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The Cinderella Particle

The lowly muon provides insight into the dark spaces between atoms.

By Hans Christian Von Baeyer
Dec 1, 1993 6:00 AMNov 12, 2019 5:54 AM


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Sometimes when Nature poses a problem of seemingly insurmountable difficulty, she simultaneously reveals a subtle phenomenon in an unexpected quarter that opens the door to a clever solution. In the nineteenth century, for example, the French philosopher Auguste Comte stated unequivocally that the composition of stars was something not merely unknown but forever unknowable. Comte could not have foreseen that in 1860, just three years after his death, dark absorption lines would serendipitously be discovered in starlight and would be used to read the elements of star stuff as clearly as words in a book.

A century later a less remote yet far more fundamental mystery was resolved in a similarly unexpected way. In 1952 the great mathematician and physicist Hermann Weyl, a colleague of Einstein’s at the Institute for Advanced Study in Princeton, published Symmetry, a beautifully illustrated little book for the general public, in which he declared categorically that in all physics nothing has shown up indicating an intrinsic difference of left and right. Just as all points and all directions in space are equivalent, so are left and right. The true difference between left and right, Weyl thought, was unknowable. But in 1957, just two years after his death, a team of physicists at the National Bureau of Standards in Washington, D.C., found that the nuclei of cobalt 60 atoms, when cooled to a sufficiently sluggish state and lined up in a magnetic field, display such a geometric property: their spins can be distinguished as left- handed or right-handed. This discovery caused a revolution in the understanding of elementary particles and immediately earned a Nobel Prize for the young Chinese-American theoreticians, Chen Ning Yang and Tsung-Dao Lee, who had suggested the experiment.

A modern example of the unexpected ways in which nature’s innermost secrets come to light concerns the determination of the strengths of magnetic fields in the inaccessible regions between atoms in solid materials--a world as remote as the interiors of stars. Since internal magnetic fields affect the behavior of electric currents, such measurements are urgently needed by the designers of integrated circuits and other electronic devices. However, these measurements are extremely difficult to make with conventional techniques. (Nuclear magnetic resonance, for example, reveals only the magnetic fields in the immediate vicinity of nuclei, not those that fill the outlying spaces between atoms. Worse, the technique doesn’t work at all in metals, because metals shield the microwave signals that carry out the information.) Where the dimensions of the materials are microscopic, as in the billionth-of-a-meter-thick structures on the surfaces of computer chips, the internal magnetic fields have defied measurement altogether--at least until now. But an elegant solution to this apparently intractable problem may be at hand. It is provided by the little-known technique of muon spin rotation, which makes use of an exotic misfit, called the muon, in the elementary particle zoo. Since the muon’s name derives from the Greek letter µ (pronounced mew), the method is abbreviated µSR.

Muons were discovered by accident during a search for the glue that keeps the atomic nucleus from being blown apart by the repulsion between the positive charges of its constituent protons. In the 1930s theoretical physicists had speculated that this glue, like everything else in the world, could be regarded as granular, the way light could be imagined as consisting of particles called photons. The hypothetical glue particles were expected to have masses lighter than that of the proton (the lightest of all nuclei) but heavier than that of the electron (into which they eventually decay), so they were called mesons, from the Greek for intermediate. When objects in this mass range actually showed up in the shower of cosmic rays that continuously rains down on Earth, the theorists were jubilant. But in 1947, just after the end of World War II, they learned of a simple experiment, performed with primitive equipment in a university laboratory in bombed-out Rome, that proved those cosmic rays interacted with nuclei about a trillionth as strongly as they were supposed to. If this was glue, it wasn’t sticking! The inevitable conclusion, swiftly though reluctantly arrived at, was that the real glue hadn’t been found yet, and that the cosmic ray particles, dubbed µ mesons, were something altogether unexpected and novel that didn’t fit into anybody’s world picture. When the venerable American Nobel laureate Isidor Isaac Rabi learned of the strange beasts, he exclaimed in frustration: Who ordered that?

