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DOE OSTI2024

Exotic edge states of C 3 high-fold fermions in honeycomb lattices

A generalization of the graphene honeycomb model to the case where each site in the honeycomb lattice contains a n -fold degenerate set of eigenstates of the C 3 symmetry has been recently proposed to describe several systems, including triangulene crystals and photonic lattices. These generalized honeycomb models are defined by ( n a , n b ) , the number of C 3 eigenstates in the a and b sites of the unit cell, resulting in n a + n b bands. Thus, the (1,1) case gives the coventional honeycomb model that describes the two low-energy bands in graphene. Generalizations, such as (2,1), (2,2), and (3,3) display several nontrivial features, such as coexisting graphenelike Dirac cones with flat bands, both at zero and finite energy, as well as robust degeneracy points where a flat band and a parabolic band meet at the Γ point. Here we explore the edge states of this class of crystals, using as reference triangulene crystals, and we find several types of edge states absent in the conventional (1,1) honeycomb case, associated to the nontrivial features of the two-dimensional bands of the high-fold case. First, we find dispersive edge states associated to the finite-energy flat bands, that occur both at the armchair and zigzag termination. Second, in the case of noncentrosymmetric triangulene crystals that lead to a S = 1 Dirac band, we have a bonding-antibonding pair of dispersive edge states, localized in the same edge so that their energy splitting is reduced as their localization increases, opposite to the conventional behavior of pairs of states localized in opposite edges. Third, for the (3,3) case, that hosts a gap separating a pair of flat conduction and valence bands, we find nondispersive edge states with E = 0 in all edge terminations. Published by the American Physical Society 2024

Madail, L. (ORCID:0000000208457748)↗

DOE OSTI2024

Extracting off-diagonal order from diagonal basis measurements

Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. Here, we show that a multiscale complexity measure can pinpoint the transition to and from the bond ordered wave phase of the one-dimensional extended Hubbard model with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors. We study the model directly in the thermodynamic limit using the recently developed variational uniform matrix product states algorithm, and draw our samples from degenerate ground states related by global spin rotations, emulating the projective measurements that are accessible in experiments. Our results will have important implications for the study of exotic phases using optical lattice experiments. Published by the American Physical Society 2024

1-dimensional systems↗

DOE OSTI2025

Emergent Dimer-Model Topological Order and Quasiparticle Excitations in Liquid Crystals: Combinatorial Vortex Lattices

Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological phases and topological order has been introduced in the context of spin liquids to investigate emergent phenomena like quantum Hall effects and high-temperature superconductivity. Here, we bridge these two seemingly disparate perspectives on topology in physics. Combining experiments and simulations, we show how topological defects in liquid crystals can be used as versatile building blocks to create complex, highly degenerate topological phases, which we refer to as “combinatorial vortex lattices” (CVLs). CVLs exhibit extensive residual entropy and support locally stable quasiparticle excitations in the form of charge-conserving topological monopoles, which can act as mobile information carriers and be linked via Dirac strings. CVLs can be rewritten and reconfigured on demand, endowed with various symmetries, and modified through laser-induced topological surgery—an essential capability for information storage and retrieval. We demonstrate experimentally the realization, stability, and precise optical manipulation of CVLs, thus opening new avenues for understanding and technologically exploiting higher-hierarchy topology in liquid crystals and other ordered media.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Optimal filtering and generation of entangled photons for quantum applications in the presence of noise

Filtering is commonly used in quantum optics to reject noise photons, and also to enable interference between independent photons. However, filtering the joint spectrum of photon pairs can reduce the inherent coincidence probability or loss-independent heralding efficiency. Here we investigate filtering for multiphoton applications based on entanglement and interference (e.g., quantum teleportation). We multiplex C-band entangled photons and C-band classical communications into the same long-distance fibers, which enables scalable low-loss quantum networking but requires filtering of spontaneous Raman scattering noise from classical light. Using tunable-bandwidth filters, low-jitter detectors, and polarization filters, we distribute wavelength-degenerate time-bin entangled photons in the C band (1536.5 nm) over 25 km/25 km standard fibers (50 km) each carrying 10 Gbit/s C-band classical data signals. Narrow filtering enables milliwatt-level C-band power, which exceeds the power achieved by comparable studies by roughly an order of magnitude and could feasibly support terabit per second classical rates. We evaluate how performance depends on pump and filter bandwidths, multipair emission, filter shapes, loss, phase matching, and how quantum information is measured. We find a trade-off between reducing noise impact and increasing single-mode purity, and discuss mitigation methods toward optimal multiphoton applications. Importantly, these results apply to noise in free space and in quantum devices (sources, frequency converters, switches, detectors, etc.) and provide insight into filter-induced degradation of single-photon purity and rates even in noise-free environments.

