Nuclear Quadrupole Interaction Research Articles

Comparison of triple quantum (TQ) TPPI and inversion recovery TQ TPPI pulse sequences at 9.4 and 21.1 T.

Both sodium T1 triple quantum (TQ) signal and T1 relaxation pathways have a unique sensitivity to the sodium molecular environment. In this study an inversion recovery time proportional phase increment (IRTQTPPI) pulse sequence was investigated for simultaneous and reliable quantification of sodium TQ signal and bi-exponential T1 relaxation times. The IRTQTPPI sequence combines inversion recovery TQ filtering and time proportional phase increment. The reliable and reproducible results were achieved by the pulse sequence optimized in three ways: (1) optimization of the nonlinear fit for the determination of both T1-TQ signal and T1 relaxation times; (2) suppression of unwanted signals by assessment of four different phase cycles; (3) nonlinear sampling during evolution time for optimal scan time without any compromises in fit accuracy. The relaxation times T1 and T2 and the TQ signals from IRTQTPPI and TQTPPI were compared between 9.4 and 21.1 T. The motional environment of the sodium nuclei was evaluated by calculation of correlation times and nuclear quadrupole interaction strengths. Reliable measurements of the T1-TQ signals and T1 bi-exponential relaxation times were demonstrated. The fit parameters for all four phase cycles were in good agreement with one another, with a negligible influence of unwanted signals. The agar samples yielded normalized T1-TQ signals from 3% to 16% relative to single quantum (SQ) signals at magnetic fields of both 9.4 and 21.1 T. In comparison, the normalized T2-TQ signal was in the range 15%-35%. The TQ/SQ signal ratio was decreased at 21.1 T as compared with 9.4 T for both T1 and T2 relaxation pathways. The bi-exponential T1 relaxation time separation ranged from 15 to 18 ms at 9.4 T and 15 to 21 ms at 21.1 T. The T2 relaxation time separation was larger, ranging from 28 to 35 ms at 9.4 T and 37 to 40 ms at 21.1 T. The IRTQTPPI sequence, while providing a less intensive TQ signal than TQTPPI, allows a simultaneous and reliable quantification of both the T1-TQ signal and T1 relaxation times. The unique sensitivities of the T1 and T2 relaxation pathways to different types of molecular motion provide a deeper understanding of the sodium MR environment.

The germanides ScTGe2 (T = Fe, Co, Ru, Rh) – crystal chemistry, 45Sc solid-state NMR and 57Fe Mössbauer spectroscopy

Abstract The TiMnSi2-type (space group Pbam) germanides ScTGe2 (T = Fe, Co, Ru, Rh) were synthesized from the elements by arc-melting. Single crystals were grown by annealing sequences of the arc-melted buttons in an induction furnace. The structures of ScFeGe2, ScRuGe2 and ScRhGe2 were refined from single-crystal X-ray diffraction data. In ScRuGe2, the ruthenium atoms have distorted octahedral germanium coordination (242–268 pm Ru–Ge). Three trans-face-sharing octahedra form a sub-unit which is condensed via common edges in c direction and connected via common corners with four adjacent blocks, forming a three-dimensional [RuGe2 type] substructure. The two crystallographically independent scandium sites have coordination numbers 15 (Sc1@Ge8Ru4Sc3) and 17 (Sc2@Ge7Ru6Sc4). Electronic band structure calculations for ScCoGe2 and ScRuGe2 show a net charge transfer from the scandium to the transition metal and germanium atoms, leading to a description with polyanionic networks Sc δ+[TGe2]δ−. The two crystallographically independent Sc sites are easily distinguishable by 45Sc magic-angle spinning (MAS)-NMR spectroscopy. Isotropic chemical shift values and nuclear electric quadrupolar interaction parameters were deduced from an analysis of the triple-quantum (TQ)-MAS NMR spectra. The electric field gradient parameters deduced from these experiments are in good agreement with quantum-chemical calculations using the Wien2k code. Likewise, the two crystallographically independent iron sites in ScFeGe2 could be discriminated in the 57Fe Mößbauer spectra through their isomer shifts and quadrupole splitting parameters: δ = 0.369(1) mm s−1 and ∆E Q = 0.232(2) mm s−1 for Fe1 and δ = 0.375(2) mm s−1 and ∆E Q = 0.435(4) mm s−1 for Fe2 (data at T = 78 K).

