APPLIED PHYSICS LETTERS 89, 252505 共2006兲
Temperature dependence of intrinsic switching current of a Co nanomagnet T. Yang,a兲 A. Hirohata, and M. Hara Frontier Research System, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
T. Kimura and Y. Otani Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 227-8581, Japan and Frontier Research System, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
共Received 22 September 2006; accepted 15 November 2006; published online 20 December 2006兲 The temperature dependence of the switching current of a magnetic nanopillar is investigated from 10 to 290 K. According to the switching probability measurement with the pulsed current, and the differential resistance measurement with sweeping the dc current, the intrinsic switching currents increase with decreasing the temperature. Transport calculations show that this temperature dependence is closely related to the reduced spin accumulation and spin polarization of the electrical current at low temperatures, attributed to the varied transport parameters. The conclusion is in accordance with the temperature dependence of the resistance difference between antiparallel and parallel magnetic configurations. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2420789兴 The spin-transfer-induced magnetization switching has been extensively studied1–7 since the theoretical predictions.8,9 The basic mechanism is that the transverse spin angular momentum is transferred to the local magnetic moment when a spin current traverses a magnet. Thus a spin torque is applied on the local magnetic moment, initiating the magnetization precession and finally the magnetization switching when the spin torque overcomes the magnetic damping. Most of the studies were carried out at room temperature 共RT兲 with a nanopillar structure including a ferromagnet 共FM兲/nonmagnet/FM trilayer, whose switching behavior has also been revealed to be significantly affected by the thermal activation.10–12 For a thermally activated switching process under the existence of a dc current I, the relaxation time can be written as11,12
= 0 exp关共1 − I/IC0兲Eb/kBT兴,
共1兲
where IC0, Eb, and 0 = 1 / f 0 are the intrinsic critical switching current, the energy barrier, and the inverse of the attempt frequency f 0 共=109 Hz兲, respectively. The intrinsic switching current is the current to realize a switching completely through uniform precession, very important for both the mechanism study and the practical application. Equation 共1兲 can also be written as I = IC0关1 − 共kBT/Eb兲ln共 f 0兲兴.
共2兲
With the linear relationship between I and ln共 f 0兲, Eq. 共2兲 provides a convenient way to estimate the intrinsic switching current. By approximately replacing with the width of a pulsed current, the intrinsic switching current13,14 and its temperature dependence15 between 100 and 300 K have been studied with pulsed currents longer than 1 s. The intrinsic switching current was observed to increase with reducing the temperature, contradict to the results obtained by measuring the switching rate with pulsed currents of several nanoseconds or shorter.15 On the other hand, another report measuring the switching rate between 4.2 and 160 K supports the increased switching current at a reduced temperature.16 For the possible application at low a兲
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temperatures,15 further experimental investigations and explanations are still absent for the temperature dependence of current-induced magnetization switching. With the pulsed current, we measured the intrinsic switching current of a magnetic nanopillar in a wide temperature range from 10 to 290 K. Different from previous reports replacing with the pulse width, the relaxation time in our measurement is evaluated with = −t / ln共1 − p兲,12 where t is the pulse width and p is the switching probability under a pulsed current of t. Thus, Eq. 共2兲 is transformed into I = IC0兵1 − 共kBT/Eb兲ln关− tf 0/ln共1 − p兲兴其.
共3兲
With pulse widths from 10 s to 1 s, the switching probability is measured at varied pulsed current amplitude I. Then, the intrinsic switching current is estimated utilizing the linear relationship between I and ln关−tf 0 / ln共1 − p兲兴. The measured magnetic nanopillar device has the layered structure of 共Cu共60 nm兲/Co 共20 nm兲/Cu 共6.5 nm兲/Co 共2.5 nm兲/Au 共20 nm兲. The fabrication process is described in a previous report.17 Besides the measurement with the pulsed current, the differential resistance loop dV / dI ⬃ Idc is also measured at each temperature by sweeping the dc current Idc at a step of 0.2 mA, as plotted in Fig. 1共a兲. The measuring time at each dc current is 2 s. It can be seen from Fig. 1共b兲 that the resis-
FIG. 1. 共a兲 dV / dI loops at various temperatures measured with sweeping the dc current. 关共b兲 and 共c兲兴 are the temperature dependences of resistance and ⌬R, respectively.
