Magnetization Dynamics in Spintronic Structures and Devices

Transcription

1 Japanese Journal of Applied Physics Vol. 45, No. 5A, 2006, pp #2006 The Japan Society of Applied Physics Magnetization Dynamics in Spintronic Structures and Devices Structure, Materials and Shape Optimization of Magnetic Tunnel Junction Devices: Spin-Transfer Switching Current Reduction for Future Magnetoresistive Random Access Memory Application Yiming HUAI, Dmytro APALKOV, Zhitao DIAO, Yunfei DING, Alex PANCHULA, Mahendra PAKALA, Lien-Chang WANG and Eugene CHEN Grandis Inc., 1123 Cadillac Court, Milpitas, CA 95035, U.S.A. (Received December 7, 2005; revised January 28, 2006; accepted February 8, 2006; published online May 9, 2006) We present a systematic study of spin transfer switching in magnetic tunneling junctions (MTJs). Several ways to decrease the switching current density through material and stack engineering and MTJ element shape optimization are explained in detail. The data are presented for switching on MgO-based MTJ with high tunnel magnetoresistance (TMR) of 150% and low intrinsic switching current density J c0 of ð2{3þ10 6 A/cm 2. Micromagnetic modeling is used to study the spin transfer switching mechanism in nanosecond regime for spin transfer torque random access memory (STT-RAM) pillar. The importance of current-induced Oersted field on the initial onset of precession is discussed. [DOI: /JJAP ] KEYWORDS: spin transfer torque, current induced magnetization switching, magnetic tunnel junction, MgO barrier, magnetoresistive random access memory 1. Introduction Recently discovered spin transfer phenomenon has stimulated considerable research activity not only because of the interesting physics involved but also due to its potential application to magnetoelectronic devices. The theoretical prediction of this effect was made independently by Slonczewski and Berger. 1,2) The possibility to use this effect as a switching scheme in a new generation of magnetic random access memory devices (MRAM) is very intriguing. The basic structure of the devices used to study the spin transfer effect have the form of a pillar with elongated crosssection. 3) The pillar consists of at least two ferromagnetic layers separated by non-magnetic metallic or insulating layer. One of the ferromagnetic layers is a thinner free layer and the other thicker layer is usually pinned by exchangebias interaction with an adjacent antiferromagnetic layer. Another method is to fix the thicker layer by increasing its thickness and making it extended. The shape anisotropy of the free layer determines two possible states for the device: low resistance parallel (P) state with magnetization of the free layer aligned in the direction of the pinned layer magnetization and high resistance antiparallel (AP) state with free layer magnetization aligned in the direction opposite to pinned layer magnetization. The switching between the two stable states is achieved by passing a current perpendicular to the plane of the layers. The reading of the state of the device is done by measuring the resistance of the pillar. The pinned layer often has a synthetic antiferromagnet structure (SAF) two ferromagnetic layers antiferromagnetically coupled through a thin Ru layer via Ruderman Kittel Kasuya Yosida (RKKY) exchange interaction. This structure serves to increase the uniformity of the magnetization of the pinned layer as well as to decrease the magnetostatic field experienced by the free layer due to the pinned layer. 4) When the electron passes through the thick layer, it becomes spin-polarized with electron spins preferentially pointing along the magnetization of the pinned layer. As this spin-polarized electron enters the free layer, it exerts a torque on the magnetization of the free layer, which 3835 can cause the generation of spin waves or even complete switching of the magnetization. Implementation of the spin transfer switching as a recording mode for spin transfer torque random access memory (STT-RAM) will provide a number of important advantages over the field switched MRAM, e.g., eliminating the half-select problem, increasing the bit density and improving scalability. 