Magnetoelectronic components and measurement method

Abstract

Magnetoelectronic components comprise at least one oblong working structure made of a ferromagnetic material, along which magnetic domain walls can migrate, means for applying an electric current to this working structure, and at least one magnetic field sensor for the magnetic field generated by the working structure. The working structure is designed so that it is able to form domain walls, the transverse magnetization direction of which in the center has no preferred direction in the plane perpendicular to the migration direction thereof along the working structure, and/or can form massless domain walls. It was found that the kinetic energy of such moving domain walls vanishes. These walls are thus not subject to the Walker limit nor to intrinsic pinning. As a result, the components can read, store or process and finally output information more quickly. The invention also relates to a method for measuring the non-adiabatic spin transfer parameter of a ferromagnetic material. This method was developed as part of a more in-depth examination of the phenomena that were found.

Claims

1. A method for measuring the nonadiabatic spin transfer parameter of a ferromagnetic material, comprising: measuring angular velocity wherein magnetization direction of domain walls rotates about a direction of migration when the domain walls pass through a working structure made of the ferromagnetic material and wherein a non-adiabatic component of said angular velocity results from a local maladjustment between spin and magnetization in the ferromagnetic material.

2. The method according to claim 1, wherein the value of the Gilbert damping factor is determined based on the velocity at which the domain walls pass through the working structure under the influence of an external magnetic field.

3. A method according to claim 1, wherein the value of the spin polarization P is determined based on the velocity at which the domain walls pass through the working structure under the influence of an electric current.

4. A method according to claim 1, wherein the non-adiabatic spin transfer parameter b is determined based on the frequency at which the magnetization direction of domain walls undergoes dipole oscillations under the influence of a current flowing, through the working structure.

5. A magnetoelectronic component, comprising: a longitudinally-extending working structure made of a ferromagnetic material that generates a magnetic field, and at least one magnetic field sensor for sensing the magnetic field generated by the working structure, wherein the working structure, when an electric current is received at the working structure, is configured to comprise: magnetic first domain walls that migrate along the working structure, and massless domain walls having a transverse magnetization direction of which in a center has no preferred direction in a plane perpendicular to a migration direction along the working structure, and wherein the massless domain walls have a predominant direction of magnetization in a center of the working structure so as to comprise frontal domain walls having a magnetization, along a migrating direction through the working structure, that is rotated by 180 degrees.

6. A magnetoelectronic component according to claim 5, wherein the working structure has no shape anisotropy perpendicular to the migration direction of the massless domain walls.

7. A magnetoelectronic component according to claim 5, wherein the working structure has material anisotropy.

8. A magnetoelectronic component, comprising: a longitudinally-extending working structure made of a ferromagnetic material that generates a magnetic field, and at least one magnetic field sensor for sensing the magnetic field generated by the working structure, wherein the working structure, when an electric current is received at the working structure, is configured to comprise: magnetic first domain walls that migrate along the working structure, and massless domain walls having a transverse magnetization direction of which in a center has no preferred direction in a plane perpendicular to a migration direction along the working structure, and wherein the massless domain walls have a predominant direction of magnetization in a center of the working structure so as to comprise transverse domain walls having a magnetization, along a migrating direction through the working structure, that is rotated by 90 degrees.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1: is a configuration of a transverse domain wall in a cylindrical wire having a length of 4 m and a diameter of 10 nm;

(2) FIG. 2: is a sketch of the characteristic rotary motion of the magnetization direction of domain walls in a cylindrical wire;

(3) FIG. 3: shows the linear velocity of the domain wall as a function of the current density in a cylindrical wire (sub-image a); the displacement of the domain wall as a function of time for various current density values (sub-image b); a comparison of the velocities of the domain walls in cylindrical wires having two different diameters (sub-image c); and

(4) FIG. 4: shows the dynamics of the magnetization direction in the domain wall.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

(5) The particularly preferred embodiment of a cylindrical working structure was examined both by way of micromagnetic simulations and analytically. The simulation was carried out for the normalized local magnetization {right arrow over (m)} using a finite element algorithm based on the aforementioned Gilbert equation.

(6) In the exemplary embodiment that was examined, the working structure is a wire made of Permalloy (Py) having the material parameters .sub.0M.sub.s=1 T (saturation magnetization), vanishing anisotropy and exchange constant A=1.3*10.sup.11 J/m. Such a working structure can be used as a magnetic shift register, for example.

(7) FIG. 1 shows the configuration of a transverse domain wall in a cylindrical wire having a length of 4 m and a diameter of 10 nm, which was obtained as the result of the simulation. The Cartesian coordinate system that was used for the simulation and a spherical coordinate system that was employed for the analytical examination are shown on the bottom left of FIG. 1. For comparison, the configuration of a transverse domain wall in a Permalloy strip having a width of 100 nm and a thickness of 10 nm is shown as an inserted image at the top right of FIG. 1. For the simulation, the volume of the wire was discretized into 259,200 tetrahedrons having a cell size of approximately 1.25 nm1.25 nm5 nm. Given the axial symmetry, the structure of the wall and the energy thereof are invariant with respect to the rotations of the magnetization in the xy plane.

