UPPSALA UNIVERSITY

MASTER THESIS

Magnetic Coupling and TransportProperties of Fe/MgO Superlattices

Author:Tobias Warnatz

Supervisor:Dr. Fridrik Magnus

Materials PhysicsDepartment of Physics and Astronomy

Thesis Number:FYSMAS1036

Series:FYSAST

September 8, 2015

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Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 X-Ray Reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Polarized Neutron Reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Magneto-Optical Kerr Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.5 Four-Terminal Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.1 Structural Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2 Magnetic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Magnetic Ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.4 Magnetotransport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3

SammanfattningMagnetiska strukturer med multilager är intressanta både för applikationer (hårddiskar, magnetfältssen-

sorer etc.) och för fundamental forskning (exempelvis koppling mellan magnetiska lager). Material medpassande gitterparametrar kan tillväxas epitaxiellt och forma ett supergitter. Den mycket kristallina kvalitetetenav såna materialprover kan leda till en bättre förståelse av den magnetiska kopplingsmekanismen och äventill uppkomsten av helt nya magnetiska fenomen.

I den här avhandlingen används Fe/MgO supergitter som skapats via en kombination av likströms-och radiofrekvens-katodförstoffning. Tjockleken hos de omagnetiska lagren av MgO varierades för attundersöka kopplingsmekanismen. Den strukturella karaktäriseringen utfördes med röntgenreflektivitetetoch röntgendiffraktion. Mätningarna med röntgenreflektivitet anpassades med GenX för att erhålla exaktavärden på lagrens tjocklek och ojämnhet. En hög kristallinitet och mycket jämna gränsytor mellan lagrenerhölls för samtliga tjocklekar på MgO-lagren.

Den longitudinella magnet-optiska Kerreffekten användes för att studera supergittrens magnetiska egen-skaper. Ovanliga steg i hystereskurvan erhölls för alla prover. Vi fann att varje enskilt steg svarade mot att ettindividuellt Fe-lager bytte riktning. Kopplingen favoriserar en antiparallell linjering i rumstemperatur ochkopplingens styrka beror kraftigt på MgO-lagrets tjocklek. Kopplingsmekanismen kommer från utbytetmellan lagren genom spinnpolariserad kvanttunnling. Dock avslöjade temperaturberoende mätningar enmagnetisk koppling assisterad av materialorenheter vid höga temperaturer och även av kopplingsbeteendetav en perfekt tunnelförbindelse vid låga temperaturer.

Genom mätningar med polariserad neutronreflektivitet var det möjligt att bekräfta en periodisk, vinkel-rät och antiparallell linjering i de ferromagnetiska lagren för de tjocka respektive tunna lagren. Den vinkel-räta kopplingen verkar vara ett resultat av kampen mellan svagare, antiparallell koppling och den magne-tokristallina anisotropin.

Mätningar av elektron-transport i planet påvisade steg i magnetoresistansen som svarade mot stegenuppmätta i hystereskurvan huvudsakligen genom den anisotropa magnetoresistanseffekten. Dock upp-mättes ett svagt bidrag från tunnelmagnetoresistanseffekten vilket gör att dessa prover också är lovandeför framtida mätningar av elektron-transport ur planet.

AbstractMagnetic multilayer structures are interesting for applied science (hard-drives, magnetic field sensor

etc.) as well as for fundamental research (coupling mechanism of the magnetic layers). Materials withsuitable lattice parameters can be epitaxially grown to form a superlattice. The high crystalline quality ofthose samples may lead to a better understanding of the coupling mechanism as well as to the emergenceof novel phenomena.

In this thesis, Fe/MgO superlattices were grown via a combination of direct-current and radio-frequencysputtering. The thickness of the MgO spacer layers was varied to investigate the coupling mechanism.The structural characterization was done via x-ray reflectivity and x-ray diffraction. The x-ray reflectivitymeasurements were fitted via GenX to obtain precise thickness and roughness values of the layers. A highcrystalline quality and very smooth interfaces were found for all MgO thicknesses.

The longitudinal magneto-optical Kerr effect was used to study the magnetic properties of the super-lattices. Unusual steps in the hysteresis curve were found in all samples. It was found that each stepcorresponds to the switching of an individual Fe layer. The coupling favors an antiparallel alignment atroom temperature and its strength highly depends on the spacer layer’s thickness. The coupling mechanismwas assigned to the interlayer exchange by spin-polarized quantum tunneling. However, temperature depen-dent measurements revealed an impurity assisted coupling at high temperatures and the coupling behaviorof a perfect tunnel junction for low temperatures.

Through polarized neutron reflectivity measurements, it was possible to confirm a periodic, perpendicu-lar and antiparallel alignment of the ferromagnetic layer for thick and thin MgO spacer layers, respectively.The perpendicular coupling seems to be a result of the competition between weaker, antiparallel couplingand magnetocrystalline anisotropy.

In-plane transport measurements revealed steps in the magnetoresistance corresponding to the steps inthe hysteresis curve mainly due to the anisotropic magnetoresistance effect. However, also a small con-tribution of the tunnel-magnetoresistance effect was measured making these samples promising for futureout-of-plane transport measurements.

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1. Introduction

In 1986, Peter Grünberg demonstrated antiferromagnetic coupling of Felayers in Fe/Cr/Fe multilayers [1], which led subsequently to the discoveryof the giant magnetoresistance effect (GMR). Due to the giant resistance dif-ference observed for parallel and antiparallel alignment of the ferromagneticlayers, the effect was quickly adapted in commercial devices for magnetic fieldsensing (e.g. in hard drives). In 2006, a multi-stepwise reversal of magneticlayers in Fe/Cr/Fe superlattices was observed leading to a partitioned GMReffect [2]. Such structures are of particular interest since not only two binarystates (high and low resistance), but also intermediate resistance values couldbe used for reading out digital information leading to a higher storage density.However, this publication raised little attention mainly because the resistancechange in this partitioned GMR effect was rather small (max. 2.4% at 300K)making it impractical for commercial devices.

Even though it was already proposed in 1975 [3] and experimentally provenin 1995 [4] that a magnetoresistance effect can also be achieved with an insu-lating spacer layer it was not until 2004 [5, 6] that Fe/MgO/Fe junctions raisedmajor attention. This was because the achieved magnetoresistance effect wasmuch larger than any other reported effect through metallic or non-metallicspacer layers. Optimization in the growth led to astonishing magnetoresistancevalues of 500% at room temperature [7]. Hence, the tunnel-magentoresistanceeffect (TMR) replaced the GMR in most devices and even led to other noveldevices (like MRAMs [8]). The size of the TMR effect in single Fe/MgO/Fejunctions opens up the question whether a significant partitioned TMR can beobtained in MgO-based multilayers.

A partitioned TMR effect can only be achieved if an interlayer coupling ex-ists through the insulating layer. Replacing the metallic Cr spacer layer withinsulating MgO eliminates the coupling mechanism discovered by Grünberg.However, a different coupling mechanism occurs. This coupling mechanismwas first proposed in 1989 by a method based on spin current [9]. A laterapproach described the coupling based on quantum interference due to spin-dependent reflections at the interfaces [10, 11]. The experimental proof ofthis interlayer exchange by spin-polarized quantum tunneling came in 2002[12]. In contrast to the ferromagnetic-antiferromagnetic-oscillating couplingof metallic spacer layers depending on the spacer layer thickness, an insu-lating layer exhibits a non-oscillating coupling behavior. However, similarto the metallic spacer layer one observes an exponential decay in the cou-pling strength with increasing spacer layer thickness [13]. Recently, we have

7

demonstrated the possibility for a partitioned TMR by a multi-stepwise rever-sal in Fe/MgO/Fe superlattices [14]. However, even though the main couplingmechanism was attributed to the aforementioned spin-polarized quantum tun-neling, it was not possible to be certain about the main coupling mechanism.

In the present work, high quality MgO[Fe/MgO]10Pd superlattices with avariation in the MgO thickness have been prepared to distinguish betweendifferent coupling mechanisms. Structural characterization was done usingx-ray reflectivity (chapter 3.1), magnetic characterization was done using themagneto-optical Kerr effect (chapter 3.2) and polarized neutron reflectivity(chapter 3.3) was used to determine the magnetic ordering of ferromagneticlayers. Finally, in-plane magneto-transport measurements were performed toinvestigate the magnetoresistance. Furthermore, samples with a comparablehigh quality grown on SrTiO3 will be characterized to investigate if such sub-strates can be used for out-of-plane TMR measurements in Fe/MgO/Fe super-lattices.

8

2. Methods

In this chapter basic methods will be explained in order to understand andinterpret the presented results in chapter 3.