5) However, one of the biggest challenges that need to be overcome in STT-RAM is the high amplitude of current density required to switch the magnetization of the free layer in nanosecond regime. Substantial reduction of the switching current density from 10 7 to 10 5 MA/cm 2 is critical for several reasons. First, small current is needed to decrease the size of metal oxide semiconductor field-effect transistors (MOSFET) in series with magnetic tunneling junction (MTJ) cell (in 1T-1MTJ design) to achieve high capacity. Second, smaller voltage across the device decreases the probability of tunneling barrier breakdown, increases the endurance of the device, and increases the yield of STT-RAM array. One good measure of the switching current density in the device is given by on-axis magnetization instability current density, introduced by Sun 6) for a monodomain small particle under the influence of spin transfer torque: J c0 ¼ 2eM St F ðh þ H K þ 2M S Þ ; ð1þ h where e is electron charge, is the phenomenological Landau Lifshitz Gilbert damping constant, M S is the saturation magnetization, t F is the thickness of the free layer, H is the applied field, H K is the effective uniaxial anisotropy field of the free layer (including shape and intrinsic anisotropy contributions), h is the reduced Planck s constant, and is the spin polarization factor of the incident current. At this current density value the initial magnetization position of the free layer along the easy axis (long axis of the ellipse in pillars with elliptical cross-section) becomes unstable. As the current becomes higher than the instability value, the magnetization of the free layer goes into stable precession mode, with amplitude of the precession deter-

2 mined by the current. The stability of the large angle steady precession comes from the increased effective damping for large-cone dynamics through channeling more energy into the higher frequency modes giving higher energy dissipation. The switching in this simplified single-domain model occurs when the magnetization of the free layer crosses the equator between the two energy minima. 6) However, as we shall see later, the single-domain model does not always hold for real devices (especially for high current and fast switching), even though it gives good qualitative picture for understanding spin transfer switching and estimating switching current. For the switching of the free layer magnetization in nanosecond regime, the required current is several times greater than the instability current J c0. 6,7) Several techniques and material optimization have been considered to decrease this current. 8,9) As can be seen from eq. (1) the switching current reduction can be carried out through innovative materials (decreasing M S, 8) damping constant, increasing spin polarization factor ) and MTJbased structure engineering 10) (increasing effective spin transfer efficiency, or cell shape optimization). This paper will review some of the critical steps and achievements in decreasing the spin transfer switching current. The first part of this paper is dedicated to experimental results and data for intrinsic switching current density reduction by material and MTJ stack structure engineering. The key results of which includes the MTJ s with amorphous AlO x and crystalline MgO tunneling barriers, and basic MTJ s and double spin filter (DSF) structures with two pinned layers to increase the efficiency of spin transfer. The second part of this paper discusses the dynamics of spin transfer switching by means of micromagnetic simulation, and serves the purpose of understanding the physics of switching mechanism in terms of shape optimization, which is needed for future implementation of STT-RAM technology in nanosecond regime. 2. Switching Current Density Reduction through Material and Structure Engineering Before discussing experimental data, it should be pointed out that one must be careful to meaningfully compare the switching currents between different structures and materials. Depending on the applied current two mechanism of switching can occur: fast precessional switching (nanosecond regime) or slow thermally-activated switching (switching time is greater than tens of nanoseconds). The presented experimental data correspond to the latter case, in which the main effect of spin transfer is to increase the effective temperature of the spin system of the free layer in effective temperature framework 11,12) or decrease the effective energy barrier in effective barrier framework. 