Exchange Torque Research Articles

Spin-polarized current induced magnetization switch: Is the modulus of the magnetic layer conserved? (invited)

The direct effect of spin-polarized current on magnetization states is studied on various electrodeposited single contacted nanowires (diameter about 60 nm). Three kinds of samples have been studied: (1) Homogeneous Ni nanowires, (2) nanowires composed of both a homogeneous Ni part and a multilayered Co(10 nm)/Cu(10 nm) part, (3) pseudospin-valve pillars Co(30 nm)/Cu(10 nm)/Co(10) electrodeposited in Cu wires. The magnetization reversal due to the current injection is observed in the three cases. The effect is observed with using different experimental protocols, including current activated after-effect measurements. The results obtained suggest that two different mechanisms are able to account for the magnetization reversal: exchange torque and spin transfer. We propose a definition of the two mechanisms based on the conservation or nonconservation of the magnetic moment of the ferromagnetic nanostructure.

A study of the induced anisotropy in a ferromagnetic grain from an exchange coupled antiferromagnetic grain with uniaxial anisotropy

Approximate analytic solutions for the energy of an antiferromagnetic (AF) grain, which experiences an external exchange torque from a ferromagnetic grain have been obtained for a wide range of AF thickness. The accuracy of the analytic expression is within 2.0% of the exact solution, which do not have a closed analytical form. The model predicts that there are two critical AF grain thickness for each particular exchange energy strength. Below the first critical thickness, the induced anisotropy energy is well approximated by an uniaxial anisotropy term. Above the second critical thickness the induced anisotropy is unidirectional. In the intermediate range the induced anisotropy can not be expressed simply as uniaxial or unidirectional. The exchange bias and coercivity in NiFe/IrMn films have been studied as a function of the IrMn thickness, and the results are consistent with the proposed theory.

A variational approach to exchange energy calculations in micromagnetics

This article presents a magnetization interpolation method for micromagnetic exchange energy calculations using a variational procedure to relax spins on a supplemental (refined) lattice. The approximations implicit in standard micromagnetic discretization schemes fail when angles between neighboring spins in the model become large, but the proposed approach effectively reduces the angle between neighboring spins, alleviating many of the associated problems. Moreover, this method does not introduce excessive discretization-induced vortex pinning observed with some large angle exchange energy formulations. This article includes details on proper post-interpolation exchange torque calculation, bounds on nearest-neighbor angles for interpolated lattices, a simple model predicting discretization-induced Néel wall collapse, and an example of a collapsed (1 cell wide) domain wall that can be restored by the proposed technique.

Corners and nucleation in micromagnetics

The divergence of the stray field in corners and its consequence for micromagnetic calculations was studied numerically in two dimensions for high-anisotropy materials. The results show that no atomistic theory has to be invoked because the singularity is smoothed out already within micromagnetics. The magnetic configurations and its deduced critical quantity, the coercivity, are determined correctly if the configurations are well approximated on the exchange length A/K d . The singularity in the stray field remains only visible in the torque balance where it is compensated by an exchange torque.

Analysis of 0.1 to 0.3 micron wide, ultra dense GMR memory elements

A micro magnetic analysis, has been performed for ultra dense magnetoresistive memory cells employing giant magnetoresistive materials that have array densities from 2/spl times/10/sup 8/ to 10/sup 9/ elements per square cm. The analysis shows that as elements are made smaller, it is necessary to increase the effective anisotropy constant by increasing the demagnetizing factor in the long dimension of the element (or by finding GMR materials with large anisotropy fields). With diminishing cell size, exchange torque becomes progressively more important, and depending in detail on the thickness of the magnetic and separation layers, the layers ultimately act semi-coherently. Cell widths are eventually limited to values between 0.05 and 0.1 microns by thermal considerations because the smaller cells require progressively larger word and sense fields. The analysis assumed GMR elements made from magnetic layers 50 to 60 Angstroms thick of Ni, Fe, Co alloys with Cu, Ag, or Au separation layers of 15 to 30 Angstroms and with a magnetoresistive coefficient of 6 to 9%. >

