Symmetry of wavefunction in perpendicular magnetic anisotropy films 76 Materials Science : Electronic & Magnetic Properties Recent high-density magnetic storage has been made possible by perpendicular magnetic recording (PMR) techniques. The first application of PMR to hard disk drives was achieved in Dec. 2005 [1]. PMR can achieve 5-10 times higher recording density than the previous conventional magnetic recording. The key material for PMR is a film with perpendicular magnetic anisotropy (PMA), which has a large positive magnetic anisotropy energy perpendicular to the film plane. Metallic multilayers, such as Co/Pd and Co/Pt, exhibit large PMA energies when their magnetic layer thickness is reduced to a few monolayers [2-5]. In spite of many experimental and theoretical studies toward the understanding of magnetic anisotropy, the origin of PMA in multilayered magnetic thin films remains to be clarified. Previous theoretical investigations [6,7] have shown the following. The orbital hybridization between Co-3 d and Pd-4 d (Pt-5 d ) at the interface increases the population of symmetric Co-3 d states with | m |= 2. Here, m denotes the magnetic quantum number. The angular momentum induced by the increased number of | m | = 2 states gives enhanced orbital magnetic moments perpendicular to the film plane. The enhanced orbital magnetic moments perpendicular to the film plane induce PMA. X-ray circular magnetic dichroism (XMCD) experiments have shown the presence of enhanced Co 3d orbital magnetic moments perpendicular to the film plane at the Co/Pd (or Pt) interface [8,9]. However, the contributions of the | m |=2 symmetry to PMA have not yet been confirmed experimentally. A magnetic Compton profile (MCP), J mag ( p z ), is expressed by a projection of a spin density map to the p z axis in momentum space. Here, p z denotes the z component of the electron momentum p in a solid. Because the symmetries of a wavefunction are the same in real space and momentum space, the symmetry of the spin-dependent wavefunction can be determined if MCPs are observed from different directions [10]. Recently, we have applied MCPs to the analysis of Co/Pd and Co/Pd multilayers to directly observe the | m |= 2 symmetry of Co 3 d states in multilayers with PMA. In this paper, we report the symmetry of the wavefunction in multilayers with PMA [11]. Five multilayer films (Co(0.8 nm)/Pd( x nm), x = 0.8, 1.6, 4.0, Co(0.8 nm)/Pt( x nm) x = 0.8, 4.0) were fabricated on PET film substrates of 4 μ m thickness by RF sputtering. The total film thickness of the multilayers was adjusted to about 1 μ m. The thin- film samples were folded 16 times to increase their effective thickness, and the effective thicknesses of the films and PET substrate were 16 μ m and 64 μ m, respectively. The crystal structure was confirmed by θ – 2 θ X-ray diffraction measurement. The (111) texture of the fcc structure was observed in the intermediate-angle region. Satellite peaks, which were observed around the intermediate-angle region, confirm the designed period of the multilayers. The lattice constant obtained from the peak position of (111) has a linear relation with the thickness fraction of the Co layer. Magnetization was measured in an out-of-plane configuration (applied fields were perpendicular to the sample surface) and an in-plane configuration (applied fields were parallel to the sample surface). Figure 1 shows the lattice constants and PMA energies. The present results reproduce those of previous studies [2-5]. Magnetic anisotropy changes from in plane magnetic anisotropy to PMA at a lattice constant of more than 0.372 nm. MCPs were measured at the high-energy beamline BL08W . The circularly polarized X-ray energy was set to be 174 keV. The degree of circular polarization was about 0.76. The scattered X-rays were detected by a 10-segmented Ge solid-state detector (SSD) with a scattering angle of 178° that was installed 1 m from the sample. The momentum resolution was 0.43 atomic units (a.u.). The applied magnetic field, which was supplied by a superconducting magnet, was ± 2.5 T for magnetization saturation in both the in-plane and out-of-plane configurations. All the measurements were carried out under vacuum at room temperature. 