Multiscale micromagnetic modeling of magnetic materials and devices Annual Activity Report 2010

Institut:

E138, Institut für Festkörperphysik, „Advanced Magnetics Group“,

Kontaktpersonen:

Univ.Prof. DI Dr. Josef Fidler Privatdozent DI Dr. Dieter Suess PhD Jehyun Lee DI Markus Fuger

E-Mail:

[email protected] [email protected]

Hardware :

Vienna Scientific Cluster

Software :

Wien2k Selbstentwickelte Programme (finite element micromagnetic code)

Weiterführende WWW-Links : Home-Page der Arbeitsgruppe: http://magnet.atp.tuwien.ac.at/

Multiscale micromagnetic modeling of magnetic materials and devices Josef Fidler, Markus Fuger, Jehyun Lee, Dieter Suess Advanced Magnetics Group, Institute of Solid State Physics, TU Vienna Wiedner Hauptstraße 8-10, 1040 Vienna, Austria

I. Introduction The main objectives of the studies of micromagnetic modelling in 2010 have been concentrated on the simulation of the magnetization reversal properties and the complex hysteresis behavior of magnetic materials in the view of magnetic recording applications, and spanning length scales from the atomic level to the continuum and picoseconds to long time stability. Special attention has been laid to the potential of exchange spring bilayers and graded media for magnetic recording applications. The magnetic switching field distribution is significantly reduced in bilayer media and graded media compared to single phase media. The influence of precessional switching on the reversal time and the reversal field is investigated in detail. The aim of our research activities is to combine the modelling of intrinsic magnetic properties on the atomistic level based on density functional theory and hysteresis properties including switching modes and times on mesoscopic level together with the functional behaviour of magnetic devices on the macroscopic level. Novel concepts for recording media and recording head design can be tested virtually. The guidelines for systems development can be drawn from the simulations results. Hard disk storage at high densities has to overcome a fundamental limit. With decreasing bit size thermal stability can only be achieved in recording media with highly coercive small structural units such as grains, particles or patterned elements. Used resources: • • • •

VSC Cluster MPI/openmp parallelization Intel 11.1 Compiler (+ MKL) Average resources per simulation: 8-32 cores, 4GB memory, 24-48h simulation time

II. First principle simulations of RECo5 compounds for the determination of intrinsic magnetic properties Computer simulations have become more and more important over the last years in the field of material science and development. The available computational power made it possible to apply atomic model on realistic structures even for systems with a large number of atoms in the unit cell. One of these attempts in the domain of density functional theory (DFT) is the full-potential linear augmented plane wave (FPLAPW) method which describes the wave function of the valence electrons by spherical harmonics within a certain given radius (muffin tin radius rMT) and approximates it in the interstitial regions by a superposition of plane waves. For simulating the magnetic material parameters of RECo5 compounds we used WIEN2k [1], which is capable to calculate the parameters of interest as there where the magnetization and the magnetic crystalline anisotropy for a given crystal structure.

In many cases of 3d metals the use of the local density approximation (LDA) yields to results that could not be verified by experiments. Therefore we used the approach of generalized gradient approximation (GGA) for YCo5 which should cover this disadvantage [2]. The open 4f shell of the transition metals Nd and Sm had to be treated in the framework of LDA+U, where the Hubbard U parameter has been taken from previous publications [3] [4].

a)

b)

Fig.1: RECo5 (blue Co; green RE): a) z=0; b) z=1/2

The crystal structure of RECo5 is that of CaCu5 (P6/mmm, No. 191. Fig.1) but including spin-orbit coupling will lower the symmetry to Pmmm (No. 47). The site of Co(3g) (Fig.1 b) with multiplicity 3 will be splitted into two inequivalent sites. The lattice parameters have been taken from experimental results as shown in table 1.

YCo5 NdCo5 SmCo5

a (a.u.) 9.313 9.459 9.452

c/a 0.806 0.795 0.792

rMT (RE) 2.31 2.5 2.115

rMT (Co) 2.015 2.31 2.015

Table 1: lattice and simulation parameters of the investigated compounds

As starting point the electronic structure of the systems of interest have been calculated. Figure 2 shows the density of states (a) as well as the bandstructure of YCo5 as representative for the RECo5 compounds.

a)

b) Fig.2: density of states (a) and bandstructure plot (b) of YCo5

Furthermore one can obtain some quantitative information about the magnetization of a system when looking the electronic density difference between the electrons having majority and minority spin. Figure 3a shows the crystal structure of YCo5 as well as the [110] plane and the corresponding difference of ρmajor and ρminor.

a)

b) Fig.3: crystal structure of YCo5 (a) and ρmajor - ρminor plot of the [110] plane (b)

