quantum spin liquid

The triptycene molecule resembles a three-pointed star with rigid arms. When such stars are scattered on a lead surface, they spontaneously assemble into a pattern like a woven basket: triangles and hexagons alternate, and at each node sits not one star but a pair.

In nature's workshop, there is a strange lathe: it cuts threads on screws but forbids left-handed ones. You can tighten a screw as much as you like, in any clockwise direction, but counterclockwise is not allowed. This lathe is not a fantasy but an exact quantum rule that physicists have just built for magnetic materials.

The hanmilite crystal, resembling a layered cake of copper and boron, behaves like a ladder: the copper spins are arranged in two parallel rails connected by rungs.

In a thin film of cobalt and iron deposited on a silicon substrate, a tiny magnetic vortex twists into existence.

A superfluid gas is like a crowd of people marching in step: each atom knows where to go and doesn't fall out of the common rhythm. But this crowd has three 'valleys'—three different directions it can take. In a new experiment, physicists made one valley slightly more 'favorable' than the others and watched how the crowd darted between them.

The PbCuTe₂O₆ crystal resembles a three-dimensional web of copper, tellurium, and oxygen. Inside, the magnetic moments, tiny arrows tied to electron spins, are so entangled that they can't settle into an orderly arrangement even near absolute zero.

In a world locked in a crystal lattice and cooled nearly to absolute zero, matter knows how to hide its deepest secrets. A quantum spin liquid is a state where electron spins never freeze, even at zero temperature, remaining in an eternally flickering superposition.

Inside planets and stars, in rotating oceans of plasma, turbulent flows, Coriolis forces, and magnetic tension collide. The central question is how the energy of this chaos crystallizes into a stable magnetic framework that can last billions of years.

In the conventional Heisenberg picture, spins at low temperatures are supposed to line up in a strict pattern. But there are crystals — like pyrochlore — where geometry has its own way. Each ion sits at a vertex of a tetrahedron, and the main interaction enforces a rule: two spins point inward, two outward.

In the world of magnetism, a simple dichotomy long reigned: ferromagnets, where spins point in one direction, and antiferromagnets, where they line up in a checkerboard pattern, canceling each other out. But a recent 'third player' — altermagnets — forced a rewrite of the rules.

Spintronics promises to transmit information not by charge but by spin, ridding microelectronics of its main enemy — Joule heating.

A thin magnetic film is like a row of toy soldiers with tiny magnetic arrows. In the flat world, thermal jostling quickly disrupts this formation — even the slightest heating destroys the order. This is the Mermin–Wagner prohibition: in two dimensions, continuous symmetry cannot survive at finite temperature.

In a world striving for chaos, rhythm sometimes arises. The Belousov–Zhabotinsky reaction has amazed for decades: in a test tube, color waves run on their own, as if a living organism breathing matter. Something similar lurks in crystals where iron atoms balance between two magnetic states — high-spin and low-spin.

An ordinary magnet is like a compass: its needle points north. But a quantum compass can look in both directions at once. If a magnet floating in a vacuum is gently spun, its electron 'tops' synchronize so the whole piece of metal starts living by the rules of the microworld — freezes in a superposition, like a split pointer.

A pot of water on the stove: the hotter the burner, the faster ice turns to water, and water to steam. Heat destroys order. But sometimes nature pulls a trick, and heating makes a liquid freeze, like a puddle turning to ice on a frosty morning.

Sugar dissolves in tea, and then with a single motion gathers back into the spoon. In an ordinary kitchen, you won't see that — viscosity and disorder get in the way. But in the world of ultra-slow motions, where inertia vanishes, such tricks become reality.

In an ordinary crystal, atoms stand in neat rows like soldiers on a parade ground. Any deviation from this formation is usually considered harmful: disorder scatters waves and quickly dampens collective motions of particles.

Inside a superconductor, a magnetic field typically twists into tubes, vortices, each carrying one quantum of magnetic flux. That's how the classic Abrikosov lattice works. But in LiFeAs crystals, the picture is different. Muon spectroscopy showed that the field penetrates not as individual vortices but as stripes. Each stripe contains pairs of 'coreless' vortices.

According to the Standard Model, the vacuum is not emptiness but an ocean of virtual ghost particles. An ultra-strong electromagnetic field, like a storm, yanks electron-positron pairs into reality.

A small ball with an iron core lies on a surface while a magnetic field spins around it. The ball starts rolling like a wheel and usually goes in the direction the field rotates. But sometimes it suddenly turns around and rolls the other way — against the field.

Deep inside Earth lies a solid iron core about the size of the Moon. It floats in liquid metal and sways slightly, like a pit in a peach when you shake the fruit. Such oscillations are called Slichter modes: the core shifts both along the planet's axis and perpendicular to it. Three forces act together to damp this motion.

