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:
EZeeman=−µ0µ · ~~ Hext (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 ~Hextto 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
C,T
NT<T
CJ>0 T<T
NJ<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 TN or TC. 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 TC. c: Anti-parallel antiferromagnetic configuration arises when J < 0 and the temperature is below TN.
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:
EExchange=−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 TC. Only some materials have a TC above room temperature. For example, cobalt has a TCof 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 TN. 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 anti-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 Jaand Jb, but anti-ferromagnetically coupled to each other with exchange constant Ja 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.
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 antiferromagferromag-netically coupled. The two lattices cor-respond to either the body-centered spin or corner spin in figure a. Figure adapted from [11].