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Switching field modulation of a nanomagnet by resonant microwave spin torque
Journal of Magnetism and Magnetic Materials 322 (2010) 3320–3323
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Switching field modulation of a nanomagnet by resonant microwave spin torque N. Biziere n, E. Mure , J-Ph. Ansermet Institut de Physique de la Matie re Condense´e, Ecole Polytechnique Fe´de´rale de Lausanne, EPFL, Station 3, CH-1015 Lausanne, Switzerland
a r t i c l e in f o
a b s t r a c t
Article history: Received 17 February 2010 Received in revised form 28 March 2010 Available online 9 June 2010
We report on the effect of a low amplitude microwave current on the switching field of magnetic layers in a 40 nm diameter pseudo-spin valve grown by template synthesis. We show a frequency dependence at room temperature reflecting the dynamic behavior of the switching process. This is confirmed by numerical calculation of the Landau–Lifschitz–Gilbert equation including Slonczewski Spin Transfer Torque term within a macrospin approximation. The possibility to modulate the switching fields of a nanomagnet with microwave currents offers an alternative to the magnetic switching assisted by microwave magnetic field. & 2010 Elsevier B.V. All rights reserved.
Keywords: Spin transfer torque Magnetic switching Spin dynamic
1. Introduction Future developments in magnetic data storage devices like magnetic random access memory (MRAM) and sensor applications imply the control of magnetization switching in nanomagnets on a very short timescale and with low power consumption. This issue is currently attracting much attention, and the mechanisms implied in the magnetization dynamics during the switching (coherent rotation, vortex core switching, domain wall propagation, etc.) are still open questions, as shown by the important number of experimental [1–4] and simulation studies [5–8]. In particular, it has been demonstrated that microwave magnetic fields decrease the static field required to flip the magnetization as they increase the precession angle of the magnetization prior to the switching process. In the last decade, pulsed or continuous high density spin polarized current has been proven to be able to switch the magnetization of the free layer in giant magneto resistive (GMR) or tunnel magneto resistive (TMR) sensors [9–11] by the spin transfer torque (STT) effect [12,13]. Recently, the combination of microwave (MW) and square-wave current pulses has been shown to decrease significantly the switching times at 20 K [14]. Moreover, spin wave modes of an individual nanomagnet have been excited by means of MW electrical currents [15–17]. These experiments open new perspectives for manipulating the magnetization at nanoscale with microwaves. We report experimental evidence of the effect of a continuous microwave current in the range 1–20 GHz on the amplitude of the
n
Corresponding author. E-mail address: [email protected] (N. Biziere).
0304-8853/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2010.06.016
switching field of magnetic layers in a pseudo-spin valve structure at room temperature. We demonstrate that the value of the switching field depends on the frequency of the microwave. Results are explained in terms of the non-linear dynamic response of the magnetization to the STT. Similarly to a microwave magnetic field, the microwave current increases the cone angle of the magnetization precession which is initially activated by thermal fluctuation. We expect this process to be frequency dependent because of the dynamic behavior of the switching. This assumption is supported by numerical integration of the Landau– Lifschitz–Gilbert equation within a macrospin approximation, including the Slonczewski spin torque term. Samples studied are Cu(2 mm)/Co(5 nm)/Cu(5 nm)/Co(40 nm)/Cu(4 mm) trilayers embedded into a 6 mm thick ion-track-etched polycarbonate commercial membranes. The pores have a diameter of about 40 nm. Nanowires are electroplated in the pores of the membrane from a single bath of 0.5 M/l CoSO4, 0.01 M/l CuSO4, and 0.7 M/l H3BO3. The nanowires grow on a thick gold layer sputtered on one side of the membrane. Then, samples are placed into a homemade sample holder, contacting electrically the top of one or a few nanowires, with a procedure similar to point contact geometry. Details about the growth [18] and contact procedures are described elsewhere [19].
2. Experimental results The GMR of the pseudo-spin valve is recorded by a usual lockin technique as a function of the external magnetic field. The amplitude of the lock-in current is 20 mA and its frequency is 413 Hz. Measurements are performed with and without a microwave current injected into the nanowire through a Bias
N. Biziere et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3320–3323
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Tee. We adjust the amplitude of the AC current so that it induces by Joule heating an increase of the average resistance of 1.2–1.4 O in the parallel configuration at each frequency. The AC current is large enough to cause a rise of the sample temperature due to Joule heating of about 5 K. The rms value of the current IAC is of about 100 mA and is calibrated by checking what DC current produces an equal resistance rise. Each scan is repeated ten times with and without AC current alternately in order to check the reproducibility of the effects and estimate the most probable amplitude of the switching field. About twenty nanowires have been measured showing similar behavior. Due to the instability of the contact to the nanowire and the acquisition time for each GMR curve, a full set of frequencies and power values could not be applied to each sample. Results reported here were obtained with two different samples measured with a magnetic field parallel or perpendicular to the plane of the membrane. Fig. 1a shows the GMR of a single nanowire recorded without AC current. The external magnetic field H0 is applied perpendicularly to the plane of the membrane. Mechanical instability of the electrical contact procedure prevents the sample from being rotated once it is in place. Then GMR measurements as a function of the angle of the applied field cannot be performed. As a consequence there is an average uncertainty about the relative angle between the applied field and the nanowire axis. Studies performed in our group [20] have shown that this angle can be up to 301 due to the average orientation of the pores in the membrane. The field is scanned from negative to positive saturation. We define the soft and the hard layers as the one with the smallest (Hsw1) and highest (Hsw2) switching field amplitudes, respectively. As the out of plane demagnetizing factor is bigger for the thin layer, we assume the thin and thick cobalt layers correspond to the hard and soft layers, respectively. Furthermore, simulations (not presented here) showed that a relative angle of 601 between the applied field and the thin layer plane can account for the value of the switching field of the thin layer.
