This section describes how a current can reverse the magnetization in a bilayer consisting of a strong spin Hall injection layer and an OOP magnetized ferromagnetic layer. This is done by introducing the LLG equation, which describes the time evolution of the magnetization by considering different contributions, such as applied magnetic field, damping and the influence of a spin-polarized current. Subsequently the LLG-equation is used to simulate the magnetization behavior under the influence of a spin Hall current and an external magnetic field.
3.2.1 The LLG equation
The LLG-equation describes the time evolution of a magnetization vector (∂ ~∂ tM) in three dimen-sions. It consists of different contribution from torques working on the magnetization.
The first contribution in the LLG equation describes the torque from an effective magnetic field H~eff and is given by: τp =−γµ0( ~M × ~Heff). This term results in the magnetization precessing around the magnetic field, with γ the gyromagnetic ratio and µ0 the vacuum permeability. The direction of the torque is indicated in figure 3.4. This effective magnetic field consists of all field-related contributions such as external fields. The anisotropy of the material is also incorporated as an effective magnetic field. As it is phenomenologically observed that the magnetization vector will align to the effective magnetic field, a damping torque is added: τd = Mα
s( ~M ×∂ ~∂ tM), with α the experimentally determined Gilbert damping constant. This results in the magnetization being damped towards the effective magnetic field, as seen in figure 3.4.
H
effM
Damping
Spin transfer torque Precession
Figure 3.4: Torques working on the magnetization vector ~M, consisting of preces-sion, damping and spin transfer torque.
A current can influence the magnetization via the spin transfer torque (STT), first described by Slonczewski in 1996 [37]. For simplicity, it can intuitively described as follows: If a polarized spin
current enters a ferromagnetic layer with its polarization non-collinear to the magnetization of the layer, the spins get absorbed. As angular momentum is conserved, the spins exert a torque on the magnetization. This torque of a spin Hall current can be modeled as a so-called Slonczewski-like torque τsand is given by τs= cMSHE2
s ( ~M ×σˆSHE× ~M ). With ˆσSHEdefined as: ˆσSHE= ˆJ ׈z for a current injected into an F layer from a current running through a NM layer below it. The constant cSH E describes the magnitude of the torque and is given by cSHE= JcθSHEħhγ/(2etF),in which Jc is the charge current density running through the underlying SHE layer, e the elementary charge and tFthe thickness of the ferromagnetic layer. The direction of the STT from the spin Hall effect is indicated in figure 3.4 for a spin current with a polarization perpendicular to the effective magnetic field.
The resulting LLG-equation consisting of the precession, damping and STT terms is given by:
∂ ~M
∂ t =τp+τd+τs=−γµ0( ~M × ~He f f) + α
Ms( ~M ×∂ ~M
∂ t ) +cSHE
Ms2 ( ~M ×σˆSHE× ~M ). (3.3) Many different approaches can be taken to solve the LLG equation to describe the magnetization behavior of a ferromagnetic layer. For example, the LLG equation is used in the well known OOMMF software in which an array of spins can be simulated to describe magnetization reversal including domain formation and nucleation. In this thesis, an LLG solver developed by Van den Brink is used [38]. It is a solver that describes only one magnetization vector in time by taking in to account all the previously introduced torques. For more details about the parameters used with the solver, see appendix C.
3.2.2 Simulation of deterministic magnetization reversal
In this section, deterministic magnetization reversal by spin Hall effect and an external field is shown for a NM/F bilayer. The simulations are done using the solver from Van den Brink for a rectangular ferromagnetic bit (100x100 nm) with a thickness of 1 nm. An effective anisotropy field is introduced to induce an OOP magnetization in the F-layer. The initial magnetization is set in the +~z direction. A spin Hall current pulse is sent through the F-layer, originating from a longitudinal charge current pulse running through 3 nm thick adjacent Pt layer. Due to the spin Hall effect, a spin polarized current in the +~z direction is generated with spins pointing in the +~x direction. This spin current is absorbed by the F-layer and exerts a torque in the ( ~M ×σˆSHE× ~M ) direction. As a result, the torque from the spin Hall effect changes as the magnetization rotates.
