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Spin Hall effect (SHE) – Spin Orbit Torque (SOT)
The spin Hall effect can be understood as the electron spin dependent asymmetric scattering [28] [30] [31] due to spin orbit coupling. In the direct SHE, an electrical current flowing through a material with a relativistic spin-orbit coupling will generate a transversal spin current (direct SHE). The reciprocal effect also exists and is called inverse SHE (ISHE). It happens when a pure spin current, injected through a material with spin orbit coupling properties, generates a transverse charge current. This asymmetric scattering was first proposed in 1971 by Dyakonov and Perel [32], however the interest was triggered with a new theoretical work with similar predictions by Hirsch [24] who gave the name to the phenomena and also with the fast development of spintronics. SHE was predicted and detected in semiconductors [33] [34] like GaAs [35], pSi [36], pGe [37] and nGe [38] [39] [40]; in metals [41] such as Pt [42] [43] [44] [45], Pd [46], Ta [47] [48] and W [49], and in alloys [50] [51] such as CuIr [52], CuBi [53], CuPb [54], and AuW [55]. The spin Hall effect is a bulk manifestation of the charge-spin current conversion due to spin orbit coupling. Thus the charge-spin current conversion happens in the bulk of the material but its detection should be performed at the edge of the sample. A schematic representation of the SHE and ISHE is showed in figure 1.9.
Mechanism of the SHE
As for the Anomalous Hall effect (AHE), we have intrinsic and extrinsic contributions to the SHE, all due to SOC. The intrinsic mechanism is related to the interband coherence induced by an external electric field, i.e injection of charge current. There are two kinds of extrinsic mechanisms where electrons are deflected after scattering by an impurity due to effective SOC: the skew scattering and side jump. These contributions are illustrated in fig 1.10.
For the sake of comparison, in Fig. 1.11 are shown the three effects, Hall effect, AHE and SHE. In the Hall effect (discovery by Sir Edwin Hall in 1879) a conductor develops a transverse voltage due to the Lorentz force acting on the charge current in the presence of an external magnetic field. The AHE happens in FM materials. In FM materials the transverse voltage is not simply proportional to the magnetic field, but there is an additional contribution related to the magnetization. Thus, the electrons flowing in a ferromagnetic conductor acquire a transverse velocity with opposite directions for different spin orientations. Therefore, spin dependent transverse velocity results in a net transverse voltage. As mentioned, in the SHE upon an injection of a charge current and without any external magnetic field is created no net voltage but a transverse spin accumulation is generated.
Efficiency of SHE
The conversion ratio between the charge current and spin current is called the spin Hall angle (SHE) which is a dimensionless parameter. The spin Hall angle is subsequently a key parameter to qualify a material for the integration in new experiments, and new spintronic-based devices. Large spin Hall angles can be found in 5d or 4d transition metals such as Pt, Ta, and W. Additionally in metal alloys such as CuBi, CuIr, and AuW, it will be possible to tune the magnitude of the spin Hall angle varying the composition of the alloy. Here there is a path to explore new alloys of Cu or Au host doped with impurities such as C, Bi or Os, in order to enlarge the SHE efficiency due to resonant asymmetric scattering by impurities [53] [59] as proposed already in 198144 [50]. Indeed, the spin Hall resistivity, SHE, is proportional to the longitudinal resistivity for an intrinsic and skew scattering contributions but is proportional to the square of such longitudinal resistivity for a side-jump contribution. And the spin Hall angle being also the ratio of spin Hall resistivity over the charge or longitudinal resitivity, i.e. SHE = SHE/. It is thus interesting to look for new alloy materials with strong spin-orbit coupling, where the longitudinal resistivity may be changed and therefore the spin Hall angle may be modulated. If skew scattering or intrinsic mechanism are dominant, then SHE is independent of , otherwise if side-jump mechanism is predominant, then SHE .