14N Hyperfine and nuclear interactions of axial and basal NV centers in 4H-SiC: A high frequency (94 GHz) ENDOR study

The nitrogen-vacancy (NV) centers (NCVSi)− in 4H silicon carbide (SiC) constitute an ensemble of spin S = 1 solid state qubits interacting with the surrounding 14N and 29Si nuclei. As quantum applications based on a polarization transfer from the electron spin to the nuclei require the knowledge of the electron–nuclear interaction parameters, we have used high-frequency (94 GHz) electron–nuclear double resonance spectroscopy combined with first-principles density functional theory to investigate the hyperfine and nuclear quadrupole interactions of the basal and axial NV centers. We observed that the four inequivalent NV configurations (hk, kh, hh, and kk) exhibit different electron–nuclear interaction parameters, suggesting that each NV center may act as a separate optically addressable qubit. Finally, we rationalized the observed differences in terms of distinctions in the local atomic structures of the NV configurations. Thus, our results provide the basic knowledge for an extension of quantum protocols involving the 14N nuclear spin.

Quantum coherence resourced by the strong nuclear quadrupolar interaction

We propose a setup for studying the quantum coherence properties of a quadrupolar nucleus using the nuclear magnetic resonance platforms We consider powder samples labeled with 23Na and oriented with respect to the static magnetic field. By using the l 1-norm of coherence, we examine the quantum coherence in the Zeeman basis at thermal equilibrium. Non-zero coherence is found to result from the strong nuclear quadrupolar spin interactions. It is also shown that higher coherence is created as the quadrupolar interaction coefficient increases. We also discuss the stability of coherence in a possible measurement process in order to use it as a potential resource in any quantum computation protocol.

First-Principles Calculation of the Temperature-Dependent Transition Energies in Spin Defects.

Spin qubits associated with color centers are promising platforms for various quantum technologies. However, to be deployed in robust quantum devices, the variations of their intrinsic properties with the external conditions, in particular temperature and strain, should be known with high precision. Unfortunately, a predictive theory on the temperature dependence of the resonance frequency of electron and nuclear spin defects in solids remains lacking. In this work, we develop a first-principles method for the temperature dependence of the zero-field splitting, hyperfine interaction, and nuclear quadrupole interaction of color centers. As a testbed, we compare our ab initio calculations with experiments for the nitrogen-vacancy (NV-) center in diamond, finding good agreements. We identify the major origin of the temperature dependence as a second-order effect of dynamic phonon vibrations, instead of the thermal-expansion strain. The method can be applied to different color centers and provides a theoretical tool for designing high-precision quantum sensors.

Symmetry of the Hyperfine and Quadrupole Interactions of Boron Vacancies in a Hexagonal Boron Nitride

The concept of optically addressable spin states of deep level defects in wide band gap materials is successfully applied for the development of quantum technologies. Recently discovered negatively charged boron vacancy defects (VB) in hexagonal boron nitride (hBN) potentially allow a transfer of this concept onto atomic thin layers due to the van der Waals nature of the defect host. Here, we experimentally explore all terms of the VB spin Hamiltonian reflecting interactions with the three nearest nitrogen atoms by means of conventional electron spin resonance and high frequency (94 GHz) electron-nuclear double resonance. We establish symmetry, anisotropy, and principal values of the corresponding hyperfine interaction (HFI) and nuclear quadrupole interaction (NQI). The HFI can be expressed in the axially symmetric form as Aperp = 45.5 MHz and Apar = 87 MHz, while the NQI is characterized by quadrupole coupling constant Cq = 1.96 MHz with slight rhombisity parameter n = (Pxx - Pyy)/Pzz = -0.070. Utilizing a conventional approach based on a linear combination of atomic orbitals and HFI values measured here, we reveal that almost all spin density (84 %) of the VB electron spin is localized on the three nearest nitrogen atoms. Our findings serve as valuable spectroscopic data and direct experimental demonstration of the VB spin localization in a single two dimensional BN layer.

