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A fresh perspective has always been of benefi t to science. RODERICH MOESSNER, Director at
the MAX PLANCK INSTITUTE FOR THE PHYSICS OF COMPLEX SYSTEMS, conducts research into unusual types of order in condensed matter, for example in magnets. In the process, he has discovered exotic phenomena such as magnetic monopoles.
36 MAXP LANCKR ESEARCH 1/2009 THE WORLD OF QUANTA
ight and shadow, good and bad, poles exist in magnetic materials, his colleagues Claudio Castelnovo Lyin and yang – some opposites seem astonishing. Moessner, a theo- and Shivaji Sondhi at the universi- need each other. Physics also has an retical physicist and Director at the ties of Oxford and Princeton, respec- inseparable pair of opposites: the Max Planck Institute for the Physics tively. The researchers’ theory has north and south poles of a magnet. of Complex Systems in Dresden, be- attracted attention in the scientifi c To date, physicists have never been lieves that they exist in a substance community, not least because it has able to fi nd reproducible evidence that derives its exceptionally unusu- explained mysterious experimental for the existence of a single magnet- al magnetic properties from its par- data on spin ice (see box, page 40). ic pole – what they call “a magnetic ticular crystal structure: spin ice. The fact that discrete magnetic monopole”. The majority of research- Spins are the minute magnetic mo- north and south poles occur in spin ers are not surprised by this, as all ments of the electrons in the solid, ice, however, does not mean that known magnetic building blocks of which behave like miniature bar there are two new particle types, matter, such as the electron and the magnets. These miniature bar mag- each bearing one of these magnetic neutron, always possess both north nets are arranged in spin ice in the poles in the same way that electrons and south poles. Since our environ- same pattern as water molecules in bear a negative electric charge and ment is made up of such particles, ice (see box, page 39). protons a positive one. The textbooks there should be no piece of matter In the material, magnetic north of elementary particle physics do not
(2) that constitutes a magnetic mono- and south poles can move apart by need to be rewritten. pole. That, at least, is the general any distance, as if freely mobile car- ICHALKE WATER WAVES ARE A M consensus. riers of magnetic north poles and COLLECTIVE PHENOMENON
ORBERT Against this background, the re- corresponding carriers of south poles
: N sults of Roderich Moessner’s re- existed. This is the conclusion of “Rather, the existence of magnetic HOTOS
P search, namely that magnetic mono- analyses performed by Moessner and monopoles is a collective phenome- non due to the interactions between Research into new forms of order: Roderich Moessner with a model of the the atoms and electrons of which spin-ice crystal lattice (left) and with V. Ravi Chandra from his group (bottom). spin ice is composed,” says Moess- ner. He compares the atomic team- work in spin ice with water waves: “Individual water molecules do not exhibit waves; only a great many water molecules together are able to do so, by exerting forces on their neighbors. Waves are a simple ex- ample of a collective phenomenon.” Waves in water and magnetic monopoles in spin ice are examples of the whole being potentially more than merely the sum of its parts. “Emergence” is the term that scien- tists use for the appearance of new qualities when a large number of discrete elements combine to form a new unit. An example is the combi- nation of many individual cells to form a multicellular living organism. Solid-state physicists know of nu- merous emergent phenomena, such as sound waves in crystals. Many of
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these collective phenomena do not therefore apply that cannot be de- He concluded his paper by saying: constitute elementary particles in the rived directly from the fundamental “The whole is not only more than, usual sense; like the discrete mag- formulae of elementary particle but also very different from, the sum netic poles in spin ice, however, they physics. Such fi ndings suggest that of its parts.” In order to understand have certain properties in common some materials can be regarded, in a the behavior of large and complex with such particles. For this reason, sense, as miniature worlds that ef- conglomerates of elementary parti- they are also referred to as “quasi- fectively create their own laws of cles, research must be conducted that particles”. nature. is no less fundamental than the study The magnetic monopoles are a The Dresden-based scientist is not of the smallest particles themselves. class