13) In both cases this results in decreased stability factor eff for the original (unswitched state): eff ¼ K uv k B T eff ðjþ ¼ K uv k B T 1 J ; ð2þ J c0 (effective temperature approach is used, effective external field is assumed to be zero) where K u V is the energy barrier between two (AP or P) stable states in absence of current, V is the volume of the free layer, T is the absolute temperature. As a consequence of the decreased thermal stability factor 3836 in presence of current, the switching occurs by thermal activation if the current is higher than the critical switching current which depends on the current pulse width and thermal stability factor K u V=k B T of the free layer: J c ðþ ¼J c0 1 k BT K u V ln 0 where 0 1 ns is the inverse of the activation frequency. Both K u and V are functions of cell dimensions. However, J c0 is independent of measurement temperature and pulse width and can be obtained by extrapolating experimentally obtained switching current as a function of pulse width to 0. Thus obtained value of J c ð 0 Þ¼J c0 will be used to compare spin transfer efficiency between different materials and structures. 2.1 Single AlO x -based structure First experimental observation of spin transfer effect was performed on metallic pseudo spin-valve structures with conducting spacer between the ferromagnetic layers. 3) However, the resistivity and giant magnetoresistance (GMR) of such devices are very small and the switching current was too high for STT-RAM applications. Immediately attention was drawn to MTJs, which have insulating nonferromagnetic material between the free and pinned layers. The first observation of the spin transfer switching in deep-submicometer MTJ-based device was made on Ta(3)/PtMn(20)/CoFe(2)/Ru(0.7)/CoFeB(2)/AlO x /Co- FeB(2.5)/Ta(3) (in nm) with AlO x barrier. 4) Note that the composition of CoFeB is 60 : 20 : 20 in atomic percentage throughout experiment in this paper, unless otherwise indicated. The film for the pillar was deposited using a Singulus sputtering cluster system (TIMARIS). The tunneling barrier is formed by natural oxidation of pre-deposited Al layer in a pure oxygen atmosphere. The samples were annealed at C for 2 h in a magnetic field of 1 T. The film was subsequently patterned into deep submicrometer ellipse-shaped pillars using either enhanced deep UV (DUV) lithography or by e-beam patterning with etch-back planarization of insulating layer. 4) Resistance R of the pillar structure was measured as a function of magnetic field H and current I at room temperature by a quasistatic tester with pulse current capability. The R vs I plots were obtained by sequentially increasing/decreasing the amplitude of current pulse in steps of 50 ma. The MTJ resistance value was measured after each pulse step using a low read current of 10 ma. R vs I plots were obtained for four different current pulse widths between 0.6 ms and 1 s. By using pulse mode resistance measurement, the bias dependence of R that is characteristic of tunneling junctions is reduced. The offset fields H off, experienced by the free layers due to the orangepeel coupling field and the dipolar field from the adjacent pinned layers, were balanced by applying an external field H a ¼ H off during current switching measurements. Average switching current at each pulse width is determined by repeating the measurements 25 times. A typical field hysteresis loop and current loop for such MTJ cell is shown in Fig. 1. The nominal magnetic cell dimension was nm 2. TMR of 42% was obtained from both field and current hysteresis loops. Average switching current hi c i¼ 0:35 ma was observed using a pulse width of 30 ms at room ð3þ

3 TMR: 42% H c : 35 Oe; H off =-7 Oe H (Oe) <I c >: 0.35 ma H off =-7 Oe temperature, where switching current I c is defined as ðic þ I c Þ=2, Iþ c is the current required to switch free layer magnetization from a P to AP state, and Ic is the current required to switch free layer magnetization from AP to P state. The room-temperature switching current density hj c i was calculated to be 2: A/cm 2. To compare the effect of spin transfer efficiency, we need to find intrinsic switching current density J c0 by extrapolation of the switching current to 1 ns pulse width as described above. Such plots of the switching current density as a function of the pulse width are shown in Fig. 2 for a different MTJ sample. hj c0 i for this MTJ samples was determined by extrapolation to be A/cm 2, as compared with A/cm 2 at current pulse width of 30 ms. hj c0 i for the MTJ samples of Fig. 1 was determined to be 7: A/cm Dual structures Introduction of tunneling barrier instead of conducting spacer layer in the spin transfer switching was promising and decreased the switching current density by several factors. Another important step towards the realization of required 10 5 A/cm 2 goal was the introduction of double structures, such as dual spin filter (DSF). 