2.1 Sample PreparationA structure consisting of two or more discrete layers grown with different

materials is called a multilayer. If the materials have a comparable latticeparameter, a superlattice can be formed. A superlattice is defined by a longout-of-plane structural coherence [15] (atomic registry). The lattice mismatchbetween Fe (2.866 Å [15]) and MgO (4.213 Å [15]) at first sight appears to betoo big (47.0%) to form a superlattice, but a 45◦ rotation of the Fe layer on topof MgO (fig. 2.1) leads to a sufficient small lattice mismatch of only 3.94%.An obvious choice of substrate for such a superlattice is single crystallineMgO (100). Another suitable material in terms of lattice matching wouldbe SrTiO3. The 45◦ rotation of Fe on top of this material results in an evensmaller lattice mismatch (3.65%). Furthermore, this material can be dopedwith small amounts of Nb to become conductive. By using doped SrTiO3 as asubstrate for the Fe/MgO superlattices, out-of-plane transport measurementscan be performed.

Fe [1

00]

MgO [100]

45°

Easy

Axis

Hard Axis

FeMg O

Figure 2.1. Schematic illustration of the tetragonal Fe/MgO structure formed by a 45◦

rotation of the Fe layer on top of MgO.

9

Table 2.1. Spacer layer sputtering times and thicknesses.

Sample MgO Sputtering Time in s MgO Thickness in ÅA 450 19.9B 420 17.4C 350 16.7D 300 14.6

Pd- Capping

MgO

Fe

MgO Substrate

~45 Å {~15-20 Å {~21-23 Å {

~1 mm {} x10

Figure 2.2. Schematic illustration of the superlattice samples (side view).

The Fe and MgO layers were deposited with direct-current (DC) and radio-frequency (RF) magnetron sputtering, respectively. In order to ensure the highquality of the samples, the chamber’s base pressure was below 2· 10−9 Torrand Ar with a purity of 99.99999% was used as a sputtering gas. The 1 mmthick MgO (100) and SrTiO3 (100) 10 mm x 10 mm substrates were annealedfor 40 minutes at 550◦C. After that, the temperature was reduced to the growthtemperature of 165◦C [16]. Once the temperature had stabilized, Fe was sput-tered (epitaxially grown) for 75 s with a power of 50 W and an Ar pressureof 2.00 mTorr. MgO was RF-sputtered with a power of 60 W and the sameAr pressure. The Fe magnetron was turned off during the MgO sputteringand vice versa, to avoid cross-contamination. This process was repeated 10times before Pd was deposited for 30 s with a power of 50 W and the sameAr pressure as a capping layer (fig. 2.2). In order to study the interlayer cou-pling of the ferromagnetic (Fe) layers, different MgO layer thicknesses wereprepared (tab. 2.1). High resolution transmission electron microscopy images(HRTEM) were taken to investigate the quality of the samples, as shown infigure 2.3. A nice layering is observed, indicating very smooth surfaces aswell as an atomic registry through the whole sample.

10

Figure 2.3. HRTEM cross section image of a representative Fe/MgO (bright /darklayers) superlattice grown on a MgO (100) substrate. Very smooth interfaces (a) anda structural registry of the individual layers with respect to the single crystalline sub-strate lattice (b) can be observed.

2.2 X-Ray ReflectivityX-ray reflectivity is a powerful tool for investigating thin films as well as

multilayers. The experimental data can be used to obtain thickness, roughnessand other sample specific values [17]. The x-ray source emits polychromaticphotons (Bremsstrahlung and characteristic x-rays). In order to perform x-rayreflectivity (XRR) measurements, monochromatic x-rays are needed (here:copper Kα ). A grid can be used to select the desired wavelength. Due tointerference effects at the grid, only photons with a certain wavelength are re-flected. In general, it does not matter if the grid (monochromator) is placedbefore or after the sample. A slit in front of the x-ray source is used to reducethe beam’s divergence, but reduces the beam’s intensity simultaneously. Thechosen slit size usually depends on the probed structure and the desired reso-lution. A 2θ -ω-scan in a standard Bragg-Brentano-geometry was used for allthe measurements. The sample is rotated at a rate ω and the detector is rotatedwith a rate of 2θ , which is twice that of ω . In this case, it is ensured that theangle α between the source and the sample and between the sample and thedetector is always the same (fig. 2.4). XRR measurements start at very smallangles. Thus, total reflection occurs up to the critical angle αc. After that,ordinary reflection progresses to lattice planes, at which Bragg’s law can beused

n ·λ = 2d · sin(θ) (2.1)with n as a positive integer number, λ as the incident wavelength, d as thelattice plane distance and the reflection angle θ . X-rays scatter at the inter-faces between the layers due to the variation of electron densities (differentmaterials). Reflections from different interfaces will lead to a path difference

11

Substrate

X-RaySource Slit

Sample

Detec

tor

(α( α

ω

2θ

Figure 2.4. Schematic illustration of a XRR setup.

between the reflected waves (fig. 2.4). Constructive interference occurs only ifthe reflected waves are still in phase. Hence, Bragg reflections can only be ob-served if the relation in equation 2.1 is obtained. By knowing the wavelengthof the incoming photons and the reflection angle, it is possible to calculate thespacing between different layers.

It is convenient to plot the XRR data over the momentum transfer Q insteadof the angle θ , since Q includes the used wavelength and different data sets(e.g. neutron and x-ray reflection) can be compared. The momentum transferQ can be calculated via the following equation.

Q =4πλ

· sin(θ). (2.2)

A special case occurs if XRR measurements are performed on multilayersamples. A multilayer sample consists of two or more discrete layers period-ically arranged through the whole sample. Due to the chemical modulationin the sample, the Bragg condition can be satisfied for the multilayer stack(Bragg peaks) and for the thickness of the whole sample (Kiessig fringes) [15]as illustrate in figure 2.5. By measuring the distance between two neighboringBragg Peaks (or Kiessig oscillations) one can calculate the bilayer (or total)thickness. If the XRR data is plotted over Q, the measured distance corre-sponds to 2πd with the bilayer (or total) thickness d. It is worth mentioning thatonly the bilayer thickness and not the thickness of the individual layers can beobtained by measuring the Bragg peaks spacing. The width and height of theBragg peaks correspond to the thickness of the individual layers. By using afitting software (e.g. GenX [18]) it is possible to receive information about theinterface roughness, the thickness of the individual layers and variations in thematerials densities (due to stress/strain or vacancies). As already mentionedabove, x-rays are only sensitive to a variation in the electronic density. Hence,

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0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4 1 . 61 E - 8

1 E - 7

1 E - 6

1 E - 5

1 E - 4

1 E - 3

0 . 0 1

0 . 1

1C r i t i c a l A n g l e

K i e s s i g O s c i l l a t i o n s

Inten

sity (a

rb. un

its)

Q ( 1 / Å )

B r a g g P e a k s

Figure 2.5. GenX simulation of a MgO[Fe(52 Å)/MgO(11 Å)]10Pd(20 Å) superlatticewith an interface roughness of 2 Å (Fe) and 3 Å (MgO).

it is not possible to distinguish between layers made of different isotopes sincethe electronic density would be the same.

If higher angles (Q-values) are chosen to illuminate the sample, diffrac-tion occurs. The measured peaks correspond then to the lattice parametersof the materials within the sample. The lattice parameters (d) can be cal-culated via equation 2.1. A special case occurs, if multilayers with a highout-of-plane structural coherence (atomic registry) are measured. In this case,satellite peaks (also known as superlattice peaks) occur next to the principlepeaks.

13

Figure 2.6. Schematic illustration of the PNR geometry [19]. The angles αi and α findicate the angles of the incoming and reflected neutron beam, respectively. γ is theangle between the magnetization and the polarization of the incoming neutrons, whereγ = 0◦ and 90◦ correspond to a sample’s magnetization parallel to the y-axis (up) andx-axis (right), respectively.

2.3 Polarized Neutron ReflectivityNeutron reflectivity measurements exploit the wave character of neutrons

and are therefore similar to XRR measurements. However, neutrons are sen-sitive to variations in the nuclear (not electronic) densities, which makes thecombination of both techniques a powerful tool for characterizing samples.One of the biggest advantages of neutrons for the sample characterization istheir spin. Hence, it is possible to probe unpaired electron spins (magneticmoments) in the sample. This technique is called polarized neutron reflec-tivity (PNR) and can be used to probe the direction of the magnetization ineach layer as a function of thickness (depth dependent). A distinction is madebetween spin-flip (SF) and non-spin-flip (NSF) measurements. NSF measure-ments can probe a variation in nuclear density and a magnetization parallel tothe incoming neutron’s spin (fig. 2.6).