Other simulation parameter details can be found in appendix C.
Figure 3.5 shows a result of a simulation under different applied external field in the ±~y direction.
A 2 ns spin Hall pulse is applied at a temperature of 300 K. The magnetization trajectory in three dimensions is shown. According to the simulation, a positive field in the y-direction results in full magnetization reversal. A field in the other direction, or no field at all, does not result in a switch.
It appears that an external field breaks the symmetry of the system. Intuitively this reversal of the magnetization can be thought of as the spin Hall torque pulling the magnetization to an IP position. If a magnetic field is applied perpendicular to the spin Hall torque during the pulse (along the current direction), there is some ’overshoot’ of the resulting magnetization vector which results in the magnetization having a slight component in the −~z direction. Due to the effective anisotropy field the magnetization relaxes to the −~z position. If the initial position of the
t (ns)
Figure 3.5: Results of an LLG simulation for different external fields. The initial magnetization is set in the +~z direction. Figure (a) shows the applied spin Hall pulse. Figure (b) shows magnetization reversal (of mz) by applying a field in the +~y-direction. Applying no field at all or reversing the field direction do not change the magnetization as seen in figure (c) and (d).
magnetization is in the −~z direction, either the current or the field should reverse its direction to induce switching (simulations not shown). Another symmetry-based explanation can be found in [9]. Thermal fluctuations can cause the magnetization to reverse even when no field is applied.
However, such kind of reversal is non-deterministic as the symmetry of the system is not broken by an external magnetic field.
3.2.3 Experimental evidence of deterministic switching with external magnetic field
Magnetization reversal using the SHE and an externally applied magnetic field has been exper-imentally observed for different combinations of heavy metal/ferromagnetic bilayers with OOP anisotropy.
Figure 3.6: 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 an AlOx capping layer. b: TEM image that shows two CoFe bar magnets which generate the magnetic field. c: Deterministic switching by applying current pulses of alter-nating polarity. The direction of the field generated from the bar magnet depends on the magnetization direction of the CoFe. This results in deterministic switching as predicted by the LLG-equation. Figure adapted from [5].
Miron et al. first discovered deterministic switching for OOP magnetized materials [5]. Figure 3.6 shows one of the main results from Miron. The stack depicted in figure 3.6a is placed between two bar magnets shown in figure 3.6b which apply an external magnetic field. A sequence of pulses with alternating polarity is applied to switch the magnetization, shown in figure 3.6c.
Successive pulses of the same polarity do not result in a change of the magnetization, indicating that the switching is deterministic instead of random or depending on the initial magnetization direction. Miron proposed that the reason for the deterministic magnetization reversal is mainly due to the Rashba effect in Pt/Co/AlOx.
In figure 3.7 results from Liu et al. are shown, which demonstrate deterministic magnetization reversal [36]. Liu proposed that the spin Hall effect, instead of the Rashba effect, is the driving mechanism for the reversal. With experiments they were able to determine the strength of the spin Hall torque compared to the Rashba effect and found that the Rashba effect is negligible.
b.
a.
Figure 3.7: Deterministic switching results from Liu et al. Complete reversal of the magnetization by applying a constant current and an external field on a Pt/Co/AlOx stack. Depending on the initial magnetization direction, either a negative or positive external field is needed to deterministically switch the magnetization. The field is applied along the current direction. Figure adapted from [36].
Figure 3.7a and 3.7b show the measured Hall resistance RH, corresponding to Mz, as a function of the applied current. At a certain threshold current, the magnetization reverses.
3.2.4 Replacing the symmetry-breaking field
The major problem regarding the magnetization reversal described in the previous section, is the need for an external field. While this is easy to implement in a lab environment, as done by Miron via creating two bar magnets on the sample or by Liu which uses an external magnet, such magnetic stray fields in actual memory applications are not desired. Moreover, they require a lot of energy to generate. Therefore, it hampers the practical implementation of deterministic magnetization reversal.