Current-induced displacements and precession of a Bloch wall in Ni-Fe thin films

Rectangular or exponential current pulses of duration ≂0.1 μs traversing a Bloch wall are found to induce wall displacements Δx≤10 μm/pulse in a Ni81Fe19 film of thickness ≂263 nm. The critical current density for wall displacement is jc≂1.35×106 A/cm2, about 20–200 times lower than for Néel or cross-tie walls investigated earlier. Wall motion arises probably from the precession of wall spins under the influence of the ‘‘s-d exchange torque’’ exerted by conduction electrons crossing the wall. The low jc value and easy precession of spins in a Bloch wall reflect the very small value ≂300 μT of the wall demagnetizing field which opposes spin orientation out of the wall plane in films of this thickness. A dc in-plane hard-axis field causes a linear decrease of jc. A dc easy-axis field smaller than Hc produces only a very slow decrease of jc.

Comment on ‘‘The pinning force between a Bloch wall and a planar pinning site in MnAlC’’

Pinning of a domain wall in uniaxial material by a thin layer defect is discussed. A coercivity Hc≂(2/3(3)1/2) (‖ακ−1‖/α) WfGM(K/M)((K/A)1/2) is found, where A, K, and M represent the exchange, anisotropy, and saturation magnetization of the bulk, and αA, and κK are those for the layer of thickness W≪((A/K))1/2. The Gaunt-Mylvaganam thermal excitation factor fGM≂1–0.40 K1/2A−3/2kT. This model is shown to be capable of explaining both the magnitude and temperature dependence of Hc in MnAlC for plausible values of α and κ for the layer, identified as grain boundary. Objections to the more complex treatment by Chen and Gaunt are discussed, in particular violation of exchange torque continuity.

Magnetization transport across a ferromagnetic-paramagnetic interface.

The transport of magnetization across a metallic ferromagnetic-paramagnetic bilayer is investigated using electron spin resonance. The ferromagnetic resonance and transmission electron spin resonance of films of palladium-iron alloys (${\mathrm{Pd}}_{100\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Fe}}_{\mathrm{x}}$, 0.5\ensuremath{\lesssim}x\ensuremath{\lesssim}4) on copper foils are measured. The data are analyzed using a phenomenological model with two proposed mechanisms to couple the magnetizations in the film and the copper. One mechanism is the diffusion of electrons across the interface; the other is an exchange torque across the interface. The dominant coupling mechanism is found to be diffusion of electrons. The model, in addition, accounts well for the angular variation of the spin resonance signal at a fixed temperature. Finally it describes moderately well the variations with temperature of the spin resonance signal over the temperature range in which the magnetization and ferromagnetic resonance linewidth of the ferromagnetic film are varying dramatically.

Possible existence of a Josephson effect in ferromagnets.

When a current density ${j}_{x}$ crosses a 180\ifmmode^\circ\else\textdegree\fi{} domain wall in a metallic ferromagnet, the spin s of each conduction electron exerts an s-d exchange torque on the localized wall spins. Hence, the wall moment of a Bloch wall is canted out of the wall plane by an angle \ensuremath{\psi}, given by ${j}_{x}$=(eC/\ensuremath{\Elzxh})sin(2\ensuremath{\psi}), where C is the maximum restoring torque at \ensuremath{\psi}=45\ifmmode^\circ\else\textdegree\fi{}. This equation is the exact analog of the dc Josephson effect, and 2\ensuremath{\psi} is the analog of the superconducting phase difference \ensuremath{\varphi} across a junction. For \ensuremath{\Vert}${j}_{x}$\ensuremath{\Vert}>eC/\ensuremath{\Elzxh}\ensuremath{\simeq}${10}^{6}$ A/${\mathrm{cm}}^{2}$, the s-d exchange torque overcomes the restoring torque, and the wall moment precesses with a frequency \ensuremath{\omega}=d(2\ensuremath{\psi})/dt. A dc voltage \ensuremath{\delta}V is expected to appear across the wall, satisfying the famous ac Josephson relation 2e\ensuremath{\delta}V=-\ensuremath{\Elzxh}\ensuremath{\omega}. This wall precession can be described as a translation of Bloch lines, and the Bloch lines are the exact analog of superconducting vortices. The electric current exerts a transverse force on Bloch lines.

