electron spins in a solid-state system (a crystal of malonic acid).

The idea of using pulse sequences to reduce decoherence is not new. Besides controlling electron spins6 in systems such as Du and col-leagues’, pulsing techniques have a rich history in nuclear (spin) magnetic resonance. The optimal pulse sequence studied by Du et al. was discovered only recently by Götz Uhrig7. It was then generalized8,9 for systems similar to that used by Du and colleagues and subsequently performed on trapped ions10. The decoherence corrections of the Uhrig pulse sequence scale linearly with the number of pulses applied. It therefore takes N pulses of flipping the spin to realize a decoherence suppression up to order N. Many of the predecessors of Uhrig’s pulse sequence require an exponentially increasing number of pulses to produce the same sup-pression effect, requiring prohibitively large numbers of spin flips to suppress high orders of decoherence. The Uhrig pulse sequence has the ability to suppress high orders of decoherence with a feasible number of spin-flip pulses.

Du and colleagues3 explored a number of Uhrig pulse sequences in their system. Using a seven-pulse Uhrig control scheme, they were able to improve the system’s coherence time by a factor of 750 compared with no control, and by a factor of 5 compared with the one-pulse Hahn-echo scheme. For up to seven pulses, they compared the Uhrig pulse scheme with other previously known pulse schemes11 and showed an improvement in coherence times. By varying parameters within the sample, they were also able to isolate and study various sources of decoherence present in their system. Characterizing decoherence in similar ways in future systems could help to identify, quantify and minimize its specific forms.

Quantum control schemes such as that used by Du and colleagues should prove to be a valuable asset in understanding and attack-ing the decoherence of quantum informa-tion. These achievements are vital to pushing the performance of real, physical systems closer to that required for practical quantum computing. ■

Bob B. Buckley and David D. Awschalom are

in the Center for Spintronics and Quantum

Computation, University of California,

Santa Barbara, California 93106, USA.

e-mails: awsch@physics.ucsb.edu;

buckley@physics.ucsb.edu

1. Bennett, C. H. & DiVincenzo, D. P. Nature 404, 247–255

(2000).

2. Zurek, W. Phys. Today 44 (10), 36–44 (1991).

3. Du, J. et al. Nature 461, 1265–1268 (2009).

4. DiVincenzo, D. P. Preprint at http://arxiv.org/abs/

quant-ph/0002077v3 (2000).

5. Hahn, E. L. Phys. Rev. 80, 580–594 (1950).

6. Viola, L., Knill, E. & Lloyd, S. Phys. Rev. Lett. 82, 2417–2421

(1999).

7. Uhrig, G. S. Phys. Rev. Lett. 98, 100504 (2007).

8. Lee, B., Witzel, W. M. & Das Sarma, S. Phys. Rev. Lett. 100, 160505 (2008).

9. Yang, W. & Liu, R.-B. Phys. Rev. Lett. 101, 180403 (2008).

10. Biercuk, M. J. et al. Nature 458, 996–1000 (2009).

11. Schweiger, A. & Jeschke, G. Principles of Pulse Electron

Paramagnetic Resonance (Oxford Univ. Press, 2001).

MATERIALS SCIENCE

Emerging routes to multiferroicsRamamoorthy Ramesh

Materials that combine ferroic properties — such as ferromagnetism and ferroelectricity — are highly desirable, but rare. A new class of multiferroic solids heralds a fresh approach for making such materials.

The porous crystalline materials known as metal–organic frameworks (MOFs) are cur-rently a hot topic of research, having found applications in catalysis1, hydrogen storage2, optical elements3 and more. Writing in the Journal of the American Chemical Society, Jain et al.4 describe a family of MOFs that have yet another potentially useful characteristic. They are multiferroic, combining the ferromag-netism familiar from iron bar magnets with antiferroelectricity — a property in which the molecules of a material are ordered so that adjacent molecular dipoles point in oppo-site directions. Multiferroics are attractive candidates for use in electrically controllable microwave elements, magnetic-field sensors and possibly even in spintronics.

Ferroic properties come in several forms, referred to as order parameters, all of which manifest themselves around some critical temperature. The primary order parameters are ferromagnetism, ferroelectricity (sponta-neous electric polarization that can be reversed by an electric field) and ferroelasticity (spon-taneous strain). But many other flavours also exist, including antiferroelectricity. Any mater-ial that combines more than one of these prop-erties is described as multiferroic. If the order parameters of a multiferroic are coupled to one other, then each can be manipulated by the application of a conjugate field from the other. For example, in magneto electric materi-als, the magnetic moment of the mater ial can be manipulated with an electric field, or the electric moment with a magnetic field. Such materials are of great fundamental scientific interest, and are also highly desirable for several applications.