The NSF measurement is divided into up-up (UU, spin of incoming neu-trons up, measured neutrons up) and down-down (DD, spin of incoming neu-trons down, measured neutrons down). Both measurements are sensitive to avariation in nuclear density. However, the contribution of the magnetic partvaries for both channels depending on the orientation of the magnetization(parallel or antiparallel) to the incoming neutrons spin as illustrated in figure2.6 and described in the following equations.(

Vuu VudVdu Vdd

)=

2πh2

mN[(

bn 00 bn

)+

(by bxbx −by

)](2.3)

bx = bm · sinγ (2.4)

by = bm · cosγ. (2.5)

14

V are the neutron scattering potentials, bn is the nuclear scattering length, bmis the magnetic scattering length and γ is the angle between the magnetizationand the polarization of the incoming neutrons. A magnetization along the z-axis (along the momentum transfer Qz) cannot be measured via PNR.

The SF measurement is divided in up-down (UD, incoming neutrons up,measured neutrons down) and down-up (DU, incoming neutrons down, mea-sured neutrons up). SF measurements are not sensitive to a variation in thenuclear density, but it is possible to probe the sample’s magnetization per-pendicular to the spin of the incoming neutrons. Hence, the combination ofSF and NSF measurements is a powerful method to reveal the magnetiza-tion of individual magnetic layers perpendicular to the scattering plane. BothSF channels are usually identical and lead to the same information. In somespecial cases (e.g. magnetic chirality) both SF channels may differ and leadto additional information, but these cases are beyond the scope of this thesisand discussed elsewhere [19]. Figure 2.7 shows the scattering length den-sity (SLD) profile of a Fe/MgO superlattice. Since Fe and MgO are differentmaterials, one observes the same periodicity in the nuclear and electron den-sity. Furthermore, since the magnetization of the layers are aligned parallel toneutrons guide field, one observes a magnetic periodicity identical to the nu-clear and electronic one. The biggest difference (contrast) is exhibited for theelectron density. The nuclear density difference is low and hardly gives anysignal. However, the magnetic contrast is very pronounced illustrating that acombination of both techniques is very powerful.

Figure 2.7. XRR (green), nuclear UU (red) and magnetic UU (blue) SLD for a[Fe(21.6 Å)/MgO(16.7 Å)]10Pd superlattice with a magnetization along the neutronsguide field.

15

Mα α

Mα α

Mα α

Polar Longitudinal

Transverse

Figure 2.8. Schematic illustration of the three MOKE geometries.

2.4 Magneto-Optical Kerr EffectThe Magneto-optical Kerr effect (MOKE) is widely used to measure hys-

teresis curves as well as to image magnetic domains (Kerr microscopy) ofmetallic surfaces [20]. Magnetic thin films, as well as particles or other sys-tems can be investigates. It can be separated into three different geometries.The polar (P-MOKE), longitudinal (L-MOKE) and transverse (T-MOKE) asillustrated in figure 2.8, where the magnitude of the effect decreases in thesame order.

Figure 2.9 illustrates the experimental setup of a L-MOKE measurement.To exploit the L-MOKE effect, linear polarized light has to be used. In thiscase, the electric wave vector of the incident light is normal to the scatter-ing plane (s-polarized). The electric field of the incident light couples to theunpaired electron spins in the sample’s magnetic material due to spin-orbitinteraction [15]. Hence, the reflection from a magnetic sample will lead toa rotation of the polarization (the electric wave vector is not anymore per-fectly s-polarized) and ellipticity corresponding to the magnetization of thesample. By using a second polarizer in front of the detector, which only al-lows p-polarized light to pass, the Kerr rotation can be detected. By applyingan alternating, magnetic field parallel to the surface of the sample (collinearto the magnetization M in the longitudinal MOKE setup in figure 2.8) one canmeasure the sample’s hysteresis loop. L-MOKE is only sensitive to a magneti-zation collinear to the direction of the incident light (fig. 2.9). A magnetizationperpendicular to its direction won’t lead to a Kerr rotation and can thereforenot be measured by a L-MOKE setup. However, by an in-plane rotation of thesample, it is possible to measure the magnetization collinear to the directionof the incident light for e.g. magnetic hard and easy axes.

16

H

Electromagnets

Detector Laser

Polarizer 1Polarizer 2

Sample

Figure 2.9. Schematic illustration of the L-MOKE setup.

A

V

Rwire

Rwire

Rwire

Rwire

Rsample

Figure 2.10. Schematic illustration of the four-terminal sensing setup with the am-peremeter A and the voltmeter V.

2.5 Four-Terminal SensingThe four-terminal sensing method is used to separate lead and contact re-

sistance from the sample’s resistance. The sample is contacted by four wiresas shown in figure 2.10. The outer wires are used to apply a constant current.The inner wires are used to measure the potential. The internal resistance ofthe voltmeter (around 10 MΩ) is much higher than the sample’s resistance.Hence, the current flows mainly through the sample and the measured voltagemostly depends on the potential drop in the sample and not the potential dropin the wires and contacts. A precise value of the sample’s resistance can thenbe obtained by dividing the measured voltage by the applied current.

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3. Results and Discussion

3.1 Structural PropertiesXRR measurements have been used to determine the structural quality of

the samples. The XRR measurement shown in figure 3.1 is representative forall samples and illustrates the high degree of perfection in the sample’s layer-ing. The Bragg peak position of the experimental data and fit overlap, whichmakes it possible to determine the bilayer (one Fe and one MgO layer) thick-ness. Since the width and height of these peaks are captured by the fit as well,the bilayer thickness can be divided into individual thickness values for Feand MgO leading to the values presented in table 2.1. As expected from theHRTEM images (fig. 2.3), very smooth interfaces with a roughness of only0.5-1 monolayers (tab. 3.1) were obtained from the fitting. The atomic densi-ties were first set to literature values ( formula unitsunit cell volume ) and then varied by 10% tocompensate for variation of the unit cell volume due to stress, strain or vacan-cies. The XRD measurements (fig. 3.1 inset) show satellite peaks around theFe (002) peak. Those peaks are called superlattice peaks and only appear whenthere is a high structural coherence normal to the layers, as already ascertainedfrom the HRTEM images.

The same measurements were performed on a [Fe/MgO]9Fe superlatticegrown on SrTiO3 with the exact same conditions as the sample above. Inthis sample, the superlattice was terminated with a Fe layer instead of a MgOlayer to avoid the possibility of island growth of the Pd capping layer. Pd isknown to form large islands on top of MgO which could result in the cappinglayer not fully covering the superlattice. However, this affects neither the mag-netic nor the structural properties of the sample. The quality of the layering(XRR data in fig. 3.2) is comparable to the layering of the samples grown onMgO substrates shown above (fig. 3.1). Furthermore, superlattice peaks canbe observed in the XRD spectrum indicating the formation of a superlattice.However, the Fe (002) peak is shifted by 0.7◦ in 2θ (further away from thebulk lattice constant) in the sample grown on SrTiO3. One can conclude, thatthe different substrate leads to differences in stress/strain causing this shift.

Table 3.1. Layer roughness from the GenX fit for Sample A.

Layer Roughness in ÅMgO Substrate 1.2

Fe 2.4MgO 1.8

Pd 4.8

18

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 01 01

1 0 2

1 0 3

1 0 4

1 0 5

1 0 6

1 0 7

1 0 8

5 0 5 5 6 0 6 5 7 0 7 51 00

1 0 1

1 0 2

1 0 3

Inten

sity (

arb.

units

)

2 T h e t a ( d e g r e e )

F e ( 0 0 2 )

X R R D a t a G e n X F i t

Inten

sity (a

rb. un

its)

Q ( 1 / Å )

Figure 3.1. Experimental XRR data (black dots) of sample A [Fe(20.9 Å)/MgO(19.9Å)]10 and GenX fit of the same data set (red line). The experimental XRD data (inset)exhibits superlattice peaks indicating a high structural coherence.

0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

1 0 2

1 0 3

1 0 4

1 0 5

1 0 6

1 0 7

1 0 8

5 5 6 0 6 5

1 0 2

1 0 3

Inten

sity (

arb.

units

)

2 T h e t a ( d e g r e e )

F e ( 0 0 2 )

Inten

sity (a

rb. un

its)

Q ( 1 / Å )

Figure 3.2. Experimental XRR data (black dots) of a [Fe/MgO]9Fe superlattice grownon SrTiO3. The experimental XRD data (inset) exhibits superlattice peaks indicatinga high structural coherence.

19

Easy Axes Hard Axes

Figure 3.3. Schematic illustration of Fe’s four-fold anisotropy (topview) with two easyaxes (dashed, orange lines) and two hard axes (solid, black lines).

3.2 Magnetic PropertiesFe intrinsically has a magnetocrystalline anisotropy. In the case of bcc Fe,

the easy axis is along the (100) direction and the hard axis is along the (110)direction. Hence, the magnetocrystalline anisotropy is four-fold symmetric.Since Fe is rotated by 45◦ (fig. 2.1) on top of MgO, the easy axes point alongthe diagonals and the hard axes along the sides as illustrated in figure 3.3. Itis worth to mention, that Fe’s four-fold anisotropy in thin films can only beobserved if a sufficiently good crystalline quality is ensured.