Current density functional framework for spin–orbit coupling

Relativistic two-component density functional calculations are carried out in a non-collinear formalism to describe spin-orbit interactions, where the exchange-correlation functional is constructed as a generalization of the non-relativistic density functional approximation. Contrary to non-relativistic density functional theory (DFT), spin-orbit coupling, however, leads to a non-vanishing paramagnetic current density. Density functionals depending on the kinetic energy density, such as meta-generalized gradient approximations, should therefore be constructed in the framework of current DFT (CDFT). The latter has previously exclusively been used in the regime of strong magnetic fields. Herein, we present a consistent CDFT approach for relativistic DFT, including spin-orbit coupling. Furthermore, we assess the importance of the current density terms for ground-state energies, excitation energies, nuclear magnetic resonance shielding, and spin-spin coupling constants, as well as hyperfine coupling constants, Δg-shifts, and the nuclear quadrupole interaction tensor in electron paramagnetic resonance (EPR) spectroscopy. The most notable changes are found for EPR properties. The impact of the current-dependent terms rises with the number of unpaired electrons, and consequently, the EPR properties are more sensitive toward CDFT. Considerable changes are observed for the strongly constrained and appropriately normed functionals, as well as the B97M family and TASK. The current density terms are less important when exact exchange is incorporated. At the same time, the current-dependent kernel ensures the stability of response calculations in all cases. We, therefore, strongly recommend to use the framework of CDFT for self-consistent spin-orbit calculations.

Diffusional Relaxation of Quadrupole Interactions of <sup>111</sup>In/ Cd Probes in IrIn<sub>3</sub> and Related Phases Having FeGa<sub>3</sub> Structure

Nuclear relaxation caused by diffusion of 111In/Cd probe atoms was measured in four phases having the tetragonal FeGa3 structure (tP16) using perturbed angular correlation spectroscopy (PAC) and used to gain insight into diffusion processes in phases having more than one diffusion sublattice. The three indide phases studied in this work have two inequivalent and interpenetrating In-sublattices, labeled In1 and In2, and nuclear quadrupole interactions were resolved for probes on each sublattice. The phases are line-compounds with narrow field-widths. Diffusional relaxations, fitted using an exponential damping ansatz, were measured at the two opposing boundary compositions as a function of temperature. “High” and “low” relaxation regimes were observed that are attributed to In-poorer and In-richer compositions, under the reasonable assumption that the atomic motion occurs via an indium-vacancy diffusion mechanism. Relaxation was observed to be greater for tracer atoms starting on In2 sites in the indides immediately following decay of 111In into 111Cd, which is attributed to a preference of daughter Cd-tracer atoms and/or indium vacancies to occupy In1 sites. Activation enthalpies for relaxation are compared with enthalpies for self-diffusion in indium metal.

Towards in vivo applications of 111Ag perturbed angular correlation of γ-rays (PAC) spectroscopy

111Ag-perturbed angular correlation of γ-rays (PAC) spectroscopy provides information on the nuclear quadrupole interactions, and thereby on the local structure and dynamics of the silver ion binding site. Brownian rotational motion, i.e. rotational diffusion, of 111Ag-labeled molecules will significantly affect the PAC spectra. Here we illustrate this effect, by simulating 111Ag PAC spectra for 111Ag-labeled molecules with molecular masses spanning from 102 to 106 g/mol, reflecting a span from fast (small molecules) to slow (large molecules) rotational diffusion on the PAC time scale. The simulated spectra are compared to 111Ag-PAC data obtained from a pilot study involving 111Ag(I) bound to a designed chelator exhibiting fast reorientation in solution, as well as to 111Ag-labeled species formed by 111Ag(I) in human serum, exhibiting slow (or no) reorientation on the PAC time scale. The simulated and experimental data illustrate typical PAC signals that are likely to be observed in vivo, when following the fate of 111Ag-labeled compounds. Potential in vivo applications are stability studies of 111Ag-radiopharmaceuticals, dissociation studies of 111Ag from the labeled molecule followed by binding to another (bio)molecule, or binding of 111Ag-labeled probes to larger carriers such as proteins.

