Heat Assisted Magnetization Reversal on Perpendicular Magnetized Nano-Dot

Heat assisted magnetization reversal on perpendicular magnetized nano-dots has been studied by solved Landau Lifshift-Gilbert equation for magnetic recording application. The heat assisted magnetization reversal scheme has been proven to be effectively reduces threshold field down to 90 %. Otherwise, this field doesn’t depend on heating time. To understand a read-write information process, cooling time dependence of threshold field has been evaluated. As a result, the threshold field depends on the cooling time and become constant after 300 ps. This result corresponds to data transfer of Hard Disc Drive about 30 Gb/s. Keywordsmagnetic recording, PMA, heat assisted, threshold field, heating time and cooling time AbstrakTelah dilakukan evaluasi mode magnetisasi reversal berbantukan panas pada nanodot magnetik beranisotropi tegak lurus dengan menyelesaikan persamaan Landau Lifshift-Gilbert untuk aplikasi perekaman magnetik. Skema magnetisasi reversal berbantukan panas terbukti efektif menurunkan medan threshold hingga 90%. Namun demikian, medan threshold tidak bergantung pada lamanya pemanasan. Untuk lebih memahami proses baca-tulis informasi, telah dilakukan evaluasi pola hubungan medan threshold terhadap lamanya pendinginan. Dan didapatkan bahwa medan ini bergantung pada lamanya pendinginan dan menjadi konstan setelah 300 ps. Hasil ini terkait dengan kecepatan transfer data pada Hard Disc Drive dalam orde Gb/s. Kata Kunciperekaman magnetik, PMA, berbantukan panas, medan threshold, lama pemanasan, lama pendinginan

o increase a magnetic disks density, magnetic size must be downsized to nanometer order.When the magnetic size is very small, the room temperature magnetization direction becomes unstable (the recorded magnetic domain relax due to thermal decay over time) [1,2].Large anisotropy magnetic material is required to overcome this thermal fluctuation [3].Ferromagnetic with large perpendicular magnetic anisotropy (PMA), such as Co x /Pd y , Co x /Pt y , Fe x Pt y etc are considered to be promising candidates for magnetic recording technology.Since 1990, recording densities of magnetic disks have an excellent annual growth up to 100%.In 2005, the commercial magnetic disks density is about 130 Gbit/cm 2 .Yet, writing magnetic field becomes insufficient if the media have large anisotropy [1].A promising method that can be proposed to solve this problem is a Heat Assisted Magnetization Reversal (HAMR).This method was developed since 1999.The main idea of HAMR method is using a heating pulse on nano-dots recording media to reduce the writing magnetic field [4].By the uses of HAMR method, the densities of magnetic recording exceeding Tbit/cm 2 , can be achieved [1].Therefore, comprehension about HAMR mechanism becomes important to be investigated.
In this HAMR scheme, double pulse i.e. writing field pulse and heating pulse, was adopted.The aim of this paper is to evaluate dependence of threshold field H th with respect to heating pulse configuration.The threshold field, associated with the writing magnetic field, is a field which required to aligning magnetization parallel to this field direction.
Reorientation of the magnetization process under an effective field was described by Landau Lifshift Gilbert equation (LLG) [6]: where M is a magnetization, α is a gilbert damping constant (= 0.3), γ is a gyromagnetic ratio (= 1.76.10 7 Oe -1 s -1 ), H eff is an effective field, M s is a magnetic saturation and dt is an integration time step (= 0.12 ps).First term in the right hand side of eq.( 1) describes the gyromagnetic precession and the second term is the damping term which describes the motion of the magnetic moment toward the H eff .The effective field introduced in eq.( 1) arises from the following four source [5,6]: (a) exchange field H ex , which appears from interaction between neighboring magnetic moments; (b) magneto-statics field H d , that breaks large magnetic particles into smaller magnetic domains, (c) anisotropy field H k , which appears from interaction of atomic moments with the crystal surrounding and causes the magnetic moments to be oriented along certain crystallographic direction, (d) at non zero temperatures a random stochastic field H T may be included.This H T will be discussed in numerical method.The H eff is given as the functional derivative of the energy density w respect to Interactions are expressed not as particle-particle interaction on the atomic scale, but are contained in macroscopic energy density.The form of the H eff is understood as the total energy E which is given as the integral functional of the energy density w respect to volume element dv E wdv Heat Assisted Magnetization Reversal on Perpendicular Magnetized Nano-Dot Nur Aji Wibowo 1 , Cari 2 , and Budi Purnama 3   T this total energy E has a minimum value for the equilibrium configuration.
If the magnetic size sufficiently small, large energy barrier becomes crucial aspect to ensure thermal stability.Field dependence of energy barrier defined by following equation where parameters K 0 is material anisotropy, V 0 is a volume and H 0 describe the magnet's real structure.Generally, thermal stability of small magnetic media demonstrated by Neel-Brown law where E a is the activation energy associated with the energy barrier ΔE, k B is a boltzman constant, T is a temperature and value of  0  10 -10 s. equation ( 5) can also be expressed as: when we assumed loss data stored at Hard Disc Drive (HDD) for 10 years,   10 years (10 8 s), so the corresponding ΔE for insured thermal stability at room temperature should be much larger than 40 k b T [2,6].

