Magnetic recording technology

Transcription

1 Magnetic recording technology The grain (particle) can be described as a single macrospin μ = Σ i μ i W~500nm 1 bit = 300 grains All spins in the grain are ferromagnetically aligned B~50nm Exchange length 10 nm

2 Limiting factor for magnetic recording Demagnetizing field effects: W~500nm B~50nm a) Bit coupling: Due to the dipolar field H d, a bit switch can induce the switch of a closed bit (impossible to approach indefinitely two opposite magnetic poles) H d μ = Σ i μ i Materials with low magnetic moment Co Co 67 Cr 13 Pt 20 μ = 1.7 μ B μ = 0.6 μ B b) Transition Width: Demagnetizing field increase the transition (bit) width. Grains have non-uniform boundaries that increase the magnetic noise in the read out process. Record for in-plane longitudinal recording 100 Gbits/in 2 The future -> perpendicular recording

3 Signal-to-Noise Ratio: SNR number of grains in each bit (~1000). To keep the SNR constant the number of grains is kept fixed Smaller bits imply smaller grain size Reduced stability of magnetization vs thermal fluctuations (Superparamagnetic limit) Αvg. time (relaxation time) taking to jump from one direction to the other: τ = τ 0 exp(k/kt) τ s In grain with a size of a few tens of nanometers K grain volume

4 Magnetic anisotropy energy (MAE) K Magnetic field (Oe) Exchange interaction is isotropic in space No preferred orientation for the total moment M = Σ i S i However, real materials are not fully isotropic in space -> There exist preferred spatial directions (easy axes) along which it is easier to align the magnetization E easy - B dm is minimum Fe bcc easy axis: (100) 4 3 K1 = J / m = 2.4 μev / atom Magnetization (emu/cm 3 ) Bulk systems: K depends on the crystallographic structure Magnetic field (Oe) Co hcp easy axis: (0001) 5 3 K1 = J / m = 45 μev / atom Magnetization (emu/cm 3 )

5 Microscopic origin of the MAE Two principal sources: 1) Shape anisotropy -> it is due to the dipolar interaction of the magnetic moment μ of each atom with the magnetic field generated by all the other atoms at the atom location K shape Σ j Σ i grad(μ i r ij /r ij3 ) μ j Ex: A cylinder with h >> d prefers to be magnetized along the cylinder axis, while a cylinder with d >> h (i.e. a disk) prefers to be magnetized on the surface plane 2) Magnetocrystalline anisotropy (MC) -> it is due to the interaction of the magnetic moments with the crystal field which is in general non-isotropic a) surface anisotropy -> at surface or at the interface the symmetry breaking induces an asymmetry in exchange interaction b) spin-orbit interaction -> the electron spin is coupled with the orbital moment which in turn is coupled with the crystal field d-elements: K MC m L// -m L The MAE of a system is the summation over all the contributions

6 Uni-axial monodomain system K μ B 2 E( θθ, 0, ϕ ) = μ B K cos ( easy μ) B = 0 2 E( θθ, 0, ϕ ) = Kcos ( easy μ) E K << kt θ E K >>kt θ If K << kt the magnetization vector isotropically fluctuates in the space. If K >> kt the magnetization vector can not switch the versus Αvg. time (relaxation time) taking to jump from one minimum to the other: τ = 1 year τ = 1 second K = 40 kt K = 23 kt τ = τ 0 exp(k/kt) τ s The MAE determines the thermal stability of the magnetization direction

7 Applied magnetic field 2 E( θθ, 0, ϕ ) = μ B Kcos ( easy μ) M z = Nμ V cos θ = Nμ V cos θ exp( E / kt ) exp( E / kt ) dω dω E K T = 0 Η = 0 Η < K/μ Η K/μ θ Magnetization loops M z B // Easy axis and K > kt B // Easy axis and K < kt B // hard axis and K < kt H Loop shape -> direction of the easy axis K 0 Mmax B easy dm 0 Mmax B hard dm

8 Zero field cooling Measure of the zero field susceptibility χ = dm/dh 1 χ( T) = χ 2 eq ( T) 1 + ( ωτ ) χ ( T) eq M exp( K / k T) 1 π Kk TErfi( K / k T) 2K 2 B = B B O. Fruchart et al., J. Magn. Magn. Mater. 239, 224 (2002) S. Rusponi et al., Nat. Mater. 2, 546 (2003) Experimentally: measure of the M z variation induced by a small AC field (frequency ν 0 ) as a function of the temperature When the condition 1/ ν 0 = τ 0 exp(k/kt) is satisfied M starts to flip -> peak in the χ vs T curve Blocking temperature: temperature at which the peak occurs -> It is a measure of the MAE M z M z M z H H H Blocking: K/kT >>30 Activation Superparamagnetic: K/kT <<30

