It means, when we rotate X for 0.01mm, it equal rotate 0.0163˚.
5.3 How to measure Kerr rotation curve and corresponding intensity?
In MOKE measurement, a linear polarization laser beam injects in a ferromagnetic material with an external magnetic field. By changing the external magnetic field with opposite direction, we can get two parabolic curves, as shown Fig 5.3.
Fig 5.3: Kerr rotation curve with positive and negative magnetic field Corresponding the two curves, the difference of two curves minimum is Kerr Rotation. When we fixed the analyzer angle, we can get the corresponding intensity (Δ y), like Fig 5.4.
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Fig 5.4: Analyzer angle and corresponding Kerr intensity
The minimum of the curves is called extinction angle. The physics of extinction angle comes from the magnetic optical Kerr effect (MOKE).
A linear polarization light to ferromagnetic materials with an external
magnetic field, the reflected light is ellipse polarization, like Fig 5.5. When we rotate the analyzer angle, we can get the corresponding intensity. When the analyzer angle is perpendicular to the long axis of the ellipse, it has the weakest optical signal and it is also the minimum intensity, we called it extinction angle.
Fig 5.5: Defined Extinction angle
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5.4 n ML Pd/Fe/Al
2O
3(0001) + H
2Fig 5.6: n ML Pd/Fe
First we focus on Pd/Fe system. In many studies, Pd thickness and H2
pressure are the most important parameters. If we want to see Pd lattice expanding at RT, Pd thickness needs to be thicker than 4 nm, and the H2
pressure needs to be higher than 20 mbar.
In our experiment, H2 pressure is always in 1013 mbar. Pd 3 ML and 5 ML, the Kerr rotation curve is similar after absorption H2. When we increase Pd thickness to 10 ML, two curves start to shift.
60 ML Pd /Fe has the obvious phenomenon of curve shift, so we take this sample do some analysis. The blue circle is measured in a vacuum of 10-3 mbar. The red triangle is measured after exposure to 1 atm H2, and the green square is in air.
Take vacuum curve for basis, air curve has less than 0.02˚ shift, and H2
curve has 0.6˚ shift. It all reasonable, it means H2 changing something by
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absorption H2. Even in the air, it also has a small H2, it still possibly to absorption in Pd thin films.
In the series of n ML Pd/Fe curve, we need to pay attention to two observable features. One is the extinction angle shift, the other is the curvature change after absorption H2.
Fig 5.7: Absorption H2 cause extinction angle shift and change
Fig 5.8: Physical meaning about MOKE intensity
Z. Q. Qiu and S. D. Bader, Rev. Sci. Instrum., Vol. 71, No.3, March 2000 [19]
The physical meaning of the parabolic and extinction angle comes from magnetic optical Kerr effect. [19]
Consider linear p-polarized light reflected from a sample surface. If the sample is nonmagnetic, the reflected light is purely p polarized. If the sample is ferromagnetic then the reflection beam should consist of an s component in addition to the dominant p component , with being the Kerr rotation. Therefore, measuring this s component will be the goal of the experimental setup.
Experimentally, the measurement of the s component could be realized by
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placing a linear polarizer in front of the photodetector to eliminate the p component. However, this measurement geometry has the following disadvantage. First, since the photodetector measures the light intensity , the measured quantity is proportional to the square of the magnetization. Second, it is difficult to quantify the absolute value of the Kerr rotation. This disadvantage can be circumvented by setting the polarizer at a small angle from the p axis. In this way, the intensity measured by the photodetector after the polarizer is
,
[19]
We fitting the curve by eq.
Fig 5.9: Fitting parabolic, Pd thickness V.S. extinction angle shift Right axis is the extinction angle shift =
Left axis is the curvature change after absorption H2=
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We take 60 ML Pd/Fe to analysis, some studies show the Kerr Intensity will increase by absorption H2. By measure Kerr Rotation Curve, we can know the intensity change not only in the specific angle but also in the all polarization angle in the range of Kerr rotation curve. By using this eq:
Fig 5.10: Kerr rotation curve analysis
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Fig 5.11: Discussion the intensity increase for Pd thickness and analyzer angle In Fig 5.11, When Pd is thicker enough, up to 30 ML. The enhancement of Kerr intensity and Pd thickness is a positive correlation. It increase about 10%、
20%、and 40% for Pd thickness 30 ML、45 ML、60 ML respectivity.
