Er³⁺ Defects in CrSBr: Atomic-Scale Magnetic Probes

• Er³⁺ defects in CrSBr are erbium ions substituted into the crystal lattice, enabling telecom-band photoluminescence to probe intrinsic magnetic order.
• They produce sharply resolved, long-lived spectrally narrow PL lines with temperature- and field-dependent shifts around the Néel transition.
• Confocal microscopy and cryogenic PL studies reveal nanoscale magnetic heterogeneity and dynamic domain behavior beyond conventional magnetometry.

Er³⁺ defects in CrSBr refer to erbium ions directly substituted into the lattice of chromium sulfide bromide (CrSBr), providing an internal, atomic-scale probe of static and dynamic magnetic order via telecom-band photoluminescence (PL). Unlike traditional external sensors, these lattice-embedded probes access the magnetism of the host material from within, enabling direct optical readout of nanoscale magnetic phenomena with minimal spatial averaging. The archetype is the use of Er³⁺ (4f¹¹) in the orthorhombic CrSBr lattice, as demonstrated in recent work by García-Arellano et al. (García-Arellano et al., 24 Jan 2026), where their integration gives rise to sharply resolved, long-lived PL lines, pronounced temperature-dependent effects at the Néel transition, magnetic-field-tunable spectral features, and spatially heterogeneous signals representing nanoscale order beyond bulk phase boundaries.

1. Crystal-Field Environment and Hamiltonian

Er³⁺ ions occupy sites of approximate C2v (mm2) symmetry within the crystalline CrSBr lattice. The 4f electronic manifold of Er³⁺ is subject to a crystal-field Hamiltonian expressible in the Stevens-operator formalism as

$$\mathcal{H}_{\mathrm{CF}} = \sum_{k=2,4,6}\;\sum_{q=-k}^{+k} B_k^q\,O_k^q$$

where $O_k^q$ are Stevens operators and $B_k^q$ are corresponding coefficients. Due to the C2v symmetry, only even-$q$ terms remain:

$$\mathcal{H}_{\mathrm{CF}} = B_2^0\,O_2^0 + B_2^2\,O_2^2 + B_4^0\,O_4^0 + B_4^2\,O_4^2 + B_4^4\,O_4^4 + B_6^0\,O_6^0 + B_6^2\,O_6^2 + B_6^4\,O_6^4 + B_6^6\,O_6^6$$

Although explicit $B_k^q$ values are not extracted in (García-Arellano et al., 24 Jan 2026), the low site symmetry leads to a complex manifold of Kramers doublets within each $J$-multiplet, underpinning a rich set of optical transitions. This local symmetry breaking is essential in splitting the energy levels to enable site- and field-sensitive PL signatures.

2. 4f Level Structure and Telecom-Band Photoluminescence

Within this crystal field, the ground multiplet $^4I_{15/2}$ of Er³⁺ splits into eight Kramers doublets $\{|g_i\rangle\}$ and the first excited $^4I_{13/2}$ multiplet splits into seven doublets $\{|e_j\rangle\}$. The dominant PL transitions at room temperature correspond to radiative recombination from the lowest $^4I_{13/2}$ doublet ($j=1$) to the four lowest $^4I_{15/2}$ doublets ($i=1\ldots 4$). These transitions result in a set of spectrally narrow lines between 1.50 μm and 1.60 μm (approximately 816–794 meV). The selection rules primarily permit magnetic-dipole transitions ($\Delta J = 0, \pm 1; \Delta m_J = 0, \pm 1$). The following table summarizes key transition wavelengths and energies:

Label	Wavelength (nm)	Wavenumber (cm⁻¹)	Energy (meV)
$\lambda_1$	$\approx 1520$	$\approx 6579$	$\approx 816$
$\lambda_2$	$\approx 1540$	$\approx 6494$	$\approx 804$
$\lambda_3$	$\approx 1560$	$\approx 6410$	$\approx 794$

This spectral fingerprint anchors the use of Er³⁺ as a telecom-band probe.

3. Temperature Dynamics, Photoluminescence Hysteresis, and the Néel Transition

The temperature evolution of PL intensity $I_{\mathrm{PL}}(T)$ and excited-state lifetime $\tau(T)$ is strongly correlated with the antiferromagnetic (AFM) transition at $T_N \simeq 132$ K. Cooling from 300 K to 3.5 K produces a pronounced $I_{\mathrm{PL}}$ minimum and complementary $\tau(T)$ maximum at $T_N$. Notably, the cooling and warming curves exhibit clear hysteresis; $I_{\mathrm{PL}}(T)$ on cooling lies systematically above that on warming in the 100–160 K window, reflecting different magnetic domain kinetics or local phase separation. Below and above $T_N$, PL recovers asymmetrically, with lifetimes peaking at $\sim6$ ms at $T_N$, and decreasing to $\sim5$ ms at 300 K and $\sim4$ ms at 3.5 K for a 70 nm flake. The PL minimum aligns with the thermal crossover in magnetic order.