Fig. 1b–d shows the GMR of the sample recorded with microwave currents at different frequencies fAC. Unfortunately, we could not perform measurements for each frequency in the (1–16 GHz) range and only currents with few different frequencies have been injected in this sample. We observe that Hsw2 decreases from 115to 80 mT when fAC ¼3 GHz (Fig. 1b) whereas Hsw1 decreases from 55 to 37 mT when fAC ¼13 GHz (Fig. 1d). The small change of Hsw1 in Fig. 1b is within the uncertainty of the measurements estimated by the ten GMR curves recorded without AC current. Fig. 1c shows the normalised resistance of the trilayer for different values of fAC. Since the Joule heating of the sample is set to be the same for all measurements, it cannot be responsible for the relative modification of the switching fields. All these results clearly demonstrate that the switching field of the soft or hard layers can be tuned independently by a MW current and that the MW frequency plays a key role in determining the amplitude of Hsw1 and Hsw2. We point out that changes of Hsw1, which we assume to correspond to the thicker layer switching field, was only observed at 11 (not shown) and 13 GHz for IAC ¼100 mA. As the spin torque efficiency strongly depends on the volume of the magnetic layer, we expect the thick layer to be less perturbed by the microwave current. This is confirmed experimentally for most of the current frequencies for which we did not observe any change of Hsw1. Nevertheless, the switching observed at these two particular frequencies, much higher than what is expected for the uniform precession mode of the thick layer, could be a proof that some spatially non-uniform dynamic modes, depending on the magnetic profile in the layer, are more efficient to switch the magnetization (see discussion below). Similar results were observed on a sample for which the applied magnetic field lies approximately within the plane of the membrane (Fig. 2a). The field is scanned from positive to negative saturation. The soft layer, which presents the smallest switching field amplitude Hsw1, corresponds to the thin layer due to its
Fig. 1. (a) GMR, magnetic field applied roughly perpendicular to the plane of the membrane (arrows: direction of the field sweep). (b) and (d) GMR recorded with microwave currents IAC at 3 GHz (red curve) and 13 GHz (blue curve), respectively, or without it (black curve) (blue arrow: direction of the field sweep from negative to positive saturation). Hsw1 and Hsw2 in (b) correspond to the value of the switching field of the soft and hard layers, respectively. (c) Normalised GMR with IAC at different frequencies. (blue arrow: direction of the field sweep from negative to positive saturation) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. (a) GMR, magnetic field applied perpendicular to the nanowire axis with (red curve) and without (black curve) IAC at 2 GHz (blue arrow: direction of the field sweep). Hsw1 and Hsw2 correspond to the value of the switching field of the soft and hard layers, respectively. (b) Maximum DH (square) and its standard deviation (bars) of the thin layer as a function of the frequency of IAC. The line is a guide for the eyes. The black square at 10 mT for fAC ¼ 11 GHz corresponds to 3 DH measured over the ten scans. (c) GMR for different microwave powers at 6 GHz. The blue curve was recorded at the end of the set of measurements. (blue arrow: direction of the field sweep from positive to negative saturation) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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bigger in plane anisotropy. The soft layer switches slightly before zero field because of the dipolar interactions between layers. A minor hysteresis loop performed by scanning the field from positive saturation to zero field then back to positive saturation allows estimating the coercive field of the thin layer to be about 60 mT and the dipolar field on the thin layer to be about 80–90 mT. The relatively large value of Hsw2 can be accounted for assuming an elliptic cylindrical shape of the thick layer, which is reasonable, given the uncertainty about the shape and dimensions of the layers. In this magnetic configuration and for IAC of 100 mA, only changes for Hsw1 were observed. We measured the difference DH between switching fields with and without microwave current (Fig. 2b). The spread in the data reported for measurements done at 11 GHz is as follows: 7 scans yielded similar large DH whereas 3 scans showed much smaller DH. We clearly observe that the DH value is more important for fAC ¼1.5, 2 and 11 GHz than for other frequencies. The highest value of DH of about 75 mT corresponds to a value of H0 that compensate the dipolar field induced by the thick layer (the average applied field is then close to zero). In both magnetic configurations of Figs. 1 and 2, we observe that current frequencies up to 3–4 GHz seem to be quite efficient to switch the thin layer magnetization at different values of H0. However, we also observe that some higher frequencies (for example 8 GHz in Fig. 1c and 11 GHz in Fig. 2b) allow the switching. We also observe a saturation of the effect with the microwave power (Fig. 2c), as expected for non-linear resonant processes.
