1 Copenhagen University June 23 rd 2008 Ph.D. Defence Morten Stilling Ph.D. student Nano-Science Center/Atomistix

2 Goals of the industrial Ph.D. project Scientific goal – Use Atomistix software to investigate the electronic properties of technologically relevant components Development goals – Test the software developed by Atomistix – Suggest improvements Commercial goals – Find new markets for the software – Develop the markets Scientific investigations Structural properties of Si/SiO 2 interfaces Electron transport properties across Si/SiO 2 interfaces Spin-transport properties of Fe/MgO magnetic tunnel junctions [1,4] Effects of oxide layers in Fe/MgO magnetic tunnel junctions [1,3] Effects of structural disorder in Fe/MgO magnetic tunnel junctions [2] Structural properties of MgO-based magnetic tunnel junctions [4] Tunneling mechanisms in MgO-based magnetic tunnel junctions [4] Effects of a bias voltage in MgO-based magnetic tunnel junctions [4] [1] Stilling et al., Mol. Sim. 33, (2006) [2] Stilling et al., J. Comput. Aided Mater. Des. 14, (2007) [3] Stilling et al., Proc. NSTI-Nanotech , (2007) [4] Stilling et al., Phys. Rev. B (submitted) Software development Spin-dependent transport Methods for constructing the electron density SCF convergence Transmission eigenstates (tool available in Atomistix ToolKit) Linear-response (tool available in Atomistix ToolKit) Spin-transfer torque (tool available in Atomistix ToolKit) Magnetic Tunnel Junction Builder (tool available in Virtual NanoLab) Market development Visits at IBM, Fujitsu, Hitachi, Grandis, Toshiba, Crocus, Thales Samsung, Seagate, KIST, KAIST, Spintec, TSMC, IMEC, Panasonic... Participation in MMM, MRS, Nanotech, NTNE, Nanofair, NNIN... Set up of the Magnetoresistive Storage and Memory Consortium

3 Copenhagen University June 23 rd 2008 Magnetoresistance in MgO-based magnetic tunnel junctions with Fe, Co, and FeCo electrodes Morten Stilling Ph.D. student Nano-Science Center/Atomistix

4 Here's what I want to tell you Hard disk drives with read heads incorporating MgO-based magnetic tunnel junctions are emerging in the data storage market We have modeled the spin-transport properties of MgO-based magnetic tunnel junctions using first-principles DFT/NEGF methods The tunneling magnetoresistance in MgO-based magnetic tunnel junctions is high but decreases with increasing bias voltage

5 The personal computer (PC) Two types of memory: – Random access memory (RAM, 4) RAM is volatile – Hard disk drive (HDD, 8) HDD is non-volatile

6 The world's first hard disk drive

7 The read head in the hard disk drive Zhu and Park, Materials Today 9, (2006)

8 The magnetic tunnel junction in the read head in the hard disk drive

9 Tunneling magnetoresistance in MgO-based magnetic tunnel junctions Parallel magnetization configuration – high conductance Anti-parallel magnetization configuration – low conductance A measure of the conductance difference – tunneling magnetoresistance (TMR) Zhu and Park, Materials Today 9, (2006)

10 We assume ideal crystalline structure

11 We calculate the electronic structure using density functional theory (DFT) The Hohenberg-Kohn theorem – The ground state electron density can be found by minimizing an energy functional The Kohn-Sham equations – The ground state electron density can be found by solving a series of one-electron equations Hohenberg and Kohn, Phys. Rev. 136, B864 (1964) Kohn and Sham, Phys. Rev. 140, A1133 (1965 ) Effective potential External potential Hartree potential Exchange-correlation potential

12 We calculate the current using the Landauer approach The conductance and current are related to the transmission probability of incident electrons Datta, Cambridge University Press, (1995)

13 A basis set of atomic-like orbitals is used Self energies describe the coupling between the electrodes and the central cell We calculate the transmission coefficient using non-equilibrium Green's functions Taylor et al., Phys. Rev. B. 63, (2001) Brandbyge et al., Phys. Rev. B. 65, (2002) LL RR

14 We use a “ramp approximation” The electrochemical potentials in the electrodes are shifted by ±eV/2 The effective potential falls off linearly across the barrier Majority-spin band structure of FeCo electrode (blue: left electrode – green: right electrode)

15 Reliability/accuracy of our results We seek to understand qualitative trends We do not make quantitative predictions Two levels of “accuracy” – Model accuracy – Numerical accuracy Model accuracy DFT provides a good description of structural properties DFT provides a good description of the electrode band structures DFT significantly underestimates the band gap of the MgO barrier DFT/NEGF is a good comprise between reliability and calculation time (it is the de facto standard for our type of studies) Numerical accuracy We use the following model parameters (electron density) LSDA exchange-correlation potential DZP basis sets 200 Rydberg mesh cut-off 12x12 k-point mesh tolerance We use the following model parameters (spin-transport) 301x301 k-points for conductance calculations 21x21 k-points for current calculations

16 We have calculated the TMR of three magnetic tunnel junctions 5-layer MgO barriers sandwiched between body-centered cubic electrodes – Fe/MgO – Co/MgO – FeCo/MgO The system geometries were optimized

17 Calculation results – zero-bias The TMR values are large The TMR values are of similar size (an order of magnitude larger than experimental values) Yuasa et al., Nat. Mater. 3, 868 (2004) Yuasa et al., Appl. Phys. Lett. 89, (2006) Parkin et al., Nat. Mater. 3, 862 (2004)

18 Tunneling mechanisms (transmission spectra) Transmission as function of k-vector for the parallel- and anti-parallel configurations

19 The transmission probability matrix can be diagonalized The total transmission is the sum of transmission eigenvalues A transmission eigenstate can be found for each transmission eigenvalue Tunneling mechanisms (transmission eigenstates) Parallel configuration majority to majority  1 to  1 (efficient) Anti-parallel configuration majority to minority  1 to non-  1 (inefficient)

20 Effects of an applied bias voltage

21 The transmission probability depends on the voltage and the energy: T = T(V,E) Voltage dependence of the tunneling mechanisms The transmission probability depends mostly on the energy: T ≈ T(E) The effect of an increasing bias voltage is to “sample” an increasingly larger energy window

22 Here's what I wanted to tell you Hard disk drives with read heads incorporating MgO-based magnetic tunnel junctions are emerging in the data storage market We have modeled the spin-transport properties of MgO-based magnetic tunnel junctions using first-principles DFT/NEGF methods The tunneling magnetoresistance in MgO-based magnetic tunnel junctions is high but decreases with increasing bias voltage

23 Thank you for your attention and thank you for your contribution