10) Dual structures have an additional pinned layer on top of the free layer with Fig. 1. Resistance as a function of the applied field and current for MTJ sample with AlO x tunneling barrier. TMR of the sample is 42% and average switching current hi c i¼0:35 ma. Plot was obtained at current pulse width of 30 ms and applied field (offset field) of 7 Oe. Jc (A/cm 2 ) 8.0E E+06 E E E+06 1.E-09 1.E-06 1.E-03 1.E+00 Pulse Width (s) Fig. 2. Switching current as a function of pulse width. Symbols are experimental data and lines represent the fitting curves. The average intrinsic switching current density hj c0 i¼610 6 A/cm 2. magnetization antiparallel to the magnetization of the bottom pinned layer, creating additional spin transfer torque on the top surface of the free layer due to the reflected spinpolarized current from the top pinned layer. Spin-transport model predicts 6{10 reduction in switching current in dual structure as compared to single MTJ. 14) Figure 3 shows typical field and current driven magnetization switching for a nanoscale DSF structure Ta(5)/PtMn(20)/ CoFe(2)/Ru(0.8)/CoFeB(3)/AlO x /CoFeB(3)/spacer/CoFe(2)/ PtMn(15)/Ta(5) (in nm). The magnetization directions of the pinned layers on both sides of the CoFeB 2.5 nm free layer are antiparallelly aligned. Both field and current data exhibit an identical TMR value of 25%. An average RT switching current of 0.13 ma was observed using a pulse width of 30 ms, as shown in Fig. 3. The nominal magnetic cell dimension was nm 2, resulting in a room-temperature switching current density value of hj c i¼1:310 6 A/ cm. hj c0 i for the DSF sample was determined by extrapolation to be 2: A/cm 2. 15) Thus, compared to the single MTJ, a reduction of 3 in the value of J c0 is observed for the DSF sample, which is smaller than the theoretically predicted reduction. One of the possible reasons for this discrepancy is the presence of additional damping due to the enhanced spin pumping effect in the DSF structure. 15) MgO tunneling barrier Recently it has been reported that MTJ with crystalline MgO barrier have greatly enhanced TMR values as compared to the MTJ with amorphous AlO x barrier ) The reason for such increase is directly related to the symmetry of the Bloch states in the free and pinned ferromagnetic layers and the evanescent states in the tunneling barrier. Bloch states of different symmetry decay at different rates within the barrier, resulting in high spin polarization. Because of the increased spin polarization, it is expected to observe a decrease in the switching current in MgO-based MTJs ) To study this effect, MTJ films with MgO barrier Ta(5)/ PtMn(20)/CoFe(2)/Ru(0.8)/CoFeB(2)/MgO/CoFeB(2.5)/ Ta(8) (in nm) were deposited and annealed at C for h in a magnetic field of 1 T. The MTJ films were

4 subsequently patterned into deep submicrometer ellipse shaped pillars in a similar way as described above for AlO x -based MTJ. A typical field hysteresis loop (R vs H) and a current loop (R vs I) for an MTJ cell with an MgO barrier of 1.2 nm are shown in Figs. 4 and 4, respectively. The nominal magnetic cell dimension is nm 2. TMR of 155% is calculated from the R vs H plot TMR: 24% H c : 35 Oe; H off =-50 Oe H (Oe) <I c >: 0.13 ma 3100 H off =-50 Oe Fig. 3. Resistance as a function of the applied field and current for DSF sample with AlO x tunneling barrier. The TMR of the sample is 24% and the average switching current hi c i¼0:13 ma. Plot was obtained at current pulse width of 30 ms and applied field (offset field) of 50 Oe. in agreement with R vs I plot. The average RT switching current is 0.33 ma at a pulse width of 30 ms. The RT switching current density J c was calculated from hi c i to be 1: A/cm 2 and RA is 50 mm 2. The intrinsic switching current density J c0 was obtained by extrapolating the switching current as a function of pulse width in analogy with procedure described above, and was found to be A/cm 2, which is a 3 reduction as compared to single MTJ structure with AlO x barrier. Assuming that dual MgO-based structure provides the same improvement compared to single MgO MTJ as dual AlO x -based structure over the single AlO x MTJ, we can expect to achieve the switching current density as low as ð7{8þ10 5 A/cm 2 in DSF structure with MgO tunneling barrier. Our preliminary results on dual MgO MTJ show intrinsic switching current density reduction by 2{3. 