0.37 ( × 10 -3 ) K u λ λ (J/m 2 ) Co/Pd Co/Pt Lattice Constant (nm) PMA IMA -0.5 0.35 0.36 0.38 0.39 0.4 0 0.5 1 Fig. 1. Perpendicular magnetic anisotropy (PMA) energy density per bilayer against the lattice constants of fcc Co/Pd and Co/Pt multilayers. The blue solid line denotes a least squares fitting result as a visual guide. The red vertical dashed line denotes the boundary of PMA and in-plane magnetic anisotropy (IMA). 77 Figure 2 shows the MCPs of the (Co(0.8 nm)/Pd( x nm) and (Co(0.8 nm)/Pt( x nm) multilayers with the in-plane and out-of-plane configurations. Differences in the MCP between the in-plane and out-of-plane configurations, which we call the anisotropies of the MCP, are observed for the Co/Pd and Co/Pt multilayers within the momentum region 2 a.u. The anisotropies depend on the Pd and Pt thickness, x . This dependence originates from the changes in the populations of | m | = 0, 1, and 2 states, and hence from the change in the symmetry of the wavefunctions. Then the MCPs are decomposed using the model calculation, and the populations of | m | = 0, 1, and 2 states are obtained. Figure 3 shows the lattice constants and populations of | m | = 0, 1, and 2 states. | m | =2 states dominate above 0.380 nm. This indicates that | m | = 2 states contribute to PMA. | m | = 1 states dominate between 0.372 nm and 0.380 nm. This indicates that | m |= 1 states also contribute to PMA on the boundary region. In conclusion, the lattice constants change the PMA energy and the symmetry of the wavefunction. The contributions of the | m |= 2 symmetry to PMA are confirmed experimentally. The contributions of the | m |= 1 symmetry to PMA are also experimentally observed for the first time. 0 2 4 6 8 10 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 in-plane Co (0.8 nm) / Pd (0.8 nm) Co (0.8 nm) / Pd (4.0 nm) Co (0.8 nm) / Pd (4.0 nm) Co (0.8 nm) / Pd (0.8 nm) Co (0.8 nm) / Pd (0.7 nm) Co (0.8 nm) / Pd (1.6 nm) Co (0.8 nm) / Pd (1.6 nm) Co (0.8 nm) / Pd (4.0 nm) Co (0.8 nm) / Pd (4.0 nm) Co (0.8 nm) / Pd (0.7 nm) out-of-plane in-plane out-of-plane 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 p z (a.u.) p z (a.u.) p z (a.u.) p z (a.u.) 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Co/Pd Co/Pt Jmag ( ( p z ) ) (a.u. -1 ) J mag ( ( p z ) ) (a.u. -1 ) J mag ( ( p z ) ) (a.u. -1 ) J mag ( ( p z ) ) (a.u. -1 ) J mag ( ( p z ) ) (a.u. -1 ) 0.36 0.37 0.38 0.39 0 20 40 60 80 100 Lattice Constant (nm) Population of Co-3 d (%) PMA IMA PMA by PMA by | m | = 0 | m | = 1 | m | = 1 | m | = 2 | m | = 2 Fig. 3. Population of | m |=0, 1, and 2 states in the spin-projected Co 3 d electrons against the lattice constants of fcc Co/Pd and Co/Pt multilayers. The red vertical dashed line denotes boundary of PMA and in-plane magnetic anisotropy (IMA). Fig. 2. Magnetic Compton profiles (MCPs) of Co/Pd and Co/Pt multilayers in out-of-plane and in-plane configurations. MCPs are normalized to have unit area. Hiroshi Sakurai Department of Production Science and Technology, Gunma University E-mail sakuraih@gunma-u.ac.jp References [1] Y. Shiroishi: Magnetics Jpn. 5 (2010) 312. (in Japanese) [2] P.F. Carcia et al. : Appl. Phys. Lett. 47 (1989) 178. [3] F.J.A. den Broeder et al. : Appl. Phys. A 49 (1989) 507. [4] F.J.A. den Broeder et al. : Phys. Rev. Lett. 60 (1988) 2769. [5] P.F. Carcia: J. Appl. Phys. 63 (1988) 5066. [6] G.H.O. Daalderop et al. : Phys. Rev. B 50 (1994) 9989. [7] K. Kyuno et al. : Phys. Rev. B 54 (1996) 1092. [8] D. Weller et al. : Phys. Rev. B 49 (1994) 12888. [9] N. Nakajima et al. : Phys. Rev. Lett. 81 (1998) 5229. [10] N. Sakai: "X-Ray Compton Scattering" edited by M.J. Cooper et al. , Oxford (2004). [11] M. Ota, M. Itou, Y. Sakurai, A. Koizumi and H. Sakurai: App. Phys. Lett. 96 (2010) 152505.
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