0003-6951/2006/89共25兲/252505/3/$23.00 89, 252505-1 © 2006 American Institute of Physics Downloaded 20 Dec 2006 to 134.160.214.75. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
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FIG. 2. Dependence of I on ln关−tf 0 / ln共1 − p兲兴 at various temperatures. The dashed lines are the linearly fitted straight lines.
tance of the nanopillar is decreased almost linearly as the temperature is reduced. On the other hand, the resistance difference ⌬R between the antiparallel 共AP兲 and parallel 共P兲 states shown in Fig. 1共c兲 is almost unvaried until the temperature is reduced to 160 K. After that, a decreasing can be observed. For the measurement with the pulsed current, a large opposite pulsed current of 12 mA and 1 s is firstly applied to initialize the sample, and then a pulse with varied width and amplitude is applied to switch the sample. Finally, the resistance is measured with a small ac current. For each pulsed current, the measurement is repeated for 200 times to obtain a stable switching probability. The pulsed current amplitude I is plotted in Fig. 2 as the function of ln关−tf 0 / ln共1 − p兲兴 for each temperature. The linear fitting is carried out to obtain the intrinsic switching current IC0, i.e., the intercept with the vertical axis. The temperature dependences of IC0 and IC, the switching current determined from the dV / dI ⬃ Idc loop, are shown in Fig. 3共a兲. With decreasing the temperature, either 兩IC0兩 or 兩IC兩 shows an initial slight increase, followed by a rapid increase for T ⬍ 160 K. Surprising is that the difference between them is also increased with reducing the temperature. Due to the thermal effect, 兩IC兩 should be lower than 兩IC0兩. However, with decreasing the temperature, the thermal effect should become smaller and smaller, therefore IC should become closer and closer to IC0. To explain this abnormal result, the energy barrier Eb for the switching is estimated from the slope of the fitted straight line in Fig. 2 for each measuring temperature,
Appl. Phys. Lett. 89, 252505 共2006兲
and shown in Fig. 3共b兲. More surprisingly, the estimated energy barrier is found to scale down with the temperature for both AP to P and P to AP switches. Because Eb mainly comes from the shape anisotropy energy of the switched nanomagnet, which should not decrease as the temperature is reduced, the result in Fig. 3共b兲 is apparently incorrect. If we check the data in Fig. 2 carefully, we can find that the data points for each temperature, in fact, constitute a downward concave curve rather than a straight line, as replotted in Fig. 3共c兲 in different scales. In addition, with decreasing the temperature, the deviation from a straight line increases. Such a deviation is unlikely caused by the Joule heating. It has been theoretically reported11 that the pure thermal activation occurs only when I Ⰶ IC0. When I Ⰷ IC0, the switching is realized completely through the uniform magnetization precession. In between the two asymptotic limits, the mixing mechanisms take effect. The deviation from a pure thermal activation process results in the increased I at a small and hence the deviation from the linear relationship between I and ln关−tf 0 / ln共1 − p兲兴. Therefore the slope of the fitted straight line is increased, giving rise to an overestimated IC0 and an underestimated Eb. The results in Fig. 3 suggest that the role of the thermal activation in the switching is weakened at low temperatures. Even at 290 K and with Ⰷ 0, the deviation from a straight line is small but still observable in Fig. 3共c兲. Thus, it should be very careful when estimating the intrinsic switching current and the energy barrier with Eq. 