A tiny magnet, made from just two molecules, was placed on a metal surface, and it behaved like a temperamental conductor. Normally, electrons in a metal move in a coordinated way, like a crowd on an escalator. But when cooled significantly, this order breaks down, and the motion becomes unpredictable.

Magnetic monopoles are like halves of a magnet that cannot exist alone in ordinary materials. But in spin ice, they appear in pairs connected by an invisible thread — a Dirac string. Previously, such monopoles were only seen in artificial systems at room temperature, but their quantum motion remained a mystery.

In some materials, atomic magnetic moments: their tiny 'arrows'—refuse to freeze even at ultra-low temperatures. Instead of conventional order, they form a spin liquid: a state where spins constantly flicker but do so coherently, like dancers in an intricate routine.

A woven bamboo basket is not just a household item: it's an exact blueprint for how atoms are arranged in the crystal YMn₆Sn₆. Six manganese atoms form hexagons that assemble into a pattern reminiscent of the Japanese kagome. In such a lattice, electrons usually behave uniformly, like passengers in a crowded subway car.

A drop of ink falls into a glass of water, and ripples spread out from it. Water seems simple, but if you look inside, each molecule isn't just moving forward: it's also spinning like a tiny top. Physicists call this intrinsic rotation spin. Usually, it goes unnoticed: in calm water, the tops spin every which way, and their rotation doesn't affect the fluid's overall motion.

A flat magnet is like a thin sheet with waves of magnetization running across it. Under normal conditions, these waves quickly die out, but when a strong magnetic field is switched on, an unexpected signal appears in the material — sharp and narrow, like a shadow cast by the main wave.

A ring of magnetic atoms resembles a round dance where each participant holds hands with their neighbors. In ordinary magnets, each atom has its own permanent magnetic moment, and they interact like little arrows striving to align opposite to each other.

A drop of water on the table looks calm, but inside it, quantum life is bustling. Protons in hydrogen atoms are like tiny spinning tops that constantly rotate. Each has its own direction of spin.

Magnetic atoms in a solid are like compass needles: usually, when cooled, they align in one direction: that's how magnetism arises. But in TbInO3, the terbium needles sit on a triangular lattice where it's impossible to please all neighbors at once. One needle wants to point north, another south, and in the end none can settle into a stable position.

Inside a magnet, there are regions where all the atomic magnets point in the same direction. Between such regions lies a narrow transition zone where the magnetization direction gradually rotates. This zone is called a domain wall. Previously, it was considered massless: give it a push, and it stops immediately.

The surface of the uranium compound UTe2 crystal looks like a frozen sea: in some places, electrons move freely; in others, they get stuck near atoms. A scanning tunneling microscope, a device that probes the surface with an atomically sharp tip and senses individual electrons, revealed that this landscape is not random.

A crystal the size of half a matchbox was grown in a furnace, where a molten zone slowly crept along a rod, leaving perfectly ordered layers behind. Inside this crystal, copper ions sit at the nodes of a triangular lattice, but the triangles are slightly skewed, as if someone pressed on one corner. Each copper ion behaves like a tiny magnetic needle that can point up or down.

Heat a crystal, and its atoms start to tremble more vigorously, like strings tightened or loosened. In a LaCoO3 crystal (a compound of lanthanum, cobalt, and oxygen), heating from 2 to 650 K triggers two major rearrangements: around 100 K, the magnetic state of cobalt ions changes, and around 550 K, the material transforms from an insulator into a…

Quantum entanglement works like a leash: it ties particles together, but the length of this tether is strictly limited. In a chain of particles, heat plays the role of an impatient dog tugging at the leash — the hotter it gets, the shorter the distance over which the connection holds.

Physicists took 114 rubidium atoms, cooled them to near absolute zero (as in experiments with liquid helium), and neatly arranged them in a honeycomb pattern. They then smoothly adjusted the interaction strength, as if slowly turning up the heat under a pot.

Ordinary tiles form a repeating pattern. But atoms can do more: under certain conditions, they themselves lay out a complex mosaic where the pattern never repeats, like on antique tile panels.

Three charged ytterbium atoms are arranged in a triangle inside an electromagnetic trap. Normally, they all communicate with each other, like three people at a table constantly exchanging remarks. But if one of them steps into the next room, the conversation continues between the remaining two.

An ordinary superconductor is like a squad of soldiers marching in pairs: electrons pair up, and their spins (internal 'tops') point in opposite directions. A magnetic field easily flips such pairs, destroying superconductivity. In UTe₂, things are different.

The magnets in this crystal behave like guests at a party where everyone wants the same chair. No one can settle down for good, and from this chaos, a special state emerges. In it, spin momentum (what makes an electron a tiny magnet) manages to travel 480 micrometers.