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CONDENSED-MATTER PHYSICS

Great moments in disorderSteven T. Bramwell

An array of nanomagnets has been designed to resemble the disordered magnetic state known as spin ice.

This could transform our understanding of disordered matter and, potentially, lead to new technologies.

Figure 1 | Organized disorder. a, Part of the disordered arrangement ofionic magnetic moments (spins) in spin ice, holmium titanate (Ho2Ti2O7):a network of linked tetrahedra with two spins in, two spins out pertetrahedron.b, Put a hydrogen atom on the end of every spin of spin ice,and you represent the low-temperature disordered hydrogen structure of(cubic) water ice, H2O: each hydrogen atom lies on the line connecting twoneighbouring oxygen atoms, but is shifted away from the mid-point of that

line to ensure that the whole structure is a hydrogen-bonded network ofv-shaped water molecules (oxygen atoms, large circles; hydrogen atoms,

small circles). c, Here arrows represent the magnetic moments of nanoscalemagnetic islands in the disordered state of the artificial square spin icecreated by Wang et al.1. Each corner has two arrows pointing in, and twopointing out, but within this constraint the direction of the arrows on anyone corner is arbitrary: the two in, two out condition is not sufficient todefine an ordered state. The blue circle marks a defect where the two in,two out configuration is not maintained. d, An ordered pattern in which

the arrows of alternate squares have the same configuration. This is possiblythe true minimum energy state of artificial spin ice.

a c d

b

How can we understand disordered states ofmatter such as liquids, glasses and disorderedmagnets? First, we must know how they areorganized; second, we must know how thatorganization responds to changes in external

constraints such as temperature, pressure ormagnetic field. This knowledge is beyond ourreach in most cases: disordered states are intrin-sically complicated and do not reveal them-selves clearly to experiment. But thankfully,there are exceptions. One of them is a magneticstate known as spin ice in which the magneticmoments of ions their spins, in analogyto the property of electron spin remaindisordered even at low temperatures, revealingmuch about the basic physics of disorder.

On page 303 of this issue, Schiffer andcolleagues (Wang et al.)1 report the creation ofspin-ice behaviour in an array of nanoscale

magnets. Such artificial spin ice, which isstable at room temperature and possessesmagnetic moments large enough to be

observed directly, offers a new approach tounderstanding and exploiting the propertiesof disordered systems.

In conventional spin ice2,3, magnetic ionsform a network of linked tetrahedra (for exam-

ple, ions of the lanthanide element holmium inthe compound holmium titanate). The spins ofthese ions point either in or out of the tetra-hedra (Fig. 1a). The dipolar interaction withtheir neighbours magnetic fields favoursan inout arrangement of neighbouringmoments, but not all pairs of neighbours canbe satisfied simultaneously: the system is frus-trated. The best compromise two momentspointing in, two pointing out, in any one tetra-hedron constitutes the local organizingprinciple. The same rule controls the hydrogenstructure of ice4 (Fig. 1b), and is fully satisfiedby a huge number of equivalent arrangements

of spins (or hydrogen atoms). This means thatthe chance of achieving an ordered structure iseffectively nil. So spin ice, just like normal ice,

remains disordered, with a non-zero entropy(a key measure of disorder) as its temperatureapproaches absolute zero.

Schiffer and colleagues artificial spin ice1

consists of a two-dimensional array of 80,000

elongated magnetic islands, each a few hun-dred nanometres long. The magnetic momentof every island is aligned parallel to its longaxis, as in a bar magnet, and is coupled to itsneighbours by the ubiquitous dipolar inter-action. For a square geometry, the two in, twoout rule is approximately satisfied (square ice5,Fig. 1c). But because the magnetic momentsinvolved are about three million times biggerthan those of holmium ions, they interactmore strongly and have less tendency to flip.The artificial spin-ice state is therefore stableat room temperature; for conventional spinice, this is only the case at temperatures below

1 kelvin. Schiffer and colleagues encouragedtheir system to settle into a minimum energystate by cycling the applied magnetic field, and

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then determined the directions of individualmagnetic moments using a technique knownas magnetic force microscopy. Statistical analy-sis of these directions confirmed that a spin-icestate, characterized by a preponderance ofthe two in, two out configuration, had indeedbeen created.

Conventional spin ice lends itself well toexperimentation. Its disordered spin arrange-

ments have been imaged by neutron scatter-ing, and applying magnetic fields to it hasrevealed disordered phases that respond toneutron scattering and bulk measurementsas if they consisted of stacks of independentchains or sheets so as if they have only oneor two dimensions, rather than three. Phasetransitions that, like the liquidliquid orliquidgas transitions in more complex matter,involve no change in structural symmetryhave also been observed6. In such symmetry-sustaining transitions, what is orderedremains ordered, and what is disorderedremains disordered.

But experiments on conventional spin iceraise interesting questions. First, what is the trueorigin of the two in, two out rule? The dipolarinteraction between magnetic moments islong-range, so any explanation that considersonly near neighbours must be incomplete. Thisquestion has largely been answered: remark-ably, the standard model of spin ice predicts thatthe two in, two out rule emerges from themany-bodied dipolar interaction of some 1023

magnetic moments7,8. Second, is there a trueordered ground state (Fig. 1d)? The question isalso pertinent to normal ice9, as such a mini-mum-energy state is required by the third law

of thermodynamics, which states that entropyapproaches zero as temperature tends toabsolute zero. An ordered ground state is alsopredicted by the standard model of spin ice, butis not observed experimentally. Finally, whatmicroscopic factors drive phase transitions inan applied magnetic field? This question, too,remains essentially open.

