Eindhoven University of Technology MASTER Field-free magnetization reversal by spin Hall effect and exchange bias Vermijs, G.

MASTER

Field-free magnetization reversal by spin Hall effect and exchange bias

Vermijs, G.

Award date:

2016

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netic layer can be switched by the spin Hall effect (SHE). This spin Hall switching is a major contender for the write mechanism in novel magnetic memory devices such as MRAM (Mag- netic Random Acces Memory). Unfortunately, an externally applied magnetic field is necessary to cause deterministic magnetization reversal by the SHE. Such a field is not suitable for imple- mentation in actual devices.

In this thesis, the external field is replaced by an effective magnetic field originating from the exchange bias effect between a ferromagnetic and an anti-ferromagnetic material. By creating an Pt/Co/IrMn trilayer in which the ferromagnetic Co layer is magnetized out-of-plane and the anti-ferromagnetic IrMn layer is magnetized in-plane, a novel exchange bias configuration, called orthogonalexchange bias, is successfully created. By investigating the thickness dependence of each layer, thermal stability and magnetic configurations, a thorough qualitative understanding of this system is achieved.

By nanostructuring these orthogonal exchange biased samples, field-free deterministic magne- tization reversal is observed via the SHE; a breakthrough in the field of MRAM research. The external field is successfully replaced by the intrinsic field from the exchange bias. The mag- netization reversal showed characteristic features that appear to be intrinsic to the orthogonal exchange bias configuration. These features, most notably the gradual and partial switching of the magnetization, can be explained by the polycrystalline structure of the IrMn layer and current shunting related to the sample geometry. It is discovered that the effective exchange bias field can be compensated by applying a 5 mT external field. This compensation field is an order of magnitude smaller than the actual exchange bias that is found in full sheet samples. Whether this discrepancy is due to the nanostructuring of the sample or thermal effects on the exchange bias remains open for discussion. Still, this demonstration of field-free magnetization reversal by SHE and orthogonal exchange bias greatly increases the feasibility of future SHE-based MRAM devices.

1 Introduction 1

1.1 The basics of STT-MRAM . . . 1

1.2 The challenges and improvements for STT-MRAM . . . 3

1.3 Magnetization switching by spin Hall effect . . . 4

1.4 Field-free switching with the spin Hall effect . . . 6

1.5 This thesis . . . 6

2 Exchange bias theory 9 2.1 Ferromagnetism and anti-ferromagnetism . . . 9

2.2 Magnetic anisotropy . . . 11

2.3 An introduction to the exchange bias effect . . . 13

2.4 Exchange bias beyond the Meiklejohn-bean model . . . 18

2.5 Orthogonal exchange bias . . . 24

2.6 Summary . . . 27

3 Theory of current-induced magnetization reversal 29 3.1 The spin Hall effect . . . 29

3.2 Current driven reversal in a bilayer system . . . 33

3.3 Summary . . . 38

4 Methods 39 4.1 Sample fabrication . . . 39

4.2 Field-cooling . . . 41

4.3 Sample characterization . . . 44

5 Creating an orthogonal exchange bias 51 5.1 Desired sample properties . . . 51

5.2 Demonstration of orthogonal exchange bias . . . 55

5.3 Thickness dependence study . . . 58

5.4 Comparison of different exchange bias configurations . . . 63

5.5 Stability of the orthogonal exchange bias . . . 65

6 Field-free magnetization reversal by spin Hall effect and exchange bias 69 6.1 Main results . . . 69

6.1.1 Proof-of-principle experiment . . . 70

6.1.2 Partial magnetization reversal . . . 72

6.1.3 Magnetization reversal under applied magnetic field . . . 73 ii

6.1.6 Results of a sample without exchange bias layer . . . 76

6.2 Discussion . . . 78

6.2.1 Current shunting . . . 78

6.2.2 Influence of IrMn grains . . . 79

6.2.3 Domain wall nucleation & propagation . . . 82

6.2.4 Thermal effects . . . 83

6.2.5 The influence of nanostructuring . . . 84

6.2.6 Anisotropy gradients . . . 85

6.2.7 Other explanations for deterministic switching . . . 85

6.3 Conclusion . . . 87

7 Conclusion & Outlook 89 7.1 Creating an orthogonal exchange bias . . . 89

7.2 Field-free magnetization reversal by spin Hall effect and exchange bias. . . 90

7.3 The future of MRAM . . . 92

Bibliography 93

A Domain nucleation and domain wall propagation 99

B Spin-glass model 101

C LLG parameter details 103

D Measuring IP exchange on wedge using MOKE 104

E Current-induced magnetization reversal in samples without dusting layer 106

iii

MRAM Magnetic random acces memory MTJ Magnetic tunnel junction TMR Tunnel magneto resistance

STT Spin-transfer torque

SHE Spin Hall effect

OOP Out-of-plane

IP In-plane

PMA Perpendicular magnetic anisotropy

EB Exchange bias

F Ferromagnetic

AF Anti-ferromagnetic

SG-model Spin-Glass model

LLG-equation Landau Lifshitz Gilbert equation

AHE Anomalous Hall effect

EBL Electron beam lithography MOKE Magneto-optical Kerr effect

VSM-SQUID Vibrating sample magnetometer superconducting interference device FEM-method Finite element analysis method

iv

Introduction

Nowadays, many digital devices are used by society and this will only increase further in the forthcoming decades. Besides the familiar smartphone or tablet, we will get more household smart devices such as smart-refrigerators and smart-thermostats. Moreover, cars will become smart-cars and streetlights become smart-streetlights. All these devices need to gather and pro- cess data and are connected to each other. To facilitate this, it is important that there is access to cheap data processing, a fast internet connection and very importantly: efficient, non-volatile, low power data storage options.

This thesis focuses on the data storage part, specifically on devices that store data using mag- netism. Magnets, which can be magnetized in two different directions, are ideal data storage devices as they can be designed to be inherently non-volatile. Development in magnetic memory already began in the 1960’s with the magnetic bubble memory and storage on memory tapes.

With the invention of the hard-disk, magnetism took off in becoming one of the most widely used data storage mechanisms.

In recent years, a new kind of magnetic memory has been developed, the STT-MRAM (Spin Trans- fer Torque Magnetic Random Access Memory). It is a non-volatile memory device that is finding its way onto the consumer market, currently as an SRAM replacement (fast, small, embedded memory). The STT-MRAM uses miniscule arrays of magnetic bits to store data, and uses cur- rent to read and write data. In this chapter, the basics of MRAM are explored in more detail.