共2兲. Despite the deviation in the measured intrinsic switching current, it is true that the real intrinsic switching current should be between IC0 and IC shown in Fig. 3共a兲, as schematically indicated by the solid lines. At higher temperatures, it is closer to IC0. At lower temperatures, it is closer to IC. Therefore, it can still be concluded from Fig. 3共a兲 that the intrinsic switching current is almost temperature independent for T ⬎ 160 K, and increases significantly with reducing the temperature for T ⬍ 160 K. The oxide on the sidewall has been suggested to increase the damping coefficient, and thus be responsible for the temperature dependence of the intrinsic switching current of a permalloy nanomagnet measured between 4.2 and 160 K.16 The same mechanism may also be applicable to our Co nanomagnet. However, there is another important mechanism to be considered, i.e., the transport parameters at a low temperature are much different from those at RT. Both the conductivity and the spin-diffusion length of a metal are significantly increased at 4.2 K compared to their values at room temperature.18,19 Different transport parameters lead to different spin accumulations and spin polarizations of the electrical current, producing different spin currents to switch the nanomagnet. Therefore, the intrinsic switching currents are also different. To check this effect, calculations of spin accumulation and spin polarization are carried out based on the one-dimensional spin diffusive equation with the transport parameters at 300/ 4.2 K:17–19 electric conductivities Cu = 3.5/ 7.1⫻ 107 ⍀−1 m−1, Au = 3.0/ 6.0⫻ 107 ⍀−1 m−1, and Co = 4.2/ 7.3⫻ 106 ⍀−1 m−1; spin-diffusion lengths Cu = 350/ 1000 nm, Au = 35/ 105 nm, and Co = 38/ 59 nm; Co spin asymmetry  = 0.36/ 0.36. The interfacial spin asymmetries ␥Co/Cu = 0.76 and ␥Co/Au = 0.85, as well as the interfa* * cial resistances rCo/Cu = 0.5 f⍀ m2 and rCo/Au = 0.56 f⍀ m2, are assumed to be independent on the temperature.17,18
FIG. 3. Temperature dependences of 共a兲 the switching current and 共b兲 the estimated energy barrier. Shown in 共c兲 are data in Fig. 2 replotted in different scales. Each straight line in 共c兲 is just a guide to eye. Downloaded 20 Dec 2006 to 134.160.214.75. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
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veal that the temperature dependence of the transport parameter is an important mechanism to the temperature dependence of the intrinsic switching current, supported by the result of ⌬R.
FIG. 4. Calculated 共a兲 spin polarization curves and 共b兲 spin accumulation curves at 4.2 K and RT. The dashed lines indicate the active Co/ Cu interface for spin transfer.
Figure 4 shows the calculated spin accumulation ⌬ and spin polarization JS for the P state when the electrical current is 1 A / m2. It is clear that both the spin polarization and the spin accumulation are reduced at 4.2 K. Hence, the spin current is reduced, increasing the intrinsic switching current. Similar results are obtained for the AP state. Therefore, the temperature dependence of the transport parameter significantly affects the temperature dependence of the intrinsic switching current. This mechanism is also supported by the temperature dependence of ⌬R, decided only by the transport parameters. According to the calculated electrochemical potential, theoretically ⌬R at RT is about 1.4 times as large as that at 4.2 K, roughly in agreement with the experimental results shown in Fig. 1共c兲. Notably is that the measured ⌬R starts to decrease at 160 K with reducing the temperature from RT to 10 K. On the other hand, it is also at 160 K that the intrinsic switching current starts to increase significantly. Such an agreement supports the mechanism that the temperature dependence of the transport parameter is important to the temperature dependence of the intrinsic switching current. In summary, we investigated the intrinsic switching current of a magnetic nanopillar from 10 to 290 K by measuring the switching probability. It is observed that the intrinsic switching current shows a significant increase with reducing the temperature when T ⬍ 160 K. Transport calculations re-
The authors are grateful to Tsukagoshi and the Nanoscience Development and Support Team of RIKEN for their great supports. 1
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