^a,n

, László F. Kiss

^a

, István Dézsi

^b

, Akio Nakanishi

^c

, Eamonn Devlin

^d

, Marianna Vasilakaki

^d

, George Margaris

^d

, Kalliopi N. Trohidou

^d

aInstitute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary

bInstitute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary

cDepartment of Physics, Shiga University of Medical Science, Shiga 520-2192, Japan

dInstitute of Nanoscience and Nanotechnology, NCSR“Demokritos”, Aghia Paraskevi, 15310 Athens, Greece

a r t i c l e i n f o

Article history:

Received 31 July 2015 Received in revised form 12 October 2015 Accepted 15 October 2015 Available online 23 October 2015 Keywords:

Multilayer Superparamagnetism Monte-Carlo simulation Mössbauer spectroscopy

a b s t r a c t

Multilayers of 0.4 nm Fe and 5 nm Ag with repetition number,n¼1, 2, 5, 10 and 20 were prepared by vacuum evaporation onto Si wafer. The blocking temperature was determined by measuring thefield cooled and zerofield cooled magnetization curves with a SQUID magnetometer and it was found to increase by almost an order of magnitude from around 20 K for the single Fe layer sample up to around 160 K forn¼20. Significant increase of the average size of the superparamagnetic Fe grains by increasing the number of the Fe layers was excluded by conversion electron Mössbauer spectroscopy measurements of the paramagnetic state. The role of the dipole–dipole interactions and their interplay with the out-of- plain magnetic anisotropy in the variation of the blocking temperature has been investigated by Monte- Carlo simulations.

&2015 Published by Elsevier B.V.

1. Introduction

The superparamagnetic nature of ultra-thin Fe layers in be- tween Ag layers has been observed since long[1,2], but the de- pendence of the superparamagnetic properties on the number of the alternating Fe and Ag layers in a multilayer stack has not yet been studied. Superparamagnetism of a nominally few monolayer thick magnetic layer appears due to the island growth mode of the layer and multilayers of such discontinuous layers are called granular multilayers. Different assembly of magnetic nanoparticles into larger structures is of intense interest as an approach both to understand the interactions effective between the nanoparticles and to engineer new materials and devices[3].

The effects of dipole interactions on the superparamagnetic behavior have been intensively studied since long[4], but it is only a few granular multilayer systems that were studied from this point of view experimentally. The blocking temperature,TB–the temperature above which the relaxation frequency of the mag- netic moment exceeds the frequency characteristic to the mea- surement–was shown to increase with the repetition number of the layers in case of Co/Al2O3[5], Co–HfO2[6], Fe3O4/polymer[7]

multilayers. To our knowledge systems with metallic non-mag- netic spacer layer have not yet been studied in this respect. Monte-

Carlo simulations of granular multilayers[8]are less investigated, and do not deal with magnetically disordered systems. Theoretical calculations on the anisotropy and dipolar energies[9]were made only for the ordered case; differently stacked layers of densely packed crystalline planes. Random distribution of the magnetic moment or anisotropy was studied in different nanoparticle as- semblies and the dipolar interactions were shown to be re- sponsible for the rich variety of the magnetic behavior found ex- perimentally[10–12]. The variation of the number of layers of granular multilayers offers a well controllable way of studying the effect of long range dipolar interactions between randomly dis- tributed particles[13].

In this work we study the blocking of the superparamagnetic relaxation in Fe/Ag granular multilayers with different number of Fe/Ag bilayers. The average size of the Fe granules will be esti- mated from Mössbauer spectroscopy measurements. The role of a perpendicular anisotropy component – well established in the literature[14,1,15]–in the observed unusually large variation ofTB

will be investigated by Monte-Carlo (MC) simulations.

2. Experimental

The samples were prepared by thermal evaporation in a high vacuum chamber with a base pressure of 10⁷Pa onto Si(111) wafers at room temperature. Ag and B were evaporated by Contents lists available atScienceDirect

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

Journal of Magnetism and Magnetic Materials

http://dx.doi.org/10.1016/j.jmmm.2015.10.055 0304-8853/&2015 Published by Elsevier B.V.

nCorresponding author.

