Spin-orbit Energy Research Articles

Imaging Spin-Orbit Excitation of Yttrium through High-Energy Collisions with Rare Gas Atoms.

The energy required for spin-orbit excitation plays a critical role in understanding translational-to-electronic energy conversion, particularly in chemical reactions involving changes in spin states. This is particularly important for transition metal atoms possessing d-orbitals, which result in multiple spin-orbit split energy levels at low energies. The accurate identification and characterization of spin-orbit transitions in such species require advanced experimental techniques and theoretical support. In this study, the spin-orbit excited collisions of Y(2D3/2) with rare gas atoms Ne, Ar, and Kr leading to Y(2D5/2) were observed using laser-ablated crossed-beam and time-sliced ion velocity mapping imaging techniques. Through a comparison of the forward angular distributions of Y(2D3/2) to the backward and sideway scattering distributions of Y(2D5/2) from elastic and inelastic collisions of Y(2D) with rare gas atoms, this study reveals that the spin-orbit electronic excitation occurs with high collision energy and low impact parameters from backward and sideway collisions. The effectiveness of the spin-orbit excitation process is strongly dependent on the collision energy or temperature, suggesting that energy requirements of the process have to be considered in chemical reactions involving changes in spin states.

Accurate abinitio based potential energy surface and kinetics of the Cl + NH3 → HCl + NH2 reaction.

The gas-phase reaction Cl + NH3 → HCl + NH2 is a prototypical hydrogen abstraction reaction, whose minimum energy path involves several intermediate complexes. In this work, a full-dimensional, spin-orbit corrected potential energy surface (SOC PES) is constructed for the ground electronic state of the Cl + NH3 reaction. About 52 000 energy points are sampled and calculated at the UCCSD(T)-F12a/aug-cc-pVTZ level, in which the data points located in the entrance channel are spin-orbit corrected. The spin-orbit corrections are predicted by a fitted three-dimensional energy surface from about 7520 energy points in the entrance channel at the level of CASSCF (15e, 11o)/aug-cc-pVTZ. The fundamental-invariant neural network method is utilized to fit the SOC PES, resulting in a total root mean square error of 0.12kcal mol-1. The calculated thermal rate constants of the Cl + NH3 → HCl + NH2 reaction on the SOC PES with the soft-zero-point energy constraint agree reasonably well with the available experimental values.

The influence of N and Bi on the band structure and band offsets of InAsNBi alloys

We present the electronic properties of InAsNBi with N and Bi concentrations based on 16×16 band Hamiltonian model. This model is extended from Band Anti-crossing (BAC) and the dimension of basis states used in the Hamiltonian matrix is 16. Under the condition that the quaternary compound matches the lattice configuration of the InAs substrate, the variations of band gap (Eg), spin-orbit coupling energy (ΔSO) has been examined as a dependency on the mole fractions of N and Bi. Our findings indicate the integration of N and Bi atoms in InAs gives rise to a substantial band gap energy minimization and the growth of spin-orbit coupling energy. Subsequently a crossover (ΔSO = Eg) is observed at a Bi concentration of 0.37%, which contributes to enhancing the effectiveness of photonic devices by suppress Auger recombination. We further reveal the band offset with different N and Bi concentrations and considered the influence of the substrate on the material deviation. The conduction band energy mislignment (ΔEc) of InAsNBi exceeds energy misalignment in the valence bands (ΔEv), which is required to improve thermal-insensitive characteristics of semiconductor devices. Moreover, the significant mastery over the edges of the conduction and valence bands by adjusting the concentration of N and Bi will increase the flexibility to design InAsNBi/InAs structures.

Insight into magnetically induced ring currents and photophysics of six-porphyrin nanorings.