In time it was found that in almost every conceivable respect the muon is unique. (The original name meson was changed to muon in order to distinguish the particle from the real nuclear glue particles, the mesons, which were discovered in due course. Unlike the electron and the positron, or the proton and the antiproton, which are pairs of antiparticles, the positive muon and its negative antiparticle are both called by the same name; consistency is not a hallmark of elementary particle nomenclature.) Compared with mesons, a muon interacts with nuclei incredibly feebly. Its lifetime is neither infinite, like that of a proton or an electron, nor as fleeting as that of a typical meson, which lives only one-hundredth of a millionth of a second. In fact it takes about two full millionths of a second before a muon, created in the collision of a cosmic ray from outer space with an atmospheric atom, spontaneously disintegrates into an electron (or, if it is positive, a positron) and a couple of neutrinos.

The most mysterious attribute of the muon is its mass, which is about 200 times larger than the electron’s. Despite the determined efforts of serious theorists and wild speculators over the course of half a century, there is as yet no explanation of this value, no derivation from more basic principles. In sharp contrast, the strength of the muon’s intrinsic magnetism can be calculated from relativity and quantum mechanics to a precision of a few parts per million--one of the most accurate computations in physics. Because of the muon’s family resemblance to the electron and the neutrino, it is classified with them as a lepton (from the Greek for lightweight), but its mass makes it a heavy lepton--a quintessential oxymoron.

Even in death the muon displays odd behavior. When it decays, it does so in the lopsided fashion of the cobalt 60 nucleus. If we imagine a negative muon that spins the way Earth does (counterclockwise, as seen from above the North Pole), mirror symmetry would require the electron to be emitted with equal probability above and below the equator--but it isn’t. The electron shows a strong preference for taking off in a southerly direction. Thus we could radio to an alien physicist in a distant galaxy who had never been taught the difference between left and right: Look at the decay of a negative muon. If you can curl your fingers in the direction of its spin while your thumb points in the direction of the decay electron, you are using your left hand. By reference to a muon, left and right can be unambiguously distinguished.

The very properties that render the muon exceptional among elementary particles--its intermediate mass, its long lifetime, the feebleness of its interaction with nuclei, and its skewed decay pattern-- happen to combine with its well-understood magnetism to make it an ideal probe of internal magnetic fields. When a positive muon enters a solid, it is relatively unaffected by the nuclei on account of its weak interaction with them, and by the electrons on account of its enormous weight advantage. As soon as it comes to rest in an interstitial space between atoms, it begins to precess about the direction of the locally prevailing magnetic field. Its motion resembles that of a child’s conical top spinning on a smooth floor: the top’s axis precesses slowly about the vertical--the direction of gravity. The rate of precession can be calculated from a knowledge of the top’s shape and weight, the speed with which it is spinning, and the strength of the gravitational force. The muon’s rate of precession, on the other hand, is determined by its own, known magnetic strength and by the magnitude of the magnetic field in which it is immersed: the stronger the field, the greater the force exerted on the muon and the faster the rate of precession. So if we could observe that precession, we could deduce the magnetic field surrounding the muon by a simple calculation.

If this were the end of the story, it would teach us nothing, because muons buried in a solid are hidden from the outside world. But it happens that nature has provided a way to monitor their precession. Positive muons emit their decay positrons not in random directions but preferentially along the axis of rotation. A group of precessing muons therefore behaves like a rotating lawn sprinkler that broadcasts its rate of rotation to distant places. A monitor that counts the rhythmic rise and fall of the emerging positron beam measures the rate of precession of the muons. (The image is tantalizingly reminiscent of the currently accepted model of a pulsar--a compact rotating star whose light emerges only from its magnetic axis, which is not lined up with its geographic axis and therefore sweeps past us in periodic rhythm.) By measuring the frequency of precession of the posi-tron signal, the strength and direction of the internal magnetic field at the sites of the muons can be determined. This is the technique known as µSR, which manages to put all the muon’s unique properties to use in an ingenious way.