of quasiparticles that particu- the only one with this view. As early The researchers in Roderich Moess- larly fascinate physicists, while at as 1972, American physicist Philip ner’s group have attempted to dis- the same time presenting them with W. Anderson warned in the journal cover as yet unknown principles ac- major puzzles. “Quasiparticles exist SCIENCE of the consequences of the cording to which complex physical that appear to be fragments of ele- reductionist research philosophy systems organize in space and time. mentary particles that are normally then prevailing. This philosophy as- One object of their research is topo- considered to be indivisible,” says sumes that things can be understood logical quantum liquids. In a quan- Moessner. The electron, for example, by being broken down to their small- tum liquid, matter is present in a is defi ned by, among other things, est constituent parts. This is the route special state that exists in addition two properties: its negative elemen- that particle physicists were taking to the solid, liquid and gaseous phas- tary charge and its magnetic moment at the time. es. An example is the Bose-Einstein of a certain strength. These two Anderson countered that reduc- condensate, in which, at very low properties appear as inseparable as tionism would never be able to de- temperatures, small clouds of atoms the two sides of a coin. liver a complete explanation of mac- enter a common quantum state. A roscopic phenomena, such as quantum liquid is topological when WORLDS WITH solid-state materials, plants, human certain of its properties are deter- THEIR OWN LAWS beings or the universe. mined by its geometry. “These topo- In solids, however, quasiparticles can in principle occur that, although they possess the magnetic moment of an electron, carry no charge (or vice- versa). In other words, they can be compared to one-sided coins. Against this background, it no longer seems absurd for spin ice to contain mag- netic monopoles. The deconstruction of the elemen- tary particles in the solid does not stop here: at very low temperatures and in strong external magnetic fi elds, quasiparticles can even occur at interfaces between two parts of
the solid that bear a fraction – for 22-23 (2007) 451,
example a third – of the elementary ATURE charge that is recognized as being indivisible. , S.L. N In complex physical systems, with ONDHI
their many billions of interacting , R., S atomic nuclei and electrons, laws OESSNER , C., M ASTELNOVO : C MAGE I
38 MAXP LANCKR ESEARCH 1/2009 THE WORLD OF QUANTA
logical quantum liquids are currently playing an important role in the re- search into quantum computers,” says Moessner. 451, 22-23 (2007) 451, The hidden organizing principles are, in a sense, the laws of nature of ATURE complex systems, and thus the , S.L. N foundation of new insights. Rod- ONDHI
erich Moessner and his colleagues , R., S only predicted the appearance of the magnetic monopoles after they OESSNER had observed a new form of order , C., M in spin ice. ASTELNOVO
NO MONOPOLES : C MAGE WITHOUT SPIN ICE I
This new type of order concerns the magnetism in the material. The mag- netic order of spin ice is much less evident than, for example, that in ferromagnetic metals, which can be A question of alignment: If two of the spins point into the tetrahedron and two out of it (top left), their magnetic charges cancel (bottom left). When a spin permanently magnetized. “In ferro- fl ips, two monopoles form (top and bottom right). magnets, the magnetic moments of all atoms tend to be aligned,” says combinations for the orientation of Moessner. The arrangement of the SPIN ICE AND WATER ICE the four magnetic moments at the moments can be compared to a pick- Spin ice forms in a crystal lattice of corners of the tetrahedron, and thus et fence. “To see this order, it would tetrahedra that are joined at their six different total magnetic mo- be suffi cient to observe the align- corners. Spin ice composed of the ele- ments. The magnetic moments of ment of the moments of a few dis- ments holmium or dysprosium, titanium multiple tetrahedra combine to form and oxygen. Spin ice owes its name to crete atoms,” he explains. We would the magnetization of a region under a similarity with water ice. The latter then discover that most of the mag- consists of oxygen and hydrogen atoms. consideration. Even when the ice netic moments point in a certain di- Each oxygen atom has four neighboring rule is observed, different regions in rection. This order is local. hydrogen atoms. Two of these – the spin ice may vary widely in their “In spin ice, by contrast, there is two with which the oxygen atom forms magnetization. a water molecule – are closer to the no local order,” says Moessner. But “In