Higher order surface couplings in elastic ferromagnets

The “classical” theory of elastic ferromagnetic materials is extended to the case of media able to support hyperstresses (double stresses, couple stresses), so as to take account of surface effects (curvature, role played by the magnetic anisotropy on the surface, boundary layer effect and to offer a larger choice of boundary conditions as far as magnetic spins are concerned (pinning, nonzero exchange torque,…). The field equations and the associated boundary conditions are obtained by using the generalized formulation of the principle of virtual power based on the requirement of objectivity for internal forces. Constitutive equations for nonlinear thermoelastic, magnetically saturated insulators and equations linearized with respect to small deformations are established. The set of equations obtained will permit a finer study of coupled magnetoelastic surface waves and of the resulting resonance phenomena in thin ferromagnetic deformable layers.

Observer-based Attitude Control In The Sliding Mode

With the increasing interest in small, relatively inexpensive satellites, envisaged to be produced on a large scale, there is a need to minimise development costs by embodying as many common elements as possible. The research presented here is aimed at the production of a 'universal' attitude controller in partial fulfilment of this need. Continuous momentum exchange torque actuators are assumed at present. Such a controller must maintain a specified dynamic response to changing attitude demands through a wide range of spacecraft dynamics parameters and in the presence of external disturbance torques. The sliding mode approach is pursued in view of its relative simplicity and effectiveness, especially when dealing with the continuous non-linearities of a) the kinematic differential equations for large angle slewing manoeuvres and b) the spacecraft dynamics when the angular velocities are sufficiently high for gyroscopic inter-axis coupling to be significant. Since the pointing accuracy of any attitude control system is ultimately limited by the accuracy of the attitude measurement system, a minimal requirement is on-board instrumentation for high precision measurement of attitude angles. To avoid the necessity of additional instrumentation for the measurement of other state variables such as angular accelerations, the control system is observer based. The sliding mode controller embodies two novel features: a) control smoothing integrators to eliminate actuator drive chatter and b) block control principle to facilitate straightforward design despite the non-linearities. The control system may be designed simply by eigenvalue assignment to yield a specified closed-loop dynamic performance. Three possible special observers Transactions on the Built Environment vol 19, © 1996 WIT Press, www.witpress.com, ISSN 1743-3509 640 Structures in Space are investigated which are intended to be insensitive to spacecraft dynamics modelling errors, to be compatible with the control law The control system performance is demonstrated by simulation, including sensitivity to measurement noise.

New Magnetic Anisotropy

A new type of magnetic anisotropy has been discovered which is best described as an exchange anisotropy. This anisotropy is the result of an interaction between an antiferromagnetic material and a ferromagnetic material. The material that exhibits this exchange anisotropy is a compact of fine particles of cobalt with a cobaltous oxide shell. The effect occurs only below the N\'eel temperature of the antiferromagnetic material, which is essentially room temperature for the cobaltous oxide. An exchange torque is inferred to exist between the metal and oxide which has a maximum value at 77\ifmmode^\circ\else\textdegree\fi{}K of \ensuremath{\sim}2 dyne-cm/${\mathrm{cm}}^{2}$ of interface.

Energy of a Bloch Wall on the Band Picture. I. Spiral Approach

It is shown that the band or itinerant electron model of a solid is capable of accounting for the which determines the properties of the transition region, known as the Bloch wall, which separates adjacent ferromagnetic domains with different directions of magnetization. In this treatment the constant spin function usually assigned to each running electron wave is replaced by a variable spin function. At each point of space the spin of a moving electron is inclined at a small velocity-dependent angle to the mean spin direction of the other electrons, and this gives rise to an exchange torque which makes the spin direction of the given electron precess as it moves through the transition region, the precession rate being just sufficient to keep it in approximate alignment with the macroscopic magnetization. Physical insight into the mechanisms involved is provided by a rigorous solution of the wall problem for a ferromagnetic free electron gas in the Slater-Fock approximation, although it is known that the free electron gas is not likely to be ferromagnetic in higher approximations. Rough upper limits to the exchange stiffness constants for actual ferromagnetic metals can be calculated without using any empirical constants other than the saturation moment and the lattice constant. The results are only a few times larger than the observed values.