After that, the main drawbacks of the current STT-MRAM design are given. This is followed by the introduction of a recently discovered effect, the spin Hall effect, that provides an alternative write mechanism for MRAM that can overcome many of the drawbacks of STT-MRAM. Finally, the outline of this thesis is presented in which an improvement is proposed on this new spin Hall effect writing mechanism. This improved method may lead to practical applications for the SHE, and possibly a next generation of MRAM devices.

1.1 The basics of STT-MRAM

A storage device compromises of three important parts: data storage, reading data, and writing data. In this section, these three parts are discussed regarding the STT-MRAM.

1

An STT-MRAM stores data in arrays of nano-sized magnetic bits. This is schematically shown in figure 1.1. The bits are connected between two electrodes which are arranged in row and column arrays. An individual bit can be addressed by properly biasing a specific column and row electrode.

MTJ

Row electrode

Column electrode

Figure 1.1: Schematic overview of an STT-MRAM device. A bit consists of a mag- netic tunnel junction (MTJ) which can be read and written by applying a voltage along the proper column and row electrodes.

Fixed magnetic layer Anti-parallel

High Resistance

Parallel Low Resistance

Tunnel barrier

Free magnetic layer

Memory state “0” Memory state “1”

Figure 1.2: Schematic overview of a magnetic tunnel junction, that consists of two magnetic layer separated by a tunnel barrier. The magnetization direction of the layers is indicated by the arrows. One of the magnetic layers has a fixed magne- tization direction. The free magnetic layer can have an orientation either parallel or anti-parallel to the fixed layer. Depending on this direction, the stack has either a low or high resistance due to the TMR-effect through the tunnel barrier. This is used as a read-out mechanism. The magnetization of the free magnetic layer can be changed by the spin transfer torque.

The magnetic bits in an STT-MRAM are a called magnetic tunnel-junctions (MTJ’s), schematically shown in figure 1.2. They consist of two magnetic layers, and a dielectric tunnel barrier. The top magnetic layer has a fixed orientation. The other, ’free’ magnetic layer can have a magnetic state parallel or anti-parallel to the fixed layer. Due to the Tunnel Magneto Resistance (TMR) effect through the tunnel barrier, the electrical resistance of the device depends on the relative orientation of the free and fixed magnetic layer [1]. A memory device can be created by assigning a ‘0’ and ‘1’ to the low or high resistive state and combining these bits in arrays. Data reading is done by monitoring the resistance of the individual bits.

The challenge for writing data is to efficiently switch the magnetization direction of the free layer between parallel and anti-parallel, relative to the fixed layer state. An energy barrier be- tween these states prevents spontaneous rotation of the magnetization, schematically indicated

Magnetic orientation Write

Figure 1.3: Due to the anisotropy energy of a magnetic layer, some states can have a lower energy. In the figure, the in-plane configurations correspond to these states.

The intermediate out-of-plane state has a higher energy and is therefore not the ground state of the magnetic layer. To rotate from one preferred state to the other, the anisotropy energy barrier has to be overcome.

in figure 1.3. This barrier is the result of an uniaxial anisotropy in the magnetic layer. In this case, the magnetization has a preferred direction out of the sample plane. It is caused by surface interactions with neighboring layers that lower the energy of the out-of-plane magnetic states compared to other directions. Materials with In-plane anisotropy are also used for STT-MRAM, but are lower in storage density. In this thesis, only out-of-plane STT-MRAM is considered.

The spin-transfer torque write mechanism can be used to overcome this anisotropy energy barrier and switch the magnetization direction, as shown in figure 1.4. When a non-polarized current runs through the reference magnetic layer, the current becomes spin-polarized. An non-polarized current consists of electrons with random spin distribution, while a spin-polarized current favors one of the directions, in this case corresponding to the orientation of the reference magnetic layer layer. The spin-polarized current is then directed into another magnetic layer. If this magnetic layer has a different orientation, the current gets spin-polarized in the corresponding direction.

As the spin is a microscopic angular momentum, conservation of angular momentum states that the spins should exert a torque on the magnetization. This principle is used in an MTJ to rotate the magnetization of the free layer. If they are oriented anti-parallel, a current runs through the fixed layer, becomes spin-polarized and exerts a torque on the magnetization of the free layer. In the case of parallel orientation, the mechanism is slightly more complicated and works via spin accumulation in the free layer (not shown here).

1.2 The challenges and improvements for STT-MRAM

While STT and TMR have only been discovered in the 1990’s, STT-MRAM is already commercially available. Still, there are some challenges that prevent STT-MRAM in finding wide use in actual devices. The first problem is that the STT only works by sending a current directly through the MTJ. As these current densities are quite high this can easily damage the MTJ. Another problem

Reference layer Electron flow

Free layer Spacer

Torque

Spin-polarized current

Figure 1.4: Schematic overview of the spin transfer torque effect. A non-polarized current becomes polarized by running through a magnetic layer. When the spin- polarized current is inserted into a layer with a different magnetization direction, it will exert a torque on the magnetization to conserve its angular momentum. Torque on the reference layer is neglected for simplicity.

is the speed of the device. To switch the magnetization, the spin-polarized electrons that are directed onto the free layer are oriented anti-parallel to the magnetization of the layer. If they are aligned perfectly anti-parallel, no torque is exerted. A small thermal fluctuation is therefore necessary to induce switching. This is called the incubation delay and it limits the write speed of the device.

To tackle the aforementioned challenges in MRAM, a lot of effort is put into finding ways to lower the energy barrier and reduce current densities. For example, by the use of electric fields, heating, or using multiferroic materials [2][3][4]. They all result in a temporary reduction of the anisotropy energy of the magnetic layer to ease the switching of the magnetization.

Another approach is to find a different writing mechanism to work around the problem of incu- bation delay. A breakthrough occurred in 2011 when Miron et al. conducted an experiment on a cobalt-iron alloy nano-layer sandwiched between a platinum layer and an aluminum oxide layer [5]. By sending a current through the non-magnetic platinum layer, they could deterministically switch the magnetization direction in the cobalt. This is surprising because the current is mainly running through the Pt layer, so direct STT can not be the driving mechanism. The experiment is schematically shown in figure 3.6. One important note is that they applied an external mag- netic field along the current direction via a built-in bar magnet. Without this field, deterministic switching was not observed.

Substantial debate about the responsible mechanisms for this magnetization reversal existed in the scientific community. In 2012, Liu et al. proposed the spin Hall effect (SHE) as the driving mechanism, subverting the initial proposal by Miron et al. that the Rashba-effect originating form the asymmetry of the stack is the main mechanism for the switching [6]. The SHE in Pt/Co/Pt layers was simultaneously confirmed by the work of Haazen et al., conducted at the TU/e [7].