Recent years have therefore seen a con-siderable worldwide effort to discover broad classes of multiferroics, using a combination of materials chemistry, theoretical approaches and synthetic techniques. Unfortunately, it is becoming increasingly clear that the electronic structures of molecules that are required for ferromagnetism and ferroelectricity tend to be mutually exclusive. Ferromagnetism typi-cally requires unpaired electrons that interact through a quantum-mechanical process known as exchange coupling. But typical ferro electric materials (such as barium titanate, BaTiO3, and other structurally related ‘perovskite’ com-pounds that contain transition metals) require the transition-metal ion to have an empty outer shell of electrons. This fundamental contrast is the main reason why few materials are both

ferroelectric and ferromagnetic. In the mater ials that do have both of these order parameters, one is usually much weaker and appears at much lower temperatures than the other.

Most researchers have adopted four main approaches to try to make better magnetoelec-tric materials5–7 (Table 1). All of these attempt to introduce ferroelectricity into magnetic materials, using various mechanisms to side-step the fundamental mismatch described above. Magnetoelectrics have also been created through a composite approach — by mixing a ferroelectric and a ferromagnet in such a way that strain is the coupling medium. Perhaps the most promising magnetoelectric material so far is bismuth ferrite (BiFeO3, a perovskite), in which the two coupled order parameters are ferroelectricity and antiferromagnetism. Bismuth ferrite sets the benchmark in the global search for new magnetoelectric materi-als, guiding the design of possible multiferroic architectures, and informing the use of theoret-ical approaches that seek truly ferromagnetic ferroelectrics.

Jain and colleagues’ MOF compounds4, however, represent a completely new class of multiferroics — previously reported magneto-electric perovskites were purely inorganic compounds, but MOFs are hybrid structures comprising metal ions in complex with organic molecules. The presence of organic molecules in the structures allows hydrogen bonds to form between the MOF’s components. It is these bonds that are responsible for ordering Jain and colleagues’ MOFs in such a way as to engender multi ferroic properties — a first in the field. The authors previously identified8 an antiferroelectric MOF structure that con-tained zinc ions (Zn2+). By replacing the zinc with magnetic transition-metal ions, such as iron(ii) ions (Fe2+), they were able to make multiferroic materials.

The authors observed that, on cooling, their multiferroic MOFs undergo a transition from a paraelectric phase (in which the materials become temporarily electrically polarized in an external electric field) to an antiferroelectric phase, at critical temperatures ranging from 160 to 180 kelvin. This corresponds to a change in the molecular structure of the MOF from a dis-ordered to a more ordered state. It is certainly nice to see that hydrogen-bonding effects can lead to relatively high transition temperatures. However, Jain et al. found that this transition is unaffected by a magnetic field, and so it is quite likely that there is no magnetoelectric coupling

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associated with it. But at temperatures below 10 kelvin, the compounds undergo a transition to another phase that is both antiferroelectric and weakly ferromagnetic. The fact that the transi-tion to the magnetic state occurs at much lower temperatures is typical of ferromagnetic MOFs; this is a consequence of the indirect nature of the quantum exchange interactions between electrons that occur in these compounds.

Jain and colleagues’ compounds4 are a great start. But for practical applications, the transition temperatures of these multiferroic MOFs will need to be increased to around room temperature, and the strength of the coupling between the two order parameters must be increased. The beauty of MOFs is that their structures can easily be modified, which should, in principle, allow the properties of the compounds to be readily optimized. In the meantime, Jain and colleagues’ findings dem-onstrate the important principle that electrical order in multiferroic materials can arise from

hydrogen bonding. What’s more, in a field dominated by materials that contain the toxic element lead, MOFs open up fresh opportuni-ties for the production of lead-free multiferroic compounds tailored for specific technological applications. ■

Ramamoorthy Ramesh is in the Department

of Materials Science and Engineering, and the

Department of Physics, University of California,

Berkeley, Berkeley, California 94720, USA.

e-mail: rramesh@berkeley.edu

1. Farrusseng, D., Aguado, S. & Pinel, C. Angew. Chem. Int. Edn

48, 7502–7513 (2009).

2. Rowsell, J. L. C. & Yaghi, O. M. Angew. Chem. Int. Edn 44, 4670–4679 (2005).

3. Allendorf, M. D., Bauer, C. A., Bhakta, R. K. & Houk, R. J. T.

Chem. Soc. Rev. 38, 1330–1352 (2009).

