# Measurement of the Resonant Magneto-Optical Kerr Effect Using a Free Electron Laser
## 3 Techniques for Magnetization Dynamics Capture
#### Characteristics of the TR-RMOKE Technique  
Below the UV energy range, magnetization probing techniques detect the average information of target materials, whereas element selectivity is added in techniques that are involved with the core levels of target materials. We extract the features of the (TR-)RMOKE technique with polarization analysis, such as the features for polar and longitudinal geometries, through comparison with the other element-selective methods that are described in Figure 3. Comparisons are made with the following notable techniques: TR-RMOKE in a transverse geometry, TR-XMCD, TR-RIXS, TR-SAXS, TR-FTH and TR-RSXD. The comparisons with TR-RMOKE in the transverse geometry and TR-XMCD are described in Features (1)-(3), which are presented in the next paragraph. TR-RIXS has only recently been used in combination with TR-RSXD. This technique focuses on tracing of the magnetic low-energy excitation mode. Therefore, if one is interested in the possibility that a demagnetization or magnetization reversal is affected by the magnetic correlated modes, this technique provides a deeper insight than the other methods. However, the laser-induced macroscopic magnetization dynamics, which are revealed by elastic scattering (including reflection), should be measured using other techniques, including TR-XMCD, TR-RMOKE for ferro-/ ferrimagnetic orders and TR-RSXD for antiferromagnetic orders, along with TR-RIXS. TR-SAXS and TR-FTH are powerful tools for determination of the magnetic structure on the nanometer scale. However, these techniques are mainly used in transmission geometries. During sample preparation, when trying to arrange a transmission-type experiment,  
Figure 3: Experimental methods that have been used to trace magnetization dynamics over a time scale ranging from \(+\infty\) (corresponding to static measurements) to \(10^{-15}\) s (femtosecond scale) are presented with respect to the energies and temporal ranges with which each technique has been used. The methods are limited to photon-in and photon-out schemes. With regard to the Kerr methods, longitudinal (L), polar (P) and transverse (T) represent the longitudinal, polar and transverse geometries, respectively, which are explained in the text. Above the temporal axis, the magnetization dynamics that occur for each timescale are shown. On the right side, the related optical transitions are depicted schematically. The core-state positions are those for the \(3d\) transition metals. Use of femtosecond X-ray pulses, free electron laser (FEL), high harmonic generation (HHG) laser and laser slicing sources, are indicated according to their pulse durations and energy ranges. the target magnetic system must be thin enough for a sizable transmission to be obtained. TR-RSXD is mainly used for materials with long-range magnetic orders with q \(\
eq\) 0, such as antiferromagnets. In the cases where ferro-/ferri-magnets are targeted, TR-XMCD and TR-RMOKE techniques are preferred. The TR-RMOKE technique with polarization analysis using an FEL offers the following characteristics: (1) \(M\)-edge measurement feasibility, (2) measurements of both rotation and ellipticity, (3) use of linearly-polarized pulses, (4) giant Kerr rotation when compared with that of conventional visible MOKE and (5) element selectivity. We explain (1)-(3) in detail here. Characteristic (4) is discussed in Section 5. (1) \(M\)-edge measurement feasibility:  
In TR-RMOKE measurements performed in the soft X-ray range, the \(M\)-edge region is preferred to the \(L\)-edge region when the target materials contain \(3d\) transition metals and when one is interested in the out-of-plane magnetization dynamics. In the \(L\)-edge range (100 \(\sim\) a few keV), the experimental setup in the reflection geometry is limited because the light in this energy range is strongly absorbed by the materials. To detect the out-of-plane component of the magnetization, it is important to ensure that the angle of incidence is as close to the sample surface normal as possible.