1.3 Magnetization switching by spin Hall effect

Switching of a magnetic layer with the spin Hall effect is schematically shown in figure 1.6. When a current flows through a high spin-orbit coupling material like platinum or tantalum, interactions

Pt Co

AlOx

I

–2.2 0 2.2

–1 0 1

0 2 4 6 8 10 12 14 16

–1 0 1 I (mA)Mz(a.u.)

MCoFe > 0

Mz (a.u.)

Time (s)

B = 0

MCoFe < 0 B = 0

Bar magnet

b.

c.

a.

200 nm

Figure 1.5: Deterministic switching results from Miron et al.. a: Sample stack con- sisting of a Pt layer through which the current run, a ferromagnetic Co layer and a AlOx cap. b: TEM image that shows two CoFe bar magnets which generate the external magnetic field. c: Deterministic switching by applying current pulses of al- ternating polarity. The direction of the external field generated from the bar magnet depends on the magnetization direction of the CoFe. Figure adapted from [5].

between the electrons and the lattice cause a vertical separation of electrons with opposite spin [8]. This vertical spin current is inserted into the magnetic layer and exerts a torque on the magnetization similar to the STT. As the spin-current is polarized in-plane, the magnetization of the layer will rotate towards the in-plane direction as well. After the pulse, the spins want to relax back to either perpendicular direction, where each direction is equally as favorable due to the out-of-plane anisotropy of the layer. To force deterministic reversal, a small external field has to be applied along the current flow direction. It breaks the symmetry of the system. The exact mechanism is explained in detail in section 3.2. For the correct combination of field and current direction, the magnetization only relaxes back to a specific magnetic state.

External field

Charge current

Spin current

Spin Hall effect

Figure 1.6: Schematic overview of switching via the spin Hall effect. Electron with opposite spins pointing in the plane are separated due to the spin Hall effect in a material. If a magnetic layer is adjacent to it, the polarized spins are inserted and exert a torque via the spin transfer torque. By applying an external field, the symmetry of the system is broken and the magnetization reverses.

The advantages of spin Hall driven switching are significant. First of all, due to the perpendicular orientation of the spin Hall current with the magnetization direction of the magnetic layer, no thermal fluctuation is necessary, thus removing the incubation delay. Therefore, magnetization

reversal with the spin Hall effect is theoretically much faster than using STT. An additional ad- vantage is the absence of a current flowing through the MTJ, as the current only flows through the non-magnetic Pt layer.

However, the major drawback of this technique is the need for the aforementioned in-plane external magnetic field to be present. The bar-magnet solution as seen in figure 3.6, is not scalable to the size of an actual MRAM bit. External magnetic fields are also not suitable as they can influence other magnetic parts of the device and need a lot of energy to be generated.

Therefore, the next challenge in the MRAM development is to enable the field-free spin Hall switching by replacement of this symmetry-breaking magnetic field. A few proposals have been done. For example, Yu et al. created an artificial variable anisotropy along the magnetic bit. This results in an effective magnetic field that breaks the symmetry in a similar way as an external magnetic field [9]. Torrejon et al. finds that such an anisotropy gradient can even occur naturally after using specific growth conditions [10]. Research is also conducted in the electric field effect or multiferroics combined with the SHE. In this thesis, another approach is taken to replace this external field, namely via an intrinsic effective field originating from an anti-ferromagnetic layer adjacent to the free magnetic layer. The next section elucidates on this idea.

1.4 Field-free switching with the spin Hall effect

We propose to replace the external magnetic field by an effective magnetic field originating from the exchange coupling between a ferromagnetic layer with an anti-ferromagnetic layer. The so-called exchange bias effect occurs at the interface of the two layers, and is equivalent to a effective field working on the ferromagnetic layer. As mentioned before, the effective field should be oriented in the in-plane direction, if a perpendicularly magnetized layer is to be switched. A schematic overview of the proposed idea is shown in figure 1.7. A trilayer of non-magnetic platinum, ferromagnetic cobalt and anti-ferromagnetic iridium-manganese is grown. The goal of this project is to reverse the magnetization of the cobalt layer by simply sending a current through the bottom platinum layer. The SHE in the Pt causes a spin current to flow into the cobalt layer, which has out-of-plane magnetic anisotropy. The coupling of this cobalt layer with an anti-ferromagnetic iridium-manganese layer results in an effective exchange bias field so that the magnetization reverses deterministically without any external magnetic field. For the exchange bias coupling between the Co and IrMn, a rather unusual system must be created, in which the orientation of the exchange bias is orthogonal to the magnetization of the Co layer. A large part of this work is dedicated to the fabrication and characterization of such a system.

1.5 This thesis

This section gives an overview of the different chapters in this thesis. The following chapter, chapter 2, focuses on the theory behind the exchange bias effect. First, a general theory about magneto-statics applied to magnetic layers is introduced as it is necessary to explain the exchange bias effect. Exchange bias is a complicated interaction and a lot of models exist to describe it.

A couple of these models will be introduced. The last part of the chapter focuses on the novel configuration that is necessary for this project: Orthogonal exchange bias.

Antiferromagnetic layer

Ferromagnetic layer

Spin Hall injection Sample

Effective exchange bias field

Figure 1.7: Sketch of the sample design used for the switching experiments in this thesis. The stack consists of a spin Hall injection layer, a ferromagnetic layer with perpendicular magnetic anisotropy, and an antiferromagnetic layer. The coupling be- tween the two magnetic layers causes an effective magnetic field due to the exchange bias and the magnetization can be switched with a combination of this effective field and the spin Hall effect.

The next chapter, chapter 3, describes theory relevant for current-driven magnetization reversal with the spin Hall effect. Simulations that show the dynamics of the switching procedure are included.

Chapter 4 introduces the various experimental setups that are used in this thesis. Sample growth is discussed first, followed by a brief overview of all the sample characterization methods. At the end of the chapter, the setup that is used for the current-driven switching experiments is introduced.

Chapter 5 presents the results on creating an orthogonal exchange biased sample. The desired properties are discussed and the results of an optimized sample are shown. A layer thickness dependence study and a study on the influence of temperature on the exchange bias are included.

Chapter 6 presents the results of the main goal of this thesis: current-driven magnetization rever- sal via the spin Hall effect in combination with the exchange bias to act as an effective magnetic field. In the first part of the chapter, it will be shown that the switching is successful and exhibits all expected symmetries. The second part will elaborate on the physics behind the switching, as these are remarkably different from existing switching experiments with the spin Hall effect.

Chapter 7 concludes this thesis. The main findings of the result chapters are summarized. A brief outlook on the implementation of the exchange bias and spin Hall driven switching for future MRAM devices concludes the chapter.

