IOP PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 42 (2009) 175004 (5pp)
doi:10.1088/0022-3727/42/17/175004
Current susceptibility of magnetization in spin valves Haiming Yu1,2 , Julie Dubois1,3 , S Granville1 , D P Yu2 and J-Ph Ansermet1 1 Institut de Physique des Nanostructures, Ecole Polytechnique F´ed´erale de Lausanne, Station 3, CH-1015 Lausanne-EPFL, Switzerland 2 State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, People’s Republic of China 3 Ecole des Mines, 60 bd Saint Michel, 75006 Paris, France
E-mail:
[email protected]
Received 12 March 2009, in final form 12 June 2009 Published 5 August 2009 Online at stacks.iop.org/JPhysD/42/175004 Abstract We observed the second harmonic voltage response of pseudo-spin valves subjected to currents oscillating at frequencies in the sub-kilohertz range. Peaks appear in its magnetic field dependence, with a signal-to-noise ratio equal to or greater than the magnetoresistance response of the same samples. This signal is interpreted as arising from the response of the magnetization to the spin torque induced by current when the magnetic layers are in non-collinear orientations. Thus, the method probes the current susceptibility of the magnetization which is shown to be sensitive to non-collinear states undetectable in the magnetoresistance. (Some figures in this article are in colour only in the electronic version)
magnetization dynamics and at current densities considerably lower than necessary to excite the ferromagnetic modes. This method provides a way of probing quasi-static configurations of the magnetization response to an ac current, as has been recently calculated [12]. Similarly, others have studied the low frequency displacement of a pinned domain wall in a device with perpendicular magnetic anisotropy [13]. The field dependence of the measurements in this study exhibits sharp peaks that stand out on a very weak baseline. We show that the signal results from the combined effects of GMR and spintransfer torque, and that it can probe rotations of the magnetic layers in the PSVs that do not affect the observed GMR.
1. Introduction The discovery of giant magnetoresistance (GMR) [1, 2] and its widespread use in data storage established the significance of large magnetic field responses. Much of spintronics research revolves around the search for ever greater field responses. For example, MgO was predicted to give large tunnel magnetoresistance [3], which was soon confirmed [4]. Another theme of spintronics is the exploitation of the effect of spin-polarized current on magnetization. Following the seminal theoretical predictions [5, 6], several types of observations were made: current-driven magnetization hysteresis [7], peaks in the differential resistance dV /dI as a function of field [8], and spin-transfer-driven oscillations [9]. Point contact spectroscopy with applied ac currents in the range of 108 –109 A cm−2 has been used to study the nonlinear responses of magnetic multilayers that originate from excitations of magnon modes [10]. The excitation of modes in a single magnetic layer at similar current densities has also been reported [11]. In this paper, we report observations of the linear response of the magnetization of pseudo-spin valves (PSVs) subjected to an alternating current. We detect the response at very low current frequencies compared with those typical of the 0022-3727/09/175004+05$30.00
2. Experiment For this work, nanowires of Cu containing Co/Cu/Co PSV structures have been prepared by electrodeposition in nanoporous membranes. The membranes have a pore density of the order of 108 pores cm−2 . We work with pores about 40 nm in diameter, and about 6 µm in length. Unless special measures are taken, not all pores are wetted and filled. Contact is obtained to a single nanowire by stopping the growth as soon as contact is established between the gold electrodes 1
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J. Phys. D: Appl. Phys. 42 (2009) 175004
H Yu et al
which were sputtered on both sides of the membranes prior to electroplating [14]. An alternative to the method of this work may also ensure only a single nanowire is contacted. In this alternative method, a nano-indenter is used to open up a thin resist, as done by Piraux et al [15]. Confirmation that electrical contact is made to a single nanowire is provided by GMR: a singly contacted Cu nanowire containing one Co/Cu/Co PSV demonstrates two jumps in the resistance as the field makes a single complete sweep. These jumps correspond to switching between parallel and anti-parallel orientations of the two Co layer magnetizations. Switching fields in these layers are known to be broadly distributed [16]. So, if two nanowires are connected, only four distinct jumps must be observed. Electrodeposition is from a single bath such that Cu is also plated when Co is deposited. Thus, we found that the Co layers contain about 15% Cu, and have the fcc structure [17]. Our PSVs are grown with typically 10 and 30 nm of Co, with a 10 nm Cu spacer. In order to increase the production yield of samples with the desired switching events, we sometimes grow nanowires containing several PSVs in series, sufficiently far from each other (typically 1 µm apart) so that magnetic couplings between spin valves are insignificant. The technique of measuring the linear response consists of simply driving a current of about 106 A cm−2 into one electrically contacted nanowire, at a frequency f in the range 100 Hz–2 kHz. A lock-in amplifier is used to measure the response at twice the frequency of the driving current, V 2f . The measurements reported here were carried out at room temperature using a driving current I0 of 100 µA at 814 Hz. It should be noted that the description of measurements of V 2f reported here superficially resembles point contact spectroscopy measurements of (d2 V /dI 2 ) versus V , such as those reported on pure Co in [11]. However, in that work, measurements were carried out at applied dc current densities high enough to induce excitations in the magnetic layer. The threshold for these excitations is ∼109 A cm−2 , orders of magnitude larger than the ∼1 × 106 A cm−2 current density of this work.