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Fig 5.12: Pd thickness V.S. Increase Intensity with different analyzer angle In order to discussion the relation Pd thickness, intensity and analyzer angle.
We defined the extinction angle in vacuum is 0˚.
Fig 5.13: We defined the extinction angle in vacuum is 0˚
And take X axis for Pd thickness, Y axis for increase intensity after absorption H2, like Fig 5.13. If we want to see the intensity enhancement after absorption H2. Pd thickness needed thick enough (>30 ML), and the analyzer angle were positive shift about 2~3˚.
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Fig 5.14: (60 ML Pd/Fe) (a) H2 absorption and (b) desorption V.S. time
Now we know that in Pd 60 ML/Fe system, with positive angle shift 3˚, under 1atm H2 absorption pressure, Kerr intensity can increase ~40%. But how long will it takes when H2 has been absorbed by Pd to achieve saturation?
In Fig 5.14, X axis is the absorption and desorption time. Left Y axis is the intensity increase (H2/Vac.) after absorption H2, it corresponding to the blue circle and blue line. In H2 pressure about 1atm, it can saturate less than 20 min.
Right axis is the intensity decrease after saturate sample pump down to vacuum, it corresponding to the red triangle and red line. From red line, we can know that it much difficult to desorption H2 out, it need more than 500 min.
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5.5 Pd/Fe,Co,Ni/Al
2O
3(0001) + H
2Fig 5.15: Corresponding 60ML Pd/Fe, Pd/Co, Pd/Ni
In this experiment, we combine three kinds of magnetic materials, Fe, Co, and Ni and fix the top Pd films for 60 ML. And report on the reversible change of magneto optical Kerr effect (MOKE) in Pd covered magnetic thin films by controlling H2 absorption. After H2 exposure, the extinction angle of MOKE was shifted and correspondingly Kerr signal was significantly changed. When properly choosing the analyzer angle, we can obtain large enhancement of 40%, 35% and 60% for Pd/Fe, Pd/Co and Pd/Ni bilayers, respectively.
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Fig 5.16: H2 pressure V.S. Intensity with Pd/Fe,Co,Ni system
As the before experiment, we know that absorption H2 pressure for 1 atm, Kerr intensity can increase 35%~60% for different magnetic materials with capping Pd thin films. But it has something question, does less H2 pressure still produce the same intensity increase effect?
In this picture, it shows the Kerr intensity as a function of H2 pressure, which is normalized by the initial value measured before hydrogen exposure. For Pd/Ni, the Kerr intensity drastically increased with H2 exposure and saturated at ~50 mbar. Pd/Co and Pd/Fe saturated at ~80 and ~110 mbar respectively.
Afterward the Kerr intensity always keeps invariant. In previous studies, the transmittance, reflectance, and refractive index of Pd are drastically changed by H2 absorption. The variations also saturate with H2 pressure 100 mbar, implying the similar mechanism in the MO enhancement.
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Fig 5.17: H2 pressure V.S. absorption time in Pd/Co system
In order to know the relationship of H2 pressure and saturation time, we do the two experiments. In Fig 5.17(a), H2 pressure is 1013 mbar and the saturation time is less than 10 min. In Fig 5.17(b), we absorption H2 for 20 mbar first, in Fig 5.17 (b), the saturation time is more than 60 min and the increase is only about 25%, by this we know that H2 pressure is an important factor, it has influence the accuracy for measure MOKE.
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Fig 5.18: (a) Pd/Fe, Pd/Co, Pd/Ni: H2 absorption V.S. time (b) Pd/Fe, Pd/Co, Pd/Ni: H2 desorption V.S. time
Fig 5.18 (b) shows how the Pd covered magnetic layers recover the original value of Kerr intensity after fully hydrogenated. The sample was firstly saturated by 1 atm H2, and then the MOKE chamber was pump down to vacuum for the investigation of recovery rate. The arrows in (b) indicate the time constant when Kerr intensity recovery 80% of the H2-induced enhancement. The 80% recovery took 30 min for Pd/Ni, and even longer (~175 min) for Pd/Co, and Pd/Fe.
Because Pd/Ni has the characteristic of quickly desorption H2, we do the repeated experiment for absorption and desorption H2, than we can get the reversibility result.
Fig 5.19: Reversibility effect in Pd/Ni system
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