Artificial spin ice could, in principle, help tosupply further insight into these problems. Itcould, for example, be engineered to havedifferent, controllable interactions and then besubjected to temperature changes or magneticfields to mimic the behaviour of conventional

spin ice. Direct imaging with magnetic forcemicroscopy could be used to identify andunderstand individual defects in the spin-icestate. Such defects (Fig. 1c) cannot be imaged byneutron scattering on conventional spin ice, butmight be crucial in determining its properties.

Bringing spin ice to room temperaturecould also inspire technological applications.In magnetic-memory media, information isencoded into the magnetic moments of ferro-magnetic grains. The drive to increase thedensity of memory bits in such media willmean smaller, more strongly magnetizedelements that are more closely spaced10. This

trend will amplify the dipolar interaction andits consequences11. Experiments with spin ice,

however, show how to create a dense array ofmagnetic elements, which, although theyinteract, retain many states in which informa-tion could potentially be encoded.

This is for the future. As a replica of conven-tional spin ice, artificial spin ice is not perfect:the two in, two out configuration is main-tained only approximately, and the systemshould actually prefer an alternative, ordered

state12 (Fig. 1d). Its failure to find this statemight reflect the inefficiency of the energy-minimization protocol involving magneticfield cycling. Despite its limitations, however,Schiffer and colleagues invention1 does em-phasize the potential of designed magneticarrays, not only as model systems for the studyof disorder, but also as the basis of technologi-cal applications. Steven T. Bramwell is in the Department of

Chemistry, University College London,

20 Gordon Street, London WC1H OAJ, UK, and

the London Centre for Nanotechnology,

216 Torrington Place, London WC1E 7HN, UK.

e-mail: s.t.bramwell@ucl.ac.uk

1. Wang, R. F. et al. Nature439, 303306 (2006).

2. Harris, M. J., Bramwell, S. T., McMorrow, D. F., Zeiske, T. &

Godfrey, K. W. Phys. Rev. Lett.79,25542557 (1997).

3. Ramirez, A. P., Hayashi, A., Cava, R. J., Siddharthan, R. &

Shastry, B. S. Nature 399,333355 (1999).

4. Pauling, L.J. Am. Chem. Soc. 57,26802684 (1935).5. Lieb, E. H. Phys. Rev. Lett. 18,692694 (1967).

6. Sakakibara, T., Tayama, T., Hiroi, Z., Matsuhira, K. & Takagi,

S. Phys. Rev. Lett.90,207205 (2003).

7. Melko, R. G. & Gingras, M. J. P.J. Phys. Cond. Mat. 16,

R1277R1319 (2004).

8 Isakov, S. V., Moessner, R. & Sondhi, S. L.Phys. Rev. Lett.95,

217201 (2005).

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11. Martin, J. I. et al. J. Magn. Magn. Mater.256,449501

(2003).

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cancers) and of the BRAF oncogene, the nextfactor in the pathway (mutated in some 60% ofmelanomas)4. Thus, looking for evidence of

an initiating mutation can make it hard toidentify all tumours in which this pathwayhas been activated.

Equally, looking for a single downstreamindicator of pathway activation, such as phos-phorylation of the enzyme ERK (one of thefinal steps in the RAS pathway), can also beproblematic. Negative feedback loops, suchas the induction of phosphate-removingenzymes that target ERK, can attenuate thesteady-state phosphorylation of ERK. In addi-tion, branching of the pathway can meanthat other targets might be more important incertain circumstances (Fig. 1).

One step in the RAS pathway that is beingtargeted by candidate drugs is MEK, anenzyme that is directly activated by BRAF, andthat is thought to be responsible for much ofthe downstream signalling from RAS (Fig. 1).To see whether MEK inhibitors could be use-ful for treating all tumours with aberrant RASsignalling, Solit et al. (page 358)1 tested humantumour cell lines carrying mutations in BRAFor RAS for sensitivity to these drugs. Cellsbearing an activating BRAF mutation wereextremely sensitive to MEK inhibitors, bothin vitro and when transplanted into immuno-deficient mice. By contrast, cells with an acti-

vating RAS mutation showed much lower andmore variable sensitivity to these inhibitors.

CANCER BIOLOGY

Signatures guide drug choiceJulian Downward

Cancer drugs are increasingly designed to target specific cell-signalling

pathways. When, and in what combination, these drugs should be used

might be judged by analysing the gene expression signature of the tumour.

Current approaches to the design of drugsagainst cancer assume that almost all tumoursescape normal growth regulation by usurping

a few of the dozen or so key cell-signallingpathways. However, pathways can be activatedat different points, so it is not always easyto tell which signalling mechanism hasbeen activated by looking for mutations inknown cancer-associated genes (oncogenes, ortumour-suppressor genes). If the gene at thetop of a signalling cascade is unaffected, forinstance, one cannot assume that the pathwayis not involved, as a factor further downstreammight have been activated. It can thus be hardto predict the best treatment for a particulartumour. Two papers in this issue1,2 address thisproblem in different ways, and provide a

potential strategy for choosing the most effec-tive combination of therapies based on thegene expression signature of a tumour.

Tumour cells seem to rely heavily on thecontinued activation of one or two pathways a phenomenon termed oncogene addiction whereas normal cells use a broader range ofsignals3. This, combined with the damageaccrued through the reckless lifestyle of thecancer cell, provides an Achilles heel thatmight be exploited therapeutically by targetingpathways activated by oncogenes such as RAS,SRC and MYC. The RAS pathway (Fig. 1), forexample, can be activated in many different

ways in tumours, including mutation of theRAS oncogene itself (seen in 40% of lung

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