This final section will discuss the outlook of the field-free switching for future implementation in a SHE-based MRAM device. The main challenges are scalability of the magnetic bits, thermal stability, power consumption, speed and how to combine the structure with a magnetic tunnel junction.
Scalability
For efficient data storage, small bit sizes are necessary. For example, modern SSD disk drives are already capable to store 4 Terabytes of data on a 2.5 inch disk. As a rough estimate, this corresponds to a bit size of 300 nm2. In principle, reducing to such a bit size is not a problem as it can be done by lithography procedures that are already used in the semiconductor industry on these scales. One result of this is that the bits will consist of only a few AF grains. It is critical that all grains are set in the correct exchange bias configuration. Unset or unstable AF grains can cause malfunction of certain bits, which can impose problems if this amount becomes significant.
Thermal stability
For a mass storage device, a data retention of a minimum of 10 years is required. As seen in section 5.5, the average stable time of an AF grain can be estimated by τ1 =ν0exp
−k∆E
BT. For a stability of 10 years this results in ∆ = k∆E
BT > 40. For the samples used for the switching experiments, ∆ ≈ 34.5 and ∆ ≈ 27 are found at 300 K and 400 K respectively. Hence, the thermal stability of the orthogonal exchange bias is a major problem and should be increased significantly before practical implementation. Moreover, once the exchange bias of a bit is reset due to thermal fluctuations, the bit is permanently broken as the exchange bias orientation is
now OOP. This is different in comparison to bits in a conventional storage device which can be reset by writing new data.
Speed
As there is no incubation delay in the case of a SHE-based MRAM compared to STT-MRAM (see chapter 1), write times can be very short (< 1 ns) and comparable with other RAM devices [68].
In our experiments, relatively long pulses (50 µs) are used as shorter pulses did not allow for the pulse magnitude to be measured. Pulses as short a 1 µs have been tried and did also result in a switch. Even shorter pulses have not been tested, but according to LLG simulations and literature reports pulses of ~1 ns should be sufficient to induce switching.
Power consumption
A major advantage of using the spin Hall effect as the write mechanism is the reduced power consumption compared to STT-based MRAM. The power consumption of a single 1 ns long SHE pulse to switch the magnetization of a bit can be estimated. If the current is running through a 3 nm thick, 20 nm wide (estimated bit size) and 100 nm long Pt this corresponds to a resistance of 200 Ω. Assuming the connecting wires contribute approximately 500 Ω the total resistance is 700 Ω. The current pulse density necessary to switch the bit is ~1012A/m2according to experiments which correspond to a 60 µA current assuming the aforementioned dimensions of the Pt layer.
This means that the energy needed to write one bit is ~2.5 fJ, an order of magnitude lower than conventional STT-MRAM which has write energies in the order of ~0.05 pJ [69].
Structure
To create a fully working MRAM bit, the stack used in this thesis should be combined with a magnetic tunnel junction to allow for readout of the bit. If a tunnel barrier, like MgO is grown directly on top of the IrMn layer, there is no tunnel magneto resistance. Therefore another read mechanism should be implemented.
Another idea is to use the AF-layer as the spin Hall injection layer instead of a Pt layer [40]. It has recently been discovered that materials like PtMn and IrMn can have considerable spin Hall angles [33]. This could greatly reduce the complexity of the stack as it can be easily combined with a tunnel barrier. However, as an AF-layer has generally a higher resistance than the F-layer, a significant part of the current may shunt through the F-layer which might increase the chance of device breakdown.
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Domain nucleation and domain wall prop-agation
The magnetization reversal as discussed in the theory chapters of this thesis only considered a macrospin model in which the magnetization rotates uniformly. In reality, magnetization reversal initiates at edges or defects in the material. The point at which the magnetization reverses first is called a nucleation point, and it happens when applying an external field that corresponds to the nucleation field HN. Around the nucleation point, a domain emerges, which is separated from the rest of the sample via a domain wall.
a.
b.
Domain wall motion driven reversal
Domain nucleation driven reversal
Figure A.1: Two different magnetization reversal modes. a: Domain wall motion driven reversal. The initially nucleated domain expand through domain wall motion.
b: Nucleation driven reversal. Many nucleation points cluster together, resulting in full magnetization reversal. Depending on whether the propagation or nucleation field is bigger, the corresponding reversal process occurs. Adapted from [70].
After an initial nucleation point, full reversal of the sample can happen in two ways, both indi-cated in figure A.1. The first possibility is nucleation driven reversal, in which there are many nucleation sites that cluster together to eventually from a uniform domain. The second option
99
is domain wall motion driven reversal, in which the initially nucleated domains expand due to an applied propagation field HP. Depending on whether HN or HP is bigger, either nucleation or domain wall driven reversal (or a combination of the two) occurs.
