Strong current actions on ferrimagnetic domain walls in the creep regime
Résumé
We observe domain-wall (DW) motion in ferrimagnetic TbFe wires with perpendicular anisotropy under combined field and current in the creep regime. The current action on the DW is double: Joule heating and spin-transfer torque. We propose a genuinely robust analysis of velocity, separating thermal effects and spin-transfer torque, quantifying the latter as an equivalent field in the so-called one-dimensional (1D) model. Its efficiency is much larger than in transition-metal ferromagnets above room temperature. The equivalent field reveals the large polarization-to-magnetization ratio in ferrimagnets despite a vanishing M s. The usual 1D DW model is extended to mimic creep and predicts that, in low net magnetization systems, the internal DW structure precesses with currents above a field-independent threshold, leading to two propagation regimes with different mobilities. This is another example of how the internal DW magnetization is relevant in creep. We could not detect experimentally these two regimes, possibly because of the dispersion of the data. Spintronic nanodevices that store and process nonvolatile information are based on the magnetic reversal of nanomag-nets [1,2]. Experimental results from field-driven as well as current-driven switching show that the reversal is mediated by domain-wall (DW) propagation, even in nanomagnets of just a few tens of nm [3-5]. The main mechanism for current-induced DW motion (DWM) is the relaxation of a spin current in the magnetic structure. If the current is polarized inside the magnetic material, we speak about spin-transfer torque (STT). The efficiency of the polarized current action on a magnetic structure is expressed by a drift speed [6]: u = gμ B P 2eM s J, (1) where P is the spin polarization of current of density J in the magnetic media, M s is the total (effective) magnetization of this media, g is the (effective) Landé factor, μ B is the Bohr magneton, and e is the electron charge. In the classical ferromagnetic materials that have been studied, P and M s share the same physical origin and so the same dependence on temperature, and therefore the ratio P/M s which governs the efficiency of STT is fixed [7]. To increase this quantity, a good solution is to focus on more exotic materials such as ferrimag-netic alloys. Equation (1) was developed for ferromagnets but it holds for ferrimagnetic alloys by using effective parameters away from compensation points (magnetic or angular). Rare-earth-transition-metal (RE-TM) ferrimagnetic alloys, such as TbFe, have two populations of magnetic moments that are antiferromagnetically coupled [8,9]. One population is the spin-polarized valence electrons of the RE and of the TM [8,9] and the second one is the localized 4 f electrons of RE. Even if current polarization is due to the first one, the net magnetization of this alloy M s is the sum of moments of * alexandra.mougin@u-psud.fr the two populations. That is why ferrimagnetic materials can exhibit a vanishingly small magnetization and yet a sizable spin polarization, both tunable by acting on the composition of alloys or by changing the temperature [8,10,11]. A few results exist showing clear DWM under current in ferrimag-nets [12-14]. In our case, we observe DWM in the creep regime. The study of the creep regime in current-driven DWs lead to nonconsensual interpretations [15-17]. One of the challenges is to account fully for Joule heating in a dynamical regime that relies on thermal activation [18]. We propose the first rigorous study of DW creep motion in TbFe ferrimagnets under current. Moreover, in the usual creep theory, the dynamics are assumed to be independent of the internal structure of the DW. However, recently, it was shown that the Dzyaloshinskii-Moriya interaction or the in-plane magnetic field affects the DW velocity in complex ways that can only be understood by considering the details of the DW structure [17,19]. So far, dynamic changes of the DW structure were never considered in the creep analysis. We propose a model in which the dynamics of the DW structure are relevant also in the creep. The studied film is 7 nm of the amorphous alloy Tb 21 Fe 79 with 5 nm Al cover with perpendicular magnetic anisotropy deposited by co-evaporation on a Si/SiO x (500 nm) substrate in ultrahigh vacuum. Details of growth and basic properties of the stacks are published elsewhere [20]. The film was characterized by using the magneto-optic Kerr effect (MOKE) and the anomalous Hall effect (AHE) resistivity measurements which are mainly proportional to spin polarization of electrons at the Fermi level (equivalent to P) [8,10]. The net magnetization M s was measured by vibrating sample magnetometry (VSM). The polarization and magnetization results are shown in Fig. 1(a) as a function of temperature. The magnetic compensation temperature (M s = 0) is well below the smallest experimental temperature (50 K) and was not reached. The Curie temperature is 375 K. Despite being
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