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Striking mathematical pattern uncovered in Chinese money plant leaves

Researchers in the US and Canda have discovered a naturally occurring “Voronoi pattern” in the Chinese money plant.

Voronoi diagrams were introduced in the 1600s by French philosopher René Descartes and are named after the Russian mathematician Georgy Voronoi, who defined and studied them in the early 1900s.

Voronoi diagrams are geometric patterns used to divide space into regions. The plane is divided up into tessellating polygons, known as cells, that each contain a “seed” point. Every location inside a cell is closer to its seed than any other seed in a neighbouring cell.

Voronoi patterns have numerous applications across mathematics, as well as in various other disciplines such as modelling animal territories, city planning or crystal growth.

Voronoi-like patterns are common in nature, such as giraffe stripes. However, the difference between textbook Voronoi patterns and what we see in nature is that the latter usually lacks visible seed points.

Now, Saket Navlakha from Cold Spring Harbor Laboratory in New York and colleagues have found an exception in Pilea peperomioides, the Chinese money plant.

Chinese money plants are perennials native to China’s Yunnan and Sichuan provinces. The plant has round, flat leaves that feature prominent pores called hydathodes. These points are then surrounded by looping reticulate veins that transport water and nutrients to and from the leaf.

Rooted in physics

By mapping the pores and veins, the team discovered a naturally occurring, visible, Voronoi pattern with the veins acting as the cell boundaries and the pores being the seed points. They then built a mathematical model to match the observed patterns.

“To our knowledge, this is the first demonstration of the occurrence of Voronoi diagrams in plant venation patterns, where both edges and centres are visible and functional,” they write.

The researchers now plan to use the model to understand why other plants that have similar vein structures do not stick to the Voronoi structure in the same way as the Chinese money plant.

Altermagnetic insulator shows giant magneto-optical Kerr effect

Researchers in China have developed a new way of probing the magnetic domains within altermagnetic materials and used it to study a prominent altermagnet candidate, alpha-phase iron oxide. According to their measurements, this material shares certain properties with ferromagnets despite having a near-zero net magnetization – a fact the researchers say supports its classification as an altermagnet.

In most magnetically ordered materials, the spins of atoms (that is, their magnetic moments) can either line up parallel with each other or antiparallel, alternating up and down. These arrangements are driven by spin-exchange interactions between the atoms, and they lead to ferromagnetism and antiferromagnetism, respectively.

Altermagnets, which were identified as a distinct class of magnets in 2022, behave differently. While their neighbouring spins are antiparallel, like an antiferromagnet, the atoms hosting these antiparallel spins are related to each other by rotational or mirror symmetries rather than the spatial inversion and half-lattice translation symmetries found in conventional antiferromagnets, explain physicists Luyi Yang and Wanjun Jiang of Tsinghua University, Beijing, who led this study. This unique property leads to a zero net magnetization in altermagnets while still allowing for the spin-split electronic band structures typically found in ferromagnets.

An altermagnet candidate

Alpha-phase iron oxide (α-Fe₂O₃) is a naturally occurring mineral commonly known as haematite. It was long believed to be an antiferromagnet, but recent theoretical research has suggested that it should be relabelled as an altermagnet.

To shed more light on the nature of α-Fe₂O₃, the team turned to a phenomenon known as the giant magneto-optical Kerr effect (giant MOKE). Named after the Scottish physicist John Kerr, who discovered it in 1877, it occurs when linearly polarized light reflects off the surface of a magnet. Interactions between the light and the material’s magnetic domains cause the polarization vector of the light to rotate, and the direction of rotation can be reversed by reversing the direction of magnetization. The effect therefore provides a “window” into materials’ magnetization states, enabling scientists to monitor and characterize them.

The Tsinghua University researchers say they found evidence of a connection between the material’s MOKE responses and its Néel vector, which is a parameter that defines its so-called staggered magnetic order. In altermagnets, the orientation of this Néel vector determines the material’s magnetic space group, which in turn dictates whether magneto-optical responses are allowed or not, they explain.

“By using magnetic fields to switch the Néel vector through a tiny canted magnetization in α-Fe₂O₃, we selectively measured the symmetry-permitted MOKE signals and confirmed the absence of symmetry-forbidden components on different surface orientations of α-Fe₂O₃ single crystals,” they say.