Recently, researchers have proposed different ways of replacing the external field by something that is more practically viable. One successful approach is the creation of an anisotropy gradient along the sample plane [39]. This anisotropy tilts the easy-axis slightly from its OOP orientation and makes its possible to deterministically reverse the magnetization. The anisotropy gradient is created by oxidizing a wedged sample, resulting in different oxidation levels along the sample.
Similar results are found by Torrejon et al., in which the deterministic magnetization reversal is also caused by an anisotropy gradient [10]. However, in their case they induce this gradient dur-ing material growth by placdur-ing the sample off-center. Small thickness variations cause enough asymmetry to deterministically reverse the magnetization. Options for using multiferroic mate-rials, electric fields, or precise control of the current pulse are also being researched, but will not be discussed here.
In this thesis, a new approach is taken: the external field is replaced by an effective field orig-inating from an exchange bias in the sample. By creating an orthogonal exchange bias, mean-ing that the ferromagnetic layer is oriented OOP and the antiferromagnetic layer is oriented IP, the exchange bias between the layer is equivalent to an external field in the IP direction. This should result in deterministic magnetization reversal without applying any external magnetic
field. During the writing of this thesis, preliminary results have been reported in literature in which orthogonal exchange bias is also used for symmetry-breaking. Fukami et al. uses an Co/Ni multilayer as the F-layer and PtMn as a combined spin Hall injection and in-plane AF-layer. Lau et al. takes a different approach by using an IP F-layer which is coupled via the Interlayer Exchange Coupling (IEC) to an OOP F-layer. An AF IrMn layer is used to pin the first F-layer. Both articles are not yet peer reviewed, but an Arxiv preprint is available for more details [40][41].
3.3 Summary
The theory presented in this chapter is now briefly summarized. The spin Hall effect was in-troduced which states that a longitudinal charge current through a heavy metal layer such as Pt, generates a transverse spin current. If such a spin current is inserted into an adjacent OOP Co layer, it was shown that this layer can be switched under the condition that an externally magnetic field is applied along the charge current direction. A simulation with the LLG-equation was presented that show the dynamics of this switching. Two literature examples have been pre-sented that demonstrate spin-Hall switching. Finally, it was proposed that this externally applied symmetry-breaking field can be replaced by an effective field originating from the exchange bias between an F and AF-layer.
Methods
This chapter provides an overview of the different experimental methods used in this thesis.
The first part of the chapter describes the setups and procedures used for sample fabrication, consisting of the sputtering, lithography and field-cooling procedures.
The second part describes the sample characterization methods. The Kerr effect is used to study the magnetization of full sheet samples. The anomalous Hall effect is be introduced as it is used to perform the current-driven experiments. A detailed overview of the anomalous Hall measurement scheme is given in the final part of this chapter.
4.1 Sample fabrication
In this part, the sample fabrication procedure is explained. The samples consist of a silicon substrate capped with a 100 nm silicon-oxide layer, on which materials are directly deposited using sputter deposition. On these samples, basic magnetic characterization is used to determine properties like exchange bias, coercivity and remanence. However, these samples are not suitable for the switching experiments, presented in chapter 6. Due to their large size, very high currents have to be applied to generate enough spin Hall current density to reverse the magnetization.
Therefore, micro-sized crosses of the deposited material are fabricated using lithography, see section 4.1.3. Such a cross is called a Hall cross and is further discussed in section 4.1.4. In section 4.2, the field cooling process is explained. This is used to set the exchange bias to the desired direction in a sample.
4.1.1 Sputter deposition
Sputtering is extensively used in the semiconductor science and industry and is known to be a reliable method to fabricate thin layers with sub-nanometer precision. A basic overview of the process will be given here.
