Bulk and surface excitons in the van der Waals magnet CrSBr: Magneto-optical studies to 55 tesla

By subjecting few-layer CrSBr to magnetic fields up to 55 tesla, this study confirms the existence of distinct bulk and surface excitons through their differing magnetic field responses, specifically a reduced redshift and smaller diamagnetic shift observed in the lower-energy surface exciton resonance.

The Gist

Imagine a stack of ultra-thin, magnetic sheets made of a material called CrSBr. Scientists have long known that when light hits these sheets, it creates tiny, bound pairs of electrons and holes called excitons. Think of an exciton like a tiny, energetic dance couple holding hands; they move together through the material and absorb specific colors of light.

In very recent studies, researchers noticed something strange in these stacks: there weren't just one, but two distinct types of these dance couples appearing at slightly different energy levels. They suspected that the couples dancing on the very top and bottom layers (the "surface" couples) were different from the couples dancing in the middle of the stack (the "bulk" couples).

Why would they be different?
Imagine the middle couples are dancing in a crowded room where everyone is holding hands with their neighbors on all sides. Now, imagine the surface couples are dancing on the edge of a stage. They only have neighbors on one side; the other side is open to the air (or in this case, a protective coating called hBN). Because they are on the edge, the "rules of the room" (specifically, how electricity and magnetism interact with them) are slightly different. The paper suggests this difference makes the surface couples dance to a slightly lower-pitched note (lower energy) than the bulk couples.

The Big Test: The 55-Tesla Magnet
To prove this theory, the authors didn't just look at the light; they put the material under extreme pressure using a massive magnet (55 Tesla is incredibly strong—about a million times stronger than a fridge magnet). They watched how the two types of excitons reacted to this magnetic squeeze.

They found two key differences that confirmed their theory:

1. The "Redshift" Test (Low Magnetic Fields):
   When they applied a small magnetic field, the material's internal magnetic order changed, and the excitons shifted their energy (like a guitar string loosening to a lower note).

   • The Bulk Couples: Because they are surrounded by neighbors on both sides, they could "loosen up" and spread out in two directions. This caused a big drop in their energy note.
   • The Surface Couples: Because they are stuck on the edge, they could only spread out in one direction. Consequently, their energy note dropped by only about half as much as the bulk couples. It's like a dancer who can only move their left arm versus one who can move both; the one with limited movement changes their pose less.

2. The "Diamagnetic" Test (High Magnetic Fields):
   In extremely high magnetic fields, excitons usually get squeezed tighter, causing a specific type of energy shift called a "diamagnetic shift." The size of this shift depends on how big the exciton's "dance circle" is.

   • The Result: The surface excitons showed a smaller shift than the bulk ones. This proved that the surface excitons are physically smaller and tighter. Why? Because the environment on the surface (the air/coating) doesn't "shield" them as well as the material in the middle does, forcing them to huddle closer together.

The Final Proof: Counting the Layers
To seal the deal, the researchers tested stacks with different numbers of layers (2 layers, 3 layers, 4 layers, and even thick stacks).

• The Logic: If the theory is right, a 2-layer stack should have only surface couples (no middle layers). A 3-layer stack should have two surface couples and one bulk couple.
• The Observation: In the 2-layer stack, the "bulk" signal disappeared entirely. In thicker stacks, the "bulk" signal grew stronger as more layers were added, while the "surface" signal stayed exactly the same size (because no matter how thick the stack gets, you only ever have two surfaces: top and bottom).

Conclusion
By using a super-strong magnet to watch how these microscopic dancers moved, the authors confirmed that surface excitons and bulk excitons are indeed two different species. They live in the same material but experience different environments, leading to different sizes, different magnetic reactions, and different colors of light they absorb. This discovery opens the door to potentially controlling these different groups of excitons separately in the future.

Technical Summary

Technical Summary: Bulk and Surface Excitons in CrSBr via Magneto-Optical Studies

Problem Statement
Recent investigations into the 2D magnetic semiconductor CrSBr identified two distinct optical resonances near the band edge: a fundamental transition and a lower-energy resonance approximately 20 meV below it. A hypothesis proposed by Shao et al. suggests these correspond to distinguishable populations of "bulk" excitons (confined to internal layers) and "surface" excitons (confined to the outermost monolayers). This distinction arises from CrSBr's highly anisotropic nature and weak inter-layer coupling, which confines excitons within individual monolayers. Consequently, surface excitons experience a different local dielectric environment compared to bulk excitons, potentially altering their binding energy, spatial extent, and coupling to magnetic order. While the existence of these two resonances was previously noted, their specific magneto-optical behaviors and the physical mechanisms distinguishing them had not been experimentally validated.