3. Spin Transfer Switching Dynamics and Shape Optimization Other than material and film structure as discussed above, the factors such as Oersted field, exchange stiffness of free layers and shape effect were studied through micromagnetic simulations. These factors may cause significant impact on STT switching dynamics in fast switching regime where the precession mechanism dominates. It has been shown that elliptical shape provides better fast-switching performance (faster switching and smaller switching current densities) than the rectangular shape 24) and some other shapes that are often used to study switching in conventional MRAM. In the simplified Slonczewski model describing spin transfer torque, 1) the total effective field is the sum of magnetostatic field of the other cells, Oersted field due to the current, effective intrinsic anisotropy field, and exchange field due to the nearest neighbors (we assume there is no external field and the magnetostatic field because the pinned layers is fully compensated). The magnetostatic field is computed by Cartesian Fast Multipole method. 25) For simplicity, we assume no thermal fluctuations (zero temperature), which are not very important in nanosecond switching studied here. The free layer has elliptical shape with size of nm 2 and thickness of 2.5 nm, which is TMR: 155% H c : 45 Oe; H off =30 Oe H (Oe) <I c >: 0.30 ma H off =30 Oe Fig. 4. Resistance as a function of the applied field and current for MgO MTJ sample. TMR of the sample is 155% and average switching current hi c i¼0:30 ma. Plot was obtained at current pulse width of 30 ms and applied field (offset field) of 30 Oe. 3838

5 subdivided into computational cells of size 5 5 2:5 nm 3. The height of the multilayer pillar is taken to be 100 nm for Oersted field calculation. 26) These dimensions and the value of M S ¼ 900 emu/cm 3 give approximately thermal stability of 60 and effective uniaxial anisotropy field H K ¼ H shape K þ HK int 120 Oe. One important parameter that determines the magnetization pattern during switching is the exchange length: sffiffiffiffiffiffiffiffiffiffiffiffi 2A l ex ¼ 0 MS 2 ; ð4þ where A is the exchange stiffness constant. In the simulation we have used two different values of exchange length l ex ¼ 4:4 nm (A ¼ J/m, M S ¼ 900 emu/cm 3 ) and l ex ¼ 5:4 nm (A ¼ 1: J/m, M S ¼ 900 emu/cm 3 or A ¼ J/m, M S ¼ 750 emu/cm 3 ) and compared the results. The switching current is very sensitive to the value of M S as can be seen from eq. (1) providing a means to decrease the switching current by using low-m S -materials, 8) which increases the value of exchange length. However, in the simulation rather than using lower value of M S we have used a higher value of exchange stiffness in order not to change the aspect ratio of the ellipse (to accommodate decreased anisotropy field) to look exclusively at the influence of the exchange length rather than combined effect of modified aspect ratio and exchange length. For fast switching in nanosecond regime, the initial condition of the free layer magnetization is very important. 27) For elliptical shapes the average magnetization of the cell lies along the long (easy) axis of the ellipse as shown on Fig. 5 and the initial spin transfer torque proportional to sin where is the angle between the local magnetization vector and the fixed magnetization direction of pinned layer (chosen to be along þx direction) is very small. The onset of precession and the initial motion of the magnetization in this case is created by non-uniform current-induced in-plane Oersted field (Fig. 6), which stimulates the magnetization precession at both ends A and B of the ellipse where the Oersted field is strong and approximately perpendicular to Fig. 5. Initial magnetization state for an elliptical free layer with size nm 2 and thickness of 2.5 nm for l ex ¼ 4:4 nm. The initial magnetization state for l ex ¼ 5:4 nm is very similar and not shown Fig. 6. Oersted field in free layer in the form of ellipse. The Oersted field increases almost linearly with the distance from the center. For