Independently of the value of the spin Hall angle, interfaces play also an important role in the injection of pure spin current from one layer to another due to the spin-flip scattering at the interfaces and spin resistance at the interfaces, historically called as spin memory loss (SML) [60]. The relevance of such SML effect in the correct qualification of spin Hall angle in materials was recently pointed out [61]Erreur ! Signet non défini.. One can optimize the spin Hall angle in a material, however its contribution to the spin injection could be strongly decreased by the interface. For example, in metallic-ferromagnetic/normal-metal (FM/NM) systems with large SML or poor transmission coefficient, part of the spin current injected from one layer to the other one will be lost at the interface.
Damping-like (DL) and field-like (FL) torques
The spin current injected from the HM into the FM layer has a spin polarization perpendicular to both JS and JC as displayed in Fig 1.12. This spin polarization leads to two symmetries on the torque exerted on the magnetization M of the FM layer: they are so-called DL and FL torques as displayed in 1.12. The relationship for both torques can be expressed as the last term in the following extended Landau-Lifshitz-Gilbert (LLG) equation: 𝜕𝑚̂𝜕𝑡=−𝛾𝑚̂×𝐻𝑒𝑓𝑓⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗+𝛼𝑚̂×𝜕𝑚̂𝜕𝑡+𝛾ℏ2𝑒𝐽𝑐(𝑡)𝜇0𝑀𝑆𝑡𝐹𝑀(𝜉𝐷𝐿𝑒𝑓𝑓(𝑚̂×𝜎̂×𝑚̂)+𝜉𝐹𝐿𝑒𝑓𝑓(𝑚̂×𝜎̂)) (1.15) where the effective field Heff includes any applied field, Happ and the anisotropies field. The SHE can contribute to both torques. There are also other effects that generate spin accumulation due to SOC, such as the Rashba interfaces and topological insulators, and, in similar way, they can contribute with both symmetries to the torque on magnetization M. The dimensionless parameters DLeff and FLeff represent the effective efficiency of the charge-to-spin current conversion (i.e; convoluted with loss or transparency at the interface). Hence, the parameter DLeff is indeed the efficient spin Hall angle of the HM layer in the HM/FM structure. The last term has the same form as the first term in the LLG equation and induces a precession of the magnetization if Heff ||, that explains the name of the torque as field-like. The damping-like term has a double cross product and also acts perpendicular to the magnetization as the second term in the LLG equation where the damping constant is shown. That is the reason why this term is called damping-like torque.
Elaboration of alloys by co-sputtering:
In the case of co-sputtering, the magnetron sputtering of several targets is performed at the same time. Therefore, atoms of several species are ejected towards a substrate on which they form the desired alloy. The main concerns about the materials that are grown by this method are the deposition rate and the atomic composition of the layers.
Let us determine the deposition rate in terms of thickness per deposition time. In order to determine that, we have to know first the thickness deposition rate of each material deposited. This can be achieved by growing calibration samples, at a given set of conditions concerning the argon flux and pressure, and varying the power applied to the target. Usually, whether a DC or RF deposition is performed, a linear dependence between the deposition rate and the working power applied to the cathode is found. Let us note 𝑣𝑖(𝑃𝑖) the deposition rate of the ith target (which is a linear function of the power applied to this target 𝑃𝑖). This quantity can be expressed in units of nanometers per second. Let us convert this into a molar rate. In order to do so, we use the molar volume of the species studied, that we note as 𝜌𝑖, which is expressed in units of m3/mol. We can thus express the ratio 𝑣𝑖(𝑃𝑖)𝜌𝑖=𝜏𝑖(𝑃𝑖) that can be expressed in mol.m²/sec. This quantity corresponds to the molar deposition rate per surface. By stating the previous sentence, we make an approximation considering that the calibration samples are composed of a perfect monocrystal of the material considered.
In order to tune the stoichiometry of the alloy chosen, by calling 𝑥𝑖 the molar proportion of the ith component, we have to solve the linear system: 𝜏𝑖(𝑃𝑖)Σ𝜏𝑗𝑗(𝑃𝑗)=𝑥𝑖 ∀𝑖 (2.1).
If we call n the number of materials used, this system has n degrees of freedom, and has n-1 constraints since the implicit condition Σ𝑥𝑖=1, that is a data of the problem, lets one of the equations of Eq. (2.1) be useless. Therefore, the choice on one applied power determines all the others. Since the power applied to each cathode can be tuned continuously, the choice made is often to have values of the power that are not too large, in order to prevent the heating of the materials targets, but also not too low, so that the linear dependence between the applied power and the deposition rate still holds.