A variational model for the hyperfine resolved spectrum of VO in its ground electronic state.

A variational model for the infra-red spectrum of vanadium monoxide (VO) is presented, which aims to accurately predict the hyperfine structure within the VO XΣ-4 electronic ground state. To give the correct electron spin splitting of the XΣ-4 state, electron spin dipolar interaction within the ground state and the spin-orbit coupling between XΣ-4 and two excited states, AΠ4 and 1Σ+2, are calculated ab initio alongside hyperfine interaction terms. Four hyperfine coupling terms are explicitly considered: Fermi-contact interaction, electron spin-nuclear spin dipolar interaction, nuclear spin-rotation interaction, and nuclear electric quadrupole interaction. These terms are included as part of a full variational solution of the nuclear-motion Schrödinger equation performed using program Duo, which is used to generate both hyperfine-resolved energy levels and spectra. To improve the accuracy of the model, ab initio curves are subject to small shifts. The energy levels generated by this model show good agreement with the recently derived empirical term values. This and other comparisons validate both our model and the recently developed hyperfine modules in Duo.

Diffusion of Tracer Atoms in Al4Ba Phases Studied Using Perturbed Angular Correlation Spectroscopy

The Al4Ba crystal structure is the most common structure among binary intermetallic compounds. It is well suited for accommodating large atoms of group II elements and is often the intermediate phase closest to the terminal phase. It is, therefore, of interest to characterize diffusion properties of compounds with this tetragonal crystal structure. In the present study, 111In perturbed angular correlation spectroscopy was used to study solute site occupation and atom movement in In4Ba, Al4Ba, Al4Eu, Al4Sr, and Ga4Sr. The indium tracer and its daughter cadmium were found to occupy only the two Al-type sublattices in these compounds through detection of nuclear quadrupole interactions with axially symmetric EFGs. Measurements with increasing temperature revealed merging of signals due to dynamical averaging of these interactions as Cd atoms jumped at increasing rates between alternating sublattices. The jump rates were estimated to be between 8 kHz and 2 MHz at about 350 °C for Al4Eu and at about 450 °C for In4Ba and Al4Ba. Fits of spectra using Blume’s stochastic model allowed determination of activation enthalpies for average Cd jump rates between alternating Al sublattices in Al4Sr and Ga4Sr to be 1.16(3) eV and 1.47(3) eV, respectively. This result was used to estimate transverse diffusivities of Cd.

Room-Temperature 181Ta(TiO2): An e-γ TDPAC Study

In this work, we report on the hyperfine parameters of the foreign 181Ta probe in the rutile structure of the single crystal TiO2 using the e−γ and γ−γ time differential perturbed angular correlation (TDPAC) technique. We implanted 181Hf ions into a sample of single crystal rutile TiO2 in the Bonn Isotope Separator. The implanted sample was then thermally annealed at a temperature of 873 K for 315 min in a vacuum. The 181Hf radioisotopes decayed by β− emission, followed by a cascade to the ground of γ rays or conversion electrons into a stable state 181Ta. The 181Ta probe substitutes the Ti lattice site with a unique nuclear quadrupole interaction, allowing for the precise measurement of the largest electric field gradient (Vzz) and asymmetry parameter (η). The hyperfine parameters obtained from the e−γ TDPAC spectroscopy agree with those of the γ−γ TDPAC spectroscopy at room temperature, apart from a calibration factor, both from our experiments and the literature. This suggests that the electronic recombination following the internal conversion of the L shell electron takes less time (ps) than the intermediate lifetime of the metastable 181Ta state (ns).