The researchers also observed that at large applied magnetic fields, the MOKE signals remain constant. This finding further rules out contributions from canted magnetization, which should increase with the field. These experiments therefore strengthen the idea that the MOKE signal they measured is truly driven by the Néel vector and the corresponding symmetry of α-Fe₂O₃.

Broadening methods for imaging altermagnetic domains

To date, most experimental studies on altermagnets have focused on spin transport. Yang, Jiang and colleagues say that they turned to MOKE-based measurements because they would like to study insulating altermagnets, for which electrical transport measurements are inaccessible. “We aimed to uncover the symmetry requirements for magneto-optical responses and broaden the methods for imaging altermagnetic domains,” they explain.

The main challenge they encountered was proving that the MOKE they observed predominantly originates from the Néel vector, rather than from the canted weak magnetization. The researchers say they addressed this through symmetry analysis, first-principles calculations and performing the experiment in different configurations to show that the Kerr signal remains nearly constant even as the canted magnetization keeps increasing at large applied magnetic fields. “By examining such effects on single crystals with different surface orientations, we confirmed that different Néel vector orientations produce distinct MOKE responses, which are consistent with the symmetry of magnetic space group predicted by theory,” they tell Physics World.

The researchers say their work shows that MOKE responses are not limited to ferromagnets, as is conventionally understood. Provided the symmetry requirements are satisfied, altermagnets can also exhibit giant MOKE. “We have shown that standard MOKE imaging microscopy can be used to visualize altermagnetic domains and domain walls in α-Fe₂O₃,” they say. “This could accelerate the development of altermagnetic spintronics based on these structures, with potential applications in advanced memory and logic devices.”

The researchers now plan to extend their approach to other altermagnetic insulators and metals and to use the magneto-optical response to study the (presumably) ultrafast dynamics of domain walls. Their present study is detailed in Chinese Physics Letters.

Paul Howarth: IOP president highlights the need to raise the profile of physics in society

This episode of the Physics World Weekly podcast features an interview with Paul Howarth, who became president of the Institute of Physics (IOP) in February.

The IOP is the professional body and learned society for physics in the UK and Ireland. Representing 21,000 members, it supports physicists at all stages of their careers and seeks to make physics accessible to people from all backgrounds.

With a PhD in nuclear physics, Howarth has had a long career in the nuclear sector working on the European Fusion Programme and at British Nuclear Fuels, as well as co-founding the Dalton Nuclear Institute at the University of Manchester and serving as chief executive officer of the National Nuclear Laboratory.

He talks to Physics World’s Michael Banks about his career in nuclear energy and his priorities now as president of the IOP. These include improving physics education and raising the profile of physics and physicists across society.

Howarth also voices concerns about recent funding cuts to particle physics, astronomy and space science in the UK, saying it could hamper the flow of students into the subject, with a potential impact on burgeoning areas such as quantum tech.

The Institute of Physics owns IOP Publishing, which brings you Physics World.

Physicists spot signs of an atom-like system bound by the strong force alone

Signs of an exotic atom-like system made up of a neutral meson bound to an atomic nucleus via the strong interaction have emerged in experimental data from two international collaborations. If confirmed, this hitherto unobserved system could shed light on the origins of hadron masses and provide new insights into the fundamental symmetries of quantum chromodynamics in nuclear matter.

The strong interaction is one of the four fundamental forces of nature, alongside gravity, electromagnetism and the weak interaction. It is responsible for binding quarks into hadrons, which are three-quark particles such as protons and neutrons, and for holding protons and neutrons together within atomic nuclei. Electrically neutral mesons – short-lived particles made up of a quark and an antiquark – are likewise subject to the strong interaction, which can bind them to atomic nuclei in a way that is conceptually similar to an electron bound to a nucleus by the electromagnetic force.

Studying these meson-based nuclear systems is important because it helps us better understand the properties of the strong interaction, says study co-leader Yoshiki Tanaka of RIKEN in Japan. The eta prime meson, η′, is particularly interesting, Tanaka adds, because its relatively large mass cannot be explained by a simple quark model. “This U(1) problem, as it known, was raised as long ago as the 1970s by the physicist Steven Weinberg,” he notes.