Thomas, Jordan M. [Fermilab; Northwestern U.]↗

DOE OSTI2026

Computational prediction of ferromagnetic 𝐴⁢𝑇 6 ⁢𝑋 6 kagome compounds

We present a systematic high-throughput density-functional-theory investigation of the structural and magnetic stability of 312 substitutional compounds in the magnetic kagome 𝐴⁢𝑇 6⁢ 𝑋 6 family. Our screening confirms the stability of many previously reported structures and predicts several additional stable candidates. Within collinear spin configurations, we find that Fe-based systems predominantly adopt antiferromagnetic ground states, whereas Mn-based analogs exhibit a more balanced distribution between ferromagnetic and antiferromagnetic order. For compounds exhibiting several nearly degenerate collinear configurations, we analyze the nature of their magnetic ground states, assess the possible emergence of noncollinear order, and discuss the limitations and uncertainties inherent to standard density-functional approaches. Our electronic structure analysis further reveals that predicted ferromagnetic kagome systems display characteristic features of topological metals, with rich magnetic configurations that can be tuned by chemical substitution. Altogether, these ferromagnetic kagome compounds constitute a broad and still largely unexplored materials platform for the emergence of exciting magnetotransport phenomena.

Density functional calculations↗

DOE OSTI2025

𝜂 and 𝜂′ Production in 𝐽/𝜓 Radiative Decays from Quantum Chromodynamics

We present a first principles calculation within quantum chromodynamics (QCD) of the radiative decays of the 𝐽/𝜓 into the light pseudoscalar mesons 𝜂 and 𝜂′. Within a lattice computation we obtain the transition form factors as a function of photon virtuality from the timelike region, accessible experimentally via the “Dalitz” decay 𝐽/𝜓 →𝑒 + ⁢𝑒 − ⁢𝜂 (′) , through to the real photon point corresponding to 𝐽/𝜓 →𝛾⁢𝜂 (′) . This is the first calculation in lattice QCD with two (heavier than physical) degenerate flavors of light quark and a heavier strange quark, in which the 𝜂′ appears as the first excited state with pseudoscalar isoscalar quantum numbers. We access it reliably by using variationally optimized operators , the use of which also improves the purity of the 𝐽/𝜓 and 𝜂 signals, reducing systematic uncertainties. High quality results at a large number of kinematic points are obtained in a typically noisy disconnected process by using a novel correlator averaging procedure. Our results show the expected enhanced production of the 𝜂′ over the 𝜂 in this process, and suggest that the demonstrated lattice technology is suitable for future calculations considering processes in which light meson resonances are produced.

form factors↗

DOE OSTI2026

Search for Higgsinos in final states with low-momentum lepton-track pairs at 13 TeV

We present a search for the pair production of Higgsinos in final states with large missing transverse momentum and either two reconstructed muons or a reconstructed lepton (muon or electron) and an isolated track. The analyzed data correspond to proton-proton collisions with an integrated luminosity of 137 fb −1 , collected by the CMS experiment at $\sqrt{𝑠}$ =13 TeV in 2016, 2017, and 2018. The signal scenario assumes four nearly mass degenerate Higgsino mass eigenstates: two neutralino states $\tilde{𝜒}^0_2$ and $\tilde{𝜒}^0_1$ with a small mass difference in the range 1–10 GeV and two chargino states $\tilde{𝜒}^±_1$ with an intermediate mass. The analysis focuses on the decay of the heavier neutralino into the lighter one and a virtual 𝑍 boson, which decays into two same-flavor leptons. The leptons have small transverse momentum and/or a small opening angle between the identified muons. An isolated track is used to recover events in which only one of the two leptons is identified. Multivariate discriminants are used to enhance the sensitivity by efficiently rejecting backgrounds from SM processes or misreconstructed tracks and/or leptons. The search explores a unique phase space and probes a previously unexplored region of the signal model parameter space. Mass differences between the two neutralinos are probed down to 1.5 GeV, assuming a Higgsino mass of 100 GeV. The maximum excluded Higgsino mass is 115 GeV.

