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Nanoscale reversal of the longitudinal magnetization (Mz) is highly desired in the ultrahigh density perpendicular magnetic recording. In this paper, an all-optical method to realize the reversal of Mz with an ultrasmall lateral size through configuring the inverse Faraday effect (IFE) is numerically proposed. This feature is achieved by optical coherent configuration of the IFE in the central and peripheral regions of the focal spot with opposite signs. By increasing the intensity of the peripheral regions to produce destructive interference, the lateral size of the reversed Mz smaller than 30 nm in one dimension in the central region can be achieved. This result is of vital importance for realizing ultrafast nanoscale perpendicular magnetic recording.
© 2015 Optical Society of America
1. Introduction
The discovery of the giant magnetoresistance [1] has enabled the perpendicular magnetic recording [2] for high density information storage. Because of the stabilization and the smaller sizes of the magnetized bits, perpendicular magnetic recording or longitudinal magnetization reversal has replaced parallel magnetic recording method as the prevailing technique to realize magnetic data storage. The generation of a longitudinal magnetization probe (perpendicular to the surface of a recording medium) with nanoscale resolution for information recording is of vital importance. Even though electron beam lithography can generate a perpendicularly magnetized bit with an ultrasmall feature size of 35 nm [3], its practical applications are limited by the high cost, complex operations, and the long operation time.
On the other hand, all-optical switching (AOS) has emerged as a promising alternative way to realize ultrafast perpendicular magnetic recording [4–9]. All-optical helicity-dependent switching (AO-HDS) based on the IFE which was theoretically conceived in 1960s [10,11] arouses intense interests of scientists. Circularly polarized incident beams with opposite helicities can induce effective magnetic fields with opposite orientations in the perpendicular direction through the IFE, and hence control the dynamics of the spins and the reversal of Mz in the magneto-optical materials [4–7,12]. In the rare earth – transition metal amorphous alloys, such as GdFeCo, with two antiferromagnetically-coupled sublattices with different relaxation constants, the AO-HDS takes place within a narrow fluence window (approximately 10%) [6,7]. Beyond this window, all-optical helicity-independent switching (AO-HIS), namely the thermal-driven switching, may occur once the laser beam induced temperature increment across the magnetization compensation temperature [6–9]. Nevertheless, all-optical helicity-dependent magnetization control by removing the thermal-driven effect completely has been observed when the operation is performed at an ultralow temperature around 20 K [12]. Alternatively, ferromagnetic materials, such as FePtAgC, emerge as excellent magneto-optical recording media exhibiting a significantly enlarged AO-HDS window [13].
In addition to the fundamental investigation of the dynamics of AO-HDS in a variety of magneto-optical materials, beam engineering for AO-HDS with small perpendicularly magnetized bits has received enormous research efforts. In this regards, high NA objective lens [14] and solid immersion lens [15] have been introduced to confine Mz in a region of 0.46λ. Later, azimuthally polarized vortex incident beam [16,17] and annular objective lens [17] are introduced to further squeeze Mz within 0.38λ. However, as the consequence of the diffraction barrier of light, none of these approaches can result in a sub-hundred nanometer longitudinal magnetization reversal even though it is of crucial importance for the development of ultrahigh density AOMR.
In this paper, an all-optical method, which can flexibly control the polarization states in the focal region to generate the reversal of Mz with an ultrasmall lateral size through the IFE, is numerically proposed. For the transverse components of the electric field in the focal region of a high NA objective, circular or elliptical polarizations with opposite helicities can be generated in the central and the peripheral regions, respectively. The lateral size of the central region (the region to be reversed) can be reduced by increasing the weighting factor of the peripheral regions owing to the destructive interference. Applying this tailored beam to the ordered magneto-optical recording medium, magnetization reversal with a lateral size smaller than 30 nm can be achieved. This result through configuring the IFE is vital important for realizing ultrafast nanoscale perpendicular magnetic recording.