Direct experimental access to the 𝜂′-meson mass in nuclei

Modern theories attribute the η′ meson’s large mass to the presence of chiral symmetry breaking in quantum chromodynamics, which is the fundamental theory of the strong force. These theories predict that this mass should be reduced in a nuclear system, and this is what Tanaka and colleagues set out to test.

“Spectroscopy studies of 𝜂′-mesic nuclei provide direct experimental access to the 𝜂′-meson mass in nuclei and offer a unique opportunity to investigate the underlying mechanisms of how the mass of hadrons comes about,” he explains.

In the team’s study, a beam of protons strikes a ¹²C atomic nucleus at near-relativistic speeds and removes a neutron from it. This neutron, together with a proton, forms a deuteron that propagates away in a forward direction, leaving behind a nucleus of ¹¹C in a highly energetic state. It is this excess energy that gives rise to an 𝜂′-meson.

WASA experiment — The experimental setup WASA in maintenance position. (Courtesy: J. Hosan, GSI/FAIR)

In rare cases, the researchers explain, the meson then binds to the ¹¹C nucleus, forming an 𝜂′-mesic nuclear system. But because these events are so rare, they are hard to find. “One of the major challenges we encountered in the work was the very large amount of background events we registered during our measurements,” Tanaka recalls. “These were about 100 to 1000 times higher than the signal events.”

The researchers overcame this problem by developing a new experiment that allows them to efficiently select signal events associated with the formation of 𝜂′-mesic nuclei by “tagging” the particles they decay into. This enabled them to measure not only the forward-travelling deuteron, but also the decay products of the short-lived 𝜂′-mesic nuclear state.

The researchers say that their results, which they describe in Physical Review Letters, indicate that the 𝜂′-meson mass drops by about 60 MeV in nuclear matter. “This result qualitatively supports the theoretical scenario [that attributes] the origin of the 𝜂′-meson mass to chiral symmetry breaking together with the dynamics of gluons (massless particles that mediate the strong nuclear force) in general,” Tanaka says.

Members of the team, which also includes researchers from the η-PRiME Collaboration and the Super Fragment Separator Experiment Collaboration, together with physicists from Justus Liebig University Giessen in Germany with their working groups GSI/FAIR, say they are now planning follow-up experiments to confirm that they have indeed observed 𝜂′-mesic nuclei. “We also aim to increase the significance to the 5σ level, which is required to firmly establish the discovery on new quantum states in particle and nuclear physics,” Tanaka says.

Thumbs up to Artemis II: a jigsaw puzzle

There are two difficulty settings: choose between a 96-piece jigsaw and the 48-piece version.

Image courtesy: NASA

Fancy some more? Check out our puzzles page.

Final look inside the Cavendish lab’s 50-year home before demolition

The prestigious Cavendish Laboratory at the University of Cambridge in the UK has an iconic status in the history of science.

The university’s physics department was initially based in central Cambridge. It is where Francis Crick and James Watson famously worked on the double-helix structure of the DNA molecule.

Yet in 1974 – 100 years after its foundation – the Cavendish moved to a new home on the outskirts of the city.

The building was built in a drab style, covered in grey-brown pebble dash, and featured a maze of interconnected blocks. It was home to generations of physicists, and many thousands of students over the last 50 years.

But the outdated and crammed structure is no longer deemed fit for use and in October last year the lab moved to the nearby larger, brighter and airy purpose-built Ray Dolby Centre. The new centre has been designed to encourage meetings and exchanges with a single entrance, common foyer and centralized café, which are also open to the public.

The move to the Dolby Centre took almost a year to complete, during which time about 180 truckloads moved 3000 m³ of research equipment, crates and furniture belonging to the lab’s 31 research teams.

This included specialized equipment such as 47 cryostats, 98 optical tables, various molecular beam epitaxy set-ups as well a teaching laboratory and museum collection, which includes the model of DNA created by Watson and Crick as well as the cathode ray tube that was used to discover the electron.

Pending chemical and asbestos decontamination, the old building will now be demolished by third-party contractors.

Once complete, the site will host a cycle route until plans are developed for the future use of the site.

Physics World visited the old building in February and this article presents a selection of images from the site.