II. METHOD
In consideration a PMA magnetized nano-dots as a magnetic recording media, reversal mode of HAMR evaluated by solve the LLG equation.An approximation of thermal fluctuation effect occurring during magnetization is taken into account by involving randomly oriented effective fields with zero mean value,H  eff (t)=0.Whereas, strength of the random field due to the thermal fluctuation effect is calculated by using a fluctuation dissipation theorem [7]: where σ is a fluctuation factor, V is a volume of cell memory (= 50 × 50 × 20 nm 3 ) and Δt is time increment.
To evaluate heat effects with respect to threshold field and initial condition of magnetization, calculation of magnetization probability aligning to field direction was performed for 20 different series of random number.This probability reaches to 1 at threshold field H th .Temperature dependence of exchange stiffness and anisotropy constant which are related with the thermally reduced magnetization was assumed as [5]: where A is a exchange stiffness constant and K  is a perpendicular anisotropy constant.While the temperature dependence of magnetization defined by following equation [8].
Value of this physical parameters used in the simulation are exchange stiffness constant A = 1.10 7 erg/cm, anisotropy constant K  = 8.10 4 erg/cc, 4πM S = 2.1 kG which corresponds to energy barrier  150 k b T at room temperature and Currie temperature = 373 K.
Figure 1 illustrates the HAMR scheme in this paper.A bias field H w , which pulse width is 4.75 ns, was applied.And a heating pulse T w , which its pulse width is 2.5 ns, was applied after 1 ns.

A. Types Modes of Magnetization
In order to know deeply a heat fluctuation effect in Heat Assisted Magnetization Reversal mode, a change of energy barrier ΔE because of this heat fluctuation effect is evaluated for four different models.Physical properties which used in this simulation are K  = 3.10 5 erg/cc and 4πM S = 2.1 kG.Model A is the magnetization process by excluding the heat fluctuation effect in a configuration of initial magnetization and the H eff .Model B is the magnetization process by including the heat fluctuation effect in the configuration of initial magnetization.Model C is the magnetization process by including the heat fluctuation effect in the H eff .Finally, model D is the magnetization process by including the heat fluctuation effect in the configuration of initial magnetization and the H eff .Furthermore, the magnetization reversal mechanism is evaluated by observe a visualization of micrograph of magnetization.In this paper, ΔE is defined as a difference of a value between a minimum and maximum level energy as shown in Figure 1.This ΔE separates the two of difference minimum state.In the magnetic recording application, the two of difference minimum state associated with an opposite direction of magnetization (in the H w direction and the oppositely).And a switching field H swt is defined as a minimum H w which is required to overcome the ΔE so that the magnetization reverse into H w direction.
Figure 2 illustrates an energy barrier shape from four different models.From Figure 1(a-b) observed that a characteristic of ΔE is symmetric and smooth.Whereas a decreasing of the minimum level energy and the ΔE with an increasing of temperature T as shown at Figure 1(b-d).The different result was obtained if the fluctuation of H eff include in the calculation.Figure 1(c-d) shows that under the fluctuation of H eff effect, the characteristic of ΔE becomes asymmetric and ripple.And the ΔE vanish when T close to T c so that the material lose its magnetism.
From Figure 2, the T/T c dependence of the ΔE can be plotted.The decreasing of the ΔE to the increasing of the T/T c observed from Figure 3.As shown from the figure that the H eff fluctuation caused the fluctuating of ΔE.For models C and D, at T/Tc ≈ 99 %, the ΔE can still be realized with the value larger than 100 k B T. It means that the magnetization reversal possible to be realized at high temperature.
The magnetization reversal mechanism of each model can be observed from Figure 4. Figure 4(a) represents the reversal mechanism of state which excluding the heat fluctuation effect.Observed from the figure, at (i), t = 0 ns, the value of M easy /M sat is equal to zero.At this time, the magnetization saturated in the opposite direction of H w .Then, throughout a present of H w in a negative direction which the value rise linearly from 0 to 2 T, the value of M easy /M sat down towards negative value.At (ii), t = 0.83 ns, the value of M easy /M sat is equal to 0.1.And at (iii), t = 0.85 ns, the value of M easy /M sat is equal to -0.4.In this interval, the magnetization gradually turned towards H w direction.After 0.85 ns, the magnetization is saturated in the direction of H w which corresponds to the value of M easy /M sat equal to -1.
Figure 4(c-d) describes that the fluctuation of H eff caused the value of M easy /M sat drop and become ≈ 0 at T/T c ≈100%.It means that at that time, randomly magnetized state be realized.In this paper, t reversal is defined as a time which is required to reverse the magnetization so that the magnetization saturate in the H w direction.Reflected from the Figure 4(b-d) that the increasing of temperature shortening the t reversal .From this figure, the T/T c dependence of the t reversal can be plotted.The shortening of t reversal with respect to the increasing of the T/T c observed from Figure 5.By comparing the t reversal at B, C and D, observed that the presence of the H eff fluctuation shorten the t reversal .
The magnetization reversal magnetization also can be reflected on micrograph of magnetization as shown in Figure 6.Which is the magnetization parallel to the H w direction shown by black color, and white color shows the opposite direction, vice versa.This figure describes that for models A and B, the magnetization reversal mechanism begins with a smooth domain wall nucleation from a center.This domain wall expands until a single domain configuration in the H w direction has been realized.In the other side, for models C and D, the magnetization reversal mechanism begins with the domain wall nucleation from an edge.This domain wall expands until a single domain configuration in the H w direction has been realized.