2. Numerical model
For simplicity, numerical model to realize the reversal of Mz with an ultrasmall lateral size in one dimension is proposed in this paper. As illustrated in Fig. 1, Et represents the transverse component of the electric field in the focal region. Left-handed and right-handed circular or elliptical polarizations are shown in the central and peripheral regions, respectively. Then, according to the IFE, an effective longitudinal magnetic field (Hzeff) with opposite orientations in the corresponding regions is generated [5,18,19]. The magnetically ordered material is assumed to be isotropic and the initial state of Mz is down. Mz in the central region is subsequently reversed with the help of Hzeff. Due to the isotropic property of the material, the final spatial distribution of the reversed Mz is supposed to be the same with Hzeff in the central region. It is straightforward to predict that by increasing the weighting factor of the peripheral regions the lateral size of the central region can be reduced owing to the destructive interference between these regions, and hence the full width at half maximum (FWHM) of the reversed Mz in the central region can be decreased monotonically.
Fig. 1 Schematic illustration of Mz reversal with an ultrasmall lateral size by the optical coherent method.
In order to generate such configurations of the focal electric fields under a high NA aplanatic objective, Richards and Wolf vectorial diffraction theory [20–22] is introduced and its Fourier transform expression is given by Eq. (1) [23,24]
where a multiplicative constant is omitted for clarification. Equation (1) is represented in Cartesian vector components. ℱ represents the two-dimensional Fourier transform, which has been studied in detail in [23]. k is the wave vector in the focal region. m = 1, 2, 3. Circular polarization is composed of orthogonal linear polarizations with a half π phase difference. Here, E1, E2 and E3 are the focal fields needed to generate circular or elliptical polarizations with opposite helicities. E1 and E2 are the focal fields of x polarized incident beams. The dominant component of them is the x polarized component (Ex1 and Ex2). E1 and E2 supply the x polarization in the central and the peripheral regions, respectively, as shown in Fig. 2(a). Etm is the plane wave spectrum expressed by the spherical coordinates θ and ϕ with the origin at the focus. For x polarized incident plane wavesandR is the radius of the back aperture of the objective. Compared with Et1, a grating function is introduced in Et2 to generate position shifts. y0 is the coordinate within the back aperture and Δyj is the position shift in the focal region [25]. λ is the wavelength of the incident beam in vacuum. By carefully controlling Δyj, polarizations with a π phase difference from the central region can be formed in the peripheral regions. Then the superposition of E1 and E2 iswhere δ is the weighting factor of the peripheral regions.Fig. 2 The formation of x polarization with a π phase difference between the central and the peripheral regions in the focal plane. (a) The cartoon diagram illustrating the generation of the field. (b) (c) (d) The corresponding normalized calculated results. (e) The corresponding cross sections at x = 0 in the focal plane.
Figures 2(b)-2(d) illustrate the corresponding normalized calculated results. Here, Δy1 = 0.394λ, Δy2 = - 0.394λ, δ = 3, and NA = 1.4. The lateral size of the central region is obviously reduced by destructively interfering with the peripheral regions as depicted in Fig. 2(e).
Meanwhile, a y polarized component dominant focal field E3 is needed to interfere with the achieved x polarized field. For y polarized incident plane waves
Then the total superposed focal field is expressed asE3 is multiplied by an i in Eq. (6) to introduce a half π phase delay and phase lead compared with E1 and E2, respectively. Figure 3(a) shows the superposition of the light fields. The dashed arrow represents the half π phase difference between Ex.Fig. 3 Polarization conversions in the central and peripheral regions and the distribution of the reversed magnetization generated by the conversed light field. (a) The cartoon diagram illustrating the superposition of the light field. (b)(c) The cross sections of the normalized electric fields and the induced Hzeff at x = 0 in the focal plane. (d)-(f) Distributions of the reversed Mz in the focal plane, x-z plane, and y-z plane, respectively.
