Role of Magnetic Circular Dichroism in All-Optical Magnetic Recording

Using magneto-optical microscopy in combination with ellipsometry measurements, we show that all-optical switching with polarized femtosecond laser pulses in ferrimagnetic GdFeCo is subjected to a threshold ﬂuence absorbed in the magnetic layer, independent of either the excitation wavelength or the polarization of the laser pulse. Furthermore, we present a quantitative explanation of the intensity window in which all-optical helicity-dependent switching (AO-HDS) occurs, based on magnetic circular dichroism. This explanation is consistent with all the experimental ﬁndings on AO-HDS so far, varying from single- to multiple-shot experiments. The presented results give a solid understanding of the origin of AO-HDS, and give novel insights into the physics of ultrafast, laser controlled magnetism.

Controlling the magnetic state of a medium with the help of femtosecond laser pulses is a recently emerging and rapidly developing research direction in modern magnetism. The interest to the problem of the ultrafast optical control of magnetism was triggered by pioneering work by Beaurepaire et al. [1], who found that excitation of magnetic Ni with a femtosecond laser pulse resulted in the quenching of the magnetization within a few picoseconds. This is much faster than one might expect supposing that the demagnetization is defined by the characteristic time of the spin-lattice interaction in the ground state. Therefore, it was suggested that the ultrafast laser-induced demagnetization was due to ultrafast angular momentum transfer from light to the medium. Soon it was argued however, that such a mechanism is negligible since the total angular momentum of photons in realistic experiments is not large enough to contribute significantly to the observed changes of the magnetization of the media [2].
The discussion about the mechanisms of light-matter interaction in optical control of magnetism was revived after the discovery of all-optical magnetization reversal with the help of circularly polarized (CP) light [3]. Namely, it was shown that in a certain range of pulse energies M is not only quenched, but is fully reversed when the medium is exposed to one light-helicity while it is not affected if the helicity is opposite. This All Optical Helicity Dependent Switching (AO-HDS) was observed in ferrimagnetic GdFeCo in the absence of an external magnetic field. The role of light, light helicity, and angular momentum in AO-HDS are still open fundamental issues and subject of intense discussions in modern magnetism [4].
It was hypothesized that CP light acts as a strong effective magnetic field pulse B eff on the spins of the medium through the inverse Faraday effect (IFE). The direction of B eff is then defined by the helicity of the light. Atomistic spin simulations performed under the assumption that light acted as B eff ¼ 20 T were able to describe some key features of AO-HDS, such as the existence of an intensity window at which this phenomenon occurs [5].
Although the existence of such effective magnetic field was demonstrated by the experiments on dielectrics [6], so far this effective field has been described only phenomenologically. The equation describing it was derived in a nondissipative approximation and thus the microscopical origin of the IFE-field in metallic GdFeCo is still a subject of research. Furthermore, these simulations have shown only a qualitative agreement with AO-HDS.
Hence, the microscopic mechanism of the light-matter interaction responsible for AO-HDS has not been revealed yet. In general, the effects of light-matter interaction can be divided into two groups: those that result in an absorption of light and those that lead to a change of the phase of the radiation. Consequently, helicity-dependent effects in optics of magnetic media can be seen as magnetic circular dichroism (MCD) or magnetic circular birefringence (MCB), respectively. It is the aim of this Letter to reveal which one of these two groups is responsible for AO-HDS.
To achieve this goal we performed spectral studies of alloptical switching as a function of light polarization, and intensity. We compared this with the spectral dependencies of both MCD and MCB. We find that AO-HDS can be explained quantitatively with MCD. This explanation is consistent with all the experimental findings on AO-HDS so far, varying from single-to multiple-shot experiments. Furthermore, we show that all-optical switching is subjected to a threshold fluence of 2:6 AE 0:2 mJ=cm 2 , independent of the wavelength and polarization of the excitation pulse.