(8) The domain wall moves in the direction of the electron flow (negative z direction) under the influence of an electric current along the positive z axis. In addition to the linear motion along the wire axis, the magnetization direction of the domain wall rotates about the wire axis.

(9) FIG. 2 shows this characteristic rotary motion of the magnetization direction. The black cross-sections of the wire shown here in the form of a tube indicate the positions of the domain walls at various times t.sub.1 to t.sub.5. The arrows in these cross-sections indicate the orientations of the transverse magnetization direction of the domain wall at these times at these locations. The helix inscribed in the wire illustrates the precession motion of the domain wall. In the simulations, was fixed at 0.02, while the value of varied between 0 and 0.1.

(10) FIG. 3a shows the linear velocity v of the domain wall as a function of the current density j in a cylindrical wire having a diameter of 10 nm for =0.02 and four different values of . The lines in FIG. 3a represent analytically computed values of u. The velocity is linearly dependent on j and is independent of . For comparison, the motion of the domain wall in a thin strip was simulated using the same parameters (inserted image in FIG. 3a). The lines in this inserted image are merely a graphical sketch of the functional curves based on the simulated individual values. The wire behaves fundamentally differently from the strip. No intrinsic pinning is found in the wire for =0. In contrast, a minimal (critical) current must be injected in the strip in order to trigger the motion of the domain wall. For small values of j, the velocity of the domain wall was low and independent of j. This can be attributed to a magnetostatic effect, which is related to the finite sample size: If the domain wall is moved out of the center of the sample, a longitudinal magnetostatic field is obtained.

(11) It should also be noted that the domain walls in the round wire are massless. The profiles thereof do not change during the motion. The simulation did not produce any mass whatsoever for the domain wall even if unrealistically high values were assumed for j or external magnetic fields, at which the domains break down due to nucleation processes. Whether the domain walls are massless strictly mathematically or only practically, however, is irrelevant for the technical application in the magnetoelectronic component, and specifically in the shift register.

(12) The structure of the domain wall in the cylindrical wire does not break down because of the Walker limit. The Walker limit, however, is reached in the strip when >. As is indicated by the arrows in the inserted image in FIG. 3a, this results in a severe drop in velocity.

(13) The velocity of the domain wall in the cylindrical wire is not dependent on . The strip, in contrast, exhibits strong dependence on . In the round wire, the domain wall achieves a constant velocity immediately after the current is activated. This observation agrees with the domain wall having no mass or inertia.

(14) FIG. 3b illustrates this unimpaired motion of the domain wall. Here, the displacement d of the wall is plotted as a function of the time t for three different values of j.

(15) FIG. 3c shows a comparison of velocities of the domain walls in cylindrical wires having two different diameters (10 nm and 40 nm). This shows merely low dependency on the wire diameter.

(16) FIG. 4 summarizes the dynamics of the magnetization direction in the domain wall. The drawing shows the angular velocity at which this magnetization direction rotates, over the current density j, for three different values of . An inserted image on the bottom left of FIG. 4 shows a comparison of the angular velocities between the wire that is 10 nm thick and the wire that is 40 nm thick. Analogous to the linear displacement of the domain wall, the angular velocity at which the magnetization direction rotates is linearly dependent on j. However, it also depends on ; it was found that it is proportional to (). The direction of rotation changes with =, where the magnetization direction of the domain wall ideally does not rotate. In the simulation, slow rotation is also obtained in this case. This is due to a magnetostatic effect, which can be attributed to the finite length of the simulated wire.

(17) In order to examine the physical background of this simulated data, the field at which the structure of Bloch domain walls breaks down as a result of the Walker limit was computed using an analytical model, which was developed in (A. Mougin, M. Cormier, J. P. Adam, P. J. Metaxas, J. Ferr, Domain wall mobility, stability and Walker breakdown in magnetic nanowires, Europhysics Letters 78, 57007 (2007)). The spherical coordinate system shown on the bottom left of FIG. 1 was employed. The angular velocities of magnetization depend as follows on the torques lab acting on the wall:

(18) $\stackrel{.}{}=\frac{}{t}=-\frac{}{M_s}{}_{}$$\stackrel{.}{}=\frac{}{t}=-\frac{}{M_s}{}_{}$

(19) The expression for the total torque acting in the domain wall is provided in Equation 10 of Mougin et al. There, a static magnetic field H, which acts along the z direction, a demagnetization field, an equivalent damping field, which describes the torque caused by damping, and an electric current flowing in the z direction are taken into consideration. Utilizing the cylinder geometry of the wire and the simplification that only the center of the domain wall (=/2) is taken into account, all terms that belong to the demagnetization field can be eliminated, resulting in the following:

(20) ${}_{}=\frac{M_s}{}\stackrel{.}{}+\frac{M_{s}u}{}\frac{}{z}{.Math.}_{\mathrm{wc}}{}_{}=-M_{s}H-\frac{M_s}{}\stackrel{.}{}-\frac{M_{s}u}{}\frac{}{z}{.Math.}_{\mathrm{wc}},$
where the index we denotes the center of the domain wall.