3. Discussion In order to get a better understanding of these experimental results, we study the thin layer dynamics in presence of a MW current by solving numerically the Landau–Lifschitz–Gilbert (LLG) equation including the spin transfer torque @m @m ¼ gm Heff þ am þ aj cosðoAC tÞm m p @t @t
ð1Þ
where m is the thin layer magnetization vector, p is the unit vector defining the direction of the thick layer (that we consider as pinned in the calculation), Heff is the effective field comprising the applied and anisotropy fields, g (2.21 105 (A/m) 1 s 1) and a (0.03) are the gyromagnetic ratio and the damping coefficient, respectively, aj is the spin torque coefficient defined in Ref. [12] and proportional to the current density, oAC is the current pulsation. As the size of our system is very small, it is reasonable to apply the macrospin approximation. Simulations in the macrospin approximation can help to understand qualitatively the basic processes involved in the microwave current assisted switching. Calculations are performed in a very ideal case of a small ellipsoid, uniformly magnetized. The dimensions of the thin layer are set to be 40 30 5 nm3 to account for a small ellipticity that can appear in electrodeposited nanowires. Numerical calculations are performed in a similar magnetic configuration as the one encountered in Fig. 1. The x and y directions are aligned with the short and long axis of the ellipse, respectively. The field is applied in the yz plane, with an arbitrary angle of 201 with respect to the z-axis. Before solving the LLG equation, the equilibrium positions of the thin and thick layer magnetizations are calculated by minimizing the free energy. Fig. 3a presents the numerical results of the LLG integration when IAC ¼ 150 mA. Similarly to the experimental observation, the occurrence of switching at a given field depends critically on frequency. For example, at H0 ¼30 mT, switching occurs at 3 GHz, not at 2 GHz. We note high amplitude oscillations between 0 and 0.5 ns corresponding to the increase of the cone angle of the
Fig. 3. (a) Normalised my component of the thin layer magnetization for different values of fAC and H0. The field is applied with an angle of 201 with respect to the z-axis. (b) FMR frequency of the thin layer as a function of the applied field H0. (c) Angle dependence of the switching time at H0 ¼40 mT, fAC ¼3 GHz. The field is applied in the y direction.
precession due to the spin torque. Moreover, the higher the frequency, the lower is the switching field amplitude. For example, when fAC ¼3 GHz, switching occurs when H0 ¼30 mT, whereas switching occurs at 2 GHz for H0 ¼45 mT. The decrease of the current frequency needed to switch the magnetization when increase in the field is coherent with the frequency dependence of the spin dynamic modes on H0. As an example, we calculate the ferromagnetic resonance (FMR) frequency of the thin layer as a function of the applied field (Fig. 3b) in the field range of interest. We observe a decrease of the FMR frequency until the magnetization switches around 95 mT. Within this macrospin approximation, we note that the frequency of the current allowing switching is smaller than the FMR frequency. However, this is expected since switching implies high precession angles of the magnetization. It corresponds to a highly non-linear dynamic state for which it is well known that frequencies are well below the FMR frequencies [21] (which corresponds to a small angle of precession around the equilibrium position). The process of non-linear excitation of a quasi-uniform mode agrees well with the experimental results presented in Figs. 1 and 2. Indeed the maximum FMR frequency, in the field range for which assisted switching of the thin layer appears is expected to be at most 4 or 5 GHz. This range was evaluated taking into account the different uncertainties about the shape and dimensions of the thin layer. Then, the maximum frequencies which are efficient for switching the magnetization in the non-linear regime are expected to be at most around 3 or 4 GHz. A rough estimation of the non-linear resonant frequency can be given by E0.8oFMR, see Ref. [22] and reference therein for more details. Indeed, we observe switching for frequencies up to 3 GHz in Fig. 1c. Moreover, as observed in Fig. 1c for fAC ¼1–3 GHz and in Fig. 2b for fAC ¼1.5 and 2 GHz, the DH value reflects the dependence of FMR frequency vs. field (taking into account the sum of the applied and dipolar field on the thin layer in Fig. 2). According to this assumption it would be surprising that frequencies in the 3–5 GHz range seem to be quite inefficient to switch the magnetization in the ‘‘in plane’’ configuration of Fig. 2b. In order to understand this point, one has to consider the amplitude of the dipolar coupling between the hard and free