Exchange bias theory

This chapter focuses on the theory behind the exchange bias phenomena in thin magnetic lay- ers. In section 2.1, two magnetic configurations, ferromagnetism and antiferromagnetism, that can arise in magnetic thin films are introduced. Important properties of these materials such as anisotropy and spin structure are described in detail. It is a prelude to the introduction of the exchange bias effect in section 2.3. Exchange bias will be discussed extensively, ranging from a basic intuitive introduction towards an overview of different theories and experimentally ob- served effects in exchange bias systems. At the end of the chapter, orthogonal exchange bias will be introduced, which is a necessary component for the field-free deterministic magnetization reversal experiments in chapter 6 and is experimentally created in chapter 5.

2.1 Ferromagnetism and anti-ferromagnetism

On a microscopic scale, atoms have a magnetic moment ~µ [11]. The biggest contribution to the magnetic moment of an atom results from the spin of the electrons that orbit the nucleus.

In paramagnetic materials, these miniscule magnetic moments are randomly distributed due to thermal fluctuations in a way that all magnetic moments cancel each other out, see figure 2.1a.

If an external magnetic field is applied, these magnetic moments align with this field. This is described by the Zeeman energy:

E_Zeeman=−µ₀µ · ~~ H_ext (2.1)

in which µ₀ is the vacuum permeability (µ₀ = 4π · 10⁻⁷ N/A²). This equation states that the magnetic moments align with an externally applied field ~H_extto lower their energy.

However, in some materials, the magnetic moments arrange in a certain common direction even when no external magnetic field is applied. This is shown in figure 2.1b. This spontaneous magnetization of a material is called ferromagnetism.

Microscopically, the ferromagnetic ordering of a material is due to the exchange interaction be- tween spins. The exchange interaction arises from the quantum-mechanical Pauli exclusion prin- ciple that states that two electrons with equal spin have an antisymmetric orbital wave function, decreasing the effective Coulomb repulsion between the two. This mechanism, known as the

9

No applied field

Paramagnetic Ferromagnetic Antiferromagnetic

a.

T>T

T

T<T

J>0 T<T

J<0

b. c.

Figure 2.1: Different magnetic spin configurations. A competition between ther- mal energy and the exchange energy determines the configuration of a material. a:

Paramagnetic configuration arises when the temperature is above T_N or T_C. Ther- mal energy overcomes the ordering caused by the exchange J between the spins.

b: Ferromagnetic configuration in which the spins align parallel to each other arises when J > 0 and the temperature is below T_C. c: Anti-parallel antiferromagnetic configuration arises when J < 0 and the temperature is below T_N.

exchange interaction, favors a certain spin configuration. Usually, exchange interactions are very short-ranged, confined to electrons in orbitals on the same atom or their nearest neighbors. This interaction between spins ~S₁ and ~S₂ can be written in the form of the exchange energy:

E_Exchange=−2J ~S₁· ~S₂. (2.2)

If the exchange constant is positive, J > 0, and the dominating energy term, a net magnetic moment in a material arises. The temperature below which this happens is called the Curie temperature T_C. Only some materials have a T_C above room temperature. For example, cobalt has a T_Cof 1388 K, and it will be used as the main ferromagnetic material in this thesis.

In the opposing case, in which J < 0, anti-parallel ordering of spins is favored, schematically shown in figure 2.1c. A material that exhibits this kind of behavior is called anti-ferromagnetic.

The corresponding temperature below which this happens is called the Neèl temperature T_N. An example of an antiferromagnetic body-centered cubic (bcc) structure is shown in figure 2.2a.

Here the spins are located on a bcc lattice, all atoms at the corners of the unit cell are anti- ferromagnetically aligned with these on the central position and ferromagnetically aligned with the other corners. In figure 2.2b, the structure is interpreted as two sub-lattices a and b which on itself are ferromagnetically coupled by the exchange constant J_aand J_b, but anti-ferromagnetically coupled to each other with exchange constant J_{a b}. This corresponds to material combinations such as cobalt-oxide (CoO) in which each material resembles a different lattice. In some materi- als, even more complicated spin structures may arise [12].

Both anti-ferromagnetism and ferromagnetism are essential to the emergence of exchange bias in magnetic multilayers. This effect will be explained in section 2.3.

a. b.

J

J

J

a

b b

a

Figure 2.2: a:: Antiferromagnetic ordering of a bcc lattice. The body-centered spins align anti-parallel to spins on the corner. b: A 2D representation of two ferromag- netic lattices a and b which are antiferromagnetically coupled. The two lattices cor- respond to either the body-centered spin or corner spin in figure a. Figure adapted from [11].

2.2 Magnetic anisotropy

In a ferromagnetic (F) or anti-ferromagnetic (AF) material, the magnetization usually aligns itself along one or more axes of the material that are energetically more favorable than other axes. This phenomena is called magnetic anisotropy and is the reason that magnetic materials are very suitable for memory applications, as the magnetization can remain stable in its low energy state and an energy is required to rotate the magnetization from a low energy state to another state. The orientation(s) corresponding to the lowest energy are called the easy-axes of the material. The higher energies correspond to the hard-axes of the material. To rotate the magnetization from an easy-axis towards an hard-axis, the magnetic anisotropy energy barrier K (units: energy/volume) has to be overcome. If a material has an uniaxial anisotropy with both an easy and a hard axes, the magnetic anisotropy energy per unit area can be written as:

E_anisotropy= K tsin²(φ − β), (2.3)

with β the angle of the magnetization, φ the angle of the easy-axis and t the thickness of the cor- responding layer. The angles are defined relative to a predefined axis. In the following section, the anisotropy of a ferromagnet and anti-ferromagnet thin film is discussed. The main contri- butions consist of shape, surface and crystalline anisotropy. Other possible contributions to the anisotropy energy, such as strain-induced anisotropy, are not discussed as they do not contribute to the anisotropy energy in the materials used in this thesis.

In section 2.3, another kind of anisotropy, the exchange anisotropy, is introduced. This is an extrinsic contribution to the anisotropy arising from the coupling between a F and AF material.

2.2.1 The magnetic anisotropy of a thin ferromagnetic layer

The first main contribution to the anisotropy energy of a ferromagnet is caused by the shape of the material [13]. Contrary to the short-ranged exchange interaction which is isotropic, spins in

a material are also coupled by dipole-dipole interaction. The dipole-dipole interaction energy is lowest when spins align parallel to their internuclear axis. Macroscopically, this means that a ma- terial has its magnetization along its longest axis to reduce the dipole-dipole interaction energies of the whole system. It can be described by an effective field inside the material: the demag- netization field ~H_d. This field is related to the magnetic configuration via the demagnetization tensor N :

H~_d=−N ~M = −





N_x 0 0

0 N_y 0

0 0 N_z







 M_x M_y M_z



, (2.4)

in which ~M is the magnetization vector. The demagnetization tensor N solely depends on the shape of the material. For an infinite square thin film, the three components of N can be calcu- lated by using Ampere’s and Gauss’s law (see [11]). This results in N_x = 0 and N_y =0, while N_z=1. Hence, the demagnetization field counteracts an out-of-plane (OOP) configuration and the spins are pulled in-plane (IP). Considering only the shape anisotropy, OOP magnetization in ultra-thin films should not be possible. This is, however, not the case in many thin film systems.