The four-fold anisotropy can be verified by measuring the sample’s mag-netic response to an applied, alternating, magnetic field along both axes (fig.3.4). If a strong, external field is applied along the hard axis (e.g. to the lefthand side of figure 3.4a inset), all magnetic moments are aligned along theexternal, magnetic field as seen by the saturation of the sample’s magnetiza-tion (around -90 mT for sample A). When reducing the external field, a steadydecrease of the magnetization can be observed. Reducing the field leads to acoherent rotation of the magnetization towards the easy axes (e.g. upper andlower left hand side corner in figure 3.3). At zero external field, a remainingmagnetization (remanence) can still be observed. In this case, all magneticmoments are aligned along the easy axes (e.g. upper and lower left hand sidecorner in fig. 3.3) leading to a component pointing still along the hard axis(left hand side). By calculating the resulting contribution M = Ms · cos45◦,where Ms is the saturation magnetization, one gets Mr = 0.7Ms, which equalsto the observed remanent magnetization. Reversing the field leads to an abruptjump in the hysteresis curve, which can be attributed to a flipping of the mag-netization over to the easy axes in the other direction (e.g. upper and lowerright hand side corner in figure 3.3). By increasing the external field further,a coherent rotation of the magnetization towards the hard axis occurs until thesaturation can finally be observed again.

By applying a magnetic field along the easy axis (fig. 3.4b inset) one ob-serves a much lower saturation field compared to the hard axis as well as

20

- 2 0 0 - 1 0 0 0 1 0 0 2 0 0

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

- 2 0 - 1 6 - 1 2 - 8 - 4 0 4 8 1 2 1 6 2 0

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

Magn

etiza

tion (

norm

alized

)

B ( m T )

a )

Magn

etiza

tion (

norm

alized

)

B ( m T )

b )

Figure 3.4. Normalized, experimental L-MOKE data of sample A [Fe(20.9Å)/MgO(19.9 Å)]10 along the hard (a) and easy (b) axis.

clear, symmetric steps between the saturation magnetization and remanence.The steps occur before zero external field as soon as the field is reduced from-Hs (red branch) and the total number of steps is close to the number of ferro-magnetic layers in the whole sample (10). Hence, one can assume that thewell-defined steps correspond to the switching of the individual ferromag-netic layers or at least to sufficiently big domains within the probed samplearea as already reported for Fe/Cr/Fe superlattices [2]. Due to the four-foldanisotropy, the layers (or domains) have to rotate by either 90◦ or 180◦ in orderto be aligned along one easy axis. Therefore, one can conclude that a couplingof the magnetic layers is present and that this coupling is not ferromagneticsince the plateaus can be observed before the external field is reversed. More-over, one observes a remanence of 0.5Ms. Since L-MOKE cannot measurea magnetization perpendicular to the plane of the incident light, it might bethat half the layers point along one easy axis (e.g. left hand side in fig. 3.4binset) and the other half point along the other easy axis (e.g. up) resulting in anet magnetization of 0.5Ms. An antiferromagnetic interlayer coupling shouldresult in a remanent state with zero net magnetization. However, if the inter-layer coupling is of similar magnitude as the magnetocrystalline anisotropy,then it might be that the coupling is not strong enough to overcome Fe’s mag-netocrystalline anisotropy and a minimization of the energy is achieved by anangle of 90◦ between the layers. Another possibility is that the coupling acrossthe MgO in fact is biquadratic, which would lead to the same result. However,with only the L-MOKE data it is not possible to give a clear statement aboutthe occurring phenomena. The alignment of the ferromagnetic layers will bediscussed in more detail in section 3.3.

To study the coupling mechanism in more detail, different MgO spacerlayer thicknesses have been compared (fig. 3.5). Two important changes areobserved with decreasing MgO thickness. Firstly, the switching fields, includ-ing the field required to saturate the magnetization, increase with decreasingthickness. Secondly, the steps in the hysteresis become less pronounced forthinner MgO spacer layers. Since L-MOKE probes only a small area (size of

21

- 1 0 0 - 8 0 - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0 8 0 1 0 0

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

2 1 . 6 / 1 6 . 7 Å F e / M g O

Magn

etiza

tion (

norm

alized

)

B ( m T )

2 2 . 9 / 1 7 . 4 Å F e / M g O 2 0 . 9 / 1 9 . 9 Å F e / M g O

2 3 . 4 / 1 4 . 6 Å F e / M g O

Figure 3.5. Normalized, experimental L-MOKE data of sample A-D along the easyaxis.

the laser spot) it might be that thinner MgO layers lead to the formation ofmagnetic domains which are smaller than the spot size. Hence, one cannot as-sume a reversal of the whole magnetic layer, but rather a successive reversal ofsmall domains, leading to a successive Kerr rotation and therefore less abruptsteps in the hysteresis curve.

Via Kerr microscopy, the domain structure of the remanent state betweensamples with thick (22.2 Å) and thin (16.5 Å) MgO spacer layers have beencompared (fig. 3.6). Since the Fe layers are only 2 nm thick and the MgOlayers are basically transparent, one has to take into account, that the observedKerr microscope image is a superposition of different Fe layers. Differentbrightness values may correspond to different Fe layers. However, it is ob-vious that the sample with thicker MgO spacer layers forms huge domains(around 0.5 mm), whereas the other sample consists of 0.1 mm or even smallerdomains. Hence, the different domain sizes provide a good explanation for theslope of the different hysteresis curves in figure 3.5.

The changes in the switching fields can be related to the strength of the in-terlayer exchange coupling by using the following equation [21]. The negativebilinear coupling term J1 corresponds to the antiferromagnetic coupling termJAF , where Bs is the saturation field, which can be obtained from the L-MOKEmeasurements, Ms is the volume magnetization (literature value) and dFe is the

22

Figure 3.6. Kerr microscopy image of a [Fe(23.0 Å)/MgO(22.2 Å)]10 (a) and a[Fe(25.3 Å)/MgO(16.5 Å)]10 (b) superlattice at remanence. The thick MgO layer fa-vors the formation of large domains, up to 0.5 mm across. A thin MgO layer leads tothe formation of much smaller domains.

thickness of one Fe layer, which can be obtained from the XRR fit. The re-sult is plotted together with the relative remanence over the MgO thickness infigure 3.7.

− J1 = JAF =BsMsdFe

4(3.1)

Increasing the thickness of the insulating layer leads to a decrease in theantiferromagnetic coupling strength (J1 decreasing in magnitude) and an in-crease of the remanence (fig. 3.7). The coupling strength follows an expo-nential decrease with an increase of the spacer layer thickness approaching avalue of 0 (no coupling), whereas the relative remanence’s behavior may bebest described by an abrupt jump between a value either close to 50% or 0%.The smallest MgO thickness (indicated by a black arrow) follows neither thetrend of the saturation field nor the trend of the relative remanence. Due to thesmall thickness, a higher pinhole density may occur. Pinholes lead to a fer-romagnetic coupling and may weaken the antiferromagnetic coupling throughthe MgO. Since the behavior of this sample is not purely connected to thesmaller MgO thickness, this sample will be neglected in further analysis.

Previous experimental and theoretical studies have confirmed a remarkableimpact of defects or vacancies within the MgO layers on the magnetic cou-pling. Thick (8 Å [22] or 10 Å[23]) or perfect MgO spacer layers [22] shouldlead to a ferromagnetic coupling. However, impurities (e.g. oxygen vacancies)enhance the antiferromagnetic coupling strength [24]. It is worth mentioning,that even with the impurity-assisted coupling mechanism a weak, ferromag-netic behavior above 10 Å is predicted [23]. The clear evidence for a non-ferromagnetic coupling in samples above 15 Å has not been reported yet. Infact, all recent theories and experiments suggest a loss of any coupling above15 Å MgO thickness.

23

1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3

- 1 . 0 x 1 0 - 4

- 8 . 0 x 1 0 - 5

- 6 . 0 x 1 0 - 5

- 4 . 0 x 1 0 - 5

- 2 . 0 x 1 0 - 5

0 . 0

0

1 0

2 0

3 0

4 0

5 0

J 1

(J/m2

)

M g O T h i c k n e s s ( Å )

J 1

Mr/M

s (%)

M r / M s

Figure 3.7. Antiferromagnetic coupling strength (black dots) and relative remanence(orange squares) of samples A-D and older samples over the spacer layer thickness.The dashed line serves as a guide to the eye.