The structure of the material we studied is SiO 2 =AlTið10Þ=SiNð5Þ=Gd 26 Fe 65 Co 9 ð20Þ=SiNð60Þ. The values in parentheses represent the layer thicknesses in nm. The GdFeCo layer is a ferrimagnetic film with perpendicular magnetic anisotropy. The switching was studied by exciting the material with a single laser pulse ( % 60 fs) at different wavelengths using magnetooptical microscopy to determine the final magnetic state of the exposed area. Subsequently, an external magnetic field pulse was applied to bring the ferrimagnet back to its initial state. The initial magnetization was always in the ''up'' direction, while the polarization was varied from left-(LC), via linearly (LP) to right-handed circularly polarized (RC). It should be noted that it is symmetrically equivalent to fix the helicity and vary the magnetic state from ''M up'' to ''M down'' (see Table I). This procedure was repeated about 20 times at every pulse energy and allowed us to measure the switching probability P as a function of fluence F and light-polarization . We define the fluence as the pulse energy divided by the beam area (defined as the standard deviation of a Gaussian distribution). The beam area at the sample surface was measured accurately at each wavelength [8]. All measurements were performed at room temperature. Further details of the experimental setup are described elsewhere [3,5]. Figure 1 shows the results for ¼ 700 nm, demonstrating that for ''M up'' P LC P L P RC , and thus that AO-HDS occurs in a certain intensity window. In the ideal case of no pulse-to-pulse fluctuations of the laser (e.g., fluctuations in the pulse energy and/or the spatial beam profile), P is given by a step function centered at the threshold fluence F , as illustrated in the inset of Fig. 1. More generally, in the realistic case of finite pulse-to-pulse fluctuations (dashed lines in the inset of Fig. 1), P is given by an error function where is a unitless quantity representing the relative magnitude of the pulse-to-pulse laser fluctuation, which varies typically between 0.5%-2%. We define the window (Á) of AO-HDS, as Note that, while pulse-to-pulse fluctuations do affect the shape of P , the value Á is not affected by these fluctuations (see inset Fig. 1). From Fig. 1 it can be seen that at ¼ 700 nm, F RC and F LC are separated by a window of Á % 1:5%. Furthermore, it shows that switching occurs even when the system is excited with LP light. The threshold fluence at which this TABLE I. Results from single-shot magneto-optical microscopy measurements, ellipsometry measurements and from calculations at four different excitation wavelengths. F LP denotes the switching threshold fluence using LP light. The errors originate from the uncertainties in the spot sizes, which were accurately measured with the Liu method [7]. The window Á is defined in Eq. (2). From ellipsometry measurements the refractive index of GdFeCo for LP light n LP , and Án a were obtained. A LP denotes the total absorption of LP light in the GdFeCo layer, and MCD the calculated magnetic circular dichroism in GdFeCo.
Single-shot magneto-optical microscopy Ellipsometry measurements Calculations occurs, F LP , lies exactly in between F RC and F LC . The experimental results at the different wavelengths are summarized in Table I, showing that Á is almost independent of the excitation wavelength. In order to understand the origin of the window it was hypothesized that the latter is due to an effective magnetic field generated by CP light via the IFE [3,5]. Pershan et al. [9] showed using arguments of thermodynamical equilibrium that CP light may act on a medium as an effective magnetic field where denotes the magneto-optical susceptibility, and E the electric field of the incoming pulse. Note that the effective magnetic field is maximum for CP light, while it vanishes for LP light. In a nondissipative approximation, the strength of this field for CP light is given by [4] where F is the Faraday rotation at saturated magnetization,ñ and d the real part of the refractive index and layer thickness of GdFeCo, respectively, F % 5 mJ=cm 2 the fluence of the excitation pulse, M 0 % 10 5 A=m [3] the static magnetization, c the speed of light and % 60 fs the temporal pulse length. We would like to stress that although the existence of B eff has been demonstrated experimentally [6], there is no experimental evidence that Eq. (4) is an adequate representation of the effective magnetic field generated by CP light in GdFeCo. This equation intrinsically neglects effects of absorption, taking into account only those effects of light-matter interaction that are related to a phase change of the light waves. Consequently, this approach accounts for MCB and neglects MCD in a medium. Note that these two effects have different spectral dependencies.
From spectral measurements of F (inset Fig. 2) and n (Table I), we calculated B eff as a function of the wavelength. This is plotted in Fig. 2(a) (open dots) together with the switching window Á (closed dots). It can be seen that the calculated B eff has a strong wavelength dependence, similar as in Ref. [10], while the switching window is almost constant in this spectral range.
Alternatively, we will consider MCD as the possible origin of AO-HDS. GdFeCo is well known for its strong magneto-optical effect. Therefore, RC and LC pulses experience different refractive indices in this material and consequently a difference in absorption of RC and LC pulses may be present. The refractive indices of the GdFeCo layer were measured using ellipsometry. The thus obtained values for n LP , n LC , and n RC of GdFeCo are shown in Table I. We calculated [8] the total absorption in the GdFeCo layer A for each polarization , with a model based on linear absorption in a multilayer stack [11]. For the refractive indices we used for GdFeCo the measured values n given in Table I, and for the other layers the values from Palik [12]. Subsequently, we can calculate the MCD from The absorption of LP light is equal to A LP ¼ 1 2 ðA RC þ A LC Þ. The thus obtained values for MCD in GdFeCo [8] are given in Table I. These values show that the switching window in GdFeCo, expressed in terms of relative fluence Á, exactly corresponds to the relative absorption of RC and LC light, given by the MCD values. This correspondence can also be seen clearly from Fig. 2(a), where the spectral dependence of MCD and the window Á are plotted together.
Note that this correlation shows that the switching thresholds for LC and RC light are different by exactly the same amount as the difference between the total absorption in the GdFeCo layer for LC and RC light, respectively. The effective switching threshold F Ã ðÞ ¼ F ðÞA ðÞ, i.e., the actual absorbed energy density in the GdFeCo layer at which switching occurs, is therefore independent of the polarization: In fact, the effective switching threshold is also independent of the wavelength and is equal to F Ã ¼ 2:6 AE 0:2 mJ=cm 2 , as can be seen in Fig. 2(b).