Calculation of electric field gradients for CdI2 in the gas phase using BOMD simulations

The nuclear quadrupole interaction (NQI) of quadrupolar nuclei in molecules in the gas phase has recently been quantified experimentally by the technique of Perturbed Angular Correlation (PAC) spectroscopy. Interpretation of the NQI data must rely on high-level electronic structure methods for the calculation of the electric field gradient (EFG). These calculations commonly omit contributions from anharmonicity, rovibrational coupling and (if applicable) decay-induced nuclear recoil to the molecular structure and the response of the EFG. Here we choose an alternative approach, conducting Born–Oppenheimer molecular dynamics (BOMD) simulations, and account for the effects of molecular motion on the EFG. We apply this approach to the analysis of PAC spectroscopic data recorded for gas phase CdI2 (Haas et al., 2021). With this methodology, we obtain a value of the nuclear quadrupole moment Q(111Cd, 5/2+) = 0.656(7) b.

Electron-Nuclear Coherent Coupling and Nuclear Spin Readout through Optically Polarized VB- Spin States in hBN.

Coherent coupling of defect spins with surrounding nuclei along with the endowment to read out the latter are basic requirements for an application in quantum technologies. We show that negatively charged boron vacancies (VB-) in hexagonal boron nitride (hBN) meet these prerequisites. We demonstrate Hahn-echo coherence of the VB- spin with a characteristic decay time Tcoh = 15 μs, close to the theoretically predicted limit of 18 μs for defects in hBN. Elongation of the coherence time up to 36 μs is demonstrated by means of the Carr-Purcell-Meiboom-Gill decoupling technique. Modulation of the Hahn-echo decay is shown to be induced by coherent coupling of the VB- spin with the three nearest 14N nuclei via a nuclear quadrupole interaction of 2.11 MHz. DFT calculation confirms that the electron-nuclear coupling is confined to the defective layer and stays almost unchanged with a transition from the bulk to the single layer.

A Method for the Variational Calculation of Hyperfine-Resolved Rovibronic Spectra of Diatomic Molecules.

An algorithm for the calculation of hyperfine structure and spectra of diatomic molecules based on the variational nuclear motion is presented. The hyperfine coupling terms considered are Fermi-contact, nuclear spin-electron spin dipole–dipole, nuclear spin–orbit, nuclear spin-rotation, and nuclear electric quadrupole interactions. Initial hyperfine-unresolved wave functions are obtained for a given set of potential energy curves and associated couplings by a variation solution of the nuclear-motion Schrödinger equation. Fully hyperfine-resolved parity-conserved rovibronic Hamiltonian matrices for a given final angular momentum, F, are constructed and then diagonalized to give hyperfine-resolved energies and wave functions. Electric transition dipole moment curves can then be used to generate a hyperfine-resolved line list by applying rigorous selection rules. The algorithm is implemented in Duo, which is a general program for calculating spectra of diatomic molecules. This approach is tested for NO and MgH, and the results are compared to experiment and shown to be consistent with those given by the well-used effective Hamiltonian code PGOPHER.

Cu2+ and Cu3+ acceptors in β-Ga2O3 crystals: A magnetic resonance and optical absorption study