Out-of-plane magnetic anisotropy (also called perpendicular magnetic anisotropy: PMA) can be achieved in thin films due to the dominating effect of surface anisotropy. If a ferromagnetic thin film is sandwiched between materials with a high spin-orbit coupling such as platinum (Pt) or palladium (Pd), these surface effects can result in a preferred OOP configuration of the spins.

The microscopic origins of these spin-orbit coupling effects are beyond the scope of this thesis. A detailed explanation can be found in [14]. The surface anisotropy energy is given by the constant K_s in J/m².

The two previously introduced anisotropies are the main contributions to the total effective anisotropy K_F in the ferromagnetic layer used in this thesis. The shape anisotropy in a thin film pulls the magnetization towards the IP direction due to ~H_d being maximum for an OOP con- figuration (so N_z =1 and N_y,x = 0). Considering equation (2.4), the shape anisotropy energy density E_d can be written as:

E_d= 1

2µ₀M · ~~ H_d= 1

2µ₀M_s², in which M_s=| ~M |, (2.5) assuming the magnetization is fully OOP. Note that the factor 1/2 originates from the double counting of the dipole-dipole interactions which cause the demagnetization field. The total uni- axial anisotropy for a thin ferromagnetic film with thickness t_Fis thus equal to:

K_F= K_s/t_F− 1

2µ₀M_s². (2.6)

Note that K_F is defined as positive if the easy-axis is oriented OOP. Due to the two competing terms in equation (2.6), only if t_F< K_s/¹₂µ₀M_s², OOP anisotropy emerges.

2.2.2 The anisotropy of an anti-ferromagnetic layer

Although an AF-layer has no net magnetization, the spins of the sub-lattices are still aligned in an ordered way. The orientation of this ordering is mainly determined by the crystalline anisotropy of a material.

Magneto-crystalline anisotropy arises from the crystalline structure of a material. Due to the coupling of the electron spin with the electric field in a crystal lattice, a preferred direction of the spin of the electron is induced. In a first order approximation, most materials have one (or more) uniaxial easy-axes due to this crystalline anisotropy. The magneto-crystalline anisotropy energy contribution scales with the total volume of the material.

The resulting effective anisotropy of the AF is determined by this crystalline anisotropy and given by K_AF. The corresponding energy per unit area is given by:

Eanisotropy, AF= K_AFt_AFsin²(φ − δ), (2.7) with δ the angle of the AF sub-lattice magnetization, φ the angle of the AF easy-axis and t_AFthe thickness of the AF-layer. Crystalline anisotropy is also present in a ferromagnetic material, al- though not considered in section 2.2.1, as the shape and surface contributions are the dominating effects in ferromagnetic thin films.

2.3 An introduction to the exchange bias effect

Another kind of anisotropy can arise when the previously described F and AF-layer are placed adjacent to each other. This was first discovered by Meiklejohn and Bean in the 1950’s when they conducted experiments on Co particles embedded in anti-ferromagnetic CoO [15]. When ana- lyzing the behavior of Co in a magnetic field, they discovered an extra unidirectional anisotropy in the system. The ferromagnetic Co appeared to have an extra preferential direction along one specific direction, not just along one axis as discussed in section 2.2.1 (uniaxial anisotropy).

The explanation of this observation can be found at the interface between the F and AF-layer. If the AF interface layer has uncompensated spins, they can couple to the spins at the F interface layer via the exchange interaction, shown schematically in figure 2.3. The strength of this cou- pling is determined by the exchange strength J_EBand can be written in the form of the exchange anisotropy energy Eexchange anisotropy:

Eexchange anisotropy=−J_EBcos(ψ − β), (2.8) with β the angle of the F-layer magnetization, and φ the angle of the uncompensated AF spins.

This adds an extra unidirectional anisotropy to the ferromagnet. When applying an external field to the system, the added anisotropy term results in an increase in the switching field in a certain direction. This effect is called the exchange bias effect.

The exchange bias effect is one of the most widely studied effects in magnetism over the last 50 years. Subsequently, exchange bias has found its way to many modern applications in magnetic devices [16]. Still, no comprehensive theory exists to fully describe this phenomenon. In the

Antiferromagnetic layer

Exchange coupling

J_EB

Ferromagnetic layer

Figure 2.3: Exchange coupling between a F and AF-layer. Uncompensated spins at the AF interface couple to the F spins via the exchange interactions. This coupling induces an extra unidirectional anisotropy in the F-layer.

following sections, an attempt will be done to give a general overview of the exchange bias effect in magnetic multilayers. First, a simple model for magnetization reversal by magnetic fields in a F/AF bilayer system will be introduced to give a phenomenological understanding of the ex- change bias effect. This model is called the Meiklejohn-Bean model and is one of the first models which tried to grasp the effect in a simple calculation. It describes the magnetization behavior in a bilayer system by energy considerations involving the previously introduced Zeeman energy, anisotropy energy, and exchange energy. This model, however, is an extremely simplified model and cannot explain many observed effects in real systems. To get a more realistic picture of ex- change bias, more properties and observation of exchange bias have to be explored, as discussed in section 2.4.

2.3.1 Magnetization reversal in the Meiklejohn-Bean model

The Meiklejoh-Bean model describes the magnetization reversal process in a F/AF bilayer. It takes into account different energy contributions to determine the equilibrium angle β of the magnetization ~Mof the F-layer. This model is a macrospin model, in which the F-layer is described by one average spin. Hence, it assumes coherent rotation of the magnetization of the F-layer. In real systems, more complicated reversal processes might occur involving domain nucleation and domain wall motion. An introduction to domain nucleation and domain wall motion is given in appendix A. The simplistic nature of this model asks for some more assumptions regarding the F/AF system. Two important assumptions are: (i) a perfect interface between the F and AF-layer and (ii) the spins in the AF-layer remain unchanged during magnetization reversal. This implies that K_AF=∞and the AF interface is fully uncompensated.

A schematic overview of an ideal two-dimensional exchange coupled AF/F system is given in figure 2.4. Panel 2.4a shows the definition of different angles relative to the x-axis. The angles φ and ψ determine the easy-axis of the ferromagnetic and anti-ferromagnetic material, respectively.