N. Biziere et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3320–3323
layer. The minor hysteresis loop performed on this sample allows estimating that for H0 below E80 mT, the effective field applied to the thin layer points in the opposite direction of the magnetization and increases as H0 decreases. For fAC ¼2 GHz, switching occurs at H0 about 80 mT (the effective applied field to the thin layer is then close to zero). Then, 2 GHz seems to be close to the maximum current frequency inducing switching within the macrospin assumption. In Fig. 1c we observe that the difference of Hsw2 for fAC between 1 and 3 GHz is about 10 mT. This is roughly half the difference that could be expected from the FMR vs field dependence. One possible explanation is related to the efficiency of the spin transfer torque with respect to the relative angle between both layer magnetizations. Indeed, as explained in Ref. [14], as long as the precession angle of the thin layer is smaller than the relative average angle between both layers, the sign of the spin torque always acts to push away the thin layer magnetization from the thick one, leading to an increase of the precession angle until the magnetization switches. It means that for very small angles between layers, resonant spin torque is not fully efficient to switch the magnetization. For fAC ¼3 GHz, switching occurs when the relative angle between layers is about 1501 whereas it could be expected at a field corresponding to a relative angle of 1701. This assumption is confirmed by calculating the LLG equation for two different relative orientations of both magnetic layers (Fig. 3c). This point is particularly important for sensors applications since it shows that magnetic layers with crossed anisotropies are more efficient to increase the switching probability induced by the microwave current. Finally we would like to discuss the high DH value observed at frequencies up to 11 GHz in Fig. 2b and 8 GHz in Fig. 1c since it cannot be accounted for by the non-linear uniform excitation of the magnetization. Then, we assume that switching at these particular high frequencies occurs through the excitation of spatially non-uniform modes. Indeed, it has been shown in Ref. [19] that the spin wave spectrum in a similar structure is extremely complex and can span a very broad frequency range. This assumption could also explain the spread in the data reported in Fig. 2b. Indeed, from one hysteresis loop to another, the static magnetization can present small differences, especially at the edge of the sample, leading to different dynamic modes with different frequencies. Then, we assume that the difference reported at 11 GHz in Fig. 2b reflects some small changes in the static configuration of the thin layer magnetization. A better understanding of this effect implies micromagnetic modeling for which a complete knowledge of the shape, size and orientations of the layers would be needed.
4. Conclusion To summarize, we showed the effectiveness of microwave current in switching at room temperature the magnetization of
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the magnetic layers in a pseudo-spin valve grown by template synthesis. The dependence of the switching field amplitude on the frequency of the microwave current is demonstrated experimentally. Our observations can be accounted for qualitatively in a simulation of the thin layer dynamics obtained by solving the LLG equation including a spin transfer torque for current frequencies below the FMR frequencies. Moreover, observations of switching at current frequencies up to 10 GHz indicate that the switching can occur through non-uniform spin wave modes. We believe that the ability to modulate the switching fields of nano spin valves by adjusting the microwave current frequency is very attractive for the development of low power consumption MRAMs and magnetic sensors.
Acknowledgement This work has been supported by the Swiss NSF, Grant no. 200020-117588.