spin ice, one revealing quanti- oxygen than the other two. Experts call the fact that spin ice is not simply this the ice rule. Spin ice has a similar ty is the magnetization of lattice random becomes evident only when local arrangement of the magnetic planes that run through the crystal all magnetic moments in a larger re- moments of the spins located at each like fl oors through a building,” says gion are observed. “First, however, corner of the tetrahedron. Magnetic Moessner. The magnetization of moments resemble minute bar magnets, we must consider the individual tet- these planes turns out to be the same each with a north and a south pole. rahedra of which spin ice is com- Like the needle of a compass, the mag- as long as the ice rule is observed. posed,” says Moessner. Each tetrahe- netic moments are pivoted at each of “This shows that a certain order is dron is subject to the ice rule, which the four corners of the tetrahedra that still present,” he says. And only dictates that the magnetic moments make up spin ice. In the lowest-energy where an order exists can it be vio- and thus preferred state of spin ice, at two of its corners have one orien- lated. A magnetic monopole is noth- two north poles in each tetrahedron tation, the opposite to that of the point to its center, and two away from ing other than such an infringement. moments at the other two corners it – a magnetic version of the ice rule. Initially, Roderich Moessner’s interest (see box, page 41). This permits six lay not in the magnetic monopole,
A network of tetrahedra: In this structure, holmium or dysprosium, titanium and oxygen combine to form spin ice.
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but in the departure from such an or- cules align along one spatial direc- der. He considered how the magneti- A MYSTERIOUS tion; otherwise, they remain ran- zation of the entire crystal changes PHASE TRANSITION dom. The existence of these when an external magnetic fi eld acts In 2004, researchers in Japan observed electronic states was later verifi ed on spin ice in the laboratory. that a phase transition occurs in spin experimentally. ice when, at temperatures below one Moessner subsequently conducted THE SEARCH FOR Kelvin – equal to minus 272 degrees research in Hamilton (Canada) and A NEW ORDER Celsius – a magnetic fi eld was increased above a critical value. The transition at Princeton University in the US. “The magnetization can change only displayed characteristics similar to the There, he showed that – surprisingly when the ice rules are violated at condensation of water vapor. The re- simple – microscopic models exist searchers observed, for example, that certain points in the crystal. Magnet- in which the elementary charge can energy was suddenly released. But ex- ic defects are then formed at these actly what happens in the crystal was be separated from the magnetic mo- points,” explains Moessner. These still unclear. The magnetic monopoles ment of an electron – that is, the defects move through the crystal in proposed by Moessner and his col- spin. To understand how this hap- the direction of the magnetic fi eld, leagues now provide an explanation: pens, one can imagine that the elec- their density increases suddenly when and transport the change in magne- trons in the solid move on a lattice. the critical magnetic fi eld is reached. tization from one plane to another. In a sense, they change from a gaseous The negative charges of the elec- When he analyzed the properties of to a liquid state. trons are compensated by the posi- these defects, the physicist noticed tively charged ions. that they were magnetic monopoles: throughout Moessner’s research ca- In the lattice planes, each electron they behave in an analogous way to reer. While working on his doctoral is surrounded by its neighbors. It electrical charges. studies, he studied two-dimensional pairs off with one of these neighbors The special properties of spin ice electron gases, and predicted elec- such that the spins of the two elec- were not discovered by chance. The tronic states that were found to lead trons – their magnetic moments – search for hidden and exotic types to orders resembling those in liquid cancel. However, these pairings are of order has been a recurring theme crystals. In liquid crystals, mole- ephemeral. Each electron continually 451, 22-23 (2007) 451, ATURE
Spaghetti in spin ice: , S.L. N
The monopoles (red and blue ONDHI dots) can migrate through the solid as if they were connect- , R., S
ed by a tensionless spring. OESSNER , C., M ASTELNOVO : C MAGE I
40 MAXP LANCKR ESEARCH 1/2009 THE WORLD OF QUANTA