B. Heat Assisted Magnetization Reversal
Figure 7 represents the HAMR mechanism under a bias field H w .Observed from the figure that for t < 1 ns, the magnetization constant.Yet, when the heat is applied (t > 1 ns), the magnetization change quickly and disordered when the heat approximate to Curie point.This randomly magnetized state shown with the value of M easy /M sat about 0. After 3 ns, the heat is lowered to room temperature.And the magnetization aligning to H w direction at room temperature, which called reversal state.At this state, read and write information is going on and then the information saved at room temperature.
The heat assisted magnetization reversal mechanism also can be reflected on micro-magnetic-graph of magnetization as shown in Figure 8, which is the magnetization parallel to the H w direction shown by white color, and black color shows the opposite direction, vice versa.Observed from micro-magneticgraph, for t < 2 ns, the magnetization dominated by multi domain configuration.During heating process, 2 < t < 3 ns, the random magnetization realized.Whereas for cooling writing process, t > 3 ns, the magnetization reversal mechanism starts with a domain wall nucleation and continued by domain wall annihilation so that single domain to the H w direction realized.
Figure 9 exhibits a decreasing of H th as a function of a writing temperature to Curie temperature ratio (T w /T c ).At T w /T c = 80 %, 2300 Oe of H th is required to aligning the magnetization in the H w direction.However, at T w /T c ≈ 99 %, only 250 Oe of H th is needed.This HAMR scheme proven to be effectively to reduce the H th down to 90 % (=(2300-250)x100%2300).The decreased of H th can be attributed to a reduction of ΔE during heating process.The reduced of the ΔE mechanism due to heat activation is illustrated at Figure 10.
Although a heating scheme has been proven to be effectively reduces the H th , in the other hand, this field doesn't depend on heating time t h as shown at Figure 11(a).This field is constant around 250 -300 Oe in 800 ps.This t h independence of H th shows that the randomly magnetized state doesn't change with the vary of t h .However, it is possible to shorten the t h in femto seconds order.
In order to understand transfer data to or from HDD process, the cooling time t w dependences of H th has been evaluated.Observed from Figure 11(b), the H th decreases with an increasing of t w and becomes constant after 300 ps.The H th reduced about 45% (=(550-300)x100%/550) from 550 Oe at t w = 0.019 ps to 300 Oe at t w = 300 ps.This field becomes stable around 250-300 Oe after 300 ps.It can be related to static and dynamic magnetization mechanism in the magnetization reversal process.This result corresponds to data transfer of HDD about Gb/s.

IV. CONCLUSION
The Heat assisted magnetization reversal on perpendicular magnetized nano-dots has been studied by solved Landau Lifshift-Gilbert equation for magnetic recording application.The heat assisted magnetization reversal scheme has been proven to be effectively reduces threshold field down to 90 %.Otherwise, this field doesn't depend on heating time.To understand a read-write information process, cooling time dependence of threshold field has been evaluated.As a result, the threshold field depends on the cooling time and become constant after 300 ps.This result corresponds to data transfer of hard disc drive about Gb/s.magnetization reversal in rectangular MRAM cell consisted of exchange coupled bilayer", J. Magn.Soc.Japan., Vol. 30, pp.574-577, 2006.

Figure 6 .Figure 7 .Figure 8 .Figure 10 .
Figure 6.The micromagneticgraph of the magnetization reversal mechanism from four different models (A, B, C and D) calculated for K= 3.10 5 erg/cc, 4πMS = 2.1 kG.Which is the magnetization parallel to the Hw direction shown by black color, and white color shows the opposite direction, vice versa