Condensed Matter Physics • IFF Scientific Report 2006 54 I 55
Magnetooptics in the XUV Regime
H.-Ch. Mertins
1, S. Valencia
2, P. M. Oppeneer
3, S. Cramm
4, C. M. Schneider
41University of Applied Sciences Münster, D-48565 Steinfurt, Germany
2BESSY GmbH, D-12489 Berlin, Germany
3Department of Physics, Uppsala University, S-75121 Uppsala, Sweden
4Institut für Festkörperforschung IFF-9, Forschungszentrum Jülich, 52425 Jülich, Germany
The fast progress in the field of modern mag- netism and the challenges brought about by spin- electronics ask for new characterization meth- ods. Of particular importance are all-optical tech- niques, as they are compatible with high mag- netic fields. We show that by accessing the shallow core levels of a ferromagnet in a reso- nant manner, large magnetooptical effects both in transmission and reflection can be observed in the extreme ultraviolet (XUV) spectral range.
This XUV-magnetooptics forms the missing link between the magnetooptic effects in the visible and the soft and hard X-ray resonant magnetic scattering (XRMS) phenomena.
Magneto-optical (MO) spectroscopies using polar- ized high-energy photons [1] allow element selective studies due to the specific energies of the absorption edges, which are characteristic for every element. In addition, a resonant enhancement of the transition probabilities at the absorption edges occurs, which leads to MO responses exceeding those in the vis- ible range by orders of magnitude. These features explain the recent popularity of x-ray MO spectro- scopies. Currently exploited techniques are the well- known x-ray magnetic circular and linear dichroisms [2], resonant magnetic reflectometry, but also more mundane phenomena such as the x-ray Voigt [3] and Faraday effects [4]. These MO effects appear in vari- ous geometries and modes such as transmission, re- flection or absorption. The size of the MO response relates both to the spin-orbit (SO) and exchange (EX) interactions of the electronic states involved in the op- tical transitions.
Up to now, most of the magneto-x-ray spectroscopic work focused on the 2pabsorption edges of the3d transition metals. Here the SO-coupling causes the 2p3/2 and 2p1/2 states to split by ∆SO∼13-16 eV, which is larger than the EX-interaction of the 3d va- lence states (∆EX∼1-2 eV), and much larger than the EX-interaction of the 2p core levels (∆EX∼0.3- 0.9 eV). At more weakly bound (shallow) core levels e.g., at the3pstates, however, the SO-splitting is re- duced by about a factor of ten, while the EX-splitting of the 3p states increases, making these interaction energies comparable (∼1 eV). Thus, accessing the shallow core levels resonantly by extreme ultraviolet (XUV) light promises sizable MO effects paired with
elemental selectivity.
In the following, we will demonstrate the kind of magneto-optical effects that can be observed in this spectral range. The experiments have been carried out on magnetic thin films of Co in the photon energy range ofhν∼40-80 eV, using the BESSY reflectome- ter [5] and linearly polarized light delivered by the U- 125/PGM undulator beamline at BESSY (Berlin).
The first experiment addresses the magneto-optical Faraday effect in a 50 nm thick Co film. As the Fara- day effect requires a transmission geometry, the film was sputter-deposited on a 100 nm Si3N4membrane and covered by a 3 nm Al cap layer. When the light passes through the film, the Faraday effect will cause a magnetization-dependent rotation of the polariza- tion plane of the lightϕF, as well as a change in el- lipticityF. In a polar geometry this may be simply described by a complex index of refractionn±for two circularly polarized eigenmodes of the linearly polar- ized light
n±= 1−(δ±∆δ) +i(β±∆β) (1) the subscript+(−)referring to a parallel (antiparallel) alignment of photon helicity and magnetization direc- tion of the sample. The real part (δ±∆δ) describes the dispersion, while the imaginary part (β±∆β) con- tains the absorption. The effect of the magnetization is contained in the respective MO constants∆δand
∆β, being nonzero for magnetized ferromagnets.
FIG. 1: Absorption and MO constants obtained for the Ni 3p edge. Top: absorption constantβ. Bottom: MO con- stants∆δ,∆βand Faraday rotation constantk.
IFF Scientific Report 2006 • Condensed Matter Physics
54 I55 The results obtained from the Faraday effect mea-
surements are displayed in Fig. 1. The top panel clearly shows the strong variation of the absorption βacross the energy position of the Co3pcore level caused by the resonant excitation. The Faraday ro- tation and ellipticity can be determined by means of a multilayer polarization analyzer implemented into the reflectometer. In principle, fromϕF andF one can directly calculate the magneto-optical constants.