9 Ni/Pt multilayers X-ray absorption spectra for a Ni 2 Pt 2 multilayer: (a) x-ray absorption coefficients for R (µ + (E)) and L (µ - (E)) circularly polarized x-rays at the Ni L2,3 edges in the soft x-ray range, (b) (c) XMCD spectra at the Ni and Pt L2,3 edges Out-of-plane magnetocrystalline anisotropy (a) Angular dependence of the XMCD spectra (T = 10 K, B = 5 T) for a Ni 2 Pt 2 multilayer sample at normal (θ = 0 ) and grazing x-ray incidence (θ = 75 ). (b) Angular dependence of the orbital moment μ L determined from the angular dependence of the XMCD spectra. The solid line is a fit according to the equation μ L (θ) = μ L + (μ L// - μ L ) sin 2 θ -> K MC μ L// - μ L

10 Magnetization loops by XMCD Co/Pt(111) STM image 85 x 85 Å 2 out-of-plane in-plane m tot = m S + m L m S = -3 n h μ B (A 3-2A 2 ) + m T m L = -2 n h μ B (A 3 + A 2 ) m T 0.34 μ B << m S 2.1 μ B m tot A 3 (A 2 0) MAE Numerical fit of the magnetization: M K 0 Mmax B easy dm 0 Mmax B hard dm z = M 2 E( θθ, 0, ϕ ) = μ B K cos ( easy μ) sat cosθ exp [ E( θθ,, ϕ) / k T ] dθdϕ exp [ E( θθ,, ϕ) / k T ] dθdϕ 0 0

11 The substrate and the atomic coordination are the key to the MAE and magnetic moment Co/K n = 1 20 Å 40 Å n = 3 n = 8 40 Å MAE = 0 Co particles on Pt(111) with average size n magnetic anisotropy energy orbital magnetic moment P. Gambardella et al., Science 300, 1130 (2003) (B) Hard-sphere representation of the Co particles considered in the theoretical calculations. The labels indicate the values of L for nonequivalent Co sites. S, L, ΔL, and K in the table are averaged over all Co sites.

12 SMOKE: Surface Magneto Optical Kerr Effect Monochromatic linearly polarized light (generated by a laser) is sent on the sample Depending on the magnetic state of the sample the polarization of the reflected light is slightly canted (some mrad) in respect to the incident light I = I 0 (1+ a θ) θ M I 0 and I are the light intensity sent on the sample and measured by the detector, respectively Polar Longitudinal Transverse Heuristic argument: 1) The media electrons are accelerated by the incident electrical field and deviated by the Lorentz force due to the sample magnetization 2) The electrons motion contributes to the outgoing wave. 3) Therefore the outgoing wave has an addition component which rotates its polarization plane

13 SMOKE: theoretical basis The light propagation is described by the Maxwell equations: H E = μμ 0 t E H = εε 0 t At the optical frequency the permeability tensor μ can be assumed to be equal to the unit tensor, while the dielectric tensor ε is given by Right circular polarization Left circular polarization Plane electromagnetic wave propagating in the positive z direction in a birefringent medium. The indices of refraction for RCP and LCP light are different (n + and n -, respectively). If the wave has a wavelength of λ 0 in vacuum, then the wavelengths of its circular components in the medium will be λ 0 /n ±. If at the point z = 0 the wave is linearly polarized along the x axis, then in the medium the wave is given by The linear polarization direction turns of δ = π(n + -n - ) z/λ 0 M.J. Freiser, IEEE Trans. Magn. 4, 152 (1968); Z.Q. Qiu et al., Rev. Sci. Instrum. 71, 1243 (2000); M. Mansuripur, J. Appl. Phys. 67, 6466 (1990)

14 UHV system for MBE growth In situ STM -> morphology SMOKE -> magnetism Base pressure 3 x mbar Pressure during MBE growth < 8 x mbar

15 Co islands on Pt(111): edge atoms determine the MAE 0.4 ML Co T = 130 K T ann = 300 K 250 Å 1 atomic layer high islands Size about 1000 atoms Pt core and Co shell Compared to pure Co islands: 1) same total MAE 2) reduced magnetic moment S. Rusponi et al., Nature Mat. 2, 546 (2003).