A phenomenological logistic-like form can approximate the temperature profile:

$$I_{\mathrm{PL}}(T) \approx I_0 + \frac{A}{1 + \exp\bigl[(T-T_N)/\Delta T\bigr]}$$

where $I_0$, $A$, and $\Delta T$ reproduce the oscillator dip and shoulder. This thermal response provides a direct optical proxy of the AFM phase boundary.

4. Zeeman Field Effects and Field-Biased Transition Shifts

Applying a static in-plane magnetic field $B = 0.3$ T (nearly along the $a$ axis) globally suppresses the PL intensity and shifts the $I_{\mathrm{PL}}(T)$ minimum from 132 K to approximately 140 K ($\Delta T \approx +8$ K). This elevation is anomalous for canonical antiferromagnets, for which uniform fields typically suppress $T_N$, but can be rationalized if the field stabilizes short-range ferromagnetic ("FM puddle") correlations, locally enhancing the net field seen by Er³⁺. A minimal Landau-like free energy:

$F(M) = \alpha(T - T_N) M^2 + \beta M^4 - M B$

describes a scenario where the onset of local moment $M$ occurs at a field-elevated temperature. Therefore, Er³⁺ probes in CrSBr map not only uniform AFM order but also field-biased, nanoscale FM domains and their evolution with external perturbations.

5. Nanoscale Magnetic Order and Spatial Heterogeneity Beyond Bulk $T_N$

Spatially resolved confocal PL imaging reveals that the suppression of PL near $T_N$ is not homogeneous; nanoscale islands and edge regions manifest extended suppression up to 160–180 K, well beyond the nominal bulk phase transition. These islands constitute local AFM or canted FM correlations persisting above $T_N$, accessible solely by atomic-scale internal probes. Upon temperature cycling, these nanoscale PL features exhibit training-dependent hysteresis—after several thermal cycles, the local PL–$T$ loops converge, but remain broader and more long-lived in thick flakes (≥600 nm) than in thin flakes (≤100 nm). The persistence and metastability of these spatial structures would be substantially averaged out by external sensors, demonstrating the unique sensitivity of Er³⁺-doped CrSBr as a platform for internal magnetic imaging.

6. Telecom-Band Spectroscopy and Confocal Microscopy Techniques

The interrogation of Er³⁺ defects relies on a custom-built, diffraction-limited confocal microscope, achieving a 450 nm × 450 nm focal spot and employing 980 nm diode-laser excitation (4 mW at sample). Emitted telecom-band photons (≥1250 nm) are isolated by dichroic and long-pass filtering, directed either to an InGaAs array (for spectral measurements) or to a superconducting nanowire single-photon detector (SNSPD) for time-resolved PL studies. Temperature control from 3.5 K to 300 K is achieved with a closed-cycle cryostat, while a kinematically mounted permanent magnet applies static in-plane fields up to 0.3 T (alignment ≤3°). Polarization analysis shows that both the absorption (maximal along $a$) and emission (linear, ≈60° from $b$) dipoles have fixed orientation, although their magnitudes change significantly with temperature and field.

These tools enable discrimination of subtle changes in the local CrSBr magnetic landscape with high spatial, spectral, and temporal resolution. The platform is uniquely sensitive to sub-10 nm magnetic domains, capturing domain wall dynamics and enabling millisecond-scale time-tracing of local antiferromagnetic sublattice imbalances.

7. Implications and Outlook

Embedded Er³⁺ defects in CrSBr constitute an internal, fiber-compatible, atomic-scale magneto-optical sensor capable of resolving thermal hysteresis, domain wall kinetics, and field-stabilized FM correlations above the nominal AFM transition. This atomic-scale readout eliminates stand-off averaging present in external approaches and presents opportunities for integrated spin–photon–magnon platforms based on layered van der Waals magnets. These findings suggest that atomic-scale dopant probes can systematically reveal nanoscale and metastable magnetic phenomena invisible to conventional magnetometry, expanding the experimental toolkit for two-dimensional spin systems (García-Arellano et al., 24 Jan 2026).