Empty cabinets and picture frames at the Cavendish Museum. (Courtesy: Mićo Tatalović)

“An eerie” feel to what was once a bustling world-class laboratory

Following the move to the state-of-the-art Dolby Centre, it’s unlikely that the old building of the Cavendish Laboratory will be missed, except perhaps for its picturesque park and pond.

When I visited the building in February, a few bikes clung to the racks to be disposed of if unclaimed, while a sooty barbecue stood in a corridor.

The silent, empty library and still glowing “lecture in progress” sign in a long-abandoned lecture theatre lent an eerie atmosphere to the place.

Among the emptied, abandoned labs a few areas seemed untouched by the move.

Some offices were still adorned with books, pictures and lab coats, while white boards were filled with equations.

Some of the old equipment left by researchers has been donated to schools and charities, with remaining materials destined for the skip that is placed at the main entrance.

A couple of areas were wet, with water dripping from the ceiling – an indication that it is time to move on.

As I entered a communal area, half-empty liquor bottles line up on a windowsill, a reminder that good times were once had.

Mićo Tatalović

lecture theatre at the Cavendish — The small lecture theatre. (Courtesy: Mićo Tatalović)

workshop at the Cavendish Lab filled with old furniture and wooden crates — Empty cabinets at one of the workshops. (Courtesy: Mićo Tatalović)

Trapping light in open space

Photonic crystal slabs are periodic structures that confine light in two dimensions while allowing it to leak in the third. Their in‑plane periodicity forces light to behave like an electron in a crystal, forming bands rather than isolated modes.

These objects can host an array of novel physical phenomena, from ultra‑sharp resonances to exotic singularities such as exceptional points. Among the most intriguing are bound states in the continuum (BICs). These are modes that, despite lying in an energy range where radiation is allowed, remain perfectly confined.

In a new theoretical study, a team of researchers from China showed that this leakage, and its surprising absence in certain cases, can be understood from a single first‑principles viewpoint. Central to their approach are Bloch waves and the scattering matrix.

Bloch waves are the natural building blocks of waves in periodic structures. Instead of spreading freely, light inside a photonic crystal is organised into Bloch waves whose fields repeat from one unit cell to the next, up to a phase factor. Even in an open slab, only a small number of these Bloch waves propagate across the thickness and carry energy towards the surrounding medium.

The scattering matrix describes how incoming waves are converted into outgoing ones by the periodic structure. The values of frequency where the matrix becomes singular (its poles) correspond to resonant modes. For open systems, these frequencies are complex: the real part sets the resonance position, while the imaginary part measures how fast energy leaks away.

One key insight of this work is that the complexity of the problem collapses dramatically once the analysis is restricted to the minimal set of Bloch waves that actually propagate. Interference between just two waves can already explain “accidental” bound states in the continuum (BICs), where radiation vanishes despite the mode lying in an open channel. Including three waves naturally produces Friedrich–Wintgen and symmetry‑protected BICs near band crossings. Adding polarisation reveals far‑field vortices and exceptional points.

By grounding resonant photonics in a minimal scattering‑matrix picture, the authors unify a wide range of phenomena within a single, transparent framework. This should prove valuable for designing efficient resonators, lasers, and topological photonic devices.

Read the full article

Complex band structure and bound states in the continuum: a unified theoretical framework – IOPscience

Jie Liu et al 2026 Rep. Prog. Phys. 89 037901

Ferroelectric band gaps are not what we thought

Ferroelectric materials have a permanent electric dipole, an internal separation of the centres of positive and negative ionic lattices, that can be flipped by applying an electric field. They also undergo a structural change at a material dependent temperature. known as the Curie temperature, above which this dipole behaviour disappears. Despite having permanent dipoles, ferroelectrics are insulating materials. These properties make them valuable in technologies such as sensors, actuators, and memory devices.

In this work, the researchers study the band gaps of ferroelectric materials to better enable their use in energy conversion, catalysis, and optoelectronic devices, where understanding light absorption and electron behaviour is essential. Traditionally, the band gap in ferroelectrics has been treated as a single number. However, ferroelectrics are not conventional semiconductors. They contain localized charges, polarons, internal dipoles, and structural disorder. These features give rise to three distinct band gaps, not one.

