L. Berger

Exchange interaction between ferromagnetic domain wall and electric current in very thin metallic films

Since the wall thickness is at least 102 electron wavelengths, a domain wall acts, through the s‐d exchange interaction, like a very weak and smooth potential barrier of height ≂10−2 eV, which does not reflect conduction electrons appreciably. The potential energy arises from the 4s conduction electron spin making a small angle with the local s‐d exchange field. Anisotropic s‐d exchange may also contribute to the potential barrier. A solution of the electron transport equations in the wall is obtained. In order for an electron current crossing the wall to exert an appreciable drive force on it, nonzero interband electron scattering by impurities or phonons is needed. The electron density for a given band varies slightly with location inside the wall, and depends on the current. Mutual electrostatic shielding between bands is taken into account. The drive force per unit wall area is F≂2Ms  μ−1i (ve −vw), where ve and vw are electron drift speed and wall speed. In other words, this drive force at ve ≠0 is g...

Low‐field magnetoresistance and domain drag in ferromagnets

Despite common misconceptions, domain walls are too thick to ’’scatter’’ electrons appreciably. However, electrons crossing a wall apply a torque to it, which tends to cant the wall spins. This could be used to measure the conduction electron spin polarization. Most of the low‐field resistive anomalies observed in pure Fe, Ni and Co at low temperature are caused by the Lorentz force associated with the internal field B=Ms present inside each domain. The existence of low‐resistivity paths extending over many domains accounts for still unexplained magnetoresistance data in iron whiskers. In uniaxial materials, a d.c. eddy‐current loop caused by the Hall effect runs around each wall. The field Hz generated by these loops tends to ’’drag’’ the whole domain structure in the direction of the carrier drift velocity. Also, the Joule dissipation of the eddy currents manifests itself as an excess Ohmic resistance. As predicted, this excess resistance decreases as the square of the field, in amorphous Gd25Co75 films...

Low‐Temperature Magnetization of Cu(NO3)2·2.5H2O

We have measured magnetization isotherms for single crystals of monoclinic Cu(NO3)2·2.5H2O between 1.2° and 4.2°K by a ballistic method. Fields up to 43 kOe were applied along the b axis, i.e., the long axis of the needlelike specimens. The character of the M vs H curves changes rapidly in this temperature interval. They are described in first approximation by a model of this salt in which Cu+ + ions are coupled by isotropic antiferromagnetic exchange, −JS1·S2, in isolated pairs. The best fit of the data with the isolated cluster model yields J = −5.23k and g = 2.23, in reasonable agreement with earlier susceptibility, specific heat, and proton resonance results. Several modifications of the model were considered in order to remove small systematic discrepancies. The addition of a very weak intercluster coupling in a molecular field approximation yields a quantitative fit of all the data. If H = H0+nM, we find n = −1.2 mole/cgs while J = −5.14k and g = 2.35, in even closer agreement with other observation...

Motion of a magnetic domain wall traversed by fast‐rising current pulses

A Bloch wall is predicted to undergo finite displacements when traversed by a current pulse with short rise time ≤20 ns and long fall time, in thin films of metallic ferromagnets. In Ni–Fe films of thickness 85–150 nm, pulses with peak current density ≂1×107 A/cm2 are expected to induce wall displacements of order 0.1–1 μm. This effect originates from the s‐d exchange interaction. It is phenomenologically similar to the well‐known ‘‘wall streaming’’ motion of Bloch walls subjected to fast‐rising pulses of hard‐axis magnetic field. The effect is related to the existence of a novel, current‐induced, term in the expression for the momentum of a magnetic domain wall.

Observation of s‐d exchange force between domain walls and electric current in very thin Permalloy films

Large dc current pulses, ≂2 μs long, are sent through 30–40‐nm‐thick Ni87Fe13 films containing Neel walls. Wall displacements are seen for current densities ≥1.2×107 A/cm2. Displacements reverse when current sense is reversed. Walls always move in direction of charge carriers in this electronlike material. Our results agree with a theory of s‐d exchange interaction between walls and 4s conduction electrons. Hydromagnetic ‘‘domain‐drag’’ forces are too small in such very thin films to explain our data.