The series of nanorings based on Zn-porphyrins and tetraoxa-isophlorins in different oxidation states (Q = 0, 2+, 4+, 6+) have been studied studied computationally at density functional theory level (DFT) using BHandHLYP functional combined with def2-SVP basis sets. Magnetically induced ring currents of nanorings have been calculated using the GIMIC method and the Ampère-Maxwell integration scheme. Ring current calculations show that neutral nanorings sustain equal diatropic and paratropic currents of 8 nA T-1, resulting in zero net ring current strengths. The charged nanorings sustain strong ring currents with tropicity depending on the oxidation state Q. Among the considered nanorings, the nanoring composed of 6 isophlorins c-Iso66+ is the most aromatic with a ring current of IGIMIC = 81.6 nA T-1. The structure c-P62+ with a ring current of IGIMIC = 54.9 nA T-1 can be considered as the most aromatic among the synthesized porphyrin nanorings. Spin-orbit coupling matrix elements, oscillator strengths, and excitation energies calculated at the CAM-B3LYP/def2-SVP level of theory were used to estimate rate constants for radiative and nonradiative processes. The algorithm based on X-H approximation were used to calculate the internal conversion rates (kIC). The main channel for the deactivation of the excitation energy in the studied nanorings is the process of internal conversion. The deactivation of excited energy occurs due to the vibrations of certain groups of C-H bonds in the nanorings. The nanoring c-Iso6 has magnetically allowed low-lying transitions that contributes significantly to the paratropic ring current, resulting in strong local antiaromaticity in the tetraoxa-isophlorin units.

The magnetic anisotropy energy of 13-atom Fe-Pt, Co-Pt and Ni-Pt clusters

The spin-orbital coupling (SOC) effect and magnetic anisotropy energy (MAE) of 13-atom Fe-Pt, Co-Pt and Ni-Pt clusters were investigated by density functional theory. The result shows that the Fe-Pt system has a higher MAE than Co-Pt and Ni-Pt. In the Fe8Pt5 cluster, the main contribution of MAE comes from SOC interaction between d orbitals around the Fermi level in Pt atoms. The giant positive MAE is mainly due to the SOC interaction between the majority spin states of d x 2 and d x y orbitals.

Structural, vibrational and electronic properties of Nb substituted orthovanadates LaV1−xNbxO4

We investigate the structural, vibrational, morphological, and electronic properties of Nb substituted orthovanadate LaV1−xNbxO4 samples prepared by the solid-state reaction method. The x-ray diffraction (XRD) analysis reveals the presence of three crystal structures [monoclinic monazite (m − m) type for the x = 0, two-phase equilibrium of monoclinic monazite (m − m) and tetragonal scheelite (t − s) type for the 0.2 ≤ x ≤ 0.8, and monoclinic fergusonite (m − f) type for the x = 1 samples] with an increase in Nb5+ concentration. The Raman spectroscopy and x-ray photoelectron spectroscopy (XPS) were employed to study the vibrational and electronic properties of all the samples, respectively. In order to choose an excitation wavelength that does not cause undesirable fluorescence and has observable intensities of all the vibrational modes, the Raman spectra are collected using 532 nm, 633 nm, and 785 nm laser lines. With increasing the Nb5+ concentration, new Raman modes associated with Nb-bonds are clearly visible and the intensity of V-bonds assigned modes is decreasing. The XPS analysis shows the unchanged 3+ oxidation state of La ion where the intensity of the V 2p core-level decreases while the Nb 3d core-level increases with x. The equal spin-orbit energy splitting of the states is confirmed by the average energy difference (across La core-level spectra for all the samples) for state I as well as bonding and anti-bonding of state II. Interesting, the relative intensity of La 3d state I and state II show systematic change with Nb doping altering the metal ligand overlap. We discuss and provide insight into the evolution of the structural, morphological, and chemical features with Nb substitution in LaV1−xNbxO4 samples.

Spectroscopic Properties of the Alkali-Krypton Diatomic M-Kr (M = Rb, Cs, and Fr) van der Waals Systems Including the Spin-Orbit Coupling.