There is the intrinsic fundamental band gap, defined as the ground state difference between the fully occupied valence band and the completely empty conduction band. The smaller optical gap is associated with light induced transitions involving bound electron-hole pairs (excitons), and the even smaller transport gap associated with electrical conduction via localised electronic carriers.

In this study, the authors determine the fundamental, optical, and transport gaps using X‑ray photoelectron spectroscopy, optical spectroscopy, and electrical conductivity measurements, respectively, for NBT‑6BT and NaNbO₃. The fundamental gap values are further supported by DFT calculations. Because these three gaps differ by about 1 eV or more, different experiments have actually been probing different gaps all along, meaning past optical and electrical results were often compared incorrectly, leading to widespread misinterpretation. The conclusion establishes that ferroelectrics possess three fundamentally different energy gaps, explains why they differ, provides a framework for measuring them, confirms their values theoretically, and highlights why this distinction is crucial for designing future energy and electronic technologies.

Read the full article

How semiconducting are ferroelectrics: the fundamental, optical and transport gaps of Na0.5Bi0.5TiO3–BaTiO3 and NaNbO3

Pengcheng Hu et al 2026 Rep. Prog. Phys. 89 028004

Do you want to learn more about this topic?

Prospects and applications near ferroelectric quantum phase transitions: a key issues review by P Chandra, G G Lonzarich, S E Rowley and J F Scott (2017)

‘Einstein’s flying mirror’ technique opens a path towards extreme light intensities

Tests of fundamental physics that were previously impossible could become a reality thanks to a new way of producing extremely intense beams of light. Using a state-of-the-art high-power laser, researchers at the University of Oxford, UK demonstrated that they could dramatically increase the efficiency of a nonlinear optical technique called relativistic harmonic generation. According to the team, this increase could herald a paradigm shift, making it possible to achieve hitherto unheard-of electromagnetic field intensities in the laboratory.

The theory of quantum electrodynamics (QED) predicts that at very high intensities, light can interact with the vacuum, converting light energy directly into matter. “If we can achieve such intensities, we could test theories about the fundamental nature of the universe,” says Robin Timmis, who led the new study. “However, doing so requires a laser system a million times more intense than those currently available.”

Relativistic harmonic generation

In the new work, Timmis and her colleagues in Peter Norreys’ group at Oxford used the Gemini laser at the UK Science and Technology Facilities Council’s Central Laser Facility (CLF) to generate coherent extreme ultraviolet (XUV) and X-ray photons via relativistic harmonic generation. They began by firing high-frequency, ultrashort, sub-picosecond (10^-12 s) laser pulses onto a solid glass target. This creates a plasma that acts like an oscillating mirror, and Timmis likens the next step to shining a flashlight at this mirror while it is rushing towards you at near-light speed – a concept known as “Einstein’s flying mirror”. The result is that the light reflected from the plasma becomes compressed, and gains intensity.

Working with researchers from Brendan Dromey‘s group at Queen’s University Belfast in Northern Ireland, the team used a process called coherent harmonic focus to concentrate this light into a region as small as a few nanometres across. This step may have boosted the light beam’s intensities as high as 10²³ W cm⁻², although Timmis acknowledges that this is an estimate based on previous theoretical simulations, as the team was unable to measure it directly.

“If confirmed with further experiments at Gemini, or indeed even larger facilities, we may have made the most intense source of coherent light ever,” says Timmis, who received this year’s Institute of Physics Culham Thesis Prize in part thanks to this work, which is described in Nature. “The energy in our XUV beam was over three orders of magnitude brighter than previous measurements,” she adds. “By resolving a long-standing gap between theoretical expectations and experimental results, we confirmed the required energies to support a coherent harmonic focus and therefore offer a substantial boost in intensity above that of the original laser pulse.”

Towards the next generation of extreme electromagnetic field studies

According to the researchers, these results demonstrate that there is a realistic experimental pathway to next-generation laboratory studies of extreme electromagnetic fields. In particular, they say that the quantum critical field for QED tests, which is known as the Schwinger limit and has a value of >10¹⁶ V cm⁻¹ or >10²⁹ W cm⁻², is now open, paving the way towards all-optical studies of the quantum vacuum. As well as fundamental physics, Timmis says that more efficient harmonic generation could also have applications in ultrafast imaging of physical and biological systems, photolithography and fusion science.