4. Jain, P. et al. J. Am. Chem. Soc. 131, 13625–13627 (2009).

5. Ramesh, R. & Spaldin, N. A. Nature Mater. 6, 21–29 (2007).

6. Cheong, S.-W. & Mostovoy, M. Nature Mater. 6, 13–20 (2007).

7. Eerenstein, W., Mathur, N. D. & Scott, J. F. Nature 442, 759–765 (2006).

8. Jain, P., Dalal, N. S., Toby, B. H., Kroto, H. W. & Cheetham,

A. K. J. Am. Chem. Soc. 130, 10450–10451 (2008).

TABLE 1 | MECHANISMS FOR MULTIFERROICSMechanism Description Examples

Lone-pair effects In perovskites of general formula ABX3, lone pairs of

electrons on the A cation distort the geometry of the BX3

anion, resulting in ferroelectricity

BiFeO3,

BiMnO3

Geometric frustration Long-range dipole–dipole interactions and rotations

of oxygen atoms generate a stable ferroelectric

state

YMnO3

Charge ordering Certain ‘non-centrosymmetric’ arrangements of ions

induce ferroelectricity in magnetic materials

LuFe2O4

Magnetic ordering Ferroelectricity is induced by magnetic long-range order

in which the arrangement of magnetic dipoles lacks

reflection symmetry

TbMnO3, DyMnO3,

TbMn2O4

EVOLUTIONARY BIOLOGY

Arrhythmia of tempo and mode Paul B. Rainey

An exercise in experimental evolution using bacteria has been running for more than 20 years and 40,000 generations. The results to date provide a glimpse of a new world, and are cause for both delight and unease.

In his seminal book Tempo and Mode in Evolution1, palaeontologist George Gaylord Simpson argued for the value of distinguish-ing between the tempo of evolutionary change (the rate) and its mode (the process); more-over, he argued that tempo could be used to infer mode. Simpson’s primary interest was the large-scale variations in rate and pattern evident in the fossil record. But his thesis has been far-reaching, as influential to students of organismal evolution2 as to those interested in the evolution of molecules3. Indeed, despite numerous uncertainties, molecular evolu-tionists use knowledge of the tempo of DNA-sequence evolution at specific loci to infer the mode of organismal evolution. On page 1243

of this issue, a group led by Richard Lenski — Barrick et al.4 — reports the results of work that provides direct insight into the rate of genomic change and organismal adaptation over 40,000 generations of evolution.

Imagine travelling back through evolution-ary time, capturing at specific time intervals a complete record of the genome from a single evolving lineage, and recording all mutational events and the magnitude of their effects. Imag-ine that, on completion, one has a picture of not just changes in physical traits (phenotype), but also the underlying dynamic of genomic evolution. Barrick et al.4 do precisely this. In 1988, Lenski took a single archived clone of the bacterium Escherichia coli B (clone REL606,

otherwise known as the ancestor), and placed it in a simple glucose-limiting environment where it has existed ever since, being kept in a continuous state of growth by daily transfer to fresh medium5. At regular intervals, samples of derived populations have been collected, the reproductive success (fitness) of these types has been determined relative to the ancestor, and samples have been cryogenically stored for future reference.

Using ‘next-generation’ DNA-sequencing technologies, Barrick et al. determined the entire nucleotide sequence of the bacterium’s single chromosome from individual clones taken at six different time points — from one of 12 replicate populations — over the 20 years of evolution. By comparison with the ancestor, the mutations underlying 40,000 generations of evolution are revealed.

Because clones were sequenced at regu-lar intervals, the rate of genomic evolution becomes apparent: over the first 20,000 gen-erations, mutations accumulated at the rate of about 2 per 1,000 generations. This clock-like tempo is strongly suggestive of mode. Indeed, it is indicative of a neutral mode of evolution — evolution driven not by natural selection, but by random sampling of selectively neutral mutants6. According to the neutral theory6, mutations are expected to become stand-ard (fixed) in populations at a constant pace. That pace is determined by the rate at which

new mutations arise spontaneously in indi-vidual cells — a rate ultimately determined by the error rate of enzymes involved in DNA metabolism.

But this makes little sense, because the authors’ measures4 of organismal adapta-tion show overwhelming evidence of natural selection. In fact, during the course of the first 20,000 generations, the reproductive success of REL606 descendants improved dramati-cally. Moreover, the increase was strongly non linear. During the first 2,000 generations, fitness increased 1.5-fold relative to ancestral genotype — thereafter, the rate of improve-ment decreased (Fig. 1).

These discordant facts leave us in an uncom-fortable position: the clock-like tempo of genomic evolution suggests a neutral mode of organismal evolution, but the tempo of organismal evolution bears the hallmarks of evolution by natural selection. Fortunately, evolution experiments with microbes offer opportunities to delve into mechanistic detail, and Barrick et al. do just that. They present compelling evidence that the majority of muta-tions arising over the first 20,000 generations of evolution are beneficial and that their fixation is due to natural selection.

In rejecting a neutral explanation for the mutations, Barrick et al. give life to numerous questions. The relationship between genomic and organismal (adaptive) evolution is without doubt counter-intuitive (Fig. 1). From an empir-ical perspective, there is a need to know whether evolution in this single replicate population

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