Hayrapetyan, A. [Yerevan Physics Institute]↗

DOE OSTI2025

Probing Ice-Rule-Breaking Transition in Dy 2 Ti 2 O 7 Thin Film by Proximitized Transport and Magnetic Torque

While the spin-ice state of bulk pyrochlores such as Dy 2⁢ Ti 2 ⁢O 7 and Ho 2⁢ Ti 2 ⁢O 7 has been extensively studied in the past several decades due to its unique degenerate ground state and emergent monopole excitation, whether it survives in the thin-film form remains a mystery. The limited volume of the thin-film sample makes it challenging to study the intrinsic magnetic properties. Here, we synthesized 18-nm-thick Dy 2⁢ Ti 2 ⁢O 7 thin film on yttria-stabilized zirconia with 9.5 mol% Y 2 ⁢O 3 substrate and capped it by a thin conductive Bi 2 ⁢Ir 2 ⁢O 7 layer and performed the proximitized magnetoresistance measurements. Our Letter found that the ice-rule-breaking phase transition survives but with a modified effective nearest-neighbor interaction (𝐽 eff =1.054 K) and distorted Ising spin axes (𝜀 = +0.051) compared to the bulk crystal. Furthermore, the results are supported by the simultaneously measured capacitive torque magnetometry. Our Letter demonstrates that proximitized transport is an effective tool for thin films of insulating frustrated magnets.

Magnetic interactions↗

DOE OSTI2025

Constraints on neutrino physics from DESI DR2 BAO and DR1 full shape

The Dark Energy Spectroscopic Instrument (DESI) Collaboration has obtained robust measurements of baryon acoustic oscillations in the redshift range 0.1 < 𝑧 < 4.2, based on the Lyman-𝛼 forest and galaxies from data release 2. We combine these measurements with cosmic microwave background (CMB) data from Planck and the Atacama Cosmology Telescope to place our tightest constraints yet on the sum of neutrino masses. Assuming the cosmological Λ⁢ CDM model and three degenerate neutrino states, we find ∑𝑚 𝜈 < 0.0642 eV (95%) with a marginalized error of 𝜎⁡(∑𝑚 𝜈 ) = 0.020 eV. We also constrain the effective number of neutrino species, finding 𝑁 eff = 3.2⁢3$^{+0.35}_{−0.34}$ (95%), in line with the Standard Model prediction. When accounting for neutrino oscillation constraints, we find a preference for the normal mass ordering and an upper limit on the lightest neutrino mass of 𝑚 𝑙 < 0.023 eV (95%). However, we determine using frequentist and Bayesian methods that our constraints are in tension with the lower limits derived from neutrino oscillations. Correcting for the physical boundary at zero mass, we report a 95% Feldman-Cousins upper limit of ∑𝑚 𝜈 < 0.053 eV, breaching the lower limit from neutrino oscillations. Considering a more general Bayesian analysis with an effective cosmological neutrino mass parameter, ∑𝑚 𝜈,eff , that allows for negative energy densities and removes unsatisfactory prior weight effects, we derive constraints that are in 3⁢𝜎 tension with the same oscillation limit, while the error rises to 𝜎⁡(∑𝑚 𝜈,eff ) = 0.053 eV. In the absence of unknown systematics, this finding could be interpreted as a hint of new physics not necessarily related to neutrinos. The preference of DESI and CMB data for an evolving dark energy model offers one possible solution. In the 𝑤 0 ⁢𝑤 𝑎 ⁢CDM model, we find ∑𝑚 𝜈 < 0.163 eV (95%), relaxing the neutrino tension. These constraints all rely on the effects of neutrinos on the cosmic expansion history. Using full-shape power spectrum measurements of data release 1 galaxies, we place complementary constraints that rely on neutrino free streaming. Our strongest such limit in Λ ⁢CDM, using selected CMB priors, is ∑𝑚 𝜈 < 0.193 eV (95%).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Pion and kaon PDFs from lattice QCD via large momentum effective theory and short-distance factorization