E-mail address:kaptas.denes@wigner.mta.hu(D. Kaptás).

electron guns from Cu cold crucibles, and ⁵⁷Fe was evaporated from a heated W boat. The following multilayer samples were prepared;

Si(111)/5 nm Ag/[0.4 nm⁵⁷Fe/5 nm Ag]n/5 nm Ag/10 nm B, with n¼1, 2, 5, 10, and 20.

The bracket and its subscript indicate the multilayer unit and the number of repetitions, respectively. The 10 nm B cover layers were applied to increase the stability of the sample against oxi- dation of the Fe layers.

TB was determined from magnetization measurements in a superconducting quantum interference device (SQUID). It is de- fined as the cusp temperature of the magnetization measured after cooling the sample from 300 K to 5 K in zerofield, i.e. from the ZFC magnetization curve.

The room temperature conversion electron Mössbauer spec- troscopy (CEMS) measurements were carried out by using a con- ventional constant acceleration-type spectrometer, a 25 mCi⁵⁷Co.

(Rh) source and a proportional counterfilled with 96%He–4%CH4

gas mixture. The isomer shift (IS) values are given relative to that of

α

-Fe at room temperature.

3. Model calculations

We developed a model for the description of the granular multilayered system.

Random assemblies of monodispersed magnetic grains (parti- cles) of diameterDare placed on the nodes of successive two di- mensional square lattices with a particle concentration c¼60%

which is above the percolation threshold in each magnetic plane.

The grains were randomly distributed over a 21a21asize area in each layer, whereais the lattice spacing, which is supposed to be equal to the inter-grain distance. The distance between these planes was taken to be equal to 2a. In case ofD¼agrains sitting at neighbor sites of the plane touch each other, but grains of neigh- boring planes are separated. The magnetic grains are single-do- main, and each of them is represented by a three-dimensional classical unit spin vectorsiand with a uniaxial anisotropy.

The MC simulations technique with the implementation of the Metropolis algorithm has been applied to the above model for the calculation of its magnetic behavior. All the parameters were normalized to the anisotropy energy[16], therefore the anisotropy constant was taken ask¼1. The total anisotropy-reduced energy is E= ∑_{i i}ε where ε_i is the anisotropy-reduced energy per particle given by the sum of the Zeeman (due to interaction with an ex- ternalfield), the anisotropy, the nearest neighbor Heisenberg ex- change and the dipolar interaction energy terms, hence,

h s e k s e j s s g s D s

1

i i h i i

i j i j

i j i ij j 2

,

∑ ∑

ε = − ( ) − ( ) − −

( )

→⌢ →⌢

< >

→→

>

→ →

where〈i,j〉denotes summation over nearest neighbors only,le_hand le_iare the directions of the magneticfield and the anisotropy axis ofith particle, respectively, andDijis the dipolar tensor between theith andjth nanoparticle.

The dipolar strength, g=μ₀M D a_s²( / )³/24K, which depends on the saturation magnetization, Ms, and the effective anisotropy constant,K, was taken asg¼0.1, based on similar considerations [16–18]as has been given for dense Fe nanoparticlesfilms pre- pared by a special pulsed laser deposition technique[17]. In our Fe–Ag granular multilayer samples the average grain size is also around 3 nm—as it will be shown further down in the experi- mental results session—and the effective anisotropy is also esti- mated to have a value similar to that used in Ref.[15], since the Fe grains are also non-spherical objects of disc-like shape with a high aspect ratio, i.e. with height close to the nominal layer thickness

[19]. The saturation magnetization of the grains is close to the bulk value (1.710⁶A/m), as confirmed by our magnetization mea- surements. The dipolar interaction was taken into account be- tween grains within each layer and between grains of neighboring planes. We have implemented the Ewald summation technique for the calculation of the long-range dipolar interactions with periodic boundary conditions inx–yplane and free boundaries in thezaxis.

Little information is available for the value of the effective ex- change energy (j), and therefore, it is treated as a free parameter.