(21) For the sake of simplicity, initially the motion of a domain wall which is driven by a static external magnetic field acting along the z axis was examined. With u=0, this results in:

(22) $\stackrel{.}{}=-\stackrel{.}{}$$\stackrel{.}{}=\frac{H}{1+{}^2}.$

(23) In the static external field, the domain wall (apart from a prefactor 1/(1+.sup.2) that is close to one) is in precession at the Larmor frequency and moves in the field direction as a result of the damping. As far as the achievable velocity is concerned, the motion of domain walls which is driven by an external field is of lesser interest given the weak prefactor .

(24) H=0, instead of u=0, was assumed for the motion of domain walls which is driven by an electric current, resulting in the following:

(25) $\stackrel{.}{}=-\frac{\left(1+\right)u}{1+{}^2}\frac{}{z}{.Math.}_{\mathrm{wc}}\stackrel{.}{}=-\frac{\left(-\right)u}{1+{}^2}\frac{}{z}{.Math.}_{\mathrm{wc}}.$

(26) These equations show how the adiabatic term influences the linear motion of the domain wall, while the difference between the non-adiabatic term and the damping term influences the rotation of the magnetization direction. In contrast, with Bloch domain walls or transverse domain walls in strips, the damping term and/or the non-adiabatic term create a distortion of the domain wall, which is to say a non-vanishing mass. This non-vanishing mass causes various undesirable effects, such as intrinsic pinning and the Walker limit for the velocity. The critical current, or the critical field, at which the domain wall structure breaks down as a result of the Walker limit is typically defined as the point at which the center of the domain wall begins to rotate out of the original plane thereof (0). When the working structure is a wire, however, the symmetry thereof allows the magnetization of the domain wall to rotate freely, without the domain wall becoming deformed. The angular velocity here depends on (), while the linear velocity at which the domain wall moves is independent of .

(27) It is remarkable that both {dot over ()} and {dot over ()} are proportional to /z|.sub.wc, which is a measure of the width of the domain wall. The width of the domain wall is not relevant for the linear velocity v because v={dot over ()}.Math.z/. The linear velocity is thus substantially equal to u, which is plotted in FIG. 3a in the form of lines. This explains why the linear velocity, as shown in FIG. 3c, is independent of the thickness of the wire, although the thicker wire forms wider domain walls. This is consistent with the simulation in the inserted image on the bottom left of FIG. 4, which shows that the angular velocity is less in the thicker wire. The lines in FIG. 4 show analytical values of the angular velocity for various values of . These lines were obtained using a value for /z|.sub.wc that was extracted from a simulated domain wall profile. The simulation also confirms, almost perfectly, the result that was obtained analytically, which is that the same angular velocities should develop for identical () that are identical in terms of the absolute values and have differing algebraic signs.

(28) The dependence of the angular velocity on the difference between and opens up interesting possibilities for measuring the non-adiabatic spin transfer parameter , which is the prefactor for the non-adiabatic spin transfer torque term and which is typically difficult to determine. The characteristics of the field- and current-driven motions of domain walls in round wires should allow precise determination of this information, because the value of follows from the field-driven velocity. The value of can then be determined based on the frequency of the current-driven dipole oscillations, which follow from the expressions for {dot over ()} and {dot over ()} in the current-driven case. The polarization rate P, which in this case is almost identical to u, can also be determined from the current-driven velocity of the domain wall (see FIG. 3 and the corresponding explanations in the general description section).

(29) The determination of the non-adiabatic spin transfer parameter according to the method proposed here can begin with knowledge of, or when having experimentally determined, the value of the damping parameter . The value of is advantageously measured based on the measurement of the velocity at which the domain walls move along the working structure under the influence of a longitudinally applied magnetic field. According to the aforementioned dynamics, this velocity is given by

(30) $v=-\frac{}{1+{}^2}.Math..Math.\frac{1}{/z{.Math.}_{\mathrm{wc}}}.Math.H$

(31) In addition to the damping constant , the velocity is thus dependent on the gyromagnetic ratio and the magnetic field strength H of the driving field as well as on the magnetic structure of the domain wall. The /z|.sub.wc value describes the gradient of magnetization along the working structure in the center of the domain wall. It is related to the domain wall width and can be determined by analytical models, experimental measurements, or computer simulations. The value of can thus be determined according to the above equation, because this is the only unknown variable in this equation. Mathematical ambiguities that occur in solving the quadratic equation for a can be eliminated by the condition <<1.

(32) After the value of is determined, can be determined based on the frequency of the dipole oscillations that the domain walls perform while they are moved through the working structure under the influence of an electric current. The angular velocity is given by

(33) 0$=\stackrel{.}{}=\frac{-}{1+{}^2}u\frac{}{z}{.Math.}_{\mathrm{wc}}$
where the value of /z|.sub.wc can again be determined by measurement or estimated by computations. The value of u is given by

(34) $u=-\frac{g{}_{B}P}{2{\mathrm{eM}}_s}j.$
Possibilities for determining the variables that occur in u were described above. This creates a direct, simple relationship between the measurable angular velocity and the required value of the non-adiabatic spin transfer parameter .