changes partners, with the result that the elements in the periodic table. So thing important,” says the physicist. the entire arrangement of bonds is in there are many new phenomena yet He does not yet envisage direct tech- constant motion. to be discovered. nical applications of the magnetic “If a single electron is removed The results of the scientists’ re- monopoles. However, the good news, from the lattice, a hole, a positive search into miniature quasiuniverses says Moessner, is that it will hope- charge, is left behind, and next to it, should not remain purely theoretical. fully be possible to create magnetic an unpaired electron,” explains Experiments on the monopole hy- monopoles should they be needed Moessner. The remaining solitary pothesis are now on the agenda. for a specifi c application. “This dem- electron is evident only from its spin; Preparations for these are underway onstrates the level of control that we against the positive background, its at several locations. “Whatever the are now able to exercise in materials negative charge goes unnoticed, as results of the experiments, I am con- physics and the physics of complex before. The electron need not remain fi dent that they will teach us some- systems.” CHRISTIAN MEIER alone, however; it can capture a partner from an adjacent spin pair. The unpaired spin, or the magnetic SPAGHETTI INSTEAD OF SPRINGS moment, thus migrates through the Moessner and his colleagues use an as- quires only a little additional energy to lattice, without the positive charge tonishingly simple model to explain mag- overcome the attraction between the following it. netic monopoles as a collective phenom- magnetic monopoles. As the distance be- enon in spin ice. The starting point of the tween the poles increases, the energy re- PREPARATIONS FOR model are the magnetic moments at the quired drops progressively. When an adja- EXPERIMENTS corners of the tetrahedra of which spin cent dumbbell fl ips, one of the poles ice is composed. Moessner compares each migrates one tetrahedron further. Since In his book A Different Universe: Re- magnetic moment to a dumbbell, with a the procedure can be repeated indefi - inventing Physics from the Bottom north pole at one end and a south pole at nitely, the magnetic monopoles are effec- Down, published in 2005, physicist the other. Two north and two south poles tively freely mobile. In conventional mag- and Nobel laureate Robert B. Laugh- thus meet in the middle of each tetrahe- netic substances, such as iron, this is not lin predicts new discoveries of many dron. The opposing magnetic charges of the case. Although these substances con- the poles in this confi guration cancel. tain magnetic moments, the reversal of such organizing principles and laws If one of the dumbbells is now turned by each moment requires the same amount of nature in complex systems. Ac- 180 degrees, an imbalance arises in the of energy, since it is surrounded by op- cording to Laughlin, we are still un- middle of two adjacent tetrahedra. Three posing moments. For this reason, in fer- aware of the great majority of orga- poles with the same polarity meet one romagnets, the attraction between two nizing principles. So the physicists in Roderich Moessner’s group still have much work to do. Theoretical research into complex systems fascinates him for two rea- sons. “For one thing, we work in small groups, which gives us a high When one bar magnet in a chain (a) fl ips, two monopoles (b and c) are degree of fl exibility and variety,” created. In the spin ice model, such chains are jumbled up (colored lines, d). The monopoles (e) can move along these chains. says Moessner. The second reason is probably more important: “Particle with the opposite polarity: in one tetra- magnetic defects does not become weak- and astrophysicists have one large hedron, three north poles face a single er as they move apart; rather, the energy south pole, and in the adjacent tetrahe- required increases without bound, almost universe. We have many small qua- dron, three south poles a north pole. So as if they were at opposite ends of a 22-23 (2007) 451, siuniverses,” he says jokingly. “For overall, there are surplus north poles in spring being stretched apart. In spin ice, ATURE
us, every material is a potentially one tetrahedron, and surplus south poles by contrast, chains of moments are tan- N , O. new type of complex system.” The in the other. This disturbs the magnetic gled like spaghetti on a plate that can be variety within solid-state physics, neutrality at a local level, and thus re- pushed around at will. So monopoles are
quires the use of a tiny energy quantum. linked, as it were, not by a spring, but by CHERNYSHYOV says Moessner, derives from the The poles can now move apart; this re- a loose thread. : T MAGE countless possible combinations of I
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