In order to obtain the thickness deposition rate of the alloy, we use again the assumption that the materials grown in the alloy have the same volume parameters as when they are grown separately in a perfect crystal. The thickness deposition rate is thus the simple sum of the thickness rates of each material at the power considered for each cathode. We can express the thickness deposition as: 𝑣𝑎𝑙𝑙𝑜𝑦=Σ𝑣𝑖(𝑃𝑖)𝑖 (2.2).
Vibrating Sample Magnetometry (VSM)
Vibrating Sample Magnetometry (VSM) is a direct magnetic measuring technique that allow to determine the magnetic moment and other magnetic parameters of a sample with high precision. The invention of this technique dates back to 1950s by Simon Foner in MIT. Since its introduction till now, VSM is popular thanks to many advantages of accuracy, versatility and ease of use. The essential set up of VSM is described in figure 2.3.
The principle of VSM is based on Faraday’s law of induction which states that a change in flux through a coil will generate an electromagnetic force in the coil. In the measurement set up, the sample is attached to a nonmagnetic rod, which is vibrates in a gap between pick-up coils at a known frequency, usually between 50 and 100Hz, and at a fixed amplitude, typically 1-3 mm. The stray magnetic field arising from the magnetized sample moves together with the sample, thus induces a varying magnetic flux in the coils. The voltage generated by this varying magnetic flux in the coils is proportional to the magnetic moment, providing the way to read it. The VSM set up requires signal processing using a lock-in amplifier to obtain high signal-to-noise ratios. The pickup coils are desisned to ensure a linear response over the length of vibration and eliminate the signal from the applied dc field. In order to provide reliable measurement, the instrument requires calibration of the absolute scale of magnetization and the corresponding voltage by using a reference sample.
Lithography process
After the deposition with magnetron sputtering, our thin films were patterned into devices of different geometries (lines, Hall crosses or double Hall crosses) using optical lithography. For that, we took advantage of the common MiNaLor cleanroom platform (platform for micro and nano technology of Lorraine).
We have used lateral dimensions spanning from width of 20 μm down to 2 μm. So, UV lithography was sufficiently precise to achieve such dimensions. We have used two lithography steps for the whole process, which are:
a) Etching of the thin film using the photoresist as hard mask. This step involves the following sub-steps:
Put the positive photosensitive resist Microdeposit Shipley 1813 (s1813) on the sample (Fig. 2.4a)
spread uniformly the resist on the sample by spinning it at 10000 RPM during 40 seconds.
Baking it at 115°C during 1 minute. The last two steps are known as a spin coating (Fig. 2.4b).
Expose UV light through the mask (Fig. 2.4c). The UV wave length is 365 nm. We used a power of about 240 W using the appropriate mask (that we called SOT1) over a period of 20 seconds in vacuum contact mode. A SUSS MicroTec Mask Aligner MJB4 was used.
develop the resist (Fig. 2.4d). The sample is placed in MF319 developer for 40 to 45 seconds, and then rinsed in double de-ionized water for 30 seconds.
The quality of the above steps is verified by the observation in an optical microscope, where lateral dimensions can be measured and pictures can be taken.
the sample is then fixed in a holder and placed in a pre-chamber of an Ion Beam Etch machine (4Wave).
– Here we use Ar inert gas which is ionized to etch the material of our thin films until the substrate (SiO2) in our case (Fig. 2.4e).
– Typical values of etching process are: Voltage beam= 200V, current beam= 50 mA, sample voltage = 60V, etching angle =10 degree. The sample is continuously rotated to homogenize the etching.
– The etching is followed in situ by chemical detection using Secondary-ion mass spectrometry (SIMS).
– Typical etching time for a W(3 nm/CoTb(3.5 nm)/AlOx (3 nm) is about 750 seconds with the parameters mentioned.
– It is important not to over-etch the films in order to keep the SiO2 substrate (Fig. 2.4 f) which works as a barrier to avoid a shunting into Si during the magneto-transport experiments.