However, we have to consider the fact that thin films have their easy axis of magnetization in the film plane due to the shape anisotropy. Therefore, in a simple polar geometry the wave vectorkof the incident light would be perpendicular to the magnetization and the effect will vanish. Instead, we have to incline the sam- ple by an angleΘito generate a magnetization com- ponent alongk. This leads to a slightly more elabo- rate analysis procedure, which yields∆δ. The quan- tity∆βis then obtained via Kramers-Kronig transfor- mation.
For an incidence angle of Θi = 50◦ the MO con- stants∆δand∆βare displayed in the bottom panel of Fig. 1. We clearly see that both quantities ex- hibit peak values at the position of the absorption edge and more or less vanish further away from the edge. This proves that the MO response is directly related to the resonant excitation of the3plevel into the unoccupied density of states below the vacuum level. As expected, the peak position of ∆δ differs slightly from that of ∆β. The quantity ∆δ is also directly related to the Faraday rotation constant k as ∆δ = kλ/(2π). The peak value of k reaches 1.5×105deg/mm, which is about one order of mag- nitude higher than the values known for the visible range. This result proves that even in the case that spin-orbit and exchange interaction are of compara- ble magnitude, strong magneto-optical effects show up. For further details, the reader is referred to Ref.
[6].
90 80 70 60 50 40 30 20 10 0 -10 -20 MagnetodichroicAsymmetry [%]
FIG. 2: Variations of T-MOKE signal (magnetodichroic asymmetryAT) from a 50 nm thick Co film as a function of photon energyE and angle of incidenceΘ. The color code gives the magnitude ofAT.
In the second experiment we employ a reflection ge- ometry. For this purpose a similar Co thin film sys- tem was prepared on a SiO2 template. Also in this experiment we have to fulfill a certain geometrical re- lationship to access the magnetooptical effects. We have therefore chosen the electric field vector of the
incident light to be parallel to the scattering plane, whereas the magnetization vector of the sample is perpendicular to this plane. This is also known as transverse Kerr geometry, giving rise to the trans- verse magneto-optical Kerr effect (T-MOKE). A par- ticular feature of the T-MOKE in the visible regime is that the magneto-optical response shows up directly as an intensity modulation in the reflected beam, due to the influence of the metal optics. Therefore, no po- larization analyzer is needed to measure the T-MOKE signal.
Exactly the same behavior is found in the XUV regime. In Fig. 2 we display the entire angular and photon energy dependence of the T-MOKE signal, which in this experiment is defined as the normalized intensity difference between opposite magnetization directionsM+andM−
AT= [I(M+)−(M−)]/[(M+) + (M−)]. (2) As we have already seen in the Faraday effect above, the data in Fig. 2 show that the magneto-optic re- sponse peaks as a function of the photon energy in a narrow interval related to the resonant excitation of the3plevel. Moreover, the T-MOKE signal exhibits also a very pronounced angular dependence, taking maximum values at aroundΘi = 45◦, correspond- ing to the Brewster angle of the system. We should note that close to the Brewster angle, the intensity of the reflected beam is reduced by 4 orders of magni- tude as compared to the specular reflection. Never- theless, in this region the T-MOKE signal may easily reach a magnetization-induced variation of close to 100%. It can therefore be conveniently employed, for example, to measure element-selective hystere- sis loops in magnetic thin film systems. As the wave- length of the XUV radiation is at least one order of magnitude higher than the individual layer thickness in functional magnetic layer stacks, which is in the nm-range, the angular variations of the T-MOKE sig- nal from such structures is much less complicated by multiple-diffraction effects.
[1] H. C. Mertins, S. Valencia, A. Gaupp, P. M. Oppe- neer and C. M. Schneider, Appl. Phys. A 80, 1011 (2005).
[2] J. St ¨ohr and H. Siegmann: Magnetism (Springer- Verlag, Berlin, 2006).
[3] H. C. Mertins, P. M. Oppeneer, J. Kun ˇes, A. Gaupp, D. Abramsohn and F. Sch ¨afers, Phys.
Rev. Lett. 87, 047401 (2001).
[4] [9] H. C. Mertins, F. Sch ¨afers, X. Le Cann, A. Gaupp and W. Gudat, Phys. Rev. B 61, R874 (2000).
[5] F. Sch ¨afers, Appl. Opt. 38, 4074 (1999).
[6] S. Valencia, A. Gaupp, W. Gudat, H.-Ch. Mertins, P. M. Oppeneer,D. Abramsohn and C .M. Schnei- der, New J. Phys. 8, 254 (2006).