Different angles of φ and ψ result in different configurations of the exchange bias. In figure 2.4b, the case of an OOP F-layer coupled to an OOP AF-layer is shown. Other configurations can also exist and will be described in section 2.5.

K

K

M

H

ψ=90o =90o

a. b.

y

x θ

β ψ ,

Figure 2.4: a: Representation of the different angles in the Meiklejohnbean modelin two dimensions. b: Example of a AF/F configuration with corresponding angles φ and ψ.

The total energy per unit area of the bilayer system consists of the Zeeman energy (the magneti- zation aligns to an external field H_ext, see equation (2.1)), the unidirectional exchange anisotropy energy at the interface between the ferromagnetic and antiferromagnetic layer, and the anisotropy energy of the ferromagnet:

E_total= E_Zeeman+ Eanisotropy,F+ Eexchange anisotropy. (2.9) This energy can be written as a function of the angle β, the magnetization angle of the ferromag- net. For an infinite sheet of material with a thickness t_F, the total energy per unit area can now be written as:

E_total(β) = −µ₀H_extM_st_Fcos(θ − β) + K_Ft_Fsin²(φ − β) − J_EBcos(ψ − β), (2.10) in which θ is the external magnetic field angle.

To find the equilibrium position of the magnetization vector, the energy is minimized with respect to β:

∂ E_total(β)

∂ β =0, (2.11)

and the stability condition:

∂²E_total(β)

∂ β² >0. (2.12)

If both conditions are satisfied, the magnetization angle β is in a stable regime. Equations (2.11) and (2.12) can be numerically solved to find the magnetization behavior under various applied magnetic fields.

Two important limiting cases are an external magnetic field applied along the easy-axis or hard- axis of the material. First, the case is considered in which (i) the magnetic field is applied along the easy-axis (θ = π/2, y-direction), (ii) no coupling between the F-layer and AF-layer (J_EB=0) exists and (iii) the easy-axis of the F-layer is oriented out-of plane (φ = π/2). For each magnetic field value, one or more local energy minima are found. A plot of the energy function E_total(β) is shown in figure 2.5. By increasing the external field, the magnetization can switch from one energy minimum corresponding to β = +π/2 to another energy minimum corresponding to β = −π/2. In other words, the magnetization in the y-direction switches.

β

E

(β )

Figure 2.5: The energy function plotted as a function of the magnetization angle β.

The sphere indicates a stable configuration for the magnetization. By applying an external field of −2K_F/µM_sthe magnetization switches from β = π/2 to β = −π/2.

The curves have been shifted vertically for clarity. Figure adapted from ??.

The resulting normalized magnetization in the y-direction M_y/M_s can be related to β via M_y = sin β and can be plotted as a function of the applied magnetic field H_{ext, y}, see figure 2.6a. The resulting graph is called a hystresis curve along the easy-axis of the material. Due to the uniaxial anisotropy of the F-layer, the history of the applied field determines the magnetization at zero applied field. This is called the remanent magnetization M_R. It is generally given as a percentage of the total saturation magnetization M_s. In the case of the easy-axis hysteresis curve, this value is 100%. The field at which the magnetization switches between the states is called the coercive field H_C. For an ideal easy-axis hysteresis curve H_C can be calculated with equation (2.11) with φ = π/2, θ = π/2 and J_EB=0:

µ₀H_C=±2K_F

M_s . (2.13)

Note that only a slight deviation in applied field direction or, for example, thermal fluctuations can significantly reduce the coercive field in real systems. The anisotropy constant K_Fis therefore hard to determine from a easy-axis hysteresis curve. For applied fields smaller than the coercive field, two local minima exist and the initial condition determines in which state the magnetization is.

In figure 2.6b, the same system is analyzed except the field sweep direction is along the x-axis instead of y-axis (θ = 0). This results in a so-called hard-axis loop of the magnetization. The uniaxial anisotropy is now perpendicular to the field direction resulting in no hysteresis and no coercive field. The remanence is also equal to zero. For strong applied fields the magnetization is completely saturated. The field at which this happens is called the anisotropy field H_K. Solving equation (2.11) for φ = π/2, θ = 0 and J_EB=0 results in the following equation for H_K:

µ₀H_K=±2K_F

M_s . (2.14)

With this equation it is generally possible to estimate the effective anisotropy K_Ffrom a hard-axis loop.

0

0 -H_ext/H_c +H_ext/H_c

H_C

M_R M_R

H_C

a.

0

0 0

-H_ext/H_K +H_ext/H_K Magnetic field Magnetic field

Magnetization

M_x/M_S

-M_x/M_S

Magnetization

M_y/M_S

-M_y/M_S

Magnetization

M_y/M_S

-M_y/M_S +2K_F/μ₀M_S

-2K_F/μ₀M_S

0

Magnetic field (a.u.) H_EB

H_EB

H_ext H_ext

b. _H

ext c.

Figure 2.6:Hysteresis curves for an F-layer with OOP anisotropy. The magnetization and field sweep direction is indicated for each figure. a: Due to the OOP anisotropy in the F-layer, magnetic hysteresis is present. The field sweep direction corresponds to the easy-axis of the material. The coercivity H_Cand remanence M_Rare indicated in the figure. b: A hard-axis hysteresis loop of an OOP F-layer is found when the field is swept in the x-direction. The magnetization is saturated at large applied fields, corresponding to the saturation magnetization M_s.c: Resulting easy-axis hysteresis curve when an F-layer is combined with an AF-layer. Due to the induced unidirec- tional anisotropy, the curve is shifted to the left compared with figure a. This shift is called the exchange bias H_EB.

Important results from the Meiklejohn-bean model are found when the coupling between the F and AF-layer is taken into account (J_EB>0). The field is swept in the y-direction corresponding to the easy-axis, just as in figure 2.6a. As shown in figure 2.6c, the hysteresis curve shifts to the left. The magnitude of this shift is called the exchange bias field H_EB. This field is a direct result of the unidirectional anisotropy induced by the exchange coupling between the F and AF-layer.

Solving equation (2.11) for φ = π/2, θ = π/2 and J_EB= J_EBresults in:

µ₀H_EB=− J_EB

µ₀M_st_F. (2.15)

This gives the possibility to calculate the exchange constant strength J_EBfrom an exchange biased easy-axis loop.