As simulation parameter for the LAPW RKmax and Gmax have been set to 9.0 and 14.0 respectively. Due to the fact, that in FLAPW all electrons are taken into account, the magnetization is an intrinsic property of any simulation. The results that have been obtained by a converged self consistent field (SCF) circle are given in table 2. After convergence an external magnetic field has been applied in (001) and (100) and the new energy eigenvalues have been calculated by using the force theorem. The magnetocrystalline anisotropy energy (MAE) between these two directions is then defined as the difference of the sum of the eigenvalues as they were found above. Table 2 gives a summary of the result for the three RECo5 systems. spin moment [μB] YCo5 NdCo5 SmCo5

7.17 10.12 12.67

spin moment [μB] (literature) 7.06 9.9 10.11

MAE [meV/f.u.] 0.94 0.38 4.82

MAE [meV/f.u.] (literature) 0.5-1.6 9 - 10 21.6

Table 2: Simulation results in comparison with published simulation values

One can see that the found magnetization is in good agreement with measured data. The magnetocrystalline anisotropy of YCo5 is close to previous simulations and measurements as well where as the data for NdCo5 and SmCo5 are far from the expected values. One of the reasons could be the arbitrary value of the Hubbard U, another the electrons for the 4f shell should be treated in another way. Future simulations will be adopted to achieve more realistic results in order to explain the nature of the rather high anisotropy values found in these compounds. III. Numerical finite element simulations For the detailed numerical simulation of the magnetic recording process a finite element software package has been developed which takes into account the detailed microstructure of a magnet and the interactions between the different magnetic parts of a magnetic device. The micromagnetic software solves the equation of motion for the magnetization of an entire

magnetic device (Landau-Lifshitz-Gilbert equation). For example in magnetic recording simulations, the input for the finite element simulations are the detailed microstructure of the recording media, the geometry of the write head, the layer stack and shield geometry of the read head, the intrinsic magnetic properties and the current wave form of the write current. Macropscopic properties like current wave form, read back voltage, transition jitter are input/output of a multiscale simulation that treats the functional behaviour of a recording system while taking into account the microscopic magnetization processes during recording and read back. Due to the small distance between the head’s air bearing surface and the patterned elements it is required to take into account the mutual interaction between head and magnetic islands. A new concept of storing information in three dimensions was investigated with micromagnetic simulations on the “vsc.zserv.tuwien.ac.at cluster”. The possibility of applying spin torque in magnetic layers via spin polarized currents gives rise to improved Magnetic Random Access Memory (MRAM) devices. Florez et al. [5],[6] showed experimentally frequency locking phenomena if the injected AC frequency is marginal below the eigenfrequency of the magnetic layer. In the work performed on the vsc-cluster we implemented the spin transfer torque (STT) using an additional contribution [7] to the LLG equation in our finite element micromagnetic package. Switching is triggered by a combination of DC and AC. Using free layers with different resonance frequencies which are realized by altering the anisotropy constants (K1,freelayer1 = 305 kJ/m3 and K1,freelayer2 = 277 kJ/m3) allows for selective switching of the two layers by tuning the AC frequency. The eigenfrequencies of the two free layers can be calculated by f = (γ*K1)/(Js*π*f0) leading to ffreelayer1 = 9.98 GHz and ffreelayer2 = 9.06 GHz. STT is triggered by an AC with an amplitude of 200 GA/m2 and a DC with an amplitude of 320 GA/m2. To avoid metastable states the angel between the effective uniaxial anisotropy axes of the free layer and the polarizer is 10°. Fig. 4 shows the two phase diagrams of these two layers. The distinct resonance frequencies can be clearly distinguished. Fig.5 shows a possible technical realization of a magnetic devices with 2 fixed polarizer and 2 free ferromagnetic layers with different anisotropy constants.

Fig. 4: Phase diagram of two magnetic layers with two different anisotropy constants is investigated as function of the DC-current strength and the AC-current frequency.

Fig. 5: Schematic drawing of the magnetic stack that allows storing information in two different layers.

References [1] P. Blaha, K. Schwarz et. al, WIEN2k An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties, 2001 [2] P.Larson et. al, Calculation of magnetic anisotropy energy in YCo5, JMMM 264 (2003) 7-13 [3] H. Pang et. Al, Calculation of magnetocrystalline anisotropy energy in NdCo5, Phys. Stat. Solidi B 246 (2009) 1245-1350 [4] P. Larson et al, Calculation of magnetic anisotropy energy in SmCo5, Phys. Rev. B 67 (2003) [5] S.H. Florez, J.A. Katine, M. Carey, L. Folks, B.D. Terris, Modification of critical spin torque current induced by rf excitation, Journal of Applied Physics 103, 07A708, 2008. [6] S.H. Florez, J.A. Katine, M. Carey, L. Folks, O. Ozatay, B.D. Terris, Effects of rf Current on Spin Transfer Torque Induced Dynamics, arXiv:0803.3791v2 [cond-mat.mes-hall], 2008 [7] J.C. Slonczewksi, Current-driven excitation of magnetic multilayers, Journal of Magnetism and Magnetic Materials 159, L1-L7, 1996