These results demonstrate that given a 60 fs excitation pulse, all-optical switching depends only on the amount of energy absorbed by the magnetic system, independent of the wavelength or helicity of the laser pulse. A natural consequence is that switching can be achieved with any polarization as long as the absorbed intensity in the GdFeCo layer is sufficiently strong. Because of different absorption coefficients for RC and LC light in GdFeCo, the switching threshold is helicity dependent. We can conclude unambiguously that AO-HDS originates from MCD. Considering the errors in our measurements, possible contributions of other mechanisms to AO-HDS are at least 10 times smaller than MCD.
The observation that all-optical switching relies on absorption only, supports the recent simulations showing that a heat pulse can be sufficient to switch the magnetic state of GdFeCo [13]. It was shown that strongly nonequilibrium conditions in multisublattice magnetic systems such as GdFeCo, due to an ultrashort heating pulse, can lead to sublattices that evolve temporarily against their intersublattice exchange interaction. This results in a transient ferromagneticlike state within a picosecond after excitation [14]. On a longer time scale, the sublattices will align antiparallel again due to their intersublattice exchange interaction. This results in an overall reversal of the net magnetization.
It is interesting that with multiple-shot exposures it is possible to obtain helicity-dependent switching of large areas, even for intensities much higher than the regime where AO-HDS occurs with a single pulse [3]. This observation is illustrated in Fig. 3. CP pulses are swept over the surface (from left to right in Fig. 3) with a 1 kHz repetition rate. For the given helicity, more energy is absorbed in the black (''M down'') than the white domain (''M up'') due to MCD. In the center of the excited area, the intensity is high enough to switch both magnetic states. Near the edge of the excited area however, there is a small ring-shaped region where only black domains switch to white. The left side of the white ring will not switch back to black when sweeping the beam to the right. Hence, the beam will leave a trail of white domain. This trail is visible when the underlying M is ''down'' (black) but invisible when it is up (white), in exact agreement with the observations in Ref. [3]. In the same article another multipleshot experiment on GdFeCo is shown. The beam was fixed at a position near a domain wall with a repetition rate of 1 kHz. In the Supplemental Material we illustrate how MCD can also explain very accurately the observations in this experiment [8].
The effective switching threshold F Ã % 3 mJ=cm 2 , compares favorably with the 2 Â 10 4 mJ=cm 2 of writing fluence per bit in current hard drives and FLASH solid state memories, and even with the 10 mJ=cm 2 in magnetic random access memory [15]. The present switching area, however, is on the order of micrometers compared to tens of nanometers of bit size in the afore-mentioned technologies. Reducing the spot size of the excitation pulse, for example, with optical near-field microscopy [16] or plasmonic antennas [17], could lead easily to a smaller switched area, as was recently demonstrated [18]. This would make all-optical magnetic recording a promising alternative to conventional recording technologies with respect to both writing speed [5] and energy per bit.
The new understanding of AO-HDS may have far reaching consequences for the realization of all-optical magnetic recording. The intensity regime at which this phenomenon occurs is the most relevant parameter for possible applications of all-optical magnetic recording, as in this regime the final magnetic state is completely determined by the helicity of the excitation pulse. For such applications, however, it is necessary to overcome pulse-to-pulse fluctuations of the laser intensity to have fully controllable switching. The ultimate solution would be the enhancement of the switching window, or equivalently the MCD value in the GdFeCo layer. The latter could be easily enhanced by optimizing the design of the multilayer structure, even without changing the properties of the magnetic layer. As an example, we calculated the MCD in GdFeCo for different structures of the capping layer, see Fig. 4. In the calculations, the 60 nm thick SiN capping layer was replaced by SiNðyÞ=amorphous-SiðxÞ=SiNð5Þ, where the values between parentheses represent the layer-thickness in nm. For y ¼ 5 and x ¼ 40 the window appears to be more than doubled, i.e., from 1.5% to roughly 3.5%. Adjusting the material and/or thickness of other layers, including the magnetic layer, could enhance the window even further.
Summarizing, we have shown that all-optical switching in GdFeCo is subjected to a threshold fluence of 2:6 AE 0:2 mJ=cm 2 absorbed by the magnetic layer, independent of either the wavelength or the polarization of the excitation pulse. With MCD we can quantitatively explain AO-HDS. Furthermore, this explanation is consistent with all the FIG. 3 (color online). Illustration of multiple-shot switching with CP excitation pulses. In the center of the excited area, both magnetic states can switch because of the high fluence, while at the edges (i.e., between the dashed borders) helicity-dependent switching occurs and therefore a single domain state is formed. Hence, by sweeping multiple CP excitation pulses over the surface, a large area can be switched.