2.4 Exchange bias beyond the Meiklejohn-bean model

We now have a basic understanding of the exchange bias effect in an AF/F bilayer, and how to describe it with the Meiklejohn-Bean model. However, this interpretation of exchange bias can- not interpret most of the observed effects in such systems. The Meiklejohn-Bean model does not explain deviations in exchange bias magnitude, temperature dependence, F or AF-layer thickness dependence, enhanced coercivity in the F-layer or the polycrystalline structure of the AF-layer, all of which are observed experimentally in different exchange bias systems [17]. In the following sections, exchange bias observations from literature will be discussed and explained by alterna- tive exchange bias theories, if possible. Many of these observation are also observed in the results presented in chapter 5.

2.4.1 Exchange bias magnitude

For a simple Co/CoO system, as studied by Meikljohn and Bean themselves, the theoretical ex- change bias magnitude can be calculated via the Meiklejohn-bean model with equation (2.15).

A 10 nm thick Co layer with a saturation magnetization of 1.4 · 10⁶A/m is assumed. J_EBcan be calculated directly from the direct exchange interaction at the F/AF interface via: J_EB= N J_AF,F/A with N the number of atoms per lattice unit area A. Theoretical values for Co/CoO are: N = 4, A =3.2 nm and J_AF,F=2.98 · 10⁻²²J. This results in a value of µ₀H_EB=270 mT.

While this may look as a reasonable value, the result of this simple calculation of H_EBis much larger compared to the values found in almost all experimentally studied systems [18]. The first explanation for the discrepancy is the simplification of the coupling between the F and AF-layer.

In the Meikljohn-Bean model it is assumed that all the AF-spins are fully compensated with the F-spins (all spins are directly coupled).

A second explanation can be found considering the interface between the F and AF-layer. A perfectly flat surface without any defects is assumed, in which the F-layer is only considered as one rotating spin (macrospin model). In reality, the AF or F-layer can consist of different grains and surface effects can play a considerable role.

Over the last 50 years, many researchers have tried to improve on the simple calculation of Meiklejohn-bean to get a more realistic value of the exchange bias. Most models take a more realistic approach to the interfacial coupling between the F and AF-layer [17].

For example, Malozemoff et al. [19], introduced random defects in the interface between the F and AF-layer. In figure 2.7 these defects are schematically shown. They form a rough interface, effectively decreasing the energy of the exchange coupling. This results in a more realistic value of H_EB.

Another approach is taken by Mauri et al. [20]. They introduced a gradual rotation of the AF spins parallel to the interface. Such a domain wall can also lower the interfacial energy between the F and AF-layer. This assumption results in more reasonable values of H_EB. However, this model assumes AF-layers thick enough to form a domain wall, while exchange bias is also observed in very thin layers of only a few atoms thick [21].

More of these interface theories are proposed during the last 30 years, but most of them are only applicable to certain F/AF systems in which they predict the exchange bias correctly. A small

Antiferromagnetic layer

Ferromagnetic layer

H_ext

Figure 2.7: Schematic representation of random interface defects according to the Malozmoff model. The dashed line represents the rough interface.

deviation in system conditions can cause unpredictable results. Until now, no comprehensive theory of exchange bias exists that can predict the exchange bias magnitude in all system equally as good.

2.4.2 Enhanced coercivity

The previously introduced interpretations of the F/AF interface can explain the value of H_EBrea- sonably well. However, the common experimental observation of an increase in coercive field H_C of the F-layer when an AF-layer is placed on top of it is not explained by these theories. A literature example of such an increase is shown in figure 2.8, in which Pt/Co multilayers are studied, coupled to a CoO AF-layer at 10 K. In the experimental part of this thesis, such a coer- civity increase is also observed. A particularly successful model called the Spin-Glass (SG) model proposed by Radu et al. tries to explain this coercivity enhancement [17].

Figure 2.8: Observed coercivity enhancement and exchange bias with the insertion of a CoO AF-layer. Figure adapted from [22].

Just as many alternative theories, this theory tries to describe the interface between the F and AF-

AF-layer

Rotatable AF spins Frozen AF spins

Low K_AF High K_AF

F-layer

H_ext H_ext

Figure 2.9: Schematic representation of the F/AF interface according to the Spin- Glass model. A low anisotropy region at the interface is present, caused by impurities and surface roughness. This low anisotropy region can rotate together with the F- layer under an applied field.

layer in a more realistic manner. More specifically, the SG-model states that at the interface, the AF has a lower anisotropy than in bulk of the AF. This results in AF spins that rotate freely when external field is applied which is strong enough to rotate the F spins. This is schematically shown in figure 2.9. Two applied field directions are sketched in which a part of the AF-layer with a low anisotropy rotates coherently with the F-layer. Arguments for such a low anisotropy region can be derived from the imperfect nature of the AF/F interface. For example, chemical intermixing or other defects are likely present at such an interface. Moreover, structural inhomogeneities at the interface can lead to a frustrated spin-glass like state. Such a frustrated SG-state can be the result of a spin structure in which there is no perfect AF ordering such as seen in figure 2.2, but where there is an energy competition between spin configurations or crystalline anisotropies.

Due to this instability, a part of the spins will have a random orientation, resulting in a lower anisotropy. The transition from the F to AF-layer is therefore not immediate, but gradual in the form of a low anisotropy region, in which the AF spins are in a frustrated spin-glass like state.

This SG-like behavior can be modeled by adding an effective anisotropy energy constant to the Meiklejohn-bean model in equation (2.10), which describes the rotatable part of the AF-layer and the resulting imperfect interface. In appendix B, more details about the extended SG-model are given.

In figure 2.10, the SG-model is compared to the standard Meiklejohn-Bean model. The following parameters are used for the F-layer: M_s =1.4 MA/m, K_F=4 · 10⁴ J/m³, t_F =1.25 nm, which correspond to a typical Co layer. The exchange constant is estimated to be J_EB=1 · 10⁻⁴J/m². The SG-model adds an extra energy term that describes the gradual rotation of a part of the AF- layer. A clear coercivity enhancement and exchange bias reduction are seen for the SG-model, which resemble the experimental observations (figure 2.8).

2.4.3 Thickness dependence

Another experimental observation, is the exchange bias dependence on the thicknesses of the F and AF-layer. Because exchange bias is an interface effect, the magnitude of the exchange bias is expected to decrease if the thickness of the F-layer increases. An 1/t_F dependence is found in the Meiklejohn-bean model, see equation (2.15). Surprisingly, considering the failure

MB-model SG-model

Figure 2.10: Calculation of hysteresis loops of a F/AF bilayer with the SG-model compared to the MB-model. For the SG-model, corresponding to a less ideal inter- face, a coercivity enhancement and a exchange bias reduction is found. The field is swept along the easy-axis of the F-layer.

of the prediction of H_EB, this dependence is actually observed experimentally in a vast amount of systems, see for example figure 2.11[20]. Deviation from this dependence is found in very thin (a few nm) or very thick (> 1µm) F-layers. Noguès et al. suggests that the derivation for thin F-layers is due to the F-layer becoming discontinuous [18] .