We consider that the grains that are in contact interact via the nearest neighbor Heisenberg exchange interaction with an aniso- tropy-reduced exchange coupling constantj¼2.0.

Two cases of anisotropy axes orientation have been considered:

(1) randomly oriented in each of thex–yplanes and (2) vertical to the x–y plane along the z axis (perpendicular anisotropy). The magneticfield was applied along thexaxis and we have calculated the magnetization,Mxper spin, along thefield axis with the im- plementation of the Metropolis MC algorithm. For eachfield and temperature value, thefirst 500 MC steps per spin were used for equilibration, and the subsequent 710³ were used to obtain thermal averages. The measurements were averaged over 10–20 different initial conditions, random configurations of the occupied

0 50 100 150 200 250 300

-10 0 10 20 30

n= 10 n= 5

M(emnu/g)

T(K)

Fig. 1.Magnetization of granular multilayers with the different number of Fe/Ag bilayers measured after cooling in 10 Oefield (full symbols) and in zero field (empty symbols).

0 10 20 30 40

0 50 100 150

n = 20 n = 10

n = 5

n = 2 n = 1

T

B

(K)

H(Oe)

Fig. 2.Dependence of the temperature of the maxima of the measured ZFC curves (TB) for different number of Fe/Ag bilayers.

lattice sites and initial spin orientations. The simulations of the ZFC magnetization versus temperature (t) curves were performed starting from a temperaturetmaxmuch higher than the blocking temperature, so all the particles are in the superparamagnetic region for all the simulated systems. Then the system is cooled down to low temperature (t¼0.002) in zerofield (h¼0). Finally, a smallfield is applied (h), and the system is heated up slowly while

the ZFC magnetization is calculated at several temperatures.

4. Experimental results

Two representative magnetization curves measured in 10 Oe appliedfield after cooling the sample in the same or in zerofield, i.e. the FC/ZFC magnetization curves, are shown for then¼1 and 10 samples inFig. 1. The blocking temperatures measured in dif- ferent appliedfields are shown for all the samples inFig. 2. As it can be seen from thefigure there is a large, almost an order of magnitude, increase of the blocking temperature as the number of bilayers is increased from 1 to 10. Upon further increasing the number of bilayers (n¼20) no change of the blocking temperature is observed.

The CEMS spectra measured at room temperature are shown in Fig. 3. All the spectra exhibit only paramagnetic components, which can befitted by two doublets with largely different quad- rupole splitting (QS) and isomer shift (IS) values (IS1¼0.09(1), QS₁¼0.12(2) mm/s and IS₂¼0.16(2) mm/s, QS₂¼0.50(3) mm/s).

QS1is small compared to the linewidth, so it is not resolved and thefirst component appears as a single line. The measured width of the lines is about 50% broader than the experimental linewidth (0.24 mm/s), indicating a distribution of the atomic environments and the respective hyperfine parameters, but with the exception of then¼1 sample, the spectra can befitted not only by similar hyperfine parameters but similar spectral intensities (I1¼0.38(5), I2¼0.62(5)) of the two components, as well. For n¼1 a third component (IS₃¼0.27 mm/s, QS₃¼1.03 mm/s) was also necessary to obtain a goodfit.

Magnetization curves obtained by the MC simulations are shown inFig. 4for a system of 5 granular magnetic layers. The ZFC magnetization curves for differenthvalues are shown both for in plane random anisotropy (a) and out of plane perpendicular ani- sotropy (b). In spite of the uniform size of the grains the super- paramagnetic transitions are broad, which is due to the interac- tions between the grains. The insets ofFig. 4show the measuring- field dependence of the blocking temperature, T_B, which is col- lected for all the calculations with different number of magnetic layers and anisotropy directions inFig. 5.

5. Discussion

In case of a non-interacting particle assembly the increase ofTB

can result from the increase of the average grain size and/or the

(0.4 nm Fe + 5 nm Ag) _n

n=1

In te ns ity (arbi tr ar y uni ts )

n=2

n=5 n=10

n=20

-2 -1 0 1 2

velocity (mm/s)

Fig. 3.CEMS spectra measured at 300 K. Thefitted components are indicated be- low each spectrum.