Electron paramagnetic resonance (EPR) and optical absorption are used to characterize Cu2+ (3d9) and Cu3+ (3d8) ions in Cu-doped β-Ga2O3. These Cu ions are singly ionized acceptors and neutral acceptors, respectively (in semiconductor notation, they are Cu− and Cu0 acceptors). Two distinct Cu2+ EPR spectra are observed in the as-grown crystals. We refer to them as Cu2+(A) and Cu2+(B). Spin-Hamiltonian parameters (a g matrix and a 63,65Cu hyperfine matrix) are obtained from the angular dependence of each spectrum. Additional electron-nuclear double resonance (ENDOR) experiments on Cu2+(A) ions give refined 63Cu and 65Cu hyperfine matrices and provide information about the nuclear electric quadrupole interactions. Our EPR results show that the Cu2+(A) ions occupy octahedral Ga sites with no nearby defect. The Cu2+(B) ions, also at octahedral Ga sites, have an adjacent defect, possibly an OH− ion, an oxygen vacancy, or an H− ion trapped within an oxygen vacancy. Exposing the crystals at room temperature to 275 nm light produces Cu3+ ions and reduces the number of Cu2+(A) and Cu2+(B) ions. The Cu3+ ions have an S = 1 EPR spectrum and are responsible for broad optical absorption bands peaking near 365, 422, 486, 599, and 696 nm. An analysis of loops observed in the Cu3+ EPR angular dependence gives 2.086 for the g value and 22.18, 3.31, and −25.49 GHz for the principal values of D (the fine-structure matrix). Thermal anneal studies above room temperature show that the Cu3+ ions decay and the Cu2+ ions recover between 75 and 375 °C.

Hydrogen-Bonded Complexes of Neutral Nitroxide Radicals with 2-Propanol Studied by Multifrequency EPR/ENDOR

The hydrogen bond plays a key role in weak directional intermolecular interactions. It is operative in determining molecular conformation and aggregation, and controls the function of many chemical systems, ranging from inorganic, organic to biological molecules. Although an enormous amount of spectroscopic information has been collected about hydrogen-bond formation between molecules with closed-shell electronic configuration, the details of such interactions between open-shell radicals and closed-shell molecules are still rare. Here we report on an investigation of hydrogen-bonded complexes between pyrroline-type as well as piperidine-type neutral nitroxide radicals and an alcohol, i.e., 2-propanol. These nitroxide radicals are commonly used as EPR spin labels and probes. To obtain information on the geometry of the complexes and their electronic structure, multi-resonance EPR techniques at various microwave frequencies (X-, Q-, W-band, 244 GHz) have been employed in conjunction with DFT calculations. The planar five-membered ring system of the pyrroline-type nitroxide radical was found to form exclusively well-defined in-plane σ-type hydrogen-bonded complexes with one 2-propanol molecule in the first solvation shell in frozen solution. The measured hyperfine parameters of the hydrogen-bridge proton and the internal magnetic parameters describing the electron Zeeman and the electron-nuclear hyperfine and nuclear quadrupole interactions are in good agreement with values predicted by state-of-the-art DFT calculations. In contrast, multi-resonance EPR on the non-planar six-membered ring system of the piperidine-type nitroxide radical (TEMPOL) reveals a more complex situation, i.e., a mixture of a σ-type with, presumably, an out-of-plane π-type complex, both present in comparable fraction in frozen solution. For TEMPOL, the DFT calculations failed to predict magnetic interaction parameters that are in good agreement with experiment, apparently due to the considerable flexibility of the nitroxide and hydrogen-bonded complex. The detailed information about nitroxide/solvent complexes is of particular importance for Dynamic Nuclear Polarization (DNP) and site-directed spin-labeling EPR studies that employ nitroxides as polarizing agents or spin labels, respectively.

Engineering local strain for single-atom nuclear acoustic resonance in silicon

Mechanical strain plays a key role in the physics and operation of nanoscale semiconductor systems, including quantum dots and single-dopant devices. Here, we describe the design of a nanoelectronic device, where a single nuclear spin is coherently controlled via nuclear acoustic resonance (NAR) through the local application of dynamical strain. The strain drives spin transitions by modulating the nuclear quadrupole interaction. We adopt an AlN piezoelectric actuator compatible with standard silicon metal–oxide–semiconductor processing and optimize the device layout to maximize the NAR drive. We predict NAR Rabi frequencies of order 200 Hz for a single 123Sb nucleus in a wide region of the device. Spin transitions driven directly by electric fields are suppressed in the center of the device, allowing the observation of pure NAR. Using electric field gradient-elastic tensors calculated by the density-functional theory, we extend our predictions to other high-spin group-V donors in silicon and to the isoelectronic 73Ge atom.