Using an ab initio approach based on pseudopotential technique, pair potential approach, core polarization potentials, and large Gaussian basis sets, we investigate interaction of heavy alkali-krypton diatomic M-Kr (M = Rb, Cs, and Fr) van der Waals dimers. In this context, the core-core interactions for M+-Kr (M = Rb, Cs, and Fr) are calculated at coupled-cluster single and double excitation (CCSD) level and included in the total potential energy. Therefore, the potential energy curves are performed for 14 electronic states: eight of 2Σ+ symmetry, four of 2Π symmetry, and two of 2Δ symmetry. Furthermore, for each M-Kr dimer, the spin-orbit coupling has been considered for the B2Σ+, A2Π, 32Σ+, 22Π, 52Σ+, 32Π, and 12Δ states. In addition, the transition dipole moment has been determined, including the spin-orbit effect using the rotational matrix issued from the spin-orbit potential energy calculations.

Exploring optical properties of 2H- and 1T′−MoTe2 single crystals by spectroscopic ellipsometry

Molybdenum ditelluride $(\mathrm{Mo}{\mathrm{Te}}_{2})$ has received considerable attention as a two-dimensional material due to its intriguing physical properties and potential for applications in a variety of devices. The optical properties of $2\text{H-}$ and $1{\mathrm{T}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{MoTe}}_{2}$ single crystals are investigated in this study using spectroscopic ellipsometry over the spectra range 0.73--6.42 eV and at temperatures of 4.2--500 K. According to the optical absorption spectra at 4.2 K, $2\text{H-MoT}{\mathrm{e}}_{2}$ has an indirect band gap of $1.06\ifmmode\pm\else\textpm\fi{}0.01$ eV, whereas $1{\mathrm{T}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{MoTe}}_{2}$ exhibits semimetal behavior. Furthermore, $2\text{H-MoT}{\mathrm{e}}_{2}$ has three distinct intralayer ${A}_{1\mathrm{s}},\phantom{\rule{0.16em}{0ex}}{A}_{2\mathrm{s}},\phantom{\rule{0.16em}{0ex}}\mathrm{and}\phantom{\rule{0.16em}{0ex}}{B}_{1\mathrm{s}}$ excitons, and one interlayer ${A}_{\mathrm{IL}}$ exciton at $1.136\ifmmode\pm\else\textpm\fi{}0.002, 1.181\ifmmode\pm\else\textpm\fi{}0.001, 1.469\ifmmode\pm\else\textpm\fi{}0.006$, and $1.21\ifmmode\pm\else\textpm\fi{}0.01$ eV, respectively. The spin-orbit coupling energy of $2\text{H-MoT}{\mathrm{e}}_{2}$ is 333 meV and is independent of temperature. By contrast, $1{\mathrm{T}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{MoTe}}_{2}$ has two low-energy optical transitions at $0.78\ifmmode\pm\else\textpm\fi{}0.01$ and $1.45\ifmmode\pm\else\textpm\fi{}0.01$ eV, which are redshifted and broadened upon an increase in temperature, indicating the increased electron-phonon interaction. We characterize the optical transitions of both phases of $\mathrm{Mo}{\mathrm{Te}}_{2}$ by comparing experimental data with the results of first-principles calculations.

Voltage-controlled magnetic anisotropy in heterostructures with a two-dimensional magnetic material

The advent of two-dimensional (2D) magnetic materials significantly expand the scope of voltage-controlled magnetization-switching scheme as their integration in diverse magnetic tunnel junctions (MTJ) offers a highly attractive perspective for designing future magnetoelectric random access memory (MeRAM). Here, we propose the utilization of 2D ferromagnetic ${\mathrm{Fe}}_{2}{\mathrm{I}}_{2}$ to substitute traditional magnetic thin films for assembling energy-efficient MTJs combined with Ir capping layers. We find these multilayers exhibit both giant perpendicular magnetic anisotropy (PMA) and voltage controlled magnetic anisotropy (VCMA) efficiency depending strongly on the Ir thickness and epitaxial strain effect. Furthermore, the spin reorientation has also been achieved with increased Ir thickness, and the magnitude and slope of VCMA behavior are dominated by the biaxial strain. We elucidate that the underlying mechanism is the electric-field-induced modifications of the spin-orbit coupling energies of the spin-polarized $\mathrm{Ir}\text{\ensuremath{-}}d$ orbitals. These findings not only reveal new approaches controlling 2D magnetism, but also pave the way of an alternative strategy for the design of nonvolatile and ultralow power spintronics and magnetic memory storage devices.