The 90◦ coupling between the ferromagnetic layers observed for sampleswith thick MgO spacer layers may have different origins. One possibility is thecompetition between antiferromagnetic coupling and Fe’s four-fold anisotropy.The thicker spacer layer weakens the antiferromagnetic coupling so that thecoupling is not strong enough to overcome the second hard axis to form anantiferromagnetic alignment. Hence, a minimization of the energy is achievedwith a biquadratic-like (90◦) alignment of the magnetization. This theory isexperimentally confirmed for thinner MgO (6 Å) spacer layers [25]. Anotherpossibility is the transition from an antiferromagnetic to a biquadratic cou-pling due to oxidation of the Fe/MgO interfaces and magnetic impurities inthe spacer layer as shown for MgO thicknesses between 4.6 and 8.1 Å [26].The biquadratic coupling can then be described by the loose spin model, whichis described elsewhere [19].

To distinguish between both possibilities, temperature dependent L-MOKEmeasurements have been performed. The biquadratic coupling should becomedominant at low temperatures if an oxidation of the interfaces is present [26].Hence, samples exhibiting an antiferromagnetic alignment at room tempera-ture (thin MgO layers) should exhibit a biquadratic behavior at lower tem-peratures and samples exhibiting a perpendicular alignment of the magneti-zation at room temperature should exhibit a higher saturation field (strongercoupling) at low temperatures. Furthermore, temperature dependent L-MOKE

24

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

- 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0

3 0 K

Magn

etiza

tion (

norm

alized

)

B ( m T )

1 5 6 K

a )

2 6 9 K 3 8 2 K

- 4 0 0 - 3 0 0 - 2 0 0 - 1 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0 3 0 K

Mag

netiza

tion (

norm

alized

)

B ( m T )

b )

1 5 6 K 2 6 9 K 3 8 2 K

Figure 3.8. Hysteresis loop along the easy axis of a [Fe(23.0 Å)/MgO(22.2 Å)]10 (a)and a [Fe(21.6 Å)/MgO(16.7 Å)]10 (b) superlattice at various temperatures.

measurements are suitable to prove if impurities and defects are present withinthe MgO layers. The quantum interference model predicts an increase ofthe coupling strength with higher temperatures due to the thermal populationof the excited electronic states [24] (higher tunneling probability) and a de-crease with lower temperatures (smaller tunneling probability). However, theimpurity-assisted interlayer exchange coupling across a tunnel barrier predictsthe inverse behavior [24].

The temperature dependent hysteresis loops are shown in figure 3.8. Thesample with the thick MgO spacer layer (fig. 3.8 a) exhibits a square hystere-sis loop at low temperatures (typical for bulk Fe) indicating the absence ofany coupling mechanism. At higher temperatures, the formation of the char-acteristic hysteresis steps and a reduced remanence occurs. It seems that thecoupling is present above 60 K with a maximum (highest saturation field) be-tween 120 and 160 K. By increasing the temperature further, the saturationfield is reduced and the steps become less pronounced. It is worth mentioning,that even above 380 K characteristic hysteresis steps can be observed.

The sample with the thin MgO follows a similar behavior. However, thesaturation field is at all temperatures higher than the saturation field of thesample with the thick spacer layer. Below 200 K, the sample’s hysteresis looplooks similar to a hysteresis loop of Fe’s hard axis as shown in figure 3.4a. Athigher temperatures, the characteristic steps occur and the saturation field isreduced as already reported for the other sample. The steps occur together withthe sharp drop of the remanence, indicating the antiferromagnetic coupling.Even at 380 K, the steps can be observed. The relative remanence as well asthe saturation field of both samples are plotted over the temperature in figure3.9 a and b, respectively.

The interpretation of the temperature dependent data is not trivial. First ofall, the coupling of both samples seems to vanish below 60 K (thick MgO) and200 K (thin MgO), which is consistent with the quantum interference model

25

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 00 . 00 . 10 . 20 . 30 . 40 . 50 . 60 . 70 . 80 . 91 . 0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 00 . 00 . 10 . 20 . 30 . 40 . 50 . 60 . 70 . 80 . 91 . 0

2 2 . 2 Å M g O

Mr/M

s

T e m p e r a t u r e ( K )

a ) 1 6 . 7 Å M g O

Mr/M

s

T e m p e r a t u r e ( K )

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 005

1 01 52 02 53 03 54 04 5

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 02 2 . 2 Å M g O

Satur

ation

field

(mT)

T e m p e r a t u r e ( K )

b )1 6 . 7 Å M g O

Satur

ation

field

(mT)

T e m p e r a t u r e ( K )

Figure 3.9. Relative remanence (a) and saturation field (b) of a [Fe(23.0 Å)/MgO(22.2Å)]10 (orange circles) and a [Fe(21.6 Å)/MgO(16.7 Å)]10 (green squares) superlatticeat various temperatures between 10 K and 390 K.

26

for perfect spacer layers. However, before the coupling vanishes, a steady in-crease of the saturation field (coupling strength) is observed, which indicatesrather an impurity-assisted interlayer exchange coupling. It seems that at leastfor the thick MgO layers a superposition of the impurity-assisted couplingand the behavior of a perfect tunnel-junction exists, whereby the impurity-assisted coupling wins at higher temperatures. It is predicted that an increasein the MgO thickness will lead to a coupling comparable to the one of an idealtunnel-junction [13]. Hence, the impurity-assisted coupling becomes less im-portant for thicker MgO spacer layers. This is consistent with the low tem-perature data of the thick MgO spacer layer. First an absence of coupling dueto a smaller tunneling probability (below 60 K) and then an increase of thesaturation field (coupling strength) up to 100 K. After 100 K, the saturationfield is constant up to 170 K. In this region, the impurity-assisted coupling andthe coupling of a perfect tunnel barrier seems to be equally strong. For tem-peratures above 160 K, a steady decrease of the saturation field indicates thedominance of the impurity assisted coupling. The relative remanence of thissample exhibits values above 0.5Ms only during the absence of any coupling(below 60 K) and is apart from that almost constant. Hence, even at low tem-peratures (60 K) the 90◦ coupling between the ferromagnetic layers is present.It seems that the coupling is still too weak to overcome the second hard axisto form the antiferromagnetic alignment of the Fe layers.

The low temperature behavior of the thin MgO spacer layer is even morepuzzling. For temperatures above 200 K it follows similar to the thick MgOlayers the behavior of the impurity-assisted coupling. However, below 200 Kthe hysteresis loops look like loops along the hard axis. An explanation mightbe, that the different thermal expansion coefficients between Fe and MgO mayinduce a lattice distortion at low temperatures swapping the magnetic easy andhard axes. Due to this exchange, it is impossible to find traces of a superpo-sition of the impurity-assisted and the coupling of a perfect MgO layer asinterpreted for the thick MgO spacer. To confirm this interpretation and tofind traces, one has to rotate the sample by 45◦ (hard axis at room tempera-ture) and perform the same L-MOKE measurement, but this has yet to be done.

Finally, L-MOKE measurements along the easy axis (fig. 3.10) were per-formed for the sample grown on SrTiO3 first presented in figure 3.2. Oneobserves similar magnetic properties compared to samples grown on MgO.The remanence is reduced to 0.34Ms indicating a different layer configurationat zero external field. Furthermore, one observes a hysteresis step around 40mT, which is far away from the other steps indicating a stronger coupling ofone of the layers.

27

- 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

Magn

etiza

tion (

norm

alized

)

B ( m T )

Figure 3.10. Experimental L-MOKE data (black squares) of a [Fe/MgO]9Fe superlat-tice grown on SrTiO3.

28

Figure 3.11. Descending branch of sample A’s hysteresis loop along the easy axis toillustrate the chosen field steps for the PNR measurements.

3.3 Magnetic OrderingTo study the magnetic alignment of individual layers, PNR measurements at

different external field steps have been performed. Before each measurement,the sample was saturated along the neutron guide field (up) to start with a well-defined magnetic history of the sample. Both NSF channels (UU and DD) aswell as one SF channel (DU) were measured and fitted together with the XRRdata. Furthermore, both NSF were measured at saturation to obtain a precisevalue for Fe’s magnetic moment which may vary with the thickness of theFe layers [27] and was then used for the fitting of the PNR data at differentexternal fields. The raw data was reduced by Gunnar K. Palsson’s Super AdamReduction program (SARED, unpublished). The reduction process included(i) redefinition of the region of interest to reduce the noise (ii) dividing bythe monitor to compensate fluctuations in the neutrons flux (iii) direct beamnormalization to obtain the reflectivity values and (iv) background subtractionto further improve the signal to noise ratio.