parts A and B (grey area) of the ellipse the torque acting on the magnetization due to Oersted field is the highest, whereas it is very small for the central part C of the figure. the local magnetization as shown on Fig. 5, however creating very marginal torque at the central region C where either the field is small (center) or the angle between the field and local magnetization is small (boundary parts of central region). As a result, the Oersted field drives the onset of precession in the end domains of the ellipse, which is amplified by the spin-transfer torque, creating the C-type state of the magnetization as shown on Fig. 9. Moreover, as the amplitude of end domain precession increases, the central region of the ellipse still experiences very little torque and is in a minimum energy state when the magnetization of this region is aligned in the long direction of the ellipse. This energy minimum is created by effective local field, which due to the mirror symmetry of the C-state of the magnetization is along the long axis of the ellipse, creating pinning of the central region. In order to cause the switching of the magnetization, the induced symmetry of the magnetization distribution needs to be overcome. As a result, the average magnetization experiences large amplitude precession shown on Figs. 7 and 8 for two different values of exchange length even becoming negative whereas the central region of the ellipse still has the magnetization pointing in the original direction. This effective pinning of the central region limits the device performance and introduces dependence on the variation in shape, size, and defects due to fabrication process, which affects the symmetry of the magnetization distribution and consequently the time required to break-up the symmetry and cause the switching. This is nicely seen from Figs. 7 and 8: the system with higher exchange (stronger central region pinning) is slower to switch. Figure 9 shows a series of magnetization state snapshots observed during spin-transfer driven switching with current applied at t ¼ 0 ns. The initial precession takes the form of magnetization precessing between two C states (clockwise and counterclockwise). The spin transfer torque acts to increase the amplitude of the precession. At t ¼ 1:08 ns a clearly visible 180 -domain wall is formed at both halves

6 (c) - - time, ns Fig. 7. Switching curves for elliptical free layer for l ex ¼ 4:4 nm and J ¼ 11 MA/cm 2, J ¼ 9 MA/cm 2, and (c) J ¼ 8 MA/cm 2. Note that the switching time for J ¼ 11 and 9 MA/cm 2 is approximately the same (c) - - time, ns Fig. 8. Switching curves for elliptical free layer for l ex ¼ 5:4 nm and J ¼ 16 MA/cm 2, J ¼ 14 MA/cm 2, and (c) J ¼ 12 MA/cm 2. of the ellipse. The central region has the magnetization pointing in the original direction for 2 ns until it finally switches causing the magnetization reversal of the free layer. The switching time is defined as the time at which average reduced magnetization component along X axis is equal to zero for the last time before it switches to 1. The switching time thus defined is a good approximation to the minimal pulse width required to switch the system as was confirmed by simulations with different pulse widths at fixed amplitude of the current. As has been seen, the detailed dynamics of switching due to spin transfer and the role of Oersted field complicates optimization of the element shape. Further experiments are in progress and the relevant data will be published in a separate paper. 4. Spin Transfer for Advanced MRAM Application As can be seen above, spin transfer switching provides an excellent write scheme for STT-RAM with low power consumption, fast read and write time (nanosecond regime), 3840 Fig. 9. Snapshots of free layer magnetization during switching for elliptical shape. The numbers near snapshots represent the time the snapshots were taken. The switching current was applied at t ¼ 0 ns Gb/cm 2 100Mb/cm 2 MRAM J c0 =5x10 6 A/cm 2 STTRAM J c0 =1x10 6 A/cm Magnetic Cell Width (nm) Fig. 10. Scaling of write current with magnetic cell width for conventional MRAM and STT-RAM spin-transfer switching. J c0 1 and A/cm 2 together with thermal factor of 60 is used in STT calculation. A distance of 0.4 mm between the clad word line and magnetic cell is used in the field switching case. and excellent scalability. Figure 10 provides a comparison of scaling of write current with magnetic cell size for magnetic-field writing and writing using spin transfer torque. STT-RAM exhibits an excellent scalability in term of write current, showing more than 10 write current reduction at 65 nm nodes as compared to the current induced magnetic field writing for conventional MRAM. In addition to low power consumption, STT-RAM has also simpler magnetic cell architecture by eliminating the word line and bypass