In this paper, we present a first-principles lattice-QCD calculation of the unpolarized quark PDF for the pion and the kaon. The lattice data rely on matrix elements calculated for boosted mesons coupled to non-local operators containing a Wilson line. The calculations on this lattice ensemble correspond to two degenerate light, a strange, and a charm quark (𝑁 𝑓 = 2 + 1 + 1), using maximally twisted mass fermions with a clover term. The lattice volume is 32 3 × 64, with a lattice spacing of 0.0934 fm, and a pion mass of 260 MeV. Matrix elements are calculated for hadron boosts of |𝑃 3 | = 0, 0.41, 0.83, 1.25, 1.66, and 2.07 GeV. To match lattice QCD results to their light-cone counterparts, we employ two complementary frameworks: the large-momentum effective theory (LaMET) and the short-distance factorization (SDF). Using these approaches in parallel, we also test the lattice data to identify methodology-driven systematics. Results are presented for the standard quark PDFs, as well as the valence sector. Beyond obtaining the PDFs, we also explore the possibility of extracting information on SU(3) flavor-symmetry-breaking effects. For LaMET, we also parametrize the momentum dependence to obtain the infinite-momentum PDFs. Since the present calculation is performed on a single ensemble at a pion mass of 260 MeV and fixed lattice spacing, the uncertainties reported are statistical only, and systematic uncertainties remain to be addressed in future multi-ensemble studies.

Miller, Joshua [Temple University, Philadelphia, P↗

DOE OSTI2024

Chiral flat-band optical cavity with atomically thin mirrors

A fundamental requirement for photonic technologies is the ability to control the confinement and propagation of light. Widely used platforms include two-dimensional (2D) optical microcavities in which electromagnetic waves are confined in either metallic or distributed Bragg reflectors. Recently, transition metal dichalcogenides hosting tightly bound excitons with high optical quality have emerged as promising atomically thin mirrors. In this work, we propose and experimentally demonstrate a subwavelength 2D nanocavity using two atomically thin mirrors with degenerate resonances. Angle-resolved measurements show a flat band, which sets this system apart from conventional photonic cavities. We demonstrate how the excitonic nature of the mirrors enables the formation of chiral and tunable optical modes upon the application of an external magnetic field. Moreover, we show the electrical tunability of the confined mode. Our work demonstrates a mechanism for confining light with high-quality excitonic materials, opening perspectives for spin-photon interfaces, and chiral cavity electrodynamics.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Topological photonic crystal fiber

Photonic crystal fibers (PCFs) provide a versatile platform for various applications, thanks to the flexibility with which light guiding can be customized by modifying the fiber geometry. We realize a PCF with guided modes produced by photonic band structure topology rather than conventional mode-trapping mechanisms. The design, which is compatible with the stack-and-draw fabrication process, consists of a cross-sectional photonic topological crystalline insulator with a disclination. A bulk-defect correspondence produces degenerate topological modes, lying below the cladding light line. We use various theoretical methods to confirm their topological origins, including a spectral localizer that makes minimal assumptions about the band structure. Our experiments on the fabricated fiber show it transmitting visible to near-infrared light with low losses of 10 to 20 decibels per kilometer, which do not increase substantially when the fiber is bent. A comparable solid-core PCF of conventional design exhibits substantially higher bending losses. Optical fibers based on topological modes hold promise for improved performance and versatile functionalities.

Zhu, Bofeng [Nanyang Technological Univ. (Singapor↗

DOE OSTI2026

Programmable Phase Selection between Altermagnetic and Noncentrosymmetric Polymorphs of MnTe on InP via Molecular Beam Epitaxy