16 Ultra-high density Co clusters superlattices on Au(788) A A 0.75 ML Co B B 1.1 ML Co A B Two island populations -> two blocking temperature N. Weiss et al., Phys. Rev. Lett. 95, (2005)

17 Magneto-optical data storage To store a bit, the magnetization has to be oriented in a certain direction in a well defined area on the disc. The process used for this is so-called thermo-magnetic writing. As it is not possible to apply a field only locally to a portion on the disc as small as the desired bit size, one combines the magnetizing field with application of a heating step which can be applied locally by using a semiconductor laser focused to a spot of about 0.5 μm. The laser radiation (>10 mw) raises the temperature locally reducing the coercive field below the magnitude of the applied field. Therefore, the region heated by the laser pulse changes its magnetization, whereas the surrounding remains unchanged. The same laser, operated at lower power (about 1mW), is used to read back the stored information. The Kerr rotation is about 0.1 A. Partovi et al., Appl. Phys. Lett. 75, 1515 (1999); H. F. Hamann et al. 84, 810 (2004)

18 1D magnetism: Co/Pt(997) THEORY Finite system (N localized moments): ground state: E=E 0 = -J(N-1) M tot 0 lowest excited state: E=E J ( N-1 such states) M tot = 0 change in free energy: ΔF= Δ(U-TS) = 2 J - kt ln(n-1) ΔF<0 no ferromagnetism for N-1 > exp(2j/kt) Infinite chain -> no magnetism (M tot = 0) at any temperature 0 Heisenberg model -> no FM state in 1D and 2D 1 Hheisen = Jijsi s j μ si H 2 i, j Ising model -> no FM state in 1D 1 H = J s s μh s z z z ising i j i 2 i, j i i

19 Finite chain Interatomic exchange energy for Co 2J 15 mev ferromagnetism is allowed only for N < 50 atoms at T = 50 K Ising model + anisotropy-> FM state in 1D 1 1 H = J s s s K s z z z easy μh ( ) 2 i ising i j i 2 i, j i 2 i Spin blocks oriented along the easy axis by the external field have to overcome the MAE barrier to reverse the orientation K The MAE stabilizes the direction of the spin blocks -> M tot 0 when the external field is put back to 0

20 Pt(997) 10 nm 2nm 0.1 ML of Co deposited at 260 K: array of parallel cobalt monatomic chains FM coupled atoms: N = 15 short-range FM K = 2.1 mev/atom P. Gambardella et al., Nature 416, 301 (2002).

21 Easy axis oscillates with the chain thickness Φ 0 0 Θ P. Gambardella et al., Phys. Rev. Lett. 93, (2004) Co wire magnetization M measured at a field B r in the plane perpendicular to the wire axis (left column) and parallel to the wire axis and the (111) direction right column). The data points represent the XMCD signal at Co L 3 edge (779 ev). The solid lines evidence a cos(x-x 0 ) behavior with x = Φ, Θ, respectively, measured with respect to the (111) normal direction, as expected for uniaxial anisotropy. (a) 1-wires, T =10 K, B r = 0.25 T; (b) 2-wires, T =10 K, B r = 1 T; (c) 4-wires, T =10 K, B r = 2.5 T. No data were recorded in the plane parallel to the wires; (d) 1.3 ML, T = 45 K, Br =1.5 T.

22 MAE oscillates with the chain thickness K = 2.0 mev/atom K = 0.33 mev/atom K = 0.45 mev/atom K = 0.15 mev/atom Magnetization loop of (a) 1-wires, Φ 1 = + 43 (solid squares), Φ 2 = - 57 (open circles); (b) 2-wires, Φ 1 = - 67, Φ 2 = + 23 ; (c) 3-wires, Φ 1 = - 7, Φ 2 = +63 ; (d) 1.3 ML, Φ 1 = - 7, Φ 2 = +63. The data points represent the XMCD at the Co L 3 edge (779 ev) normalized by the L3 absorption edge jump; solid lines are fits to the data. P. Gambardella et al., Phys. Rev. Lett. 93, (2004).

23 Orbital moment decreases increasing chain thickness m L 0.68 μ B 0.37 μ B 0.33 μ B 0.31 μ B chain in respect to bulk hcp: - Narrowing of the d-band - increasing of the spin splitting LSDA: Local Spin Density Approximation LSDA+U: LSDA + electron correlations A. B. Shick et al., Phys. Rev. B 69, (2004).