Multilayer configuration for experiments of spin precession induced by a dc current

Until now, most predictions about spin precession induced by a CPP dc current have concerned a simple “asymmetric” configuration consisting of a free magnetic layer and of a thicker pinned magnetic layer. In the present work, we propose a different configuration where the precessing free magnetic layer is sandwiched between two thicker pinned magnetic layers having opposite magnetizations. In this “antisymmetric” configuration, the spin current and accumulation arising from expansion/contraction are nearly three times as large as in the asymmetric configuration, for given current and layer thickness. Moreover, both interfaces of the free magnetic layer are now active to generate drive torques. This should result in a reduction of the critical current density needed for spin oscillations, by a factor of about six.

Exchange forces between domain wall and electric current in permalloy films of variable thickness

Wall displacements are induced by large current pulses crossing a wall, in Ni81Fe19 films. In films of thickness w<35 nm containing Neel walls, the sense of wall motion is found to be independent of the magnetization sense in the two domains adjacent to the wall, and is identical to the sense of motion of the electronlike charge carriers. This shows that the wall motion is not caused by stray magnetic fields, but rather by s‐d exchange forces generated by conduction electrons. The value ≂5×107 A cm−2 of the needed current density agrees with predictions of a theory based on s‐d exchange. In the case of cross‐tie walls in films with 35 nm <w<86 nm, the sense of wall motion does depend on the sense of the domain magnetizations. The force of the circumferential magnetic field of the current is probably important, here.

New origin for spin current and current-induced spin precession in magnetic multilayers

In metallic ferromagnets, an electric current is accompanied by a flux of angular momentum, also called spin current. In multilayers, spatial variations of the spin current correspond to drive torques exerted on a magnetic layer. These torques result in spin precession above a certain current threshold. The usual kind of spin current is associated with translation of the spin-up and spin-down Fermi surfaces in momentum space. We discuss a different kind of spin current, associated with expansion and contraction of the Fermi surfaces. It is more nonlocal in nature, and may exist even in locations where the electrical current density is zero. It is larger than the usual spin current, in a ratio of 10 or 100, at least in the case of one-dimensional current flow. The new spin current is proportional to the difference Δμ≃10−3 eV between spin-up and spin-down Fermi levels, averaged over the entire Fermi surface. Conduction processes, spin relaxation, and spin-wave emission in the multilayer can be described by...

Effect of interfaces on Gilbert damping and ferromagnetic resonance linewidth in magnetic multilayers

In magnetic multilayers, the presence of sharp interfaces causes a local increase of the interaction between spin waves and conduction electrons. This leads to an increase of the Gilbert spin-damping parameter near an interface. In turn, the ferromagnetic-resonance linewidth is increased over its value in single-layer films. In addition, the precession of magnetic spins during ferromagnetic resonance induces conduction-electron transitions from the spin-up to the spin-down band. As a result, the spin-up Fermi level differs from the spin-down Fermi level by an amount Δμ. At high precession amplitudes, the existence of Δμ causes a measurable decrease of the Gilbert parameter. At precession-cone angles exceeding 4°, the Gilbert parameter returns nearly to its single-layer value. Ferromagnetic-resonance line shapes are predicted to be non-Lorentzian, narrower and sharper near the top. This line-narrowing effect increases with increasing microwave power. The effect of Δμ spreads into the entire multilayer, ...

Multilayers as spin-wave emitting diodes

Magnon-electron interaction is enhanced in the vicinity of an interface between ferromagnetic and normal layers, in metallic thin films. When a dc current crosses this interface, stimulated emission of spin-waves is predicted to take place. Beyond a certain critical current density ≃107 A/cm2, a spontaneous precession of the magnetization is predicted to arise. This SWASER (Spin Wave Amplification by Stimulated Emission of Radiation) is the magnetic equivalent of the injection laser. In the earlier theories, the thickness of the precessing magnetic layer was assumed to be larger than the electron mean free path. We now treat the case of general value of that thickness L2x. The current-induced amplification rate of spin-waves is proportional to L2x in the limit L2x≃0, and goes through a maximum for L2x≃π/|k↑−k↓|. Here, k↑ and k↓ are the spin-up and spin-down Fermi wave numbers. At larger L2x, the amplification rate of spin-waves decreases towards zero. On that general decrease are superposed damped periodi...