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Domain wall and Dzyaloshinskii Moriya Interaction (DMI)

The presence of magnetic domain wall results from the competition between anisotropy and exchange energies. In ultra-thin films with perpendicular anisotropy, the energetically favorable structures are Bloch domain walls where the magnetization in the domain wall center is parallel to the domain wall plane. When the films are patterned into small wires, Néel walls are favored where the magnetization in the center is perpendicular to the domain wall plane, in order to reduce the magnetostatic energy due to magnetic charges at the edges of the wires. In both cases, Bloch and Néel walls are not chiral, i.e, they have the same probability to be left-handed or right-handed.
In presence of the Dzyaloshinski-Moriya interaction, chiral Néel walls are favored as described below. The asymmetry exchange effect in interfacial asymmetric structures was first proposed by Dzyaloshinskii based on Landau theory in 1958 to explain the weak magnetism in anti-ferromagnetic materials [DZY58]. Later, Moriya explained this effect by considering SOC, where a super-exchange interaction is present for neighboring spins of asymmetry magnetic insulator [MOR60]. As a result, it was later called Dzyaloshinskii-Moriya Interaction (DMI). Prof. A. Fert predicted the existence of interfacial DMI in heavy metal/ferromagnetic metal thin film structures, where an indirect exchange effect is induced between the non-linear spin in ferromagnetic layer and the heavy metal atom with strong SOC, due to the broken inversion asymmetry [FER90].
where μ0 is the vacuum permeability, HDM is the effective field of DMI, MS is the saturation magnetization, ΔDW is the domain wall width. As shown before, ΔDW is given by ΔDW = (A/Keff)1/2, where A is the exchange stiffness, Keff is the effective anisotropy. As shown in Figure 1-10, the direction of Dij is determined by rij×x, which is perpendicular to the plane formed by Si, Sj and the neighbor atoms.
For the measurement of DMI, Brillouin Light Scattering (BLS) is commonly used [COR13], which measures the frequency shift of two spin waves with opposite directions to extract the DMI factor. This method is accurate, because the DMI is directly obtained without the use of magnetic parameters, such as the exchange constant Aex, the effective anisotropy Keff. However, the BLS equipment is relatively complex, which limits the application scope of this method.
The more convenient way to measure the DMI value is to measure the velocity of domain wall asymmetry expansion in the creep mode when an in-plane field is applied, as proposed by Je et al. in 2013 and experimentally demonstrated in Pt/Co/Pt structure [JE13]. Figure 1-12 shows typical Kerr images of domain wall expansion without and with the in-plane field measured by Kerr microscopy.
In a structure without DMI or applied in-plane field, the center magnetization direction is parallel to the domain wall plane, resulting in a Bloch wall that reduces the domain wall surface energy, as shown in Figure 1-13 (a). When DMI is present, the center magnetization direction is perpendicular to the domain wall plane, as shown in Figure 1-13 (b). The DMI induces an effective field HDM perpendicular to the domain wall plane, which favors a Néel type domain wall. When an in-plane field HX is applied in a structure with DMI, if HX = HDM, the effect of DMI will be cancelled out to favor a Bloch wall. As a result, the velocity driven by perpendicular field will reach its minimum. Therefore, the applied HX could be regarded as the DMI effective field.

Domain wall motion regimes

Domain walls could be driven by several excitations including magnetic field [MET07], polarized current [KOY11, RYU13, EMO13, YAN15], spin wave [TAT04, KIM12, WAN14], thermal gradient [SCH14], electric field [SCH12, FRA15], light [QUE18], etc. Magnetic-field-induced domain wall motion is the basic method to study the rich dynamics of domain wall motion. The research on current-induced domain wall motion has started from the discovery of STT effect. Ever since, spin-polarized current has become the most promising way to manipulate domain wall motion for future applications.
The dynamics of domain wall motion is usually divided into three different regimes (Figure 1-14): a low velocity creep regime where the DW interacts very strongly with pinning defects, a depinning transition regime and a high velocity flow regime [MET07]. Due to the presence of structural inhomogeneities (grain boundaries, grain texture, interface roughness, interface intermixing…), a spatial distribution of magnetic properties is present in the films, which results in a spatial distribution of DW energy responsible for pinning. At zero temperature, a minimum depinning field Hdep has to be applied to move the pinned DWs. At T > 0 K, DWs can move even at Hext < Hdep by thermal activation. In the very low field regime, the thermally activated behavior is described by the very well know creep law corresponding to the competition between an elastic energy (DW energy) and random disorder under a low driving force:
where Uc is the pinning energy barrier, kB is the Boltzmann constant, T is the temperature, v0 is the initial velocity, μ = 1/4 is a universal exponent corresponding to the motion of 1D interface (ultra-thin PMA film) in a 2D random disorder.
For Hext > Hdep, the dynamics of DW motion can be described by an intermediate depinning regime. When Hext equals to Hdep, the velocity is given by:
When Hext >>Hdep, the DW move in the flow regime that can be divided into three regimes: the steady regime, an intermediate chaotic regime above the Walker field HW and a precessional regime.