Exploring the luminescence properties and sensing mechanism of a turn-on TADF probe for sulfite.

Fluorescent probes with a microsecond lifetime have attracted much attention in biological detection. The luminescence properties and responsive mechanisms of a probe [DCF-MPYM-lev-H]- for detecting sulfite and its corresponding product [DCF-MPYM-2H]2- are studied based on density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations as well as the thermal vibration correlation function method. It is found that the luminescence efficiency of the probe increases obviously after reacting with sulfite, which is induced by increased radiative decay rates and decreased nonradiative rates. In addition, the thermally activated delayed fluorescence (TADF) properties of products are confirmed by analyzing the spin-orbital constants and energy gaps between the singlet excited states and the triplet excited states. The calculation results favor the understanding of the luminescence properties and responsive mechanism of a turn-on TADF probe for sulfite, which may provide a theoretical reference for the development of new TADF probes.

Chiral Majorana modes via proximity to a twisted cuprate bilayer

We propose a novel heterostructure to achieve chiral topological superconductivity in two dimensions. A substrate with a large Rashba spin-orbit coupling energy is brought in proximity to a twisted bilayer of thin films exfoliated from a high-temperature cuprate superconductor. The combined system is then exposed to an out-of-plane magnetic field. The rare $d+id$ pairing symmetry expected to occur in such a system allows for nontrivial topology; specifically, in contrast to the case of the twisted bilayer in isolation, the substrate induces an odd Chern number. The resulting phase is characterized by the presence of a Majorana zero mode in each vortex.

Magnetism Studies of Bis(acyl)phosphide-Supported Eu3+ and Eu2+ Complexes.

A series of bis(acyl)phosphide-supported Eu complexes were synthesized (bis(acyl)phosphide = BAP). In this study, BAP ligands proved to be excellent ligands for the synthesis of both Eu3+ and Eu2+ molecular complexes. Sodium bis(mesitoyl)phosphide (Na(mesBAP)) and sodium bis(2,4,6-triisopropylbenzoyl)phosphide (Na(trippBAP)) were employed as ligand precursors for the synthesis of the Eu3+ complexes Eu(bis(mesitoyl)phosphide)3(thf)2 (Eu(mesBAP)3(thf)2) and Eu(bis(2,4,6-triisopropylbenzoyl)phosphide)3 (Eu(trippBAP)3), as well as the Eu2+ complex, Eu(bis(2,4,6-triisopropylbenzoyl)phosphide)2(dme)2 (Eu(trippBAP)2(dme)2) (thf = tetrahydrofuran, dme = 1,2-dimethoxyethane). All complexes were characterized using a combination of UV-vis-NIR-IR and NMR spectroscopies, and single-crystal X-ray diffraction (SC-XRD). The magnetic properties of these three monomeric Eu complexes were investigated by variable-temperature magnetic susceptibility. The magnetic data are typical for these ions, with Eu(trippBAP)2(dme)2 displaying Curie-type behavior. Both Eu(trippBAP)3 and Eu(mesBAP)3(thf)2 possess similar 7F0-7F1 spin-orbit energy gaps and a similar zero-field splitting of the 7F1 state.

Orbital Angular Momentum of Magnons in Collinear Magnets.

We study the orbital angular momentum of magnons for collinear ferromagnet (FM) and antiferromagnetic (AF) systems with nontrivial networks of exchange interactions. The orbital angular momentum of magnons for AF and FM zigzag and honeycomb lattices becomes nonzero when the lattice contains two inequivalent sites and is largest at the avoided-crossing points or extremum of the frequency bands. Hence, the arrangement of exchange interactions may play a more important role at producing the orbital angular momentum of magnons than the spin-orbit coupling energy and the resulting noncollinear arrangement of spins.

