🔬 mesoscale physics

Quantum Noise Spectroscopy of Criticality in an Atomically Thin Magnet

This study utilizes nitrogen-vacancy center noise magnetometry to quantitatively characterize the critical dynamics of a two-dimensional CrSBr magnet, revealing that its phase transition is Ising-like but significantly modified by long-range dipolar interactions rather than adhering to a standard short-range universality class.

Original author: Mark E. Ziffer, Francisco Machado, Benedikt Ursprung, Artur Lozovoi, Aya Batoul Tazi, Zhiyang Yuan, Michael E. Ziebel, Tom Delord, Nanyu Zeng, Evan Telford, Daniel G. Chica, Dane W. deQuilettes, Xiaoy

Published 2026-11-05

📖 4 min read☕ Coffee break read

CC BY 4.0

Original author: Mark E. Ziffer, Francisco Machado, Benedikt Ursprung, Artur Lozovoi, Aya Batoul Tazi, Zhiyang Yuan, Michael E. Ziebel, Tom Delord, Nanyu Zeng, Evan Telford, Daniel G. Chica, Dane W. deQuilettes, Xiaoyang Zhu, James C. Hone, Kenneth L. Shepard, Xavier Roy, Nathalie P. de Leon, Emily J. Davis, Carlos A. Meriles, Jonathan S. Owen, P. James Schuck, Shubhayu Chatterjee, Abhay N. Pasupathy

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the author. For technical accuracy, refer to the original paper. Read full disclaimer

Matter changes its character when it gets hot or cold. A solid metal becomes a liquid, a magnet loses its pull, or a superconductor suddenly conducts electricity without resistance. These dramatic shifts, known as phase transitions, are not random; they are governed by deep mathematical rules that describe how tiny particles interact over long distances. When a material nears one of these critical points, its internal parts stop acting independently and begin to move in large, coordinated waves. These waves, called fluctuations, are the heartbeat of the transition. Understanding them tells scientists not just how a specific material behaves, but how entire classes of matter organize themselves. For decades, studying these fluctuations in materials that are only a few atoms thick has been nearly impossible. The samples are too small for traditional tools, and the signals are too faint to catch. Yet, knowing how these ultra-thin magnets work is crucial for the future of computing and data storage, where shrinking components to the atomic limit is the goal.

A team of researchers has now solved this problem by using a unique tool: a tiny defect inside a diamond crystal that acts as a microscopic sensor. They turned their attention to a material called CrSBr, a magnetic crystal that can be peeled apart into layers just three atoms thick. In its bulk form, this material is a magnet that orders itself in a specific way, but scientists have long debated how it behaves when reduced to a single few-layer sheet. Does it follow the standard rules of magnetism, or does the extreme thinness change the game entirely? To find out, the researchers placed a flake of this three-layer magnet directly on top of a diamond chip. Inside the diamond, just a few dozen nanometers below the surface, they had implanted a dense collection of nitrogen-vacancy centers. These are atomic-scale imperfections that behave like tiny magnets themselves, capable of sensing the magnetic field of the material above them with incredible precision.

The researchers did not just look at the magnet; they listened to its noise. As the temperature of the sample changed, the magnetic atoms in the CrSBr flake began to jitter and fluctuate. These jitters created a fluctuating magnetic field that reached down into the diamond. The team used a specific sequence of microwave pulses to measure how quickly the tiny sensors in the diamond lost their own magnetic alignment, a process called decoherence. When the material was far from its critical temperature, the sensors held their alignment for a long time. But as the researchers warmed the sample to a specific point, around 139 Kelvin, the sensors suddenly began to lose their alignment much faster. This sharp spike in the loss of alignment was the fingerprint of the critical fluctuations, revealing exactly where the phase transition occurred.

By analyzing the shape of this spike and how the sensors responded at different speeds, the team was able to test two competing theories about how the magnet was behaving. One theory suggested the material was undergoing a transition typical of two-dimensional magnets where the order is maintained by a specific type of swirling motion. The other theory suggested a more standard type of magnetic ordering. The data showed a very sharp, distinct peak in the noise, which ruled out the swirling motion theory. Instead, the behavior matched a model where the magnetic atoms align along a preferred axis, similar to how a compass needle points north. However, the numbers the team extracted from the data did not match the standard textbook values for this type of ordering. The fluctuations were stronger and behaved differently than expected for a simple, short-range interaction.

The researchers concluded that the magnet was indeed following the standard rules of alignment, but with a significant twist. The magnetic atoms in the thin flake were influencing each other over longer distances than usual, likely due to the way their magnetic fields stretch out through space. This long-range influence changed the fundamental nature of the transition, making it distinct from the simple models used to describe most magnets. The study proves that these atomic-scale sensors can act as a precise microscope for the invisible dynamics of critical matter. By measuring the noise of a magnet that is only three atoms thick, the team has opened a new window into understanding how the most complex magnetic behaviors emerge in the thinnest possible materials, providing a clear path to studying other exotic states of matter in the future.