Solid-State Nuclear Magnetic Resonance Techniques for the Structural Characterization of Geminal Alane-Phosphane Frustrated Lewis Pairs and Secondary Adducts.

The first comprehensive solid‐state nuclear magnetic resonance (NMR) characterization of geminal alane‐phosphane frustrated Lewis pairs (Al/P FLPs) is reported. Their relevant NMR parameters (isotropic chemical shifts, direct and indirect 27Al‐31P spin‐spin coupling constants, and 27Al nuclear electric quadrupole coupling tensor components) have been determined by numerical analysis of the experimental NMR line shapes and compared with values computed from the known crystal structures by using density functional theory (DFT) methods. Our work demonstrates that the 31P NMR chemical shifts for the studied Al/P FLPs are very sensitive to slight structural inequivalences. The 27Al NMR central transition signals are spread out over a broad frequency range (>200 kHz), owing to the presence of strong nuclear electric quadrupolar interactions that can be well‐reproduced by the static 27Al wideband uniform rate smooth truncation (WURST) Carr‐Purcell‐Meiboom‐Gill (WCPMG) NMR experiment. 27Al chemical shifts and quadrupole tensor components offer a facile and clear distinction between three‐ and four‐coordinate aluminum environments. For measuring internuclear Al⋅⋅⋅P distances a new resonance‐echo saturation‐pulse double‐resonance (RESPDOR) experiment was developed by using efficient saturation via frequency‐swept WURST pulses. The successful implementation of this widely applicable technique indicates that internuclear Al⋅⋅⋅P distances in these compounds can be measured within a precision of ±0.1 Å.

Mössbauer spectroscopy of superparamagnetic Fe3O4 nanoparticles

Spherical, mono-disperse, non-interacting iron oxide (Fe3O4) nanoparticles, synthesized by high-temperature hydrolysis of chelated iron alkoxide complexes, have been studied by Mössbauer spectroscopy. The critical diameter for room temperature superparamagnetism, an important parameter for high frequency biomedical (MRI) and IT applications, was about 11 nm. Particles of diameter 11.9 nm and greater are ferrimagetic and showed magnetic splitting. Particles of diameter 10.6 nm and smaller are superparamagnetic and gave a non-magnetic spectrum at room temperature. The lines narrow as the particle size decreases and the spin relaxation rate increases. For the smallest particles (8.6 nm or less) the room temperature spectra could be resolved into two partially overlapping lines, one from the A-sites and one from the B-sites, the latter being broadened by the nuclear quadrupole interaction. Similar spectra have been previously reported for bulk Fe3O4 above the Curie point. The isomer shifts showed anomalies possibly arising from magnetostrictive atomic displacements. On applying a magnetic field of 20 kG, hyperfine splitting was observed, confirming that the particles are single-domain with large magnetic moments of the order of 104 μB. The in-field spectrum was similar to that of bulk crystals above the Verwey temperature with Fe3+on the A-sites and Fe2.5+ on the B-sites, characteristic of the inverse cubic spinel structure. The lines narrowed as the temperature was decreased until magnetic splitting was observed at temperatures below the blocking temperature TB, where the magnetic fluctuations are blocked. The transition to the magnetic state is smooth, confirming that the particles are mono-disperse. At the lowest temperature (6 K) the spectra resemble those of bulk Fe3O4 with Fe3+on the A-sites and both Fe2+ and Fe3+ on the B-sites corresponding to the local monoclinic distortion, indicating that the nanoparticles have undergone a Verwey transition. The values of TB found are lower than those reported by most other researchers, suggesting that magnetic interactions between our particles are small. The non-stoichiometry parameter, x, defined by the formula Fe3-xO4, was estimated from the relative amounts of Fe3+/ Fe2+ and from isomer shifts to be less than 0.1 in the different samples.