Scanning Tunneling Microscopy Reveals Spin Information in Altermagnetic Lieb Lattices

The subtle interplay of magnetism and electronic structure governs the behaviour of many advanced materials, and understanding this relationship requires increasingly sophisticated techniques. Eric Petermann, Kristian Mæland, and Björn Trauzettel from the Institute for Theoretical Physics and Astrophysics at the University of Würzburg demonstrate how standard, non-spin-resolved scanning tunneling microscopy can reveal hidden magnetic information within a specific class of materials called altermagnets. Their theoretical work shows that carefully placed impurities within these materials create interference patterns which, when analysed, effectively map out the spin-dependent electronic structure. This discovery is significant because it offers a pathway to probe magnetism at the nanoscale without the need for specialised, spin-sensitive equipment, potentially simplifying the characterisation of future electronic devices and materials.

Unique Magnetic Order and Quantum Properties

Altermagnetism represents a recently discovered and intensely studied quantum state of matter, distinct from conventional magnetism. This unique form of magnetic order differs from ferromagnetism, antiferromagnetism, and ferrimagnetism, and arises from specific arrangements of electron spins. The concept is closely tied to the Lieb lattice, a two-dimensional structure with unique electronic properties that can host flat bands, crucial for realizing altermagnetic behavior. A specific type, d-wave altermagnetism, has been observed in several candidate materials, demonstrating its potential for realization.

Altermagnetism isn’t simply a different spin arrangement, but a fundamentally different state of electrons, impacting their behavior. Researchers are actively searching for materials exhibiting altermagnetic behavior, with promising candidates including metal-organic frameworks designed to mimic the Lieb lattice and layered materials like La2O3Mn2Se2. Recent discoveries have even revealed materials displaying room-temperature altermagnetism. Creating these materials with the precise structure and properties needed to realize altermagnetism presents a significant challenge, requiring materials with flat bands in their electronic structure, leading to strong electron correlations that can stabilize the altermagnetic phase.

Strong electron correlations and the quantum geometry of electronic bands also play vital roles in determining the properties of these materials, with theoretical interest in the possibility of superconductivity and quantum critical behavior arising from altermagnetic interactions. Detecting and characterizing altermagnetism experimentally requires specialized techniques. Quasiparticle interference (QPI) is a powerful method for imaging electronic structure, revealing unique signatures of altermagnetism through specific scattering patterns. Analyzing Friedel oscillations, spatial modulations of electron density induced by impurities, provides further information about the altermagnetic order.

Scanning tunneling microscopy (STM) is used to image electronic structure and probe local density of states, while angle-resolved photoemission spectroscopy (ARPES) maps the electronic band structure. Magnetometry measures the magnetic properties of materials, providing a comprehensive picture of altermagnetic behavior. Computational methods, including efficient matrix inversion algorithms, are essential for modelling and understanding these complex materials. Ongoing research focuses on understanding the fundamental properties of altermagnets and exploring their potential applications. Key areas of investigation include the role of impurities, the possibility of superconductivity, topological properties, and behavior at interfaces. Altermagnetism is a novel quantum state of matter with unique magnetic and electronic properties, and the field is rapidly evolving, promising new insights into materials science and quantum physics.

Impurity Effects Reveal Altermagnet Spin Structure

Researchers have developed a unique method to investigate altermagnetic materials, combining theoretical modelling with concepts applicable to scanning tunneling microscopy (STM). This approach simulates how imperfections, introduced as impurities, affect electron flow and reveal hidden details about magnetic order. This is innovative because it extracts spin-resolved information using a standard, non-spin-polarized STM tip, avoiding the need for complex instrumentation. The investigation begins with a detailed computational model representing the material’s crystal structure and electronic behavior, built upon a ‘tight-binding’ framework that describes electron interactions within the lattice.

This model incorporates the ability to tune the material’s magnetic properties by adjusting energy levels, effectively switching between antiferromagnetic and altermagnetic states. By strategically placing simulated impurities, researchers observe how these imperfections scatter electrons and create interference patterns, known as quasiparticle interference. A key aspect involves analyzing these patterns through a Fourier transform, converting real-space images of electron density into momentum space and revealing the shape of the material’s Fermi surface, a boundary separating occupied and unoccupied electron states. Crucially, the location of the impurity dramatically influences the resulting interference pattern, acting as a filter for electron spin.

Impurities placed on specific sublattices preferentially highlight electrons with a particular spin orientation, along a specific direction on the Fermi surface. By comparing Fourier-transformed interference patterns obtained from impurities placed on different sublattices, researchers reconstruct a complete, spin-resolved map of the altermagnet’s Fermi surface. This innovative approach allows determination of electron spin orientation without requiring a spin-polarized STM tip, offering a simpler and more accessible experimental route to characterize these complex magnetic materials. The method leverages the sensitivity of quasiparticle interference to impurity location, transforming a standard technique into a powerful tool for probing subtle magnetic order.

Impurity-Driven Spin Sensitivity in Lieb Lattices

Researchers have demonstrated a novel method for extracting spin-dependent information from materials using scanning tunneling microscopy, even without directly measuring spin polarization. This breakthrough centers on carefully studying how impurities disrupt electron flow within an altermagnetic Lieb-like lattice and analyzing the resulting patterns. The team discovered that the placement of an impurity on one of four distinct sites dramatically alters how electrons scatter, and crucially, this scattering is not identical for spin-up and spin-down electrons. The research reveals that impurities placed on certain sites preferentially scatter electrons of a specific spin, creating a directional bias in the scattering pattern.

For example, an impurity on one site might strongly affect spin-up electrons along one direction, while having minimal impact on spin-down electrons, or vice versa. This effect is particularly pronounced when the material is tuned into an altermagnetic state, where the magnetic properties differ from traditional magnets. By analyzing these subtle differences in scattering, researchers can effectively “decode” the spin orientation of electrons without needing to directly measure their spin. The team further showed that the degree of anisotropy, the directionality of the scattering, can be precisely controlled by manipulating the material’s properties.

In a specific limit, where one site becomes energetically inaccessible to electrons, the scattering becomes almost entirely polarized, with impurities scattering electrons of only one spin along a single direction. This level of control opens possibilities for designing materials with tailored spin-dependent properties. Importantly, the researchers extended their analysis from real space to momentum space, mapping electron behavior in terms of momentum. This momentum-space analysis reveals characteristic patterns related to the altermagnetic state, confirming the spin-dependent nature of the scattering process. The ability to extract spin information from these patterns represents a significant advancement, potentially enabling new techniques for characterizing and manipulating magnetic materials at the nanoscale.

Mapping Spin Texture via Impurity Scattering

This research demonstrates a method for extracting spin-dependent information from scanning tunneling microscopy measurements of an altermagnetic Lieb-like lattice. By introducing impurities into the lattice and analyzing the resulting changes in local electron density, the team shows that the scattering patterns effectively reveal the spin orientation of electrons. Specifically, the placement of an impurity on one sublattice highlights spin-up electrons, while placement on another favors spin-down electrons, providing a way to map the spin texture of the material. The key finding is that this technique allows researchers to discern spin information without needing spin-polarized probes, which are often difficult to implement. The.