References [1] G. Woltersdorf, C.H. Back, Phys. Rev. Lett. 99 (2007) 227207. [2] M. Laval, J.J. Bonnefois, J.F. Bobo, F. Issac, F. Boust, J. Appl. Phys. 105 (2009) 073912. [3] C. Thirion, W. Wernsdorfer, D. Mailly, Nature Mater. 2 (2003) 524. [4] H.T. Nembach, P. Martn Pimentel, S.J. Hermsdoerfer, B. Leven, B. Hillebrands, S.O. Demokritov, Appl. Phys. Lett. 90 (2007) 062503. [5] R. Yanes, R. Rozada, F. Garc a-Sanchez, O. Chubykalo-Fesenko, P. Martin Pimentel, B. Leven, and B. Hillebrands, arXiv: 0906.0263v1,(2009). [6] S. Okamoto, N. Kikuchi, O. Kitakami, Appl. Phys. Lett. 93 (2008) 142501. [7] Y. Nozaki, M. Ohta, N. Narita, K. Matsuyama, J. Appl. Phys. 105 (2009) 07B901. [8] G. Bertotti, I.D. Mayergoyz, C. Serpico, M. d’Aquino, R. Bonin, J. Appl. Phys. 105 (2009) 07B712. [9] J.A. Katine, F.J. Albert, R.A. Buhrman, E.B. Myers, D.C. Ralph, Phys. Rev. Lett. 84 (2000) 3149. [10] T. Devolder, P. Crozat, J.-V. Kim, C. Chappert, K. Ito, J.A. Katine, M.J. Carey, Appl. Phys. Lett. 88 (2006) 152502. [11] T. Aoki, Y. Ando, D. Watanabe, M. Oogane, T. Miyazaki, J. Appl. Phys. 103 (2008) 103911. [12] J.C. Slonczewski, J. Magn. Magn. Mater. 159 (1996) L1. [13] L. Berger, Phys. Rev. B. 54 (1996) 9353. [14] Y.-T. Cui, J.C. Sankey, C. Wang, K.V. Thadani, Z.-P. Li, R.A. Buhrman, D.C. Ralph, Phys. Rev. B. 77 (2008) 214440. [15] S.H. Florez, J.A. Katine, M. Carey, L. Folks, O. Ozatay, B.D. Terris, Phys. Rev. B. 78 (2008) 184403. [16] Jack C. Sankey, Yong-Tao Cui, Jonathan Z. Sun, John C. Slonczewski, Robert A. Buhrman, Daniel C. Ralph, Nature Phys. 4 (2008) 67. [17] W. Chen, J.M.L. Beaujour, G. de Loubens, A.D. Kent, J.Z. Sun, Appl. Phys. Lett. 92 (2008) 012507. [18] D. Doudin, A. Blondel, J.-P.h Ansermet, J. Appl. Phys. 79 (1996) 6090. [19] N. Biziere, E. Mur, J.-P.h Ansermet, Phys. Rev. B 79 (2009) 012404. [20] D. Doudin, J.E. Wegrowe, S.E. Gilbert, V. Scarani, D. Kelly, J.P. Meier, J.-P.h Ansermet, IEEE Trans. Magn. 34 (1998) 968. [21] H. Suhl, J. Phys. Chem. Solids 1 (1957) 209. [22] Thibaut Devolder, Hans Werner Schumacher, Claude Chappert, Precessional switching of thin nanomagnets with uniaxial anisotropy, in: B. Hillebrands, A. Thiaville (Eds.), Spin Dynamics in Confined Magnetic Structures III, Topics Applied Physics, 101, 2006, pp. 1–55.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Switching field modulation of a nanomagnet by resonant microwave spin torque N. Biziere n, E. Mure , J-Ph. Ansermet Institut de Physique de la Matie re Condense´e, Ecole Polytechnique Fe´de´rale de Lausanne, EPFL, Station 3, CH-1015 Lausanne, Switzerland
a r t i c l e in f o
a b s t r a c t
Article history: Received 17 February 2010 Received in revised form 28 March 2010 Available online 9 June 2010
We report on the effect of a low amplitude microwave current on the switching field of magnetic layers in a 40 nm diameter pseudo-spin valve grown by template synthesis. We show a frequency dependence at room temperature reflecting the dynamic behavior of the switching process. This is confirmed by numerical calculation of the Landau–Lifschitz–Gilbert equation including Slonczewski Spin Transfer Torque term within a macrospin approximation. The possibility to modulate the switching fields of a nanomagnet with microwave currents offers an alternative to the magnetic switching assisted by microwave magnetic field. & 2010 Elsevier B.V. All rights reserved.
Keywords: Spin transfer torque Magnetic switching Spin dynamic
1. Introduction Future developments in magnetic data storage devices like magnetic random access memory (MRAM) and sensor applications imply the control of magnetization switching in nanomagnets on a very short timescale and with low power consumption. This issue is currently attracting much attention, and the mechanisms implied in the magnetization dynamics during the switching (coherent rotation, vortex core switching, domain wall propagation, etc.) are still open questions, as shown by the important number of experimental [1–4] and simulation studies [5–8]. In particular, it has been demonstrated that microwave magnetic fields decrease the static field required to flip the magnetization as they increase the precession angle of the magnetization prior to the switching process. In the last decade, pulsed or continuous high density spin polarized current has been proven to be able to switch the magnetization of the free layer in giant magneto resistive (GMR) or tunnel magneto resistive (TMR) sensors [9–11] by the spin transfer torque (STT) effect [12,13]. Recently, the combination of microwave (MW) and square-wave current pulses has been shown to decrease significantly the switching times at 20 K [14]. Moreover, spin wave modes of an individual nanomagnet have been excited by means of MW electrical currents [15–17]. These experiments open new perspectives for manipulating the magnetization at nanoscale with microwaves. We report experimental evidence of the effect of a continuous microwave current in the range 1–20 GHz on the amplitude of the
n
Corresponding author. E-mail address: [email protected] (N. Biziere).