R (Ω)
74.40 74.35 74.30 74.25
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Figure 1. V 2f and MR of a nanowire containing two Co(10 nm)/ Cu(10 nm)/Co(30 nm) PSVs in series, with the magnetic field applied parallel to the nanowire ramping up (black) and down (red). (Colour online.)
up to 0.5 µV on a baseline of 0.75 µV(67%), whereas the maximum GMR ratio of the same sample at a sharp transition is ∼0.05 /74.25 = 0.06%. V 2f changes of over 100% are common in many examples of PSVs investigated as a part of this study. We discuss the origin of the changes in V 2f based on considerations of how the resistance of a PSV depends on the quasi-static perturbation of the configuration of the two magnetic layers. The second harmonic of the voltage generated in response to an applied ac current has also been calculated from a theoretical description based on a diffusive model of spin transport in PSVs [18]. In that work the magnitude of the calculated voltage response closely agrees with the size of the peaks reported in the V 2f signal of this work. Nonlinearity in the voltage response V versus current I is expected whenever the resistance depends on the magnetization, which also depends on time. This simple idea was exploited by Juretschke [19] to obtain a dc voltage when electromagnetic irradiation is at resonance with the fundamental ferromagnetic resonance mode [20] or spin wave modes [21] in homogeneous thin films. In order to make explicit the non-linear voltage response at frequencies that are very low compared with the resonance modes, we refer to the work of Kovalev et al [12], who calculated the voltage response of spin valves to an applied ac current. They start with a generalized Landau–Lifshitz– Gilbert equation dM α dM = −γ M × Heff + M× dt Ms dt h ¯ I (t) (1) η1 m × (mfixed × m) , +γ 2e Vm where M is the magnetization of the free layer and m and mfixed are the magnetization unit vectors for the free and fixed magnetic layers, respectively. There is a time-dependent current I (t) flowing in the system, η1 denotes the strength of the spin-transfer torque and the other constants take their usual definitions. We have omitted the effective-field-like term arising from a ‘spin-transfer exchange field’, as this term is thought to be relevant in tunnel junctions, but negligible in metallic structures [22]. Heff contains terms including
3. Results and discussion Figure 1 presents the magnetoresistance (MR) and V 2f data obtained for a Cu nanowire containing two PSVs in series, separated by several micrometres within the nanowire, with the field applied parallel to the axis of the wire. The presence of sharp V 2f peaks shows that the second harmonic voltage signal is just as sensitive to an applied magnetic field as the MR response of the same sample. A significant feature of the data is that the peaks of V 2f appear when the layer magnetization switches over a finite field range (near ±70 mT), but not at all at a sudden switch (∼±40 mT). As the field is applied parallel to the wire, it is perpendicular to the plane of the layers, and typically the magnetization rotates over a finite field range, though it may be small. It is worth noting that, due to the very weak baseline, the relative magnitude of the peaks in the second harmonic signal is very large compared with the sharp MR transitions. In figure 1, V 2f changes by 2
J. Phys. D: Appl. Phys. 42 (2009) 175004
H Yu et al
MR (Ω)
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Figure 3. V and magnetoresistance of a nanowire containing a single PSV, magnetic field applied perpendicular to the nanowire, measured with field ramped up (black) and down (red). The inset shows a close-up around 140 mT of the field ramp-up curve, demonstrating the V 2f peak is outside the field range of the magnetoresistance switching. (Colour online.)