Methodology
To test the hypothesis of distinguishable bulk and surface exciton populations, the authors performed polarized optical absorption spectroscopy on few-layer CrSBr samples (ranging from 2 to ~18 layers) encapsulated in hexagonal boron nitride (hBN). The study utilized a "sample-on-fiber" approach to enable measurements in high magnetic fields (up to 55 T) at low temperatures (4 K).

• Low-Field Regime: The team measured absorption spectra as magnetic fields ($B \parallel \hat{c}$) were increased from 0 to 2 T. This range induces a transition from antiferromagnetic (AFM) to ferromagnetic (FM) order, allowing observation of field-induced redshifts associated with spin reorientation and inter-layer delocalization.
• High-Field Regime: Absorption spectra were measured in pulsed magnetic fields up to $\pm 55$ T to quantify the quadratic diamagnetic shifts ($\Delta E_{dia} \propto B^2$). Circularly polarized light was used in this regime to avoid artifacts from Faraday rotation in optical components.
• Analysis: The absorption spectra were fitted to Lorentzian oscillators to extract resonance energies and oscillator strengths. The diamagnetic shift coefficients ($\sigma$) were extracted to infer the characteristic mean-squared radius ($\langle r^2_\perp \rangle$) of the excitons. Theoretical modeling using the Rytova-Keldysh potential was employed to correlate dielectric screening environments with expected exciton sizes and shift ratios.

Key Results

1. Distinct Redshifts in Low Fields: Upon transitioning from AFM to FM order (0 to 2 T), the fundamental resonance ($X_{bulk}$) exhibited a parabolic redshift of approximately 14 meV. In contrast, the lower-energy resonance ($X_{surf}$) redshifted by only ~6 meV. This factor of roughly two difference is consistent with the theoretical expectation that bulk excitons can delocalize in both the $+\hat{c}$ and $-\hat{c}$ directions as inter-layer hopping is permitted, whereas surface excitons can delocalize in only one direction.
2. Differential Diamagnetic Shifts: In high fields (up to 55 T), both resonances exhibited quadratic diamagnetic shifts. The bulk exciton ($X_{bulk}$) had a shift coefficient of $\sigma_{bulk} = 45 \pm 2$ neV/T$^2$, while the surface exciton ($X_{surf}$) showed a significantly smaller coefficient of $\sigma_{surf} = 34 \pm 5$ neV/T$^2$. This ~25% reduction in the shift coefficient indicates that surface excitons possess a smaller characteristic spatial radius, consistent with weaker dielectric screening due to the adjacent hBN encapsulation ($\epsilon_{hBN} < \epsilon_{CrSBr}$).
3. Thickness Dependence: Measurements across 2L, 3L, 4L, and thick (~18L) samples confirmed the assignments. The 2L sample lacked the $X_{bulk}$ resonance entirely, as it contains no internal "bulk-like" layers. For $N \ge 3$, the oscillator strength of $X_{bulk}$ increased with layer number, while the oscillator strength of $X_{surf}$ remained constant, consistent with the presence of exactly two surface layers regardless of total thickness.

Significance and Claims
The paper claims to provide the first magneto-optical validation of the distinguishable bulk and surface exciton scenario in CrSBr. By demonstrating that the two resonances respond differently to both magnetic ordering (low-field redshift) and dielectric screening effects (high-field diamagnetic shift), the authors confirm that these are distinct physical populations rather than artifacts or different electronic transitions.
The authors state that these findings offer quantitative evidence that surface excitons in CrSBr are physically smaller and less screened than their bulk counterparts. They conclude that this spectral distinguishability, despite the excitons originating from proximal atomic layers, establishes a platform for future studies on inter-species exciton interactions, exciton-magnon dynamics, and the dielectric engineering of excitonic properties in 2D magnets. The work does not propose new applications but rather solidifies the fundamental understanding of exciton behavior in this material system.