0304-8853/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2010.06.016
switching field of magnetic layers in a pseudo-spin valve structure at room temperature. We demonstrate that the value of the switching field depends on the frequency of the microwave. Results are explained in terms of the non-linear dynamic response of the magnetization to the STT. Similarly to a microwave magnetic field, the microwave current increases the cone angle of the magnetization precession which is initially activated by thermal fluctuation. We expect this process to be frequency dependent because of the dynamic behavior of the switching. This assumption is supported by numerical integration of the Landau– Lifschitz–Gilbert equation within a macrospin approximation, including the Slonczewski spin torque term. Samples studied are Cu(2 mm)/Co(5 nm)/Cu(5 nm)/Co(40 nm)/Cu(4 mm) trilayers embedded into a 6 mm thick ion-track-etched polycarbonate commercial membranes. The pores have a diameter of about 40 nm. Nanowires are electroplated in the pores of the membrane from a single bath of 0.5 M/l CoSO4, 0.01 M/l CuSO4, and 0.7 M/l H3BO3. The nanowires grow on a thick gold layer sputtered on one side of the membrane. Then, samples are placed into a homemade sample holder, contacting electrically the top of one or a few nanowires, with a procedure similar to point contact geometry. Details about the growth [18] and contact procedures are described elsewhere [19].
2. Experimental results The GMR of the pseudo-spin valve is recorded by a usual lockin technique as a function of the external magnetic field. The amplitude of the lock-in current is 20 mA and its frequency is 413 Hz. Measurements are performed with and without a microwave current injected into the nanowire through a Bias
N. Biziere et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3320–3323
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Tee. We adjust the amplitude of the AC current so that it induces by Joule heating an increase of the average resistance of 1.2–1.4 O in the parallel configuration at each frequency. The AC current is large enough to cause a rise of the sample temperature due to Joule heating of about 5 K. The rms value of the current IAC is of about 100 mA and is calibrated by checking what DC current produces an equal resistance rise. Each scan is repeated ten times with and without AC current alternately in order to check the reproducibility of the effects and estimate the most probable amplitude of the switching field. About twenty nanowires have been measured showing similar behavior. Due to the instability of the contact to the nanowire and the acquisition time for each GMR curve, a full set of frequencies and power values could not be applied to each sample. Results reported here were obtained with two different samples measured with a magnetic field parallel or perpendicular to the plane of the membrane. Fig. 1a shows the GMR of a single nanowire recorded without AC current. The external magnetic field H0 is applied perpendicularly to the plane of the membrane. Mechanical instability of the electrical contact procedure prevents the sample from being rotated once it is in place. Then GMR measurements as a function of the angle of the applied field cannot be performed. As a consequence there is an average uncertainty about the relative angle between the applied field and the nanowire axis. Studies performed in our group [20] have shown that this angle can be up to 301 due to the average orientation of the pores in the membrane. The field is scanned from negative to positive saturation. We define the soft and the hard layers as the one with the smallest (Hsw1) and highest (Hsw2) switching field amplitudes, respectively. As the out of plane demagnetizing factor is bigger for the thin layer, we assume the thin and thick cobalt layers correspond to the hard and soft layers, respectively. Furthermore, simulations (not presented here) showed that a relative angle of 601 between the applied field and the thin layer plane can account for the value of the switching field of the thin layer.
Fig. 1b–d shows the GMR of the sample recorded with microwave currents at different frequencies fAC. Unfortunately, we could not perform measurements for each frequency in the (1–16 GHz) range and only currents with few different frequencies have been injected in this sample. We observe that Hsw2 decreases from 115to 80 mT when fAC ¼3 GHz (Fig. 1b) whereas Hsw1 decreases from 55 to 37 mT when fAC ¼13 GHz (Fig. 1d). The small change of Hsw1 in Fig. 1b is within the uncertainty of the measurements estimated by the ten GMR curves recorded without AC current. Fig. 1c shows the normalised resistance of the trilayer for different values of fAC. Since the Joule heating of the sample is set to be the same for all measurements, it cannot be responsible for the relative modification of the switching fields. All these results clearly demonstrate that the switching field of the soft or hard layers can be tuned independently by a MW current and that the MW frequency plays a key role in determining the amplitude of Hsw1 and Hsw2. We point out that changes of Hsw1, which we assume to correspond to the thicker layer switching field, was only observed at 11 (not shown) and 13 GHz for IAC ¼100 mA. As the spin torque efficiency strongly depends on the volume of the magnetic layer, we expect the thick layer to be less perturbed by the microwave current. This is confirmed experimentally for most of the current frequencies for which we did not observe any change of Hsw1. Nevertheless, the switching observed at these two particular frequencies, much higher than what is expected for the uniform precession mode of the thick layer, could be a proof that some spatially non-uniform dynamic modes, depending on the magnetic profile in the layer, are more efficient to switch the magnetization (see discussion below). Similar results were observed on a sample for which the applied magnetic field lies approximately within the plane of the membrane (Fig. 2a). The field is scanned from positive to negative saturation. The soft layer, which presents the smallest switching field amplitude Hsw1, corresponds to the thin layer due to its