0.0 0.2 0.4 0.6 0.8

M

x

/s pi n

t

0.13 0.15 0.2 0.3

a

0.4

0.00 .2 0.4

0.0 0.2 0.4 TB

h

0 2 4 6 8 10 0.00 2 4 6 8 10

0.2 0.4 0.6 0.8

M

x

/s pi n

t

0.13 0.15 0.2 0.3

b

0.4

0.00 .2 0.4

0.4 0.6 0.8 T_B

h

Fig. 4.Simulated ZFC magnetization curves (see text for details) of 5 granular layers for different measuringfields (h) with in plane random anisotropy (kxy)(left) and out of plane anisotropy (kz)(right). Insets show the dependence of the blocking temperature onh.

anisotropy energy. Significant changes of these factors for our samples can be ruled out by the CEMS measurements.

The CEMS spectra of the samples inFig. 3do not show change with increasing layer number. The small third component ob- served only for then¼1 sample can be due the effect of the nat- ural oxide layer covering the Si substrate, which might have in- fluence across some imperfections of the thin bottom Ag layer. It might be connected to some extremely small grains, as a similar component is also present in Ref.[20]in case of 0.15 ML nominal layer thickness. The interpretation of the two main components is not certain; they might represent large and small grains of a grain size distribution and/or bulk and surface components of similar size grains, as well, but in any case the similarity of all the spectra prove that the average grain size does not change with the layer number. The evolution of the average grain size with increasing nominal Fe layer thickness over an Ag layer was studied earlier by

“in situ” scanning tunneling microscopy measurements during layer growth [20]. The Mössbauer spectra were recorded [20]

“ex situ” after covering the grains with a protective Ag layer.

Comparing the spectra ofFig. 3to those published in this study, one can estimate a grain size of around 3 nm for all the samples.

The effective anisotropy energy is also not supposed to change significantly, because according to previous Mössbauer results[15]

the alignment of the spontaneous magnetization is basically re- lated to the nominal thickness of the Fe layer, i.e. to the average grain size.

Increase of TB upon increasing the number of the granular magnetic layers has already been observed in a few similar sys- tems[5–7]and the dipolar interactions between the layers gave satisfactory explanation of the modest increase observed e.g. in the Co/Al2O3samples[5]. The much larger change for our samples is surprising, since the characteristic quantity –

μ

^2/d3 – is esti- mated to be smaller in this case (

μ

is grain moment anddis layer distance). The 5 nm thickness of the non-magnetic layer excludes the possibility that an RKKY-type coupling through the metallic Ag spacer[21]would be responsible for the enhancement. The out-of- plain alignment of the grain moments, however, can play a sig- nificant role. The observed increase ofTBwith the number of layers is well reflected in the MC simulations results which give a definite increase ofTBwith increasing layer number by considering a grain anisotropy perpendicular to the layers, while the variation is within the error limits for all measuringfield values for the in- plane anisotropy situation. Our simulations demonstrate that the out of plane anisotropy for the grains is responsible for the in- crease ofTBwith the increase of the layers number in our system.

To achieve better agreement with the measured data, further calculations will be necessary which take into account (i) possible

correlations between the anisotropy directions of the grains in subsequent layers due to the epitaxial growth within a columnar structure[19], and (ii) a grain size distribution.

6. Conclusion

An unusually large increase of the blocking temperature was observed in superparamagnetic Fe/Ag granular multilayers by SQUID measurements upon increasing the number of bilayers from 1 to 10. The Mössbauer spectra of the samples exclude a significant increase of the average grain size. Monte Carlo simu- lations show that beyond the dipolar interactions between neighboring layers, the out-of-plane anisotropy plays a decisive role in the observed large variation.

Acknowledgment

The authors acknowledgefinancial support from the BILATERAL R&D Co-operation Greece-Hungary (NSRF) project“Magnetic In- teractions in Multilayer Heterostructures”, MIS HUN 48 and TÉT_10_1_2011_0579. J.B., D.K., L.F.K. and I.D. thank for the support by the Hungarian Scientific Research Fund (OTKA) Grants K112811 and K101456.

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