Technical Summary: Quantum Noise Spectroscopy of Criticality in an Atomically Thin Magnet

Problem and Motivation
The universality class of a phase transition dictates the scaling behavior of low-frequency, long-wavelength critical fluctuations in a material. While understanding these dynamics is fundamental to condensed matter physics, experimentally characterizing them in atomically thin magnetic insulators remains a significant challenge. Conventional probes such as inelastic neutron scattering, $\mu$ SR, NMR, and EPR are limited by the small sample volumes inherent to two-dimensional (2D) van der Waals (vdW) crystals. Furthermore, optical techniques are often restricted by diffraction limits or require complex sample aggregation to increase volume. Consequently, there is a need for a quantitative probe capable of sensing low-frequency, long-wavelength fluctuations in mesoscopic 2D magnets without perturbing the sample's magnetic state.

Methodology
The authors employ Nitrogen-Vacancy (NV) centers in diamond as a quantum sensor to perform $T_2$ (spin-decoherence) noise magnetometry on a tri-layer sample of the 2D vdW magnet Chromium Sulfide Bromide (CrSBr).

Experimental Setup: A tri-layer CrSBr flake is transferred onto an isotopically pure $^{12}$ C diamond substrate containing an ensemble of NV centers implanted at shallow depths (10–80 nm). The NV centers are optically initialized and read out, with their spin coherence manipulated via microwave pulses.
Static Characterization: Using pulsed Optically Detected Magnetic Resonance (ODMR), the authors map the stray magnetic field ( $B_{flake}$ ) generated by the CrSBr flake. This confirms the expected A-type antiferromagnetic ordering (ferromagnetic intralayer, antiferromagnetic interlayer) and tracks the loss of magnetic order as temperature increases.
Dynamic Probing ( $T_2$ Noise Spectroscopy): The core technique involves measuring the spin-echo coherence decay ( $C(\tau)$ ) of the NV ensemble as a function of temperature. Unlike $T_1$ sensing, which is limited to frequencies near the zero-field splitting (~GHz), the $T_2$ protocol utilizes a spin-echo pulse sequence to filter for magnetic field fluctuations at frequencies $\sim 1/\tau$ . This allows access to the low-frequency range (kHz–MHz) where critical slowing down occurs near the phase transition.
Theoretical Modeling: The decoherence dynamics are modeled using a noise spectroscopy framework where the NV spin variance $\langle \phi^2 \rangle$ is related to the material's dynamical structure factor $S(\omega, q)$ . The model incorporates momentum and frequency filter functions ( $W_\ell(q)$ and $W_\tau(\omega)$ ) determined by the NV-sample distance and the pulse sequence, respectively. The structure factor is parametrized by critical exponents: the correlation length exponent ( $\nu$ ) and the dynamical exponent ( $z$ ).

Key Results

Observation of Critical Fluctuations: The authors observe a sharp increase in the NV spin decoherence rate ( $1/T_2$ ) as the sample temperature approaches the critical temperature. The peak in the decoherence rate identifies the critical temperature $T_C = 139$ K, consistent with the loss of static magnetization observed in ODMR imaging.
Distinction of Universality Class: The temperature dependence of the decoherence rate is used to distinguish between competing hypotheses for the magnetic transition in CrSBr: a Berezinskii-Kosterlitz-Thouless (BKT) transition (2D XY model) versus an Ising transition.
- The BKT hypothesis predicts a broad, asymmetric enhancement of the decoherence rate persisting well below $T_C$ due to quasi-long-range order.
- The experimental data shows a sharp, symmetric peak at $T_C$ , which qualitatively rules out the BKT scenario and supports an Ising-like transition.
Quantitative Extraction of Critical Exponents: By globally fitting the temperature-normalized decoherence dynamics to simulations based on the Ising universality class, the authors extract the critical exponents:
- Dynamical exponent: $z \approx 1.68$
- Correlation length exponent: $\nu \approx 0.58$
- These values are statistically distinct from the standard short-range 2D Ising universality class ( $z=2, \nu=1$ ).
Role of Long-Range Interactions: The deviation of the extracted exponents from the short-range Ising model is attributed to the presence of long-range dipolar interactions. The authors conclude that while the transition is Ising-like, it is modified by these long-range dipolar couplings and easy-axis anisotropy.

Significance and Claims
The paper establishes $T_2$ noise magnetometry using NV centers as a precise, quantitative probe for studying critical dynamics in 2D materials. The work demonstrates that this technique can:

Directly access low-frequency, long-wavelength fluctuations in atomically thin samples where conventional probes fail.
Distinguish between different universality classes (Ising vs. BKT) based on the qualitative shape of the decoherence rate near $T_C$ .
Quantitatively measure critical exponents ( $z$ and $\nu$ ) in 2D systems, revealing the impact of long-range interactions that are often difficult to disentangle in static measurements.

The authors assert that their findings clarify the nature of the magnetic transition in 2D CrSBr, indicating it is an Ising transition modified by long-range dipolar interactions. They position this work as a foundational step toward exploring strongly correlated phenomena at the atomically thin limit, offering a pathway to study criticality in a broad range of 2D materials and phases of matter.

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