For sample A (thickest MgO layer), PNR measurements were carried outat the field values corresponding to remanence, and the first and second mag-netization steps, as shown in figure 3.12. The experimental PNR data as wellas the fit are plotted in figure 3.12. For the sake of clarity, the fit and data ofthe first and second step are plotted with an offset of 1E-3 and 1E-6 respec-tively. At remanence, both data sets exhibit a clear peak at QB = 0.157 1/Åcomparable to the position of the first Bragg peak in the XRR spectrum (QB =0.162 1/Å). Furthermore, a clear peak at QB/2 = 0.0789 1/Å and another peak

29

0 . 0 0 0 . 0 5 0 . 1 0 0 . 1 5 0 . 2 0 0 . 2 51 E - 1 31 E - 1 21 E - 1 11 E - 1 0

1 E - 91 E - 81 E - 71 E - 61 E - 51 E - 41 E - 30 . 0 1

0 . 1

s e c o n d s t e p

f i r s t s t e p

U U D a t a G e n X F i t

Refle

ctivity

a )

Q ( 1 / Å )

r e m a n e n c e

0 . 0 0 0 . 0 5 0 . 1 0 0 . 1 5 0 . 2 0 0 . 2 51 E - 1 31 E - 1 21 E - 1 11 E - 1 0

1 E - 91 E - 81 E - 71 E - 61 E - 51 E - 41 E - 30 . 0 1

0 . 1b ) D U D a t a

G e n X F i t

Refle

ctivity

Q ( 1 / Å )

r e m a n e n c e

f i r s t s t e p

s e c o n d s t e p

Figure 3.12. Experimental (black dots) and fitted (red/ orange line) UU (a) and DU(b) PNR data of sample A (thick MgO) at different external fields. For the sake ofclarity, the measurement of the first and second step are plotted with an offset of 1E-3and 1E-6, respectively.

30

Figure 3.13. Schematic illustration of the first three magnetic layers at remanence forsample A. For the sake of clarity, the non-magnetic spacer layers are not shown.

at Q = 0.232 1/Å is present in both channels. The latter peak is the higherorder of the QB/2 peak. The best fit is obtained for the in-plane direction of themagnetization of the layers alternating between values close to the in figure2.6 defined angle γ = 0◦ and 90◦ (fig. 3.13) as already reported [14].

The peak at 0.157 1/Å in the NSF channel occurs due to the variation inthe nuclear density (bilayer thickness). The peak at QB/2 in the NSF channelis purely due to the magnetic periodicity, which is therefore twice the struc-tural periodicity (two bilayer thicknesses). According to equation 2.3, the NSFchannel is not sensitive to a magnetization perpendicular to the neutrons spin.Hence, the magnetic periodicity varies between no contribution (magnetiza-tion perpendicular to the neutrons spin) and high contribution (magnetizationcollinear to the neutrons spin), which is exactly twice the nuclear periodicityresulting in the QB/2 peak as illustrated in figure 3.13. The SF channel is onlysensitive to a magnetization perpendicular to the neutrons spin. Hence, theQB/2 peak there can be identically explained. The occurring QB peak seemsto be puzzling, since the variation of the nuclear density does not contributeto the SF channel. In former studies [14], this peak was explained by hugedomains. The Kerr microscope images confirmed the presence of domains.However, they should not result is such a pronounced peak. A more realisticexplanation is the constructive interference due to the second harmonics (n=2)in Bragg’s law (equ. 2.1) leading to a Q2B/2 = QB peak. The same occursof course also for the NSF channel, but the magnetic and nuclear contributionoverlap at the same position making the second harmonics (net magnetization)less obvious.

The increase of the external field leads to a clear reduction and broadeningof the QB/2 peak in both channels indicating a reduced magnetic periodicity.In contrast to the NSF channel, the QB peak in the SF channel becomes muchbroader. By applying an external field collinear to the incoming neutrons spinsome layers may align parallel to the external field reducing both, the contribu-tion of these individual layers as well as the measurable net magnetization to

31

Table 3.2. Azimuthal angles γ of the net magnetization of individual Fe layers forthree different applied field values (as defined in figure 3.11).

Layer Remanence First Step Second Step1 82◦ 2◦ 4◦

2 -1◦ 9◦ 2◦

3 84◦ 83◦ 20◦

4 3◦ 4◦ 7◦

5 84◦ 79◦ 64◦

6 0◦ 1◦ 1◦

7 83◦ 79◦ 72◦

8 5◦ 1◦ 0◦

9 85◦ 79◦ 85◦

10 0◦ -1◦ -18◦

the SF channel resulting in a reduction and broadening of all three SF channelpeaks. The obtained magnetic angles for the best fit are summarized in table3.2.

One notices the small offset in the γ = 90◦ angle at remanence. The smallguide field (to define the direction of the neutrons spin during the measure-ment, 1 mT) is pointing upwards (γ = 0◦). Hence, the layers forming a γ = 90◦angle are a little bit tilted upwards due to the weak external field. Furthermore,a small misalignment of the sample with respect to the guide field may alsofavor an imperfect configuration of the sample’s magnetization.

By increasing the external field to 4.5 mT, it was possible to measure thefirst plateau occurring in the hysteresis curve (fig. 3.11). The biggest changeis observed in the top layer, which is now aligned along the externally appliedfield. This layer has only one nearest neighbor and experiences therefore theweakest coupling. Hence, the applied field is strong enough to switch thewhole layer without having a major impact on the alignment of the other layersmagnetization.

By increasing the external field up to 7.5 mT, the second plateau can bemeasured. This plateau is much narrower than the one measured before mean-ing that there is some uncertainty in the exact position on the hysteresis curvefor this measurement. Furthermore, all the unchanged layers have the sameamount of nearest neighbors. If the coupling exists only between the nearestneighbors, then every layer has the same probability to switch its magnetiza-tion. Layer 3 experiences the biggest impact of the new external field. How-ever, also layer 5 and 7 are further away from the favored 90◦ alignment, whichmay be a hint that some domains have switched. It seems that the stepwise re-versal of the layers starts from the weakest coupled layer and propagates thenthrough the whole sample. That might imply that the coupling extends notonly to the nearest neighbors, but also to the next nearest neighbors or evenfurther.

32

Figure 3.14. Descending branch of sample C’s hysteresis loop along the easy axis toillustrate the chosen field steps for the PNR measurements.

The presented angles of the net magnetization correspond to the best ob-tained fit. Varying these angles will always lead to a worse fit. However, smallchanges may not have a remarkable impact. Therefore, the uncertainty of thepresented angles is estimated to be ≤ 10◦.

The same measurements were performed for sample C with a thinner MgOspacer layer. The measurement protocol was identical to the one used for theprevious measurements and the data reduction was done in the exact same way.Again, a precise value for Fe’s magnetization was obtained by a fit of a NSFmeasurement at saturation. A measurement at remanence and a measurementwith an external field of 47 mT was performed (fig. 3.14).

One of the biggest differences between the PNR results of both samples isthe missing QB/2 peak in the remanent state of the NSF channel. Since the SFchannel exhibits a clear QB/2 peak, one can conclude that a magnetic period-icity with twice the bilayer thickness exists perpendicular to the neutron spin.The GenX fit of the data set confirms the periodic, antiparallel alignment ofthe Fe layers (fig. 3.16) as already deduced from the L-MOKE measurements.Even though the sample was saturated along the neutrons guide field (up), aremanent magnetization perpendicular to the guide field was observed.

By reducing the external field, the strongest coupled layer will flip first toform an antiparallel alignment (down) to the neighboring layers. However,since the external field forces the layer to be aligned in the opposite direction(up), a 90◦ flip might be the compromise between the coupling (antiferromag-netic) and the external field (ferromagnetic). This phenomena is known as

33

0 . 0 0 0 . 0 5 0 . 1 0 0 . 1 5 0 . 2 0 0 . 2 51 E - 1 11 E - 1 0

1 E - 91 E - 81 E - 71 E - 61 E - 51 E - 41 E - 30 . 0 1

0 . 1

0 . 0 0 0 . 0 5 0 . 1 0 0 . 1 5 0 . 2 0 0 . 2 51 E - 1 11 E - 1 0

1 E - 91 E - 81 E - 71 E - 61 E - 51 E - 41 E - 30 . 0 1

0 . 1

Refle

ctivity

Q ( 1 / Å )

s t e p

U U D a t a G e n X F i t

Refle

ctivity

Q ( 1 / Å )

r e m a n e n c e

0 . 0 0 0 . 0 5 0 . 1 0 0 . 1 5 0 . 2 0 0 . 2 51 E - 1 11 E - 1 0

1 E - 91 E - 81 E - 71 E - 61 E - 51 E - 41 E - 30 . 0 1

0 . 0 0 0 . 0 5 0 . 1 0 0 . 1 5 0 . 2 0 0 . 2 51 E - 1 11 E - 1 0

1 E - 91 E - 81 E - 71 E - 61 E - 51 E - 41 E - 30 . 0 1

Refle

ctivity

Q ( 1 / Å )

D U D a t a G e n X F i t

Q ( 1 / Å )

s t e p

r e m a n e n c e

Figure 3.15. Experimental (black dots) and fitted (red/ orange line) UU (a) and DU (b)PNR data of sample C (thin MgO) at different external fields. For the sake of clarity,the measurement at remanence has an offset of 1E-3

34

Figure 3.16. Schematic illustration of the first three magnetic layers at remanence forsample C. For the sake of clarity, the non-magnetic spacer layers are not shown.

spin-flop-transition, mainly investigated in antiferromagnets, but recently alsoadapted to "artificial antiferromagnets" like magnetically coupled multilayers[28]. It precisely describes the sudden 90◦ rotation of the magnetization withrespect to the external field at a critical magnetic field [29].