One of the pioneers of µSR is physicist William J. Kossler, whose office happens to be down the hall from mine at the College of William and Mary in Williamsburg, Virginia. Jack, as his friends call him, is a slight, smiling man with a huge mop of unruly iron gray hair, great bushy eyebrows to match, and a permanently rumpled look. As often as not, his jacket collar is turned inside at the back, but what Jack lacks in sartorial refinement he makes up for in quickness of mind. At any time of the day or night--in the hallway, the office, the cafeteria, or the swimming pool--he is ready to launch into a spirited discussion of the latest development in physics or some brilliant new idea that has caught his fancy. Thanks to his engaging personality, I believe that even though I don’t exchange more than a few sentences a week with him, and although our specialties don’t overlap very much, I am better informed about his work than about that of any of my other colleagues.

Jack received his Ph.D. from Princeton almost 30 years ago, with a dissertation on the magnetic properties of atomic nuclei. The technique he used had been invented by I. I. Rabi, who passed it on to one of Jack’s thesis advisers. Thus it came about that Rabi’s own academic grandson could come up with a resounding answer to the question Who ordered that?

Years before he actually began to experiment with muons, Jack had learned about their extraordinary potential and decided that he would try to exploit it. Then, when he came to William and Mary and found himself near an accelerator capable of producing muons, he seized the opportunity. He hit pay dirt with his very first experiment, in 1973--a measurement of the magnetic field in nickel and iron: it became an important step along the road toward understanding the configuration of magnetic fields inside magnetized materials.

In the ensuing years muons have assumed a permanent place in the toolbox of solid-state physics, alongside such probes of matter as microwaves, light, X-rays, thermal radiation, electrons, positrons, and neutrons. But compared with those traditional techniques, µSR suffers from a serious drawback: it is very expensive. Cosmic rays being far too feeble and unpredictable a source, muons have to be produced artificially in order to make them useful. In principle the method is straightforward: whenever a nucleus is struck sharply enough by any projectile--an electron, a proton, or even another nucleus--it shakes off a shower of positive pi mesons, or pions, the most common of the glue particles, which in turn quickly decay into positive muons. These are corralled into a tight beam by magnets and then allowed to impinge on the sample under investigation. Detectors surrounding the target record the oscillating flow of emerging positrons. The limitation µSR therefore suffers from is that it requires the use of a powerful nuclear accelerator.

When the cyclotron operated by the College of William and Mary became obsolete in the late 1970s it was shut down, and Jack Kossler was forced to begin a pilgrimage in search of muons at other accelerators around the world. There were many capable of producing pions, but time and again he found that not all physicists shared his views on what should be done with them. Accelerators are built and operated by people with specific interests in the physics of nuclei and particles, and they often show little enthusiasm for the study of magnetism or materials. Partly because of this impediment, progress in µSR has been slow, but several impressive successes achieved in recent years by laboratories scattered around the world have caused the pace to pick up.

One particularly well-known application was to a strange class of materials called spin glasses. A spin glass sits squarely on the boundary between a magnetic material, like iron, and a nonmagnet, like gold. In the former the spins, and therefore the associated magnetic fields, of the electrons all line up like stakes in a picket fence and thus render the material magnetic. The minuteness of the strength of each individual magnet is compensated for by the immensity of the number of electrons, so that the final effect is powerful enough to pin my daughter’s paintings to the refrigerator door. In gold, on the other hand, the microscopic magnets happen to be too weak to affect the orientation of their neighbors, so they point helter-skelter in all directions, instead of lining up, and thus they cancel each other out.

Certain alloys, such as a mixture of gold with a few percent iron, form an altogether different state of matter, known as a spin glass. The magnetic iron atoms, dispersed evenly among the gold atoms, do not fully line up, but neither are they randomly directed. Instead they line up in patches, each one representing a permanently magnetized island in a sea of nonmagnetic gold. But since the magnetic directions of the various patches are randomly distributed, the macroscopic, overall magnetization is zero, just as in pure gold. The term spin glass does not imply that the material is transparent like ordinary glass--in fact, gold alloys are quite opaque. What gives spin glasses their name is the analogy between the magnetic directions of the patches in a spin glass and the orientations of molecules in ordinary glass, which are random but frozen in time. The first direct observation of these patches, made by Jack Kossler together with colleagues from AT&T; Bell Laboratories in Murray Hill, New Jersey, captured the attention of solid-state physicists and propelled interest in muons to a new level.