According to the energy considerations [5,11,16,19], the effective magnetic field induced by the IFE in the nonabsorbing isotropic magneto-optical material can be represented by the phenomenological expression as Eq. (7)
where E*total is the conjugate of Etotal. γ is a real constant proportional to the susceptibility of the material [5,11,16,19]. Especially, for Hzeff at x = 0 in the focal planeFigures 3(b) and 3(c) depict the corresponding cross sections of the normalized electric fields and the induced Hzeff. In region A, the central region, left-handed circular or elliptical polarization is formed and then induces Hzeff with + z orientation. Meanwhile, in the peripheral regions (B) right-handed circular or elliptical polarization is obtained and Hzeff with the opposite orientation (-z) is achieved in these regions. In regions C, although left-handed circular or elliptical polarization is formed as well, the amplitudes of Hzeff are reduced by the small values of Ey3 in these areas and will not affect the magnetization distribution severely.Mz with the initial state (-z) is reversed by the Hzeff in the central region. As the magneto-optical material is isotropic, the final spatial distribution of the reversed Mz is supposed to be the same with Hzeff with + z orientation. Figure 3(d) shows the distribution of the reversed Mz in the focal plane. The FWHM of the central region in the y direction is 0.19λ. It is substantially smaller than that induced by the focal fields of circularly polarized and azimuthally polarized vortex incident beams [16]. The limitation of the lateral size of Mz reversed by these two kind of incident beams is 0.25λ for NA = 1.4. By using our proposed method, reversed Mz with a lateral size of sub-hundred nanometers can be obtained if the incident wavelength is shorter than 500 nm. The realization of ultrasmall sized Mz is of great importance in the applications of ultrahigh density magnetic data storage and magnetic nanostructures fabrication. The distributions of Mz in the x-z and y-z planes are shown in Figs. 3(e) and 3(f). As Hzeff and the initial state of Mz in the peripheral regions have the same orientation, large values of Hzeff in the peripheral regions do not have detrimental effect on the reversal in the central region.
By further increasing δ, the FWHM of the reversed Mz in the central region decreases monotonically as depicted in Fig. 4(a). Figure 4(b) shows the distribution of the reversed Mz with a weighting factor of 20. In order to obtain usable distribution of the reversed Mz in the central region, a similar grating function is introduced in Et3 (Δy1 = 0.25λ and Δy2 = −0.25λ), which can ensure that only the Mz located at the central region can be reversed. Moreover, a slit parallel to the y direction can be utilized at the back aperture of the objective to make better use of the ultrasmall size by confining the focusing effect in the x direction. The width of the slit is 0.2R. In the reversed region, a lateral size of 0.0746λ is obtained in the y direction. If the incident wavelength is 400 nm, the FWHM is below 30 nm which is smaller than that achieved by the electron beam lithography. For longer incident wavelengths the FWHM can be kept below 30 nm by increasing the weighting factor.
Fig. 4 (a) The variation of the FWHM of the reversed Mz in the central region versus the change of δ. (b) The distribution of the reversed Mz by introducing a grating function in (E)t3 and inserting a slit parallel to the y direction at the back aperture when δ = 20.
3. Conclusion
In conclusion, an all-optical helicity-dependent method to realize longitudinal magnetization reversal with an ultrasmall lateral size through configuring the IFE is numerically proposed. This feature is achieved by optical coherent configuration of the IFE in the central and peripheral regions of the focal spot with opposite signs. The reversed Mz with a lateral size below 30 nm can be achieved. It is comparable to that realized by the electron beam lithography and substantially smaller than that induced by focusing circularly polarized or azimuthally polarized vortex beam through the IFE. This configured result is of crucial significance and has unquestionably potential applications in ultrahigh density magnetic recording and fabrications of nanoscale magnetic lattices for atomic trapping and spin wave operations.
Acknowledgment
This work is supported by the Australian Research Council (ARC) Laureate Fellowship scheme (FL100100099). Mr. Sicong Wang acknowledges the financial support from the National Basic Research Program of China (2012CB921904) for his study in Australia. Dr. Xiangping Li thanks ARC Discovery Early Career Researcher Award for funding support (DE150101665).
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