Another explanation might be, that an uniaxial anisotropy is embedded inthe fourfold anisotropy as was already reported for other Fe/MgO superlattices[25]. In this case, the antiferromagnetic coupling would be favored along onespecific easy axis. To confirm this assumption, PNR measurements have to beperformed on the same sample rotated by 90◦ (neutrons guide field along theother easy axis).

The enhanced external field gives rise to the QB/2 peak in the NSF channelindicating a magnetization collinear to the neutrons spin (guide field). At thesame time, a broadening of the QB and QB/2 peak in the SF channel can beobserved. That indicates a reduction in the periodic alignment perpendicularto the neutrons guide field. The obtained magnetic angles for the best fit aresummarized in table 3.3.

The remanent state exhibits a periodic, antiparallel alignment of the Fe lay-ers perpendicular to the guide field. Due to the guide field, the layers are tilteda little bit upwards. The magnetization of the first step looks at first randomlydistributed. However, a detailed analysis may reveal the occurring phenom-ena. At saturation, all magnetic moments are aligned along the external field(up). By reducing the field, the strongest coupled layer does not flip by 180◦,but rather by 90◦ (spin-flop) as already discussed above. It seems that thestrongest coupled layer is layer number 5 (the middle layer), since this layeris already in equilibrium position. Furthermore, this layer has the most near-est and next-nearest neighbors resulting in the strongest coupling. A largervariation in the magnetic angles as seen in the other sample (thick MgO) ispresent since a competition between the strong external field and the antifer-romagnetic coupling occurs. A coherent rotation from a parallel (γ = 0◦) to anantiparallel alignment (γ = ± 90◦) due to spin-flop-transition occurs leading

35

Table 3.3. Azimuthal angles γ of the net magnetization of individual Fe layers for twodifferent applied field values (as defined in figure 3.14). The numbers in red highlightare doubtful magnetizations along the hard axis.

Layer Remanence First Step1 81◦ 0◦

2 -94◦ 7◦

3 81◦ 53◦

4 -94◦ -24◦

5 81◦ 81◦

6 -94◦ -17◦

7 81◦ 67◦

8 -94◦ -4◦

9 81◦ 42◦

10 -94◦ -4◦

to a large variation in the magnetic angles. That would also explain the slopein the hysteresis curve (fig. 3.14). However, the four-fold magnetocrystallineanisotropy breaks the coherent rotation and leads to a jump over the γ = ± 45◦hard axes. After this jump, a coherent rotation of the magnetization to the val-ues γ = ± 90◦ proceeds. The angles of layer 3 and 9 are close to the value ofthe magnetic hard axis. Since the neutrons measure the whole sample it mightbe that these observed angles are an average about multiple domains leadingto the unlikely orientations.

It is not surprising that the outermost layer (1) exhibits an magnetic angle ofγ = 0◦. Again, this layer is the weakest coupled layer and will therefore onlyturn at an external field close to remanence. Hence, one can conclude that thereversal process from saturation to remanence seems to start with the rotationof the innermost layer and propagates then coherently to the outermost layers.

36

Figure 3.17. Schematic illustration of the setup for in-plane transport measurementsof a [Fe(26.0 Å)/MgO(17.0 Å)]10 superlattice in cross section. The capping layer andsubstrate are insulating.

3.4 MagnetotransportBy attaching silver contacts to the side of a sample with relatively thin MgO

spacer layers, in-plane transport measurements with external field dependencecould be performed in a standard four-terminal sensing setup. Figure 3.17 and3.18 illustrate the setup in side and top view, respectively. Such a measurementgeometry is not ideal for studying TMR effects since most of the current willpass along the low-resistance Fe layers without tunneling through the MgO.Nonetheless, if the TMR is large enough a small contribution could be detecteddue to current spreading throughout the thickness of the film.

Easy Axes Hard Axes

A

V

Figure 3.18. Top-view of the setup for in-plane transport measurements with silvercontacts on the sides.

37

3 . 8 4 4

3 . 8 4 6

3 . 8 4 8

3 . 8 5 0

3 . 8 5 2

3 . 8 5 4

3 . 8 5 6

3 . 8 5 8

3 . 8 6 0

- 2 5 0 - 2 0 0 - 1 5 0 - 1 0 0 - 5 0 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

Resis

tance

(Ohm

)0 . 3 6 %

m a g n e t i c f i e l d

Magn

etiza

tion (

norm

alized

)

B ( m T )

c u r r e n t

Figure 3.19. Magnetoresistance (upper part) with respect to the hysteresis (lower part)along the horizontal hard axis. The red line is the ascending and the black line thedescending branch.

First, in-plane transport measurements along the hard axis have been per-formed as shown in figure 3.19. A decrease in the resistance is observedwhen approaching the remanent state with a small peak at zero external field.The main effect seems to come from the anisotropic magnetoresistance effect(AMR). If the material’s magnetization is parallel to the applied current, a highresistance can be observed. A magnetization perpendicular to the applied cur-rent leads to a smaller scattering cross section of the 3d-orbitals and thereforeto a smaller resistance (fig. 3.20) [30]. As already explained in section 3.2,a magnetization parallel to the hard axis at saturation (parallel to the appliedcurrent) and therefore a high resistance is observed. By reducing the externalfield, the sample’s magnetization rotates along the easy axes, increasing theperpendicular contribution of the magnetization with respect to the appliedcurrent and therefore reducing also the measured resistance.

The peak close to zero external field cannot be explained by the AMR. Sincethe MgO layers are very thin and a very small remanence can be observed, onecan assume that the individual layers exhibit a periodic, antiparallel alignmentalong one easy axis (either top right and bottom left or top left and bottomright corner), as already shown for slightly thinner MgO spacer layers in sec-tion 3.3. Hence, at zero external field the magnetization component collinear

38

Figure 3.20. Schematic illustration of the AMR effect (left). An applied external fieldleads to a change in the sample’s magnetization inducing a change in the scatteringcross section of the 3d-orbitals (light green ellipses). The real shape of the 3d-orbitalsis illustrated on the right hand side [30].

to the applied current is smallest, which would lead to the smallest AMR value.However, the TMR exhibits a high resistance for a periodic, antiparallel align-ment (as assumed for the remanent state) and a low resistance for a periodic,parallel alignment (as assumed for the saturated state). Thus, the TMR shouldexhibit a maximum resistance at zero external field and a minimum resistanceat saturation (contrary to the AMR). Hence, one can conclude that at least asmall part of the s-(conductance)-electrons tunnels through the MgO layers toexhibit the small peak at remanence. A contribution of the TMR may alsoexist by approaching the remanent state, however since this effect is so tinyit cannot be distinguished from the AMR. The maximum magnetoresistance(mainly due to the AMR) is just 0.36%.

In-plane magnetoresistance measurements along the easy axis have beenperformed to investigate if the steps in the hysteresis curve give rise to a changein the in-plane resistance (fig. 3.21). Again, the main contribution comes fromthe AMR. A high resistance can be observed if the sample’s magnetization isparallel to the applied current (along the horizontal easy axis). By reducingthe external magnetic field, a successive switching of the layers perpendicularto the applied field (along the vertical easy axis due to spin-flop) leads to astepwise decrease in the resistance. This switching has been confirmed for asample with a slightly thinner MgO spacer in section 3.3. However, at zeroexternal field one observes a pronounced peak, which cannot be explained bythe AMR. Similar to the measurement along the hard axis, this peak can beattributed to the TMR. Since some s-electrons tunnel through the insulatingspacers, a periodic, antiparallel alignment leads to a rise in resistance. Again,the effect observed close to remanence is a superposition of a low resistancedue to the AMR (magnetization perpendicular to current) and a high resis-tance due to the TMR (periodic, antiparallel magnetization of the ferromagen-tic layers). The magnetoresistance effect is only 0.16%, but since the AMR

39

3 . 8 7 4

3 . 8 7 6

3 . 8 7 8

3 . 8 8 0

3 . 8 8 2

3 . 8 8 4

3 . 8 8 6

- 3 0 - 2 0 - 1 0 0 1 0 2 0 3 0

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

Resis

tance

(Ohm

)0 . 1 6 %

m a g n e t i c f i e l d

Magn

etiza

tion (

norm

alized

)

B ( m T )

c u r r e n t

Figure 3.21. Magnetoresistance (upper part) with respect to the hysteresis (lower part)along the horizontal easy axis. The red line is the ascending and the black line thedescending branch.

weakens the TMR contribution, one can assume that an out-of-plane measure-ment should lead to a much higher TMR effect. Firstly, because no AMRwould be present (no weakening of the TMR) and secondly more s-electronswould tunnel through the MgO barrier since no alternative path (in-plane tothe ferromagnetic layers) is available. Even though the observed effects arerelatively weak, it is remarkable that the steps in the magnetization can alsobe observed in the in-plane resistance making these structures promising forfuture out-of-plane measurements.