Spin and Orbital Spectroscopy in the Absence of Coulomb Blockade in Lead Telluride Nanowire Quantum Dots

We investigate quantum dots in semiconductor PbTe nanowire devices. Due to the accessibility of ambipolar transport in PbTe, quantum dots can be occupied both with electrons and holes. Owing to a very large dielectric constant in PbTe of order 1000, we do not observe Coulomb blockade which typically obfuscates the orbital and spin spectra. We extract large and highly anisotropic effective Landé g-factors, in the range 20-44. The absence of Coulomb blockade allows direct readout, at zero source-drain bias, of spin-orbit hybridization energies of up to 600 \muμeV. These spin properties make PbTe nanowires, the recently synthesized members of group IV-VI materials family, attractive as a materials platform for quantum technology, such as spin and topological qubits.

Tunable two-dimensional superconductivity and spin-orbit coupling at the EuO/KTaO3(110) interface

Unconventional quantum states, most notably the two-dimensional (2D) superconductivity, have been realized at the interfaces of oxide heterostructures where they can be effectively tuned by the gate voltage (VG). Here we report that the interface between high-quality EuO (111) thin film and KTaO3 (KTO) (110) substrate shows superconductivity with onset transition temperature T_{{{mathrm{c}}}}^{{{{mathrm{onset}}}}} = 1.35 K. The 2D nature of superconductivity is verified by the large anisotropy of the upper critical field and the characteristics of a Berezinskii–Kosterlitz-Thouless transition. By applying VG, T_{{{mathrm{c}}}}^{{{{mathrm{onset}}}}} can be tuned from ~1 to 1.7 K; such an enhancement can be possibly associated with a boosted spin-orbit energy varepsilon _{{{{mathrm{so}}}}} = hbar /tau _{{{{mathrm{so}}}}}, where τso is the spin-orbit relaxation time. Further analysis of τso based on the upper critical field (Hc2) and magnetoconductance reveals complex nature of spin-orbit coupling (SOC) at the EuO/KTO(110) interface with different mechanisms dominating the influence of SOC effects on the superconductivity and the magnetotransport in the normal state. Our results demonstrate that the SOC should be considered an important factor in determining the 2D superconductivity at oxide interfaces.

Theoretical study of spin-orbit coupling in Janus monolayer MA2Z4

Abstract In this paper, based on first-principles calculations, we investigate the energy valley and spin-orbit coupling properties of Janus monolayer MA2Z4. The stability of different structures is illustrated. Due to the breaking of mirror symmetry, Rashba splitting occurs at the Γ point in the band structures of Janus monolayers WSiGeN4 and WSi2(NP)2. The relationship between Rashba spin-orbit coupling strength and potential energy gradient and d-orbital composition is explored. Janus monolayer WSi2(NP)2 has stronger Rashba effect than WSiGeN4 due to the strong asymmetry of the d orbital of W atom. These results help to promote the application of two-dimensional materials in spintronics and valleytronics.

Intrinsic Ferromagnetism of Two-Dimensional (2D) MnO2 Revisited: A Many-Body Quantum Monte Carlo and DFT+U Study

Monolayer MnO$_2$ is one of the few predicted two-dimensional (2D) ferromagnets that has been experimentally synthesized and is commercially available. The Mermin-Wagner theorem states that magnetic order in a 2D material cannot persist unless magnetic anisotropy (MA) is present and perpendicular to the plane, which permits a finite critical temperature. Previous computational studies have predicted the magnetic ordering and Curie temperature of 2D MnO$_2$ with DFT+U (Density Funtional Theory + Hubbard U correction), with the results having a strong dependence on the Hubbard U parameter. Diffusion Monte Carlo (DMC) is a correlated electronic structure method that has had demonstrated success for the electronic and magnetic properties of a variety of 2D and bulk systems since it has a weaker dependence on the starting Hubbard parameter and density functional. In this study, we used DMC and DFT+U to calculate the magnetic properties of monolayer MnO$_2$. We found that the ferromagnetic ordering is more favorable than antiferromagnetic and determined a statistical bound on the magnetic exchange parameter ($J$). In addition, we performed spin-orbit MA energy calculations using DFT+U and using our DMC and DFT+U parameters along with the analytical model of Torelli and Olsen, we estimated an upper bound of 28.8 K for the critical temperature of MnO$_2$. These QMC results intend to serve as an accurate theoretical benchmark, necessary for the realization and development of future 2D magnetic devices. These results also demonstrate the need for accurate methodologies to predict magnetic properties of correlated 2D materials.