The Oxford team is now analysing data from a follow-on experiment at the CLF that will guide their next steps. “We will be shortly publishing results about a new harmonic beam that we have discovered on that run,” reveals Timmis, “and future studies will focus on actively controlling the coherent harmonic focus and directly measuring its intensity.”

Ultrasound-activated nanoparticles shine a light deep within living tissues

Researchers at Stanford University in the US have found a way to generate light deep within living tissues, potentially leading to new forms of gene and cancer therapies. The proof-of-concept approach uses ultrasound to trigger luminescence in nanoscale particles travelling through the bloodstream, and it has already been tested in tissue-mimicking “phantoms” and live mice. However, its developers caution that human trials are still some way off.

Light has numerous applications in medicine and biological research. It is widely used, for example, to stimulate cell growth and in photodynamic therapies for skin and eye conditions, as well as certain types of cancer.

The problem is that many potentially useful wavelengths of light are easily scattered by tissues and become attenuated over relatively short distances. This means they cannot penetrate very far into the body without help from invasive methods such as removing overlying tissue or inserting/injecting optical implants and light-emitting nanoparticles into the target area.

Sound and light

The new work by Stanford materials scientist and engineer Guosong Hong and colleagues involves nanoparticles made from a ceramic material with the chemical formula Sr₄Al₁₄O₂₅:Eu,Dy. This material is mechanoluminescent, meaning that it emits light when subjected to mechanical stresses and deformations. In Sr₄Al₁₄O₂₅:Eu,Dy, these mechanoluminescent effects can be induced by exposing the material to sound waves, which penetrate more deeply into tissue than light waves.

The Stanford researchers began by coating their nanoparticles with a biocompatible film. They then suspended the particles in a solution and injected the resulting colloid into the veins of mice. Thanks to the rodents’ vascular systems, the particles soon travelled to all parts of their bodies.

The researchers then showed they could make the nanoparticles emit blue light with a wavelength of 490 nm simultaneously in multiple locations (such as the brain, gut, hindlimb and spine) by applying sound waves to different parts of the mouse’s body. In addition, they showed they could create precise patterns of in-situ light generation throughout the three-dimensional volume of the animal, controlled over distances of 100 to 200-μm in the focal region. The ultrasound can also be used as a scanner to define where the light is generated.

A host of applications

The team picked the 490 nm wavelength because it has many applications, including neuron modulation and photodynamic cancer therapy. However, applying the same technique to different materials could produce other useful wavelengths, too. Indeed, Hong and his colleagues are exploring the possibility of using materials that emit ultraviolet light, which has antiviral and antibacterial properties.

The researchers say their approach is broadly applicable to virtually all therapeutic modalities that requires light to be delivered deep within the body, including optogenetics, phototherapy and photo-switchable gene editing. This last technique currently suffers from off-target effects, but the researchers say that by pairing light-producing nanoparticles with a light-activated gene-editing system, they may be able to use ultrasound to turn gene editing on and off in localized areas of the body.

“The overarching theme of my lab’s research is to develop new strategies to deliver and receive light throughout the body in its native, living state,” Hong tells Physics World. “In 2024, we reported on a method to render living tissue transparent using strongly absorbing dye molecules. In the present study we have taken a complementary approach: rather than modifying how light propagates through tissue, we leverage the intrinsic penetrative capability of ultrasound, together with the pervasive reach of the circulatory system, to generate light directly within deep regions of the body.”

Reporting their work in Nature Materials, the researchers are now working to integrate their approach with other light-activatable control systems, including photo-switchable Cas9 gene editing in collaboration with Michael Lin’s lab at Stanford. In parallel, they hope to develop alternative mechanoluminescent materials that will break down safely in the body. While the materials studied in this work did not seem to show adverse effects in mice, they also did not break down quickly, and the researchers say they could accumulate in organs such as the liver.

“What we’re demonstrating here is a proof-of-concept showing that you can produce light emission in a programmable manner deep within the body,” Hong says. “If we can replace the material with one that is safer to be used in humans, that will start to pave the way for clinical applications.”

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