Figure 2. Fixed layer Mf and free layer M0 magnetization vectors. Mf is Mf translated to O. Ox is defined as the normal to the plane containing Mf and M0 . θ is the angle between Mf and M0 . φ defines a rotation of Mf which keeps θ fixed. The shaded plane containing Ox y is a guide to the eye.
damping then becomes ∂R (ν) I0 /e γ h ¯ /2 1 Nd η1 I 0 sin2 θ xd 2 ∂ν γ Ms Vm Ms Ny
Nyd Nyd × − 1 cos φ sin φ − α sin2 φ + cos2 φ , Nxd Nxd
U2ω =
the externally applied field, anisotropy, demagnetization and dipolar fields. With reference to the diagram of figure 2, the total resistance of the spin valve is given as ∂R (cos θ) R = R (cos θ ) − sin θ θ, ∂ (cos θ )
(5) Nxd
and are the diagonal components of the where demagnetization tensor. Typically, (Nxd /Nyd ) < 1. Using (5) and figure 2, we can understand a switching process that gives rise to a sharp peak in V 2f where the change in MR is progressive, such as experimentally seen near ±70 mT in the measurements of figure 1. From (2), R is governed entirely by the angle θ between the layer magnetizations, which is in the Oy z plane in figure 2. However, U2ω is dependent on φ as well as on angle θ , which is in the Ox y plane. The rotation of the free layer magnetization M0 may in general change both θ and φ. Equation (5) shows that U2ω is sensitive to rotations of the free layer magnetization which are undetectable in R, i.e. in situations where θ is fixed and only φ varies. For a set value of θ, the first term in the square brackets of (5) gives maxima for U2ω at φ = (±)π/4, (±)3π /4, when neglecting the term proportional to α. An example of such a rotation is detected in figure 3, which shows the MR and V 2f data measured for a single PSV in a Cu nanowire, with field applied perpendicular to the wire axis. During each sweep of field either from positive or negative saturation values, there is a sharp peak in the V 2f signal measured close to but outside the field range where the MR changes abruptly (see figure 3 inset). A systematic observation representative of the many samples measured is that the V 2f response is nearly insensitive to the situations of parallel and anti-parallel orientation of the Co layers. At the fields where MR shows a sharp transition, the V 2f change from the baseline is very small at best, while a pronounced peak is observed when the MR presents a transition occurring over a larger field range. The case of sharp
(2)
where the magnetization angle θ is dependent on the applied magnetic field. Here the ac current causes a small perturbation of the relative magnetization angle θ , which to first order is equal to the oscillatory component of magnetization my . The total voltage resulting from the interaction of the resistance with the ac current is equal to a dc term plus a term proportional to I 2 at twice the frequency ω of the current I 2 sin θ ∂R (cos θ ) U2ω = 0 (3) χy I , 2Ms d (cos θ ) where χy I
−¯hγ sin θ η1 Nx y + αNx . (0) = 2eVm γ M N N − N 2 s x y xy
Nyd
(4)
I0 is the magnitude of the ac current. For equation (4) we have taken the linear response function χy I (ω) of [12] with α 1, η2 = 0, in the limit ω → 0 as appropriate for the low frequency of our applied ac current. Therefore, the signal at 2ω involves the current susceptibility of magnetization at low frequency. We transform (3) and (4) using the system of coordinates of figure 2 in order to demonstrate more clearly the sensitivity of V 2f to specific switching processes. The form of U2ω with 3
H Yu et al
151.4 151.2 151.0 150.8 150.6 150.4 150.2 3.0
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J. Phys. D: Appl. Phys. 42 (2009) 175004
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Figure 4. V 2f and MR of a nanowire containing a single PSV. The magnetic field is applied parallel to the nanowire, ramped up (black) and down (red). (Colour online.)
Figure 5. V 2f of a multilayer Co/Cu nanowire with I0 = 50 µA applied at 406 Hz and magnetic field applied parallel to the nanowire, field ramped up (black) and down (red). Inset: the magnitude of the sharp peaks versus I02 . (Colour online.)
jumps between magnetization orientations is best illustrated in figure 4, showing the V 2f and the MR of a Cu nanowire containing a single PSV. Here, only a small change in V 2f appears when the spin valve is in the anti-parallel state. This type of V 2f response is also visible in figure 1, in the field range where sharp MR jumps occur. According to the model of spin-transfer torque response, pronounced peaks in V 2f are expected only in the cases where the Co layers switch gradually, so that non-collinear orientations of the two layers occur in the quasi-static regime. In the cases where the MR switches are sharp, as seen in figures 1 and 4, θ apparently rotates by approximately 180◦ in a field range less than that of successive field values applied in the experiment (
