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The effect of pulsed currents on magnetization reversal were studied on single ferromagnetic nanowires of diameter about 80 nm and 6000 nm length. The magnetization reversal in these wires occurs with a jump of the magnetization at the switching field Hsw, which corresponds to unstable states of the magnetization. A pulsed current of about 10 7 A/cm 2 was injected at different values of the applied field close to Hsw. The injected current triggered the magnetization reversal at a value of the applied field distant from the switching field by as much as 20%. This effect of current-induced magnetization reversal is interpreted in terms of the action of the spin-polarized conduction electrons on the magnetization.

The dynamical equation of the magnetization has been reconsidered with enlarging the phase space of the ferromagnetic degrees of freedom to the angular momentum. The generalized LandauLifshitz-Gilbert equation that includes inertial terms, and the corresponding Fokker-Planck equation, are then derived in the framework of mesoscopic non-equilibrium thermodynamics theory. A typical relaxation time τ is introduced describing the relaxation of the magnetization acceleration from the inertial regime towards the precession regime defined by a constant Larmor frequency. For time scales larger than τ , the usual Gilbert equation is recovered. For time scales below τ , nutation and related inertial effects are predicted. The inertial regime offers new opportunities for the implementation of ultrafast magnetization switching in magnetic devices. The range of validity of the Landau-Lifshitz-Gilbert (LLG) equation was established one decade later by W. F. Brown, with a description of a magnetic moment coupled to a heat bath ("thermal fluctuations of a singledomain particle ", 1963 [3]). The magnetic moment is treated as a Brownian particle described by the slow degrees of freedom (10 −9 s), the angles {θ, φ}. The remaining degrees of freedom of the system relax in a much shorter time scale (< 10 −12 s). The time scale separation between the rapidly relaxing environmental degrees of freedom and the slow magnetic degrees of freedom allows the coupling between the magnetization and the environment to be reduced to a single phenomenological damping parameter η, whatever the complexity of the microscopic relaxation involved [4,5].However, important experimental advances towards very short time-resolved response of the magnetization (sub-picoseconds resolution, i.e. below the limit proposed by Brown) have been reported in the last decade [6]. In parallel, industrial needs for very fast memory storage technologies are approaching the limits imposed by the precessional switching [7]. In these experiments and in the corresponding applications, time scale separation between the conserved degrees of freedom {θ, φ} and the other degrees of freedom, assumed by Brown [3], finds its limit.The purpose of this Letter is to investigate the dynamics of the magnetization beyond this limit by extending the phase space to additional degrees of freedom expected to be also out-of-equilibrium at short time scales [5,9]. According to the well-known gyromagnetic relation [10], the next relevant degree of freedom of the ferromagnetic system (beyond the coordinates of position; i.e. the angles {θ, φ}) is the angular momentum L. As will be shown below, the consequence of considering also the conservation of the angular momentum is that inertial terms, i.e. acceleration terms proportional to d 2 M/dt 2 , appear in the equation of motion. The existence of inertial terms in the dynamics of the magnetization opens the way to deterministic ultrafast magnetization switching strategies, beyond the limitations of the precessional regime [11]. We assume however ...

The understanding of how spins move and can be manipulated at pico-and femtosecond time scales is the goal of much of modern research in condensed matter physics, with implications for ultrafast and more energy-efficient data processing and storage applications. However, the limited comprehension of the physics behind this phenomenon has hampered the possibility of realising a commercial technology based on it. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast time scales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report the first direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetisation at a frequency of approximately 0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps.