Under ultra-high vacuum, a small disc of a target material of high purity (i.e. platinum) is bom-barded with argon ions. The argon ions are accelerated by a DC voltage applied between the target and a ring-shaped anode below the target. When the ions hit the target, they will knock
39
off atoms from the target which will fall down on the sample substrate lying underneath. Highly controllable material growth rates of ~1 Å/s are reached this way.
The samples used in this thesis are all grown by using the CARUSO deposition system at the group Physics of Nanostructures. It operates at a base pressure of 10−7 mbar and consists of a main chamber with six deposition targets and a separate oxidation chamber, which is used for plasma cleaning (see section 4.1.2). To study layer thickness dependent properties of sputtered materials, a wedge mask is used. The wedge mask is a sharp-edged shutter plate placed right above the surface. The mask is moved at a constant speed while depositing a material which creates a gradient in the thickness.
Figure 4.1: Schematic representation of the sputter deposition process. The target material is bombarded by argon ions in a high vacuum, which cause atoms to whirl down on the sample substrate to grow a material layer by layer. The wedge shutter can be used to create a gradient in the thickness.
4.1.2 Plasma cleaning
The samples grown in the deposition chamber can be transported in-situ to an oxidation chamber.
In this chamber, a plasma of highly energetic oxygen ions is created which bombard the sample surface. It is used to clean the sample by removing surface contamination. Samples which are patterned with electron beam lithography are oxidized for 3 minutes with a plasma current of 15 mA. All other samples are oxidized for 5 minutes. The oxygen pressure is kept constant at 0.1 mbar during the process.
4.1.3 Electron beam lithography
To fabricate the micro-sized hall cross structures, electron beam lithography (EBL) is used. The advantage of this technique is the freedom to make structures of virtually any shape and size.
The process consists of several different steps, which are shown schematically in figure 4.2.
The first step is spin-coating the initial silicon wafer substrate with an electron sensitive polymer, called resist. For the resist, a ~300 nm thick bilayer of PMMA 495 K A2 and PMMA 950 K A4 is used. The fully coated substrate is now placed inside the EBL machine, a FEI Nova Nanolab 600i dual beam. A focused beam of electrons hits the sample and change the solubility of the resist locally. After the exposure, the whole sample is submerged in a solvent. If this is done for just
the right amount of time, only the exposed areas of the resist will dissolve. In this project, the sample is placed in a MIBK-isopropanol (ratio 1:3) solution for 45 seconds.
With dissolving this resist locally, the underlying substrate is exposed. The sample is now placed inside the sputtering chamber to deposit one or more materials on top of the whole substrate.
Subsequently, the substrate is placed in a strong solvent for the resist, for example acetone, to remove both the resist and the deposited material on top of it. Only the material deposited on the previously exposed parts stays on the substrate, resulting in the desired structure.
Micro-structuring a sample can induce anomalies in the sample which can change the properties.
This is especially prevalent along the edges of the sputtered material and should be considered when analyzing the results [42].
a) Silicon Substrate b) Resist deposition c) EBL
d) Developing e) Material deposition f ) Lift-off
Figure 4.2: Overview of the EBL process to create micro-structures. (a) A silicon substrate is (a) covered with resist after which (c) an electron beam changes the solubility of the resist locally. (d) After dissolving the exposed part, material is de-posited (e) using sputter deposition and finally (f) the lift-off procedure removes the unexposed parts.
4.1.4 Hall cross fabrication
In this thesis, so-called Hall crosses are used for current-driven experiments. Before making the actual Hall cross, gold contact pads and wires are sputtered onto a Si substrate. By using the aforementioned sputtering and EBL techniques, the desired materials are deposited as a cross between four of the deposited gold wires, as indicated in figure 4.3. The cross consists of two bars with dimensions 1x10 µm. The gold wires are connected to macrosized gold pads at the edges of the sample, which can be connected to a chip carrier to connect the vertical or horizontal bar of the Hall cross to any desired equipment, e.g. a pulse generator or Volt meter.