Spin-glass model
SG-like behavior in an exchange biased system can be modeled by an effective anisotropy energy constant KSGeffwhich can be added to the Meiklejohn-bean model of equation (2.10):
Etotal(β) = −µ0HextMFtFcos(θ − β)
+ KFtFsin2(φ − β) + KAFtAFsin2(ψ − α) + KSGeffsin2(β − γ) − JEBeffcos(β − ψ).
(B.1)
The anisotropy of the AF-layer is now also included in the model to account for the rotatable AF spins, as shown in figure 2.9. Here, α is the angle of the AF-layer. The angle γ is the average angle of the partially random frustrated SG-spins, and JEBeff the reduced exchange energy due to the previously described interface impurities. It can be related to the SG-anisotropy via the conversion factor f :
KSGeff= (1 − f )JEB, (B.2)
JEBeff= f JEB. (B.3)
The conversion factor can be seen as a measure for the amount of derivation from a perfect interface. f = 1 is equal to a perfectly ordered interface, f = 0 corresponds to perfect disorder.
In figure B.1, hysteresis curves are shown for two different values of f . The following parameters are used for the F-layer: Ms=1.4 MA/m, KF=4·104J/m3, tF =1.25 nm, which correspond to a typical Co layer. The exchange constant is estimated to be JEB=1 · 10−4J/m2. A clear coercivity enhancement and exchange bias reduction are seen for the lower value of f , corresponding to a imperfect interface.
The SG-model can explain the observed behavior shown in 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 B.2. The following parameters are used: Ms=1.4·106A/m, KF=0.4·105J/m3, KAF=1.0·105J/m3, tF=1.25 nm, tAF=6 nm, JEB=3 · 10−4 J/m2, which correspond to experimental values. The values f = 0.75 and γ = 5◦are used to account for a rough F/AF interface.
101
Figure B.1: Calculation of hysteresis loops of a F/AF bilayer with the SG-model. For lower values of f , corresponding to a less ideal interface, a coercivity enhancement is found. The field is swept along the easy-axis of the F-layer.
a. b.
Figure B.2: Layer thickness dependent exchange bias, simulated using the SG-model.
LLG parameter details
Regarding the LLG simulations in chapter 3, this appendix elaborates on the chosen parameters.
The simulation is done on a cobalt element with the following typical properties:
Parameter Variable Constant
Length l 100 nm
Width w 100 nm
Heigth d 1 nm
Damping constant α 0.1
Saturation magnetization Ms 1 · 106 A/m
Anisotropy field Bani 100 mT
Please note that the anisotropy field is much less than experimentally observed to account for micro-magnetic effects such as domain formation, to more closely resemble the experimental data.
The spin Hall current is applied via an underlying Pt layer with the following properties:
Parameter Variable Constant
Thickness d 3 nm
Resistance R 105 · 10−9Ω/m Spin Hall angle Θ 0.05
Current J 2 · 1012A/m2
An external field of 20 mT is applied to break the symmetry of the system. Temperature effects are accounted for by a random thermal field HT, corresponding to a temperature of 300 K.
The simulation runs for 10 ns. At t=0, a SH-pulse is applied for 2 ns. The field is applied during the whole simulation. For more details about the solver itself, please refer to [38].
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Measuring IP exchange on wedge using MOKE
For the full sheet sample, the IP exchange bias is determined using the VSM-SQUID, as it can apply large stable field that can pull the spin fully IP. However, the VSM-SQUID is not suitable for measuring wedged samples, as it only measures the exchange bias of the full sheet. In a wedged sample, the exchange bias needs to be determined at each point along the thickness gradient.
A solution is using the MOKE setup in the longitudinal configuration. The magnetic field is applied along the IP direction, while the Kerr rotation is measured via a laser under an angle of 45 degrees. This results in the MOKE loop shown as in figure D.1a. Because the alignment of the field is never exactly along the hard-axis, the OOP component of the magnetization can still switch. As the MOKE is also sensitive to this direction, this switch is visible. If the applied field direction is very close to the actual hard-axis, the measured exchange bias is equal to that of a VSM-SQUID measurement. The exchange bias is determined by averaging the points found at zero-magnetization. Please note that the results shown in figure D.1 are done on a sheet with a single thickness to able to compare it to a VSM-SQUID measurement.
By changing the applied IP field angle, the resulting exchange bias changes towards zero ex-change bias, as is expected.
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Figure D.1: Measuring IP exchange bias with MOKE. The angle is the external field angle relative to the IP hard-axis. When measuring a loop, a switch is still visible as the field is not aligned perfectly and the MOKE is sensitive to the OOP component.
The exchange bias corresponds to the exchange bias measured in the VSM-SQUID.
The exchange bias corresponds to the exchange bias measured in the VSM-SQUID.