This dataset contains DFT input and output files supporting the theoretical modeling in the associated publication (ACS Appl. Mater. Interfaces 2026, 18, 15654-15664). The calculations model the interfacial energetics of two MnTe polymorphs — NiAs-MnTe (hexagonal, alpha phase) and ZnS-MnTe (cubic, gamma phase) — on InP(111) substrates with two surface terminations: In-terminated InP(111)A and P-terminated InP(111)B. This gives four interface configurations: NiAs on In-terminated (experimentally observed), NiAs on P-terminated (computed for comparison), ZnS on In-terminated (computed for comparison), and ZnS on P-terminated (experimentally observed). The dataset is organized into four calculation types, each covering all four polymorph/termination combinations: (i) Slabs: Pristine MnTe/InP heterostructure slabs used to compute total energies and interface energy densities (Eint) for all four configurations, as reported in Fig. 6 of the main text. (ii) Disorder: Same slab geometries with a P_Te + Te_P antisite defect pair introduced near the interface, used to assess chemical intermixing effects on interface stability (Fig. S8, SI). (iii) Strain: Pristine slab calculations with in-plane lattice parameters strained by -1% and +1% relative to the InP lattice constant, used to evaluate strain-dependent interface energetics (Fig. S9, SI). (iv) Charge_Density: Single-point calculations on the full heterostructure, the isolated InP slab, and the isolated MnTe slab at fixed geometry, used to compute differential charge density plots showing interfacial charge accumulation and depletion as a function of surface termination (Fig. S10, SI). Each calculation folder contains INCAR, KPOINTS, POSCAR, CONTCAR, OUTCAR, and POTCAR_info.txt (PAW potential information, excluding the full POTCAR due to VASP licensing restrictions). The calculations were performed using VASP 6.4.3 with PBE exchange-correlation, PAW potentials, a Hubbard correction of Ueff = 5 eV on Mn d-states, and A-type AFM spin initialization.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Femtosecond two-photon-resonant parametric four-wave mixing detection of atomic hydrogen

Here, we demonstrate an ultrafast parametric four-wave mixing method for the collisional-quenching-free detection of atomic hydrogen. Two photons of 243 nm light resonantly excite the n = 1 to n = 2 transition of atomic hydrogen, and a third probe photon scatters from the electronic coherence to generate the parametric emission of a degenerate signal photon. Laser-induced photofragmentation fluorescence from water, also excited with the same 243 nm pulses, is used as a convenient method to visualize beam overlap in space and time. The femtosecond time resolution enables the suppression of unwanted nonresonant contributions to the signal and separation from resonant mixing in water molecules because of the significantly different coherence lifetimes. A folded BOXCARS phase-matching configuration yields a spatially isolated, laser-like, signal beam, amenable to measurements in highly luminous backgrounds. Measurements in an H 2 /CH 4 /air flame demonstrate quantitative agreement with simulated H-atom concentration profiles. A coherence decay time constant of 42 ps is recorded in the atmospheric pressure flame.

Kliewer, Christopher Jesse [Sandia National Labora↗

DOE OSTI2024

Ultrafast temporal phase-resolved nonlinear optical spectroscopy in the molecular frame

In an ultrafast nonlinear optical interaction, the electric field of the emitted nonlinear signal provides direct access to the induced nonlinear transient polarization or transient currents and thus carries signatures of ultrafast dynamics in a medium. Measurement of the electric field of such signals offers sensitive observables to track ultrafast electron dynamics in various systems. In this work, we resolve the real-time phase of the electric field of a femtosecond third-order nonlinear optical signal in the molecular frame. The electric field emitted from impulsively pre-aligned gas-phase molecules at room temperature, in a degenerate four-wave mixing scheme, is measured using a spectral interferometry technique. The nonlinear signal is measured around a rotational revival to extract its molecular-frame angle dependence from pump-probe time-delay scans. By comparing these measurements for two linear molecules, carbon dioxide and nitrogen, we show that the measured second-order phase parameter (temporal chirp) of the signal is sensitive to the valence electronic symmetry of the molecules, whereas the amplitude of the signal does not show such sensitivity. We compare measurements to theoretical calculations of the chirp observable in the molecular frame. This work is an important step towards using electric field measurements in nonlinear optical spectroscopy to study ultrafast dynamics of electronically excited molecules in the molecular frame.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Highly efficient visible and near-IR photon pair generation with thin-film lithium niobate