But a skeleton was lurking in the closet. From the very beginning, the pioneers of µSR realized that the technique had a serious shortcoming: it could not deal with samples of atomic dimensions, such as microscopically thin films. The reason was as simple as it was frustrating: the muons were too fast--instead of stopping in the thin films, the particles tore through them like bullets through gauze. Only thick, bulky targets could stop them. The excessive speed of the available muons was an inevitable consequence of their method of generation. When a pi meson decays, it converts so much of its mass into kinetic energy (via E = mc2) that the muon emerges like a speeding bullet. Thus, from the beginning, the practitioners of µSR dreamed of a beam of slow muons.

The most natural way to slow down a positive muon, or a bullet for that matter, is to shoot it through a block of solid material. (Retarding its motion by means of an opposing electric field turned out to be impossible: the voltage required to do the trick would be immense.) The trouble with the direct, brute force approach is that muons, in their passage through matter, are affected in two distinct ways. They do indeed lose energy in a smooth, controlled way as they bump against the atoms of the medium--a little like divers who quickly come to a stop on entering the water. At the same time, however, their electric charge tears loose electrons inside the material, and this more destructive process has a disruptive effect on the motion of the muons. The result is that a beam of muons entering a material at high speed emerges as a disorderly crowd with such a broad range of velocities that it is useless as a diagnostic tool.

Then Dale Harshman, while still a graduate student at the University of British Columbia in Vancouver, discovered that nature has provided a clever way around this problem. In noble gases (helium, neon, argon, krypton, and xenon--the hermits of the periodic table) the tendency of the electrons to be disturbed is much less pronounced than in other materials. Harshman reasoned that since these elements are chemically inert, the arrangement of their electrons might be impervious to disturbance by a passing muon. At extremely low temperatures most noble gases (with the exception of helium) become icelike solids, so he guessed that a slab of such a substance placed in the path of a beam of fast muons might slow them down in an orderly manner. With a group of colleagues, he tried the experiment in 1987 and found that solid argon really did have the desired effect.

As is usually the case in science and technology, the journey from the idea to its full-fledged exploitation is long and arduous. Producing a useful beam of slow muons is complicated by the extremes of temperature required to put the scheme into practice and by such technical obstacles as the tendency of a copious beam of particles to melt the solid it passes through. But progress was made. The current leaders in the international race to produce a beam of slow muons are E. Morenzoni and his colleagues at the Paul Scherrer Institute, an accelerator laboratory near Zurich, who have adapted Harshman’s idea and made it practical. Within the year they hope to conduct the first µSR experiments with their newly constructed beam.

Jack Kossler knows exactly what needs to be done. Today, seven years after the high-temperature superconductivity revolution, a complete theory of the phenomenon is still lacking. A particularly troublesome experimental obstacle is the difficulty of producing the relevant ceramic materials with precisely controlled chemical compositions--except, that is, in the form of atomically thin films, which can be made with high precision. Such films, in turn, are notoriously hard to study. In particular, how can you measure the magnetic fields inside them? Kossler knows. All you need is a beam of slow muons--and now his colleagues in Switzerland have built one. As soon as it is ready, he predicts, it will be aimed at a thin film of high-temperature superconducting material. The strength of the internal magnetic field will be measured, and then, he hopes, a study of the way this field is distributed in the material will provide the evidence needed to distinguish which of several alternative models is most promising.

The muon, the little interloper that nobody ordered, is poised to assume a place of unprecedented prominence in the physics laboratories of the world. In Switzerland, Canada, Japan, and the United States new µSR facilities are being planned that will testify to nature’s subtlety in a way that will remind us of the enigmas of stellar composition and the difference between left and right. After slyly concealing from our probing sensors the magnetic fields in the spaces between the atoms of a solid, nature has compensated by allowing the muon, aided by a block of solidified inert gas, to map them out after all. Einstein had it right, as usual, when he said: Raffiniert ist der Herr Gott, aber boshaft ist er nicht, or, in his own translation, God is slick, but he ain’t mean.

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