Current-induced domain wall motion

Current-induced domain wall motion based on STT

Domain wall motion along nanowires can be driven by spin-polarized current. Current-induced domain wall motion driven by STT was first proposed by Berger et al. [BER84]. When a polarized current goes through domain walls, the spin angular momentum of conduction electrons is transferred to the magnetization of the DWs and exerts a torque on the magnetization, which induces their motion. The STT contribution usually consists of two terms. First, the adiabatic component is given by [LI04, BOU11]:
where μB is the Bohr magneton, g is the Laudau factor, P is the polarization, J is the current density and e is the elementary charge.
Both adiabatic and nonadiabatic components may play a significant role in the DW motion [LEG17], but their respective origin is still under discussion. The nonadiabatic term proportional to the current density J acts as an effective field HSTT [BOU08].

Current-induced domain wall motion based on SOT

Emori et al. have found that the combination of DMI and SOT can enable current-induced domain wall motion in Pt/CoFe/MgO and Ta/CoFe/MgO perpendicularly magnetized heterostructures [EMO13]. Figure 1-15 (a) shows domain wall motion in Pt/CoFe/MgO wires. First, the DMI at the interface of Pt/CoFe favors a left-handed Néel type domain wall. When current is injected in the x direction, the SHE in the Pt layer induces spin accumulation along the y direction, which in turn creates a torque on the chiral DWs. The domain wall moves against the current direction, which is opposite to the domain wall motion induced by STT [MOO08, UED15]. With the stabilization of Néel type domain wall in heterostructures due to DMI, SOT can induce DW motion at higher speed. Figure 1-15 (b) illustrates the domain wall velocity as a function of current density and magnetic field along the z direction. The effect of current on domain wall motion is the same as that of magnetic field, which suggests that the effective field of SHE induced by the current is along the z direction. The domain wall motion in Ta/CoFe/MgO structure is in the direction of electrons flow, which can be explained by the opposite spin Hall angle of Ta compared to Pt [LIU12] that induces an effective field of SHE in the opposite direction compared to Pt/CoFe/MgO structure.

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Domain wall motion in Co/Ni multilayers

Co/Ni multilayers have been explored as a very promising system for current-induced domain wall motion. Current-induced domain wall motion in Co/Ni multilayers was first explored by Ravelosona et al. in nanowires based on sputtered [Co/Ni] spin valves showing PMA, as Co/Ni multilayers provides higher spin-torque efficiencies [RAV07]. The same structure was used to explore the current-induced domain wall motion by STT, where the non-adiabatic torque dominates the domain wall depinning and creep motion [BUR09]. In 2011, Koyama et al. found an “intrinsic pinning” phenomenon by demonstrating the wire width dependence of the threshold current density, where the depinning process is driven by the adiabatic torque in sputtered Co(0.2 nm)/[Ni(0.6 nm)/Co(0.2 nm)]4 nanowires. They also confirmed the intrinsic nature of current-induced domain wall motion by showing that the threshold current density is independent of the external magnetic field and the temperature [UED11, YOS12]. Current-induced domain wall motion was further explored in epitaxial [Co/Ni] multilayers consisting of Al2O3/V(5 nm)/Au(1 nm)/Ni(0.2 nm)/[Co(0.5 nm)/Ni(0.6 nm)]3/Au(1.2 nm), where both adiabatic and nonadiabatic components of the STT play a role in the domain wall motion [LEG17]. In 2013, Ryu et al. observed domain wall motion in the direction against the electron flow in a perpendicularly magnetized Co/Ni/Co tri-layered wires, which is in the opposite direction of the traditional current-induced domain wall motion by STT. As the Co/Ni/Co layers are sandwiched between Pt layers, the SHE arising from the Pt layer generates spin accumulation and induces a spin-orbit torque on the Co/Ni/Co layers. In addition, the DMI due to the structural inversion asymmetry of the film structure stabilizes a Néel wall structure. Therefore, current-induced domain wall motion driven by SOT has been observed Co/Ni multilayers [RYU13]. In 2015, a velocity up to 750 m/s for current-induced domain wall motion driven by SOT and DMI can be obtained in a synthetic antiferromagnet, which is formed from two perpendicularly magnetized Co/Ni multilayers separated by an ultrathin coupling layer of Ru. This phenomenon is due to the exchange coupling torque that is directly proportional to the strength of the antiferromagnetic exchange coupling between the two sub-layers, in addition to the stabilization of the Néel domain wall structure [YAN15].