Fig. 1. (a) GMR, magnetic field applied roughly perpendicular to the plane of the membrane (arrows: direction of the field sweep). (b) and (d) GMR recorded with microwave currents IAC at 3 GHz (red curve) and 13 GHz (blue curve), respectively, or without it (black curve) (blue arrow: direction of the field sweep from negative to positive saturation). Hsw1 and Hsw2 in (b) correspond to the value of the switching field of the soft and hard layers, respectively. (c) Normalised GMR with IAC at different frequencies. (blue arrow: direction of the field sweep from negative to positive saturation) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. (a) GMR, magnetic field applied perpendicular to the nanowire axis with (red curve) and without (black curve) IAC at 2 GHz (blue arrow: direction of the field sweep). Hsw1 and Hsw2 correspond to the value of the switching field of the soft and hard layers, respectively. (b) Maximum DH (square) and its standard deviation (bars) of the thin layer as a function of the frequency of IAC. The line is a guide for the eyes. The black square at 10 mT for fAC ¼ 11 GHz corresponds to 3 DH measured over the ten scans. (c) GMR for different microwave powers at 6 GHz. The blue curve was recorded at the end of the set of measurements. (blue arrow: direction of the field sweep from positive to negative saturation) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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bigger in plane anisotropy. The soft layer switches slightly before zero field because of the dipolar interactions between layers. A minor hysteresis loop performed by scanning the field from positive saturation to zero field then back to positive saturation allows estimating the coercive field of the thin layer to be about 60 mT and the dipolar field on the thin layer to be about 80–90 mT. The relatively large value of Hsw2 can be accounted for assuming an elliptic cylindrical shape of the thick layer, which is reasonable, given the uncertainty about the shape and dimensions of the layers. In this magnetic configuration and for IAC of 100 mA, only changes for Hsw1 were observed. We measured the difference DH between switching fields with and without microwave current (Fig. 2b). The spread in the data reported for measurements done at 11 GHz is as follows: 7 scans yielded similar large DH whereas 3 scans showed much smaller DH. We clearly observe that the DH value is more important for fAC ¼1.5, 2 and 11 GHz than for other frequencies. The highest value of DH of about 75 mT corresponds to a value of H0 that compensate the dipolar field induced by the thick layer (the average applied field is then close to zero). In both magnetic configurations of Figs. 1 and 2, we observe that current frequencies up to 3–4 GHz seem to be quite efficient to switch the thin layer magnetization at different values of H0. However, we also observe that some higher frequencies (for example 8 GHz in Fig. 1c and 11 GHz in Fig. 2b) allow the switching. We also observe a saturation of the effect with the microwave power (Fig. 2c), as expected for non-linear resonant processes.
3. Discussion In order to get a better understanding of these experimental results, we study the thin layer dynamics in presence of a MW current by solving numerically the Landau–Lifschitz–Gilbert (LLG) equation including the spin transfer torque @m @m ¼ gm Heff þ am þ aj cosðoAC tÞm m p @t @t
ð1Þ
where m is the thin layer magnetization vector, p is the unit vector defining the direction of the thick layer (that we consider as pinned in the calculation), Heff is the effective field comprising the applied and anisotropy fields, g (2.21 105 (A/m) 1 s 1) and a (0.03) are the gyromagnetic ratio and the damping coefficient, respectively, aj is the spin torque coefficient defined in Ref. [12] and proportional to the current density, oAC is the current pulsation. As the size of our system is very small, it is reasonable to apply the macrospin approximation. Simulations in the macrospin approximation can help to understand qualitatively the basic processes involved in the microwave current assisted switching. Calculations are performed in a very ideal case of a small ellipsoid, uniformly magnetized. The dimensions of the thin layer are set to be 40 30 5 nm3 to account for a small ellipticity that can appear in electrodeposited nanowires. Numerical calculations are performed in a similar magnetic configuration as the one encountered in Fig. 1. The x and y directions are aligned with the short and long axis of the ellipse, respectively. The field is applied in the yz plane, with an arbitrary angle of 201 with respect to the z-axis. Before solving the LLG equation, the equilibrium positions of the thin and thick layer magnetizations are calculated by minimizing the free energy. Fig. 3a presents the numerical results of the LLG integration when IAC ¼ 150 mA. Similarly to the experimental observation, the occurrence of switching at a given field depends critically on frequency. For example, at H0 ¼30 mT, switching occurs at 3 GHz, not at 2 GHz. We note high amplitude oscillations between 0 and 0.5 ns corresponding to the increase of the cone angle of the
Fig. 3. (a) Normalised my component of the thin layer magnetization for different values of fAC and H0. The field is applied with an angle of 201 with respect to the z-axis. (b) FMR frequency of the thin layer as a function of the applied field H0. (c) Angle dependence of the switching time at H0 ¼40 mT, fAC ¼3 GHz. The field is applied in the y direction.