Efficient on-chip entangled photon pair generation at telecom wavelengths is an integral aspect of emerging quantum optical technologies, particularly for quantum communication and computing. However, moving to shorter wavelengths enables the use of more accessible silicon detector technology, and opens up applications in imaging and spectroscopy. Here, we present high brightness ((1.6 ± 0.3) × 10 9 pairs/s/mW/nm) visible–near-IR photon pair generation in a periodically poled lithium niobate nanophotonic waveguide. The degenerate spectrum of the photon pairs is centered at 811 nm with a bandwidth of 117 nm when pumped with a spectrally multimode laser diode. The measured on-chip source efficiency of (2.3 ± 0.5) × 10 11 pairs/s/mW is on par with source efficiencies at telecom wavelengths and is also orders of magnitude higher than the efficiencies of other visible sources implemented in bulk crystal or diffused waveguide-based technologies. Further improvements in the brightness and efficiencies are possible by pumping the device with a single-frequency laser, which would also shrink the pair bandwidth. These results represent the shortest wavelength of photon pairs generated in a nanophotonic waveguide reported to date by nearly an octave.

42 ENGINEERING↗

DOE OSTI2024

State-to-State Molecular Reactions in the Ultracold Regime (Final Scientific Report)

We have achieved the proposed goal to experimentally probe the AB + CD and AB + C types of reactions with state-to-state resolution, which we also compared to advanced theoretical calculations to help elucidate the role of quantum mechanics in the processes of bond breakage and formation. Our approach uses reactants that are prepared at ultracold temperatures (< 1µK) such that the quantum effects of translational motion are an important factor. Specific example reactions, including the potassium-rubidium metathesis reaction KRb + KRb → K 2 + Rb 2 as well as the atom exchange reaction Rb + KRb → Rb2 + K, are chosen because the technology of quantum internal and motional state control of these types of molecules is particularly advanced. The results for the entire funding period are fruitful. For the majority of this grant, we have constructed a one-of-the-kind quantum degenerate gas apparatus that integrates ion detection and velocity map imaging capabilities, allowing us to explore the KRb + KRb → K 2 + Rb 2 bimolecular reaction in detail. Specifically, we first verified such a reaction indeed proceed at ultracold temperatures by direct detection of reaction products. We then mapped out the complete product state distribution, which was compared to a state-counting model based on statistical theory. Our results show an overall agreement with the statistical state counting model, but also reveal several deviating state-pairs. An exact quantum calculation for molecule-molecule collisions, that is needed to understand these deviations, is however beyond the current state-of-the-art. Beside scrutinizing the reaction products, we also directly observe the reaction intermediate complex, which was quite a surprise to us. The intermediate complexes are long-lived and can interact with the inferred light that we use to trap the ultracold gas. After molecule-molecule collisions, we then explored the more theoretically tractable Rb + KRb reaction, which is endothermic. Surprisingly, we observed an exceedingly long-lived KRb$^*_2$ collisional complexes, with our experimentally measured complex lifetime deviating from conventional theoretical calculations by five orders of magnitude. This discrepancy has motivated many explorations of possible underlying causes, though no model yet captures this phenomenon completely. In the final year and the work that continues today, we extend upon these atom-molecule collision experiments to explore the origin of the long-lived KRb$^*_2$ complex lifetime and develop means to control the outcome of the reaction complex. The 5-year funded work advanced our understanding of chemical reactions at the lowest possible temperatures and at the same time opened up many new questions that are beyond our initial imaginations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Detecting rare earth elements via optically detected magnetic resonance (ODMR) and spin-relaxometry using nitrogen vacancy centers in nanodiamonds

Nanodiamonds embedded with nitrogen-vacancy (NV) centers are emerging as powerful tools in quantum sensing due to their remarkable sensitivity to local variations in electromagnetic fields, temperature, and pressure. These point defects in the diamond lattice can be probed using optically detected magnetic resonance (ODMR) and spin relaxometry techniques, allowing for the detection and characterization of magnetic nanoparticles and ions. The sensing mechanism relies on laser-induced excitation of the NV center's non-degenerate triplet ground state, which promotes electrons to an excited state. Subsequent photoluminescence (PL) emission, which is spin-state dependent, is then measured. These spin states are highly responsive to magnetic perturbations in the surrounding environment. By analyzing changes in the ODMR spectra and spin relaxation times, we can effectively monitor how magnetic species influence the NV center's spin dynamics, thus enabling sensitive and selective characterization of nanoscale magnetic materials. These techniques have been applied for the characterization of transition metals and rare earth elements which shows natural ferromagnetic properties.

magnetic nanopartgicles and ions↗