7 line, 5) enabling much smaller memory bit cell size (possibly as small as 6 F 2 compared to 20 F 2 for conventional MRAM with 1T-1MTJ design). In summary, spin transfer torque RAM (STT-RAM) combined with newly observed high-tmr MgO MTJs 16 23) provides an excellent path to realize Gbit-scale STT-RAM with very low power consumption and very fast write and read access time (few ns). The excellent intrinsic STT-RAM attributes are not only attractive for replacing non-volatile memory products, but also for random access memory (RAM) such as SRAM and DRAM without stand-by current for wireless and embedded applications. 5. Conclusions This work discusses several ways to decrease the switching current in order to implement spin transfer switching as a writing scheme in STT-RAM. Introduction of dual structures with additional pinned layer on top of the free layer provides additional spin transfer torque on the free layer due to the spin-polarized current from the top pinned layer. Experimental results show 3 decrease of the intrinsic switching current in double structure with AlO x tunneling barrier (J c0 2: A/cm 2 ) as compared to single AlO x MTJ (J c A/cm 2 ). Another way to decrease the switching current by introduction of crystalline MgO barrier in MTJ pillar provides 3 reduction as compared to AlO x MTJ achieving low ð2{3þ10 6 A/cm 2 intrinsic switching current. Micromagnetic simulation was performed to study the fast switching. It was shown that the Oersted field is critical to onset of precession and switching. Strong exchange in the free layer was shown to have negative impact on the switching behavior by increasing the stability of the central region of the free layer. 1) J. C. Slonczewski: J. Magn. Magn. Mater. 159 (1996) L1. 2) L. Berger: Phys. Rev. B 54 (1996) ) F. J. Albert, J. A. Katine, R. A. Buhrmann and D. C. Ralph: Appl. Phys. Lett. 77 (2000) ) Y. Huai, F. Albert, P. Nguyen, M. Pakala and T. Valet: Appl. Phys. Lett. 84 (2004) ) Y. Huai: News Mag. Taiwan Inf. Storage Assoc. (Dec, 2004) 75. 6) J. Z. Sun: Phys. Rev. B 62 (2000) ) A. A. Tulapurkar, T. Devolder, K. Yagami, P. Crozat, C. Chappert, A. Fukushima and Y. Suzuki: Appl. Phys. Lett. 85 (2004) ) K. Yagami, A. A. Tulapurkar, A. Fukushima and Y. Suzuki: Appl. Phys. Lett. 85 (2004) ) Y. Huai, M. Pakala, Z. Diao and Y. Ding: Appl. Phys. Lett. 87 (2005) ) Y. Huai, M. Pakala, Z. Diao and Y. Ding: IEEE Trans. Magn. 41 (2005) 2621; M. Pakala, Y. Huai, T. Valet, Y. Ding and Z. Diao: J. Appl. Phys. 98 (2005) ) D. M. Apalkov and P. Visscher: Phys. Rev. B 72 (2005) ) Z. Li and S. Zhang: Phys. Rev. B 69 (2004) ) E. B. Myers, F. J. Albert, J. C. Sankey, E. Bonet, R. A. Buhrman and D. C. Ralph: Phys. Rev. Lett. 89 (2002) ) T. Valet: Grandis Inc. Rep. 3 (2004). 15) Y. Tserkovnyak, A. Brataas and G. Bauer: Phys. Rev. B 67 (2003) ) D. D. Djayaprawira, K. Tsunekawa, M. Nagai, H. Maehara, S. Yamagata, N. Watanabe, S. Yuasa, Y. Suzuki and K. Ando: Appl. Phys. Lett. 86 (2005) ) S. S. P. Parkin, C. Kaiser, A. Panchula, P. M. Rice, B. Hughes, M. Samant and S. H. Yang: Nat. Mater. 3 (2004) ) S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki and K. Ando: Nat. Mater. 3 (2004) ) J. Hayakawa, S. Ikeda, F. Matsukura, H. Takahashi and H. Ohno: Jpn. J. Appl. Phys. 44 (2005) L ) S. Ikeda, J. Hayakawa, Y. M. Lee, R. Sasaki, T. Meguro, F. Matsukura and H. Ohno: Jpn. J. Appl. Phys. 44 (2005) L ) Z. Diao, D. M. Apalkov, M. Pakala, A. Panchula and Y. Huai: Appl. Phys. Lett. 87 (2005) ) H. Kubota, A. Fukushima, Y. Ootani, S. Yuasa, K. Ando, H. Maehara, K. Tsunekawa, D. D. Djayaprawira, N. Watanabe and Y. Suzuki: Jpn. J. Appl. Phys. 44 (2005) L ) J. Hayakawa, S. Ikeda, Y. M. Lee, R. Sasaki, T. Meguro, F. Matsukura, H. Takahashi and H. Ohno: Jpn. J. Appl. Phys. 44 (2005) L ) K. Ito: IEEE Trans. Magn. 41 (2005) ) P. B. Visscher and D. M. Apalkov: preprint at ~visscher/mumag/cart.pdf. 26) J. G. Deak: J. Appl. Phys. 97 (2005) 10E ) D. Apalkov, M. Pakala and Y. Huai: to be published in J. Appl. Phys. 99 (2006). 3841