Current-driven magnetic domain walls gather speed

Just because a magnet has a net moment—a north pole and a south pole—that doesn’t mean that all of its unpaired spins point in the same direction. More likely, several magnetic domains having different orientations will coexist, each separated from its neighbors by thin transition regions called domain walls.

And those domain walls don’t always stay put. They shift, for example, when an external magnetic field causes some domains to expand and others to shrink. Domain walls can also be displaced by spin-polarized current. As an electron passes from one domain to the next, it exchanges a spin-transfer torque with the intervening domain wall; the electron’s spin tilts in one direction and the domain wall’s spins tilt, ever so slightly, in the other. A current of electrons acting in concert can cause the wall to propagate.

Using current to move domain walls is potentially a convenient way to toggle a nanowire’s magnetization in order to write bits to magnetic random-access memory. (For more on MRAMs, see the article by Peter Grünberg in PHYSICS TODAY, May 2001, page 31 .) It has also been proposed as a way to shuttle sequences of magnetic bits to and fro in three-dimensional memory devices. ¹

For those ideas to make the leap from the lab to laptops, however, domain walls need to be driven quickly and reliably, with minimal current. Unfortunately, the materials best suited to yield highly mobile domain walls are also the most susceptible to Walker breakdown, a turbulence-triggering instability that slows domain-wall speeds to a crawl. Now, researchers led by Gilles Gaudin and Ioan Mihai Miron of Spintec in Grenoble, France, have figured out a way to avert Walker breakdown. ² As it turns out, they didn’t have to do much of note to the magnet itself; they only had to change its packaging.

Around the Bloch

In a macroscopic magnet, individual domain moments can point virtually anywhere. As the magnet’s dimensions decrease, however, thermodynamics begins to assert orientational preferences. (See the article by Chia-Ling Chien, Frank Zhu, and Jimmy Zhu in PHYSICS TODAY, June 2007, page 40 .) In a nanowire, for example, spins typically minimize energy by pointing along the wire axis, with neighboring domains aligned head-to-head. Although the domain walls in such a wire can be moved with current, they tend to be relatively large and unwieldy, which limits the number of bits that can be stored on a wire and the precision with which those bits can be manipulated.

More recently, researchers have begun to experiment with planar nanowires crafted by sandwiching a highly anisotropic ferromagnetic material in the middle of a multilayered nanostructure. In such wires, electron spins point out of the plane and neighboring domains are separated by a Bloch wall, an outward-pointing spiral of electron spins like that illustrated in panel a of the figure on page 20.

Among other advantages, Bloch walls are smaller, and they are predicted to propagate with more ease than the walls of axially magnetized wires. A simple model helps to illustrate the process: If conduction electrons are assumed to realign instantly with their local magnetic field, conservation of angular momentum requires that the electrons exert clockwise torques on counterclockwise Bloch walls, and counterclockwise torques on clockwise walls. Their effect, then, is to “untwist” the domain wall, propelling it forward in orderly fashion.

The true picture, though, is more complicated. The clockwise and counterclockwise conformations are degenerate, and bestowed with enough energy, a Bloch wall is free to sample both. That’s exactly what happens when the driving current density becomes large—the wall begins to flip back and forth, wasting energy in the process. A form of Walker breakdown, that instability marks the onset of an inefficient turbulent-flow regime.

Sustained stability

When Gaudin and company began conducting domain-wall experiments a few years ago, they fully expected to see the signatures of Walker breakdown at high current densities. During their initial tests using platinum-coated cobalt nanowires, however, they couldn’t get the domain walls to move at all. They then tried a different recipe: From sandwich structures of Pt, Co, and aluminum oxide that another Spintec group had been using for magnetic tunnel junctions, they crafted nanowires like those shown in panel b of the figure.

To the team’s surprise, with each pulse of current, the domain walls—housed in the ferromagnetic Co layer—zipped along the nanowires at speeds upwards of 100 m/s, well above those of previous experiments. ³ “We didn’t understand it,” recalls Miron. “At those current densities, the domain walls should have been in the turbulent regime.” In the team’s most recent experiments, domain-wall speeds were greater still, nearly 400 m/s, with no hint of Walker breakdown.

The researchers now believe they have a grasp on the underlying physics. They note that sandwiching Co between Pt and AlO_x introduces a structural inversion asymmetry, which in turn gives rise to an out-of-plane electric field. A fortuitous spin–orbit effect results: Due to the so-called Rashba effect, electrons experience an effective magnetic field H_R that causes their spins to tilt to one side. That tilt lifts the chiral degeneracy of the Bloch wall. Rather than flip back and forth between clockwise and counterclockwise conformations, the wall aligns permanently with H_R.

A follow-up experiment seemed to confirm the group’s hypothesis. The researchers used an external magnetic field to set the domain walls’ initial states—some were fixed to point away from H_R, others were fixed to point toward it. The domain walls that pointed away from H_R responded sluggishly to a pulse of current, the implication being that only after aligning with H_R could a domain wall propagate efficiently at high current densities.

More to learn

Still, Gaudin and company can’t yet claim a detailed understanding of what goes on in their nanowires. For one thing, although the domain wall resides in the 0.6-nm-thick Co layer, the thicker Pt layer likely provides the least resistive path for electrons. “We don’t know how the current divides between the nanolayers,” says Miron. “It’s possible that almost all of it goes through the platinum.” That wouldn’t necessarily be a bad thing. It would suggest that the actual domain-wall mobility, the wall speed per unit current density in the ferromagnetic layer, is higher than the team’s measurements indicate.

More puzzling is that although the team observed uniform, reproducible domain-wall motion, the walls seemingly traveled in the wrong direction. The simplest models predict that a Bloch wall should move in the direction of the electron flow. The walls in Gaudin and company’s experiments moved in the opposite direction. “We had to check several times to convince ourselves,” says Gaudin. “It’s strange but it’s not inconceivable.” Indeed, other groups have observed the same behavior.

At around 3 × 10⁸ A/cm², the current densities Gaudin and company used in their experiment are still an order of magnitude or so above the targets for market applications. With Walker breakdown no longer a nuisance, however, the team is free to focus on finding the ferromagnetic materials that most efficiently convert current to domain-wall motion.

Stuart Parkin of IBM’s Almaden Research Center in San Jose, California, sees the work as a key step in the right direction: “[Gaudin and colleagues’] work shows that the motion of the domain walls can be even more robust than we previously thought. It makes the possibility of domain-wall memories that much more exciting.”