All-optical switching

In 1996, Beaurepaire et al. demonstrated ultra-fast demagnetization in ferromagnetic thin film using ultrafast laser pulses, which raised the interest of the researchers. They observed the ultrafast demagnetization of Ni thin films within 1 picosecond (ps) by femtosecond (fs) laser pulses [BEA96]. As the demagnetization duration is much smaller than the spin precession time of around 100 ps, the performance of magnetic memory may be improved greatly. Hereafter, the ultrafast demagnetization of other magnetic materials has been found, such as 3d ferromagnetic metals and rare-earth magnetic metals. All-optical helicity-dependent switching (AO-HDS) was then demonstrated in 2007 by Stanciu et al. in Radboud University, where left-circularly (σ-) or right-circularly (σ+) polarized fs laser pulses can deterministically switch the magnetization of perpendicularly magnetized Gd22Fe74.6Co3.4 thin films to the up or down direction [STA07]. In 2011, Radu et al. discovered a magnetization switching in Gd25Fe65.9Co9.4 by a single 60-fs linearly-polarized laser pulse, which can be called as all-optical helicity-independent switching (AO-HIS) [RAD11].
The differences between AO-HIS and AO-HDS are that: AO-HIS can realize magnetization switching with a single pulse independent of the laser helicity, while AO-HDS needs multiple pulses and the magnetization switching direction depends on the helicity. AO-HIS occurs only in ferrimagnetic materials containing Gd, while the materials for AO-HDS was found to be broader when it was observed in ferromagnetic multilayers as Co/Pt and Co/Ni, rare-earth metals as CoTb and CoDy, FePt granular films, etc. [LAM14, MAN 14] Recently, transparent ferrimagnetic dielectric was also found to be appropriated for all-optical switching [STU17]. These researches provide rich material choices for the application of all-optical switching in the magnetic storage and move one step closer to the application of all-optical switching.
AO-HDS has the advantages of faster writing speed and lower power consumption, compared to the current magnetic storage [ELH17]. Instead of magnetic field or current, the use of laser helicity for magnetization switching of magnetic materials lays a foundation for the realization of magnetic storage with all-optical switching based on ultrafast laser. Therefore, all-optical switching can be an important approach for the realization of novel magnetic memory, magnetic sensors and magnetic logic devices, which reveals broad application potentials and great commercial values in the near future.

Table of contents :

1.1 MRAM
1.1.1 STT-MRAM
1.1.2 SOT-MRAM
1.2 Dynamics of domain wall motion
1.2.1 Domain wall and Dzyaloshinskii Moriya Interaction (DMI)
1.2.2 Domain wall motion regimes
1.2.3 Current-induced domain wall motion
1.2.4 Domain wall motion in Co/Ni multilayers
1.3 All-optical switching
1.3.1 All-optical helicity-dependent switching in ferromagnetic materials
1.3.2 Helicity-dependent all-optical domain wall motion in ferromagnetic materials
1.4 Summary
2.1 Sample deposition and fabrication
2.1.1 Magnetron sputtering
2.1.2 Molecular Beam Epitaxy (MBE)
2.1.3 Magnetic characterization
2.1.4 Optical lithography
2.1.5 Ion Beam Etching (IBE)
2.1.6 E-beam evaporation
2.1.7 Microwire fabrication
2.2 Magneto-optical Kerr microscopy
2.2.1 Field configuration for field-driven domain wall motion
2.2.2 Field configuration for DMI measurement
2.3 Femtosecond pulse laser
2.4 Electrical characterization
2.5 Summary
3.1 Sputtered Pt/Co/heavy metal (HM) structure
3.1.1 Magnetic properties
3.1.2 All-optical switching results
3.2 Epitaxial Au/Co/Ni/Co/Au structure
3.2.1 Magnetic properties
3.2.2 All-optical switching results
3.3 Sputtered Pt/Co/Ni/Co/Pt structure
3.3.1 Magnetic properties
3.3.2 DMI in thin films
3.3.3 All-optical switching results for thin films
3.3.4 Criterion for the observation of all-optical switching by domain size calculation
3.3.5 Current-induced domain wall motion in Ta(3 nm)/Pt(3 nm)/Co(0.3 nm)/Ni(0.6 nm)/Co(0.3 nm)/Pt(3 nm) structure
3.3.6 Current-induced domain wall motion in Ta(3 nm)/Pt(5 nm)/Co(0.3 nm)/Ni(0.6 nm)/Co(0.3 nm)/Pt(2 nm) structure
3.3.7 All-optical switching results for microwires
3.4 Summary
4.1 Combined effect of helicity-dependent optical effect and SOT in Ta(3 nm)/Pt(5 nm)/Co(0.3 nm)/Ni(0.6 nm)/Co(0.3 nm)/Pt(2 nm) structure
4.1.1 Experimental set-up
4.1.2 Domain wall motion combining synchronized femtosecond laser pulses and short current pulses
4.1.3 Effect of synchronization delay between the electron and light stimuli on domain wall motion
4.1.4 Energy consumption
4.1.5 Modeling
4.2 Combined effect of helicity-dependent optical effect and STT in Ta(3 nm)/Pt(3 nm)/Co(0.3 nm)/Ni(0.6 nm)/Co(0.3 nm)/Pt(3 nm) structure
4.2.1 Domain wall motion combining synchronized femtosecond laser pulses and short current pulses
4.2.2 Modeling
4.3 Domain wall logic based on the combined effect
4.4 Summary


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