Abstract. We present an overview of template synthesis as it applies to our nanomaterials research. This bottom-up approach is motivated by our desire to find an alternative to the big, top-down approaches to nanoscience, such as clean-rooms and X-ray lithography. Using universally available templates and materials, and very modest synthesis techniques, we have created a variety of interesting and useful structures. Starting with homogeneous ferromagnetic nanowires, we were able to study and manipulate spin-dependent transport. Next, we branched into multi-layer GMR and spin-valve structures for spintronics. As a side trip, we put carbon-encapsulated fullerene nanoparticles into nanopores for ballistic magnetoresistance studies. Carbon nanotube molecules were grown in templates by CVD self assembly. The carbon nanotubes grown using a cobalt catalyzer show spin-valve, ballistic transport, and Coulomb blockade effects. Very recently, we have started to study templated semiconductor nanorods with the amazing result that their behaviour is very similar to that of the carbon nanotubes and can be reduced to a scaling law. Essentially, the template acts as a skeleton for the nanoscale synthesis and macroscale contact of an infinite variety of materials and structures. It is our hope that by the following examples we demonstrate that high quality nanoscience research is available to everybody. PACS

The gyromagnetic relation -i.e. the proportionality between the angular momentum L (defined by an inertial tensor) and the magnetization M -is evidence of the intimate connections between the magnetic properties and the inertial properties of ferromagnetic bodies. However, inertia is absent from the dynamics of a magnetic dipole (the Landau-Lifshitz equation, the Gilbert equation and the Bloch equation contain only the first derivative of the magnetization with respect to time).In order to investigate this paradoxical situation, the lagrangian approach (proposed originally by T. H. Gilbert) is revisited keeping an arbitrary nonzero inertial tensor. A dynamic equation generalized to the inertial regime is obtained. It is shown how both the usual gyromagnetic relation and the well-known Landau-Lifshitz-Gilbert equation are recovered at the kinetic limit, i.e. for time scales above the relaxation time τ of the angular momentum.PACS numbers:

In order to describe the recently observed effect of current induced magnetization reversal in magnetic nanostructures, the thermokinetic theory is applied to a metallic ferromagnet in contact with a reservoir of spin-polarized conduction electrons. The spin-flip relaxation of the conduction electrons is described thermodynamically as a chemical reaction. In the two-current approximation, the diffusion equation of the chemical potential, the giant magnetoresistance at the interface, and the usual Landau-Lifshitz-Gilbert ͑LLG͒ equation is obtained from the entropy variation in the absence of current. The description of the conservation laws, including spin dependent scattering and spin injection, leads to the derivation of a generalized LLG equation. The equation is applied to the measurements obtained on single magnetic Ni nanowires.An unexpected and spectacular effect due to spin polarization of conduction electrons in metallic ferromagnets, the giant magnetoresistance ͑GMR͒, appeared with transport studies on magnetic nanostructures. 1 The spin-diffusion length of conduction electrons being of some few tens of nm, the relaxation of the conduction electron spins becomes observable when the magnetization can be controlled over this typical length. Some predictions about the inverse effect, namely the influence of spin-polarized current on the dynamics of the magnetization, were also proposed. Berger predicted the existence of some surprising phenomena due to the action of spin-polarized conduction electrons on domain walls 2 or spin waves 3 in magnetic thin films. Slonczewski predicted the rotation of the magnetization due to polarized current in multilayered systems, 4 and Bazaliy, Jones, and Zhang derived from microscopic considerations a generalized Landau-Lifshitz-Gilbert equation. 5 All the abovementioned approaches are microscopic and based on the ballistic approximation.From an experimental point of view, Freitas and Berger, Hung and Berger, 6 and Salhi and Berger 7 show the action of a high current density on domain walls in thin films. Recent experiments on nanostructured samples bring interesting evidence for the interpretation in terms of the action of the spin of the conduction electrons. Tsoi et al. 8 show an effect of a high current density on spin-wave generation in Co/Cu multilayers, Sun reported on current-driven magnetic switching in manganite, 9 and Myers et al. reported an effect of current induced switching in magnetic multilayer device. 10 In a recent work, we have evidenced an effect of current induced magnetization reversal in magnetic nanowires, 11,12 where the reversal of the magnetization is induced by a high current at an applied field 20% smaller than the normal reversal field. The ballistic approximation is, however, difficult to justify in all these experiments.A phenomenological approach based on the thermokinetic theory 13,14 of a metallic ferromagnet in contact with a reservoir of spin-polarized conduction electrons is proposed. In contrast to the pioneering works of Johnson and...

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