precession due to the spin torque. Moreover, the higher the frequency, the lower is the switching field amplitude. For example, when fAC ¼3 GHz, switching occurs when H0 ¼30 mT, whereas switching occurs at 2 GHz for H0 ¼45 mT. The decrease of the current frequency needed to switch the magnetization when increase in the field is coherent with the frequency dependence of the spin dynamic modes on H0. As an example, we calculate the ferromagnetic resonance (FMR) frequency of the thin layer as a function of the applied field (Fig. 3b) in the field range of interest. We observe a decrease of the FMR frequency until the magnetization switches around 95 mT. Within this macrospin approximation, we note that the frequency of the current allowing switching is smaller than the FMR frequency. However, this is expected since switching implies high precession angles of the magnetization. It corresponds to a highly non-linear dynamic state for which it is well known that frequencies are well below the FMR frequencies [21] (which corresponds to a small angle of precession around the equilibrium position). The process of non-linear excitation of a quasi-uniform mode agrees well with the experimental results presented in Figs. 1 and 2. Indeed the maximum FMR frequency, in the field range for which assisted switching of the thin layer appears is expected to be at most 4 or 5 GHz. This range was evaluated taking into account the different uncertainties about the shape and dimensions of the thin layer. Then, the maximum frequencies which are efficient for switching the magnetization in the non-linear regime are expected to be at most around 3 or 4 GHz. A rough estimation of the non-linear resonant frequency can be given by E0.8oFMR, see Ref. [22] and reference therein for more details. Indeed, we observe switching for frequencies up to 3 GHz in Fig. 1c. Moreover, as observed in Fig. 1c for fAC ¼1–3 GHz and in Fig. 2b for fAC ¼1.5 and 2 GHz, the DH value reflects the dependence of FMR frequency vs. field (taking into account the sum of the applied and dipolar field on the thin layer in Fig. 2). According to this assumption it would be surprising that frequencies in the 3–5 GHz range seem to be quite inefficient to switch the magnetization in the ‘‘in plane’’ configuration of Fig. 2b. In order to understand this point, one has to consider the amplitude of the dipolar coupling between the hard and free
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layer. The minor hysteresis loop performed on this sample allows estimating that for H0 below E80 mT, the effective field applied to the thin layer points in the opposite direction of the magnetization and increases as H0 decreases. For fAC ¼2 GHz, switching occurs at H0 about 80 mT (the effective applied field to the thin layer is then close to zero). Then, 2 GHz seems to be close to the maximum current frequency inducing switching within the macrospin assumption. In Fig. 1c we observe that the difference of Hsw2 for fAC between 1 and 3 GHz is about 10 mT. This is roughly half the difference that could be expected from the FMR vs field dependence. One possible explanation is related to the efficiency of the spin transfer torque with respect to the relative angle between both layer magnetizations. Indeed, as explained in Ref. [14], as long as the precession angle of the thin layer is smaller than the relative average angle between both layers, the sign of the spin torque always acts to push away the thin layer magnetization from the thick one, leading to an increase of the precession angle until the magnetization switches. It means that for very small angles between layers, resonant spin torque is not fully efficient to switch the magnetization. For fAC ¼3 GHz, switching occurs when the relative angle between layers is about 1501 whereas it could be expected at a field corresponding to a relative angle of 1701. This assumption is confirmed by calculating the LLG equation for two different relative orientations of both magnetic layers (Fig. 3c). This point is particularly important for sensors applications since it shows that magnetic layers with crossed anisotropies are more efficient to increase the switching probability induced by the microwave current. Finally we would like to discuss the high DH value observed at frequencies up to 11 GHz in Fig. 2b and 8 GHz in Fig. 1c since it cannot be accounted for by the non-linear uniform excitation of the magnetization. Then, we assume that switching at these particular high frequencies occurs through the excitation of spatially non-uniform modes. Indeed, it has been shown in Ref. [19] that the spin wave spectrum in a similar structure is extremely complex and can span a very broad frequency range. This assumption could also explain the spread in the data reported in Fig. 2b. Indeed, from one hysteresis loop to another, the static magnetization can present small differences, especially at the edge of the sample, leading to different dynamic modes with different frequencies. Then, we assume that the difference reported at 11 GHz in Fig. 2b reflects some small changes in the static configuration of the thin layer magnetization. A better understanding of this effect implies micromagnetic modeling for which a complete knowledge of the shape, size and orientations of the layers would be needed.
4. Conclusion To summarize, we showed the effectiveness of microwave current in switching at room temperature the magnetization of
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the magnetic layers in a pseudo-spin valve grown by template synthesis. The dependence of the switching field amplitude on the frequency of the microwave current is demonstrated experimentally. Our observations can be accounted for qualitatively in a simulation of the thin layer dynamics obtained by solving the LLG equation including a spin transfer torque for current frequencies below the FMR frequencies. Moreover, observations of switching at current frequencies up to 10 GHz indicate that the switching can occur through non-uniform spin wave modes. We believe that the ability to modulate the switching fields of nano spin valves by adjusting the microwave current frequency is very attractive for the development of low power consumption MRAMs and magnetic sensors.
Acknowledgement This work has been supported by the Swiss NSF, Grant no. 200020-117588.
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