Field-driven phase transition crossover in kagome antiferromagnet Mn$_{3-x}$Co$_x$Sn

Magnetism is often thought of as a simple toggle between on and off, but in certain materials, the story is far more intricate. Deep inside the atomic structure of some solids, tiny magnetic arrows called spins arrange themselves in complex patterns, and these patterns can shift dramatically when the temperature changes or when an external magnetic field is applied. When these shifts happen, the material absorbs or releases heat, a phenomenon known as the magnetocaloric effect. This effect is the engine behind magnetic refrigeration, a technology that promises to cool things down without the harmful gases used in traditional fridges. However, to harness this power, scientists need to understand exactly how these magnetic shifts occur. Are they smooth, gradual changes, or are they sudden, sharp jumps? The difference matters immensely for designing efficient cooling devices, and it is here that the behavior of a specific family of materials called kagome antiferromagnets becomes a fascinating puzzle.

In a recent study, researchers at the Indian Institute of Technology Kanpur turned their attention to a crystal called Mn3Sn. This material is famous for its unique internal architecture, where manganese atoms sit at the corners of triangles that form a honeycomb-like pattern known as a kagome lattice. At room temperature, the magnetic spins in this crystal are arranged in a non-collinear triangular structure, meaning they point in different directions within the same plane rather than lining up neatly. As the crystal cools, it undergoes a transformation where these spins rearrange themselves into a spiral pattern. This transition happens at a specific temperature, around 278 Kelvin, and it is a sharp, sudden event. The researchers wanted to know if they could tame this sharpness and perhaps even change the nature of the transition by slightly altering the crystal's recipe.

To test this, the team grew high-quality single crystals of Mn3Sn and then created a new version by replacing a small portion of the manganese atoms with cobalt. They kept the cobalt concentration low, at just 8 percent, to ensure the fundamental kagome structure remained intact while still introducing subtle changes. The results were striking. In the pure crystal, the magnetic transition at 278 Kelvin was a sharp, sudden jump, characteristic of a first-order phase transition. This kind of abrupt change is often accompanied by a thermal hysteresis, meaning the material behaves slightly differently when heating up compared to when it is cooling down, much like how a door might stick when you push it open but slide smoothly when you pull it shut. The pure crystal also showed a specific type of magnetic response where the entropy, or disorder, decreased in a way that is considered "inverse" to what is typically expected in standard magnetic cooling materials.

When the cobalt was added, the story changed completely. The sharp transition temperature dropped significantly to 175 Kelvin, and a new, weaker magnetic behavior appeared around 210 Kelvin. The cobalt atoms, being slightly smaller than the manganese they replaced, squeezed the crystal lattice, causing it to contract. This physical tightening altered the way the atoms interacted with one another, effectively breaking the perfect symmetry of the kagome pattern. This symmetry breaking induced a new magnetic state where the spins tilted slightly out of their flat plane, creating a weak ferromagnetic character. Instead of the sharp, sudden jump seen in the pure crystal, the cobalt-doped version showed a much broader, smoother transition. However, the researchers observed that the thermal hysteresis, which was a clear sign of a sudden jump in the pure sample, persisted in the doped sample at lower fields, indicating that the first-order phase transition signature remained across a wide temperature range before evolving under higher fields.

The most significant discovery, however, was how the material responded to an external magnetic field. In the pure crystal, applying a magnetic field did not change the fundamental nature of the transition; it remained a sharp, first-order event regardless of the field strength. But in the cobalt-doped crystal, the magnetic field acted as a switch. At low field strengths, the transition still behaved like a sharp jump. Yet, as the researchers increased the magnetic field, the transition began to smooth out. Above a certain threshold, the sharp jump did not disappear entirely but rather gave way to a crossover where the material exhibited a mix of behaviors, eventually evolving into a continuous, second-order transition. This means the material could be tuned from one type of magnetic behavior to another simply by adjusting the strength of the magnetic field applied to it.

To confirm this crossover, the team analyzed how the magnetic entropy changed across different temperatures and field strengths. They found that in the pure crystal, the data points scattered widely when scaled, a signature of a sharp, first-order transition. In contrast, the cobalt-doped crystal showed a remarkable collapse of data points onto a single, universal curve when the magnetic field was strong enough. This collapse is the hallmark of a smooth, second-order transition, though at lower fields, the data indicated a coexistence of both first-order and second-order characteristics. The researchers mapped these findings into a new phase diagram, which clearly shows the boundaries where the material switches from a sharp, first-order transition to a smooth, second-order one. This field-driven crossover suggests that by carefully choosing the amount of cobalt and the strength of the magnetic field, scientists can control the order of the phase transition.

The implications of this work extend beyond just understanding a single crystal. It demonstrates that the order of a magnetic phase transition is not a fixed property of a material but can be manipulated through chemical doping and external fields. For the field of magnetic refrigeration, this is a crucial insight. Materials that undergo smooth, second-order transitions are often preferred for cooling applications because they can operate over a wider temperature range without the energy losses associated with sharp jumps. The study shows that by introducing a small amount of cobalt into Mn3Sn, the material can be engineered to exhibit these desirable smooth transitions under the right conditions. The researchers have successfully grown these crystals, measured their properties with high precision, and constructed a detailed map of how they behave, providing a clear path for future exploration in magnetic materials.