While the thickness t_AF of the AF-layer is not included in simple exchange bias models, in most experiments a dependence on this thickness is found. See for example figure 2.11b in which a temperature and thickness dependent exchange bias is found for an FeMn AF-layer.

Some theories, such as the previously introduced SG-model, can model the observed behavior of figure 2.11ab, as it includes both the F and AF thickness in its model. The result of the SG-model is shown in figure 2.12. For details about the parameters or the SG-model, see appendix B.

As expected, the exchange bias follows a 1/t_F dependence. This can intuitively explained by it being a surface effect. Increasing the volume of the F-layer reduces this relative strength of this surface. The t_AF dependence is more complicated. For small thicknesses, the AF-layer rotates with the F-layer due to its low total anisotropy. As a result, the exchange bias disappears, and an increase in coercivity below a critical thickness is observed. The behavior is comparable to the experimental results in figure 2.11. For thicker AF-layers, the exchange bias can decrease. This can be explained by the AF domain wall model from Mauri et al. as discussed in section 2.4.1.

A change in anisotropy due to the increase in F-layer thickness is not taken into account in this model, but will of course play a role in experimental results.

2.4.4 Temperature dependence & field-cooling

Temperature can have a strong effect on the exchange bias. An important parameter of exchange bias systems is the blocking temperature T_B. At this temperature, the exchange bias completely

a. b.

Figure 2.11: Literature examples of observed F and AF-layer thickness dependence on coercivity and exchange bias. a: F-layer thickness dependence. Note the non- linear scale. Figure taken from [20]. b: AF-layer thickness dependence. The ex- change bias emerges after a critical thickness. Figure taken from [23].

a. b.

Figure 2.12: Layer thickness dependent exchange bias, simulated using the SG- model.

vanishes. One might expect that this is equal to the previously introduced Neèl temperature T_N, which describes the temperature at which the AF-layer becomes paramagnetic (disordered).

However, studies show that for thin (< 10 nm) AF-layers, the blocking temperature can be con- siderably lower than the Neèl temperature [24]. Causes for this behavior have been sought in finite size effects, AF grains or super-paramagnetic behavior [25]. An example of low blocking temperature for thin AF-layers is shown in figure 6.11 for a CoO antiferromagnet.

The discrepancy between T_N and T_B appears to be very useful when setting the exchange bias in a desired direction. This can be done by a so-called field-cooling procedure, in which the temperature is heated to above T_B and subsequently cooled under a strong applied magnetic field. This sets the direction of the exchange bias parallel to that of the applied field. As T_Bis usually lower than T_N, lower field-cooling temperatures are needed. This process is extensively discussed in section 4.2.

The models that are considered in this thesis do not include any temperature dependence. In light of the previously introduced SG-model, the discrepancy between the blocking and Neèl temperature can be interpreted as follows: The SG model is based on frustration at the interface, resulting in a low anisotropy region. The conversion factor f that describes this, is probably temperature dependent, as thermal energy can influence the frustration. For thin AF-layers, this can result in a large low anisotropy region and the disappearance of exchange bias. AF grains can also play a role in the temperature dependence of AF-layers. This will be further explored in the next section.

Figure 2.13: Blocking temperature T_B as a function of the AF thickness in a Fe₃O₄/CoO bilayer. The curve is a guide to the eye. Figure taken from [25].

2.4.5 Polycrystalline antiferromagnetic thin films

Most of the experimentally observed effects can be explained by theory quite well. However, they still consider only a macrospin model of the magnetization reversal. Some AF materials such as IrMn (which is used extensively in this thesis) tend to grow in a polycrystalline manner (especially with the fabrication method used in this thesis). A macrospin model can only account for the average of such differences and does not account for the microscopic behavior of the AF-layer and the observed magnetization reversal. Such a polycrystalline structure can result in vastly different results [26]. Crystalline grains can have different sizes and crystal orientations.

Therefore, the AF spins direction can differ among grains as they are bound to the crystalline axis at which the crystalline anisotropy energy is lowest. Likewise, this can also have an effect on the local exchange bias, blocking temperature or on an underlying ferromagnetic layer. More details on the effects of AF grains will follow with the interpretation of results in chapter 5 and 6.

2.5 Orthogonal exchange bias

Until now, only an exchange bias system in which the F and AF-layer are oriented parallel have been discussed. Most literature reports consider exchange bias systems for IP ferromagnetic ma- terials, the configuration shown in figure 2.14a. With the emergence of OOP magnetic layers, OOP exchange bias has become a field of interest (also called perpendicular exchange bias in various sources) [27][28]. The OOP spins are coupled to an AF-layer with OOP unidirectional anisotropy, schematically shown in figure 2.14b. The properties of both systems are very compa- rable, although some differences can exist. Obviously, OOP exchange bias can only emerge when the F-layer is thin enough to give rise to PMA. As discussed, the 1/t_F dependence can diverge in very thin layers. Is is also reported that a difference in exchange bias magnitude can exist.

Either an increase, decrease or comparable exchange bias are reported for OOP exchange biased systems compared to IP exchange biased systems [22][28][29].

a. c.

AF F

b.

Figure 2.14: Different exchange bias configurations. a: IP exchange bias. b: OOP (perpendicular) exchange bias. c: Orthogonal exchange bias

In this thesis, a new exchange bias configuration is studied consisting of an F-layer with PMA coupled to AF-layer with an IP anisotropy, see figure 2.14c. The spins are coupled orthogonally, resulting in an orthogonal exchange bias. Chapter 5 focuses on creating such an exchange bias.

Only a few reports in literature exist about comparable exchange bias configurations. In 2001, Maat el al. reported a combination of OOP and IP exchange bias [22], shown in figure 2.15. The exchange bias of a sample with OOP (sample 1) and one with IP (sample 2) anisotropy are set in either OOP (H_⊥) or IP (H_k) direction with a field-cooling temperature of 10 K. Figures 2.15bc demonstrate that it is possible to create an exchange bias (partly) orthogonal to the magnetization direction of the F-layer, as they shown an exchange bias is the hard-axis loop. An explanation for this effect is shown schematically in figures 2.15ef. The spins of the AF CoO are bound to different crystallographic easy-axes depending on the field-cooling direction, this results in both IP and OOP exchange bias to be present in the sample.

Figure 2.16 shows a result from Sun el al. [30]. Here, an (FeNi/FeMn)_N ferromagnetic multilayer with IP anisotropy is coupled to a FeMn AF-layer. The sample is field-cooled in either IP or OOP