The analysis of future TMR measurements is not trivial since the TMRis expected to be weakened, but also enhanced by different effects. It wasshown that the main coupling mechanism at room temperature is impurity-assisted spin-polarized tunneling. The impurities (probably O-vacancies) leadto a sharp decrease in the theoretically possible TMR. An ideal tunnel junc-tion can exhibit a TMR of more than 1800%, whereas the TMR of a defectafflicted junction is reduced to 800% or less [13]. This reduction is attributedto the incoherent scattering of the tunneling electrons. On the other hand,the smooth interfaces in the samples (confirmed by XRR measurements) willhave a positive effect on the TMR, which highly depends on the interfacequality [15] and structural relaxation [31]. Furthermore, the TMR increases

40

with increasing MgO thickness, where a peak in the TMR can be observed atdifferent MgO thicknesses ("hot spots"). One of these "hot spots" is a MgOthickness around 22 Å [32] close to the thickness of sample A. A 25 Å thickMgO spacer leads to a TMR of 67% [33]. By increasing the MgO thickness to30 Å a TMR of even 150% at room temperature can be observed [34]. How-ever, no coupling was observed in these studies. Therefore, the top Fe layerhad to be magnetically hardened with a Co layer to perform TMR measure-ments. Hence, only a trilayer (hard Fe/MgO/Fe) could be measured. All thehere presented MgO thicknesses exhibit a coupling, which makes out-of planemagentotranport measurements through several layers possible.

41

4. Conclusions and Outlook

[Fe/MgO]10 superlattices have been studied. The structures were grown bysputter deposition, where the sputtering time for the MgO deposition was var-ied for different samples. The different sputtering times led to different MgOthicknesses between the samples, which influenced the magnetic interlayerexchange coupling mechanism. By fitting XRR measurements, it was possi-ble to obtain precise values for the thickness of the individual layers as wellas to extract further information like interface roughness or variations in thedensity. These measurements confirmed the high degree of perfection in thelayering. XRD measurements were performed to examine the structural qual-ity. Every sample exhibited superlattice peaks, illustrating a high out-of-planecoherence.

L-MOKE measurements were carried out to study the magnetic propertiesof the samples. It was found that unusual steps occur in the hysteresis curves.Each step corresponds to the switching of large domains in individual Fe lay-ers. Kerr microscopy measurements confirmed that a thick MgO spacer layerleads to the formation of larger domains. Furthermore, a thicker spacer layerleads to a weaker magnetic coupling between the Fe layers. The coupling isfound to be antiferromagnetic, whereby samples with relatively thick MgOspacer layers exhibit a perpendicular alignment of the individual layers at re-manence due to a competition between the antiferromagnetic coupling andFe’s fourfold magnetocrystalline anisotropy. Temperature dependent measure-ments revealed that the dominant coupling mechanism at high temperatures isthe impurity-assisted interlayer exchange coupling due to spin-polarized tun-neling. However, it seems that samples with a thick spacer layer follow ratherthe behavior of a perfect (no defects) tunnel junction at low temperatures.Samples with thin MgO spacer layers exhibit a typical hysteresis loop of ahard axis for low temperature measurements along the easy axis. It seems thatinternal strain swaps the magnetic anisotropy axes at low temperatures makingit impossible to investigate the coupling at low temperatures. At higher tem-peratures the coupling could be assigned to the impurity-assisted interlayer ex-change coupling due to spin-polarized tunneling. It is worth mentioning, thatneither in theory nor in experiments has a coupling across such thick MgObarriers been reported previously.

PNR measurements have been performed to confirm the periodic couplingof the individual layers. The occurring QB/2 peak confirmed the periodic mag-netic alignment at remanence, which was found to be antiparallel and perpen-dicular for thin and thick MgO spacer layers, respectively. By fitting the PNR

42

data together with the XRR data and by performing measurements at differentexternal fields, it was possible to confirm that the hysteresis steps correspondto the switching of individual layers and to get an impression of the switchingsequence. It was found that the reversal of the layers starts with a weakly cou-pled outermost layer (only one nearest neighbor) and propagates then throughthe whole sample.

In-plane transport measurements showed mainly an AMR, however somefeatures can be assigned to a TMR. Unfortunately, the TMR contribution wasreduced by the AMR and a quantification of this effect was not possible. Thisis perhaps not surprising as the in-plane resistivity is not strongly affected bythe TMR across the MgO layers. Hence, out-of-plane transport measurementsare of utmost importance to get solely a TMR contribution. Therefore, thegrowth on SrTiO3 substrates has been studied, as this material can be dopedto become conductive. It was found that samples grown on SrTiO3 exhibitsimilar XRR and XRD data and similar steps in the hysteresis curve makingit suitable for out-of-plane transport measurements. However, the growth hasto be optimized and the magnetic properties have to be studied more carefullyexceeding the scope of this thesis.

Looking ahead, temperature dependent measurements of the sample withthe thin MgO spacer layers along the hard axis have to be performed in or-der to confirm the swapping of the magnetic axes at low temperatures and tostudy the coupling mechanism at these temperatures. The next step wouldbe the growth optimization on doped SrTiO3 substrates. Once a sufficientlyhigh sample quality is achieved, L-MOKE and PNR measurements similar tothe ones carried out for samples grown on MgO have to be performed. Out-of-plane transport measurements can then be performed through the wholesample. Additionally, a patterning of individual islands can be performed. Bychoosing the size of the islands according to the domains size one can ensurethat each hysteresis step corresponds to the switching of the whole layer. Inthis case, PNR measurements may be also easier to fit. To exploit the fullpotential of such samples, one could also combine different MgO but alsoFe thicknesses to create novel devices (e.g. a shift-register). Such a devicemay have more stable states than just the antiparallel or perpendicular coupledstates shown in this thesis.

43

5. Acknowledgment

First of all, I would like to thank Dr. Fridrik Magnus for fulfilling his su-pervision duties flawlessly. Without his assistance during the measurements,contagious enthusiasm, permanent availability (particularly during the holi-days) and helpful explanations as well as critical remarks, this thesis wouldnot exist in its current state.

Furthermore, Dr. Gunnar Karl Palsson has to be honored for his supportduring the PNR measurements as well as for his indispensable assistance dur-ing the following data reduction and analyzes processes.

Prof. Bengt Lindgren has to be named for teaching me the GenX basics,helping me tirelessly improving the XRR and PNR fits as well as explainingme mysterious PNR data nobody else understood.

Moreover, Dr. Spyridon Pappas deserves my gratitude for sacrificing a lotof his time to help me with the temperature dependent L-MOKE measure-ments.

Also, Sotirios Droulias sacrificed a lot of his time to teach me XRR andXRD basics (and advanced stuff). Thank you!

Additionally, I appreciate Emil Melander’s help with the Swedish abstractas well as his organized after-work group activities.

Besides, I would like to express my deepest gratitude to Dr. Vassilios Ka-paklis, who introduced me to this group, awakened my interest in materialsscience and gave me valuable feedback on an almost final version of this the-sis.

I would like to thank Dr. Reda Moubah for teaching me the sputteringtechnique as well as providing me with a sputter recipe, which was used togrow the superb samples.

I am grateful for fruitful fist-and second-hand discussions with Prof. BjörgvinHjörvarsson, which led to a much deeper understanding of the occurring cou-pling mechanism and occurring phenomena of the PNR measurements, re-spectively as well as for his constant support and motivation.

Finally, I want to thank the materials physics group of Uppsala Universityfor supporting me whenever I needed help, half-serious, half-humorous dis-cussions at the coffee table and activities apart from academia.

Last, but not least I want to thank my family for both, the financial andmoral support during all the years of study (almost 6), my friends for draggingme away from work and you, dear reader, for reading my thesis (or at least theacknowledgment).

44

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1 Introduction2 Methods2.1 Sample Preparation2.2 X-Ray Reflectivity2.3 Polarized Neutron Reflectivity2.4 Magneto-Optical Kerr Effect2.5 Four-Terminal Sensing

3 Results and Discussion3.1 Structural Properties3.2 Magnetic Properties3.3 Magnetic Ordering3.4 Magnetotransport

4 Conclusions and Outlook5 AcknowledgmentReferences