Samples and magnetic properties
To investigate the impact of temperature on SOT magnetization swiching in RE-TM alloys, we study a series of CoxTb1−x ferrimagnetic alloys deposited on a tungsten heavy metal film using DC magnetron sputtering. Deposition was done at room temperature. The full sample stack is Si−SiO2/W(3 nm)/CoxTb1−x(3.5 nm)/Al(3 nm) with 0.71 𝑥 0.86. We used silicon substrates covered by an oxidized silicon layer of 100 nm thick to minimize the leakage current that might go through Si substrates in the measurements. The CoxTb1−x alloys were fabricated by co-sputtering pure Co and Tb sources. The relative concentration of the two elements Co and Tb was controlled by varying the sputtering powers. A 3 nm thick Al layer that naturally oxidized is used to protect the sample from oxidation. The W and CoTb layers have amorphous structure. This was confirmed by X-ray diffraction measurements where only broad amorphous contributions were observed even for films as thick as 20 nm.
In this section, I discuss the magnetic properties of CoxTb1−x alloys. Alloys of rare earth (RE) and transition metal (TM) have been studied for a long time and there are detailed reports on their properties (e.g. [10]). However, a thorough characterization of our particular samples is essential because the magnetic properties are very sensitive to the specific growth technique and conditions. Also, for RE-TM alloys, a small fluctuation of the sample composition can lead to important changes in magnetic properties of the system.
The magnetism of CoTb alloys is due to the itinerant magnetism of the Co sublattice and the localized 4f electrons of the Tb atoms. The moments of the two sublattices are antiparallel. The exchange constant between the Co moments or between the Tb moments is positive while the exchange constant between a Tb and a Co moment is negative. This coupling between Co and Tb happens in an indirect way via the conducting 5s electrons of the Tb atoms.
The total magnetization 𝑀𝐶𝑜𝑇𝑏 of CoTb alloy is described by the sum of the two sublattice contributions: |𝑀𝐶𝑜𝑇𝑏(𝑥𝑣𝑜𝑙,𝑇)|=|𝑀𝐶𝑜(𝑇).(1−𝑥𝑣𝑜𝑙)−𝑀𝑇𝑏(𝑇).𝑥𝑣𝑜𝑙|.
Table of contents :
Chapter I – Basics of magnetism and spin orbit torque
1.1 Origin of magnetization
1.2 Magnetic interactions
1.2a) Zeeman interaction
1.2b) Dipolar interaction
1.2c) Magnetocrystalline and effective anisotropy
1.2d) Exchange interaction
1.2e) DMI interaction
1.3 Magnetic orders
1.4 Spintronics
1.5 Spin Hall effect (SHE) – Spin Orbit Torque (SOT)
1.5.1 Spin Hall effect (SHE)
1.5.2 Mechanism of the SHE
1.5.3 Efficiency of SHE
1.5.4 Spin Orbit Torque
1.5.4 Damping-like (DL) and field-like (FL) torques
1.6 All Optical Switching
Chapter II – Experimental methods and samples
2.1 Thin film deposition by DC magnetron sputtering
2.2 Vibrating Sample Magnetometry (VSM)
2.3 Lithography process
2.4 Magneto-transport (spin-orbit torque) setup
Chapter III – Spin-orbit torque induced switching in ferrimagnetic alloys: Experiments and modeling
3.1 Introduction
3.2 Samples and magnetic properties
3.3 Theoretical model
3.4 Results of transport measurements
3.5 Analytical model
3.6 Conclusion
Chapter IV – The effect of temperature on magnetization switching by spin-orbit torque in metal/ferrimagnetic system
4.1 Introduction
4.2 Samples and magnetic properties
4.2.1 Magnetic compensation point xMcomp
4.2.2 Compensation temperature TMcomp
4.2.3 Angular momentum compensation temperature TAcomp
4.2.4 Field – induced magnetization switching
4.2.5 Determination of Hall angle AHE in CoxTb1-x (3.5nm)
4.3 Current – induced spin orbit torque switching
4.4 Characteristic temperatures of switching
4.5 T-x switching phase diagram
4.6 Conclusions
References