BODIPY-Based Polymers of Intrinsic Microporosity for the Photocatalytic Detoxification of a Chemical Threat.

Effective heterogeneous photocatalysts capable of detoxifying chemical threats in practical settings must exhibit outstanding device integrity. We report a copolymerization that yields robust, porous, processible, chromophoric BODIPY (BDP; boron-dipyrromethene)-containing polymers of intrinsic microporosity (BDP-PIMs). Installation of a pentafluorophenyl at the meso position of a BDP produced reactive monomer that when combined with 5,5,6,6-tetrahydroxy-3,3,3,3-tetramethyl-1,1-spirobisindane (TTSBI) and tetrafluoroterephthalonitrile (TFTPN) yields PIM-1. Postsynthetic modification of these polymers yields Br-BDP-PIM-1a and -1b─polymers containing bromine at the 2,6-positions. Remarkably, the brominated polymers display porosity and processability features similar to those of H-BDP-PIMs. Gas adsorption reveals molecular-scale porosity and Brunette-Emmet-Teller surface areas as high as 680 m2 g-1. Electronic absorption spectra reveal charge-transfer (CT) bands centered at 660 nm, while bands arising from local excitations, LE, of BDP and TFTPN units are at 530 and 430 nm, respectively. Fluorescence spectra of the polymers reveal a Förster resonance energy-transfer (FRET) pathway to BDP units when TFTPN units are excited at 430 nm; weak phosphorescence at room temperature indicates a singlet-to-triplet intersystem crossing. The low-lying triplet state is well positioned energetically to sensitize the conversion of ground-state (triplet) molecular oxygen to electronically excited singlet oxygen. Photosensitization capabilities of these polymers toward singlet-oxygen-driven detoxification of a sulfur-mustard simulant 2-chloroethyl ethyl sulfide (CEES) have been examined. While excitation of CT and LEBDP bands yields weak catalytic activity (t1/2 > 15 min), excitation to higher energy states of TFTPN induces significant increases in photoactivity (t1/2 ≅ 5 min). The increase is attributable to (i) enhanced light collection, (ii) FRET between TFTPN and BDP, (iii) the presence of heavy atoms (bromine) having large spin-orbit coupling energies that can facilitate intersystem crossing from donor-acceptor CT-, FRET-, or LE-generated BDP singlet states to BDP-related triplet states, and (iv) polymer triplet excited-state sensitization of the formation of CEES-reactive, singlet oxygen.

Influence of the spin-orbit split-off valence band on the hole g factor in semiconductor nanocrystals

We present results of $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ calculations of the effective $g$ factor of holes confined in spherical, cube, and planar semiconductor nanocrystals (NCs). We use the six-band Luttinger model for semiconductors with the zinc-blende crystal structure and study the size dependence of the ${\mathrm{\ensuremath{\Gamma}}}_{8}$ top valence subband hole $g$ factor caused by the admixture of the spin-orbit split-off valence subband ${\mathrm{\ensuremath{\Gamma}}}_{7}$. We present semianalytical expressions for the hole $g$ factor which depends on the light- to heavy-hole effective mass ratio $\ensuremath{\beta}$ and on the ratio between spin-orbit energy splitting of valence band ${\mathrm{\ensuremath{\Delta}}}_{\text{SO}}$ and the hole quantization energy ${E}_{h}$. The admixture of ${\mathrm{\ensuremath{\Gamma}}}_{7}$ states is significant for small ${\mathrm{\ensuremath{\Delta}}}_{\text{SO}}/{E}_{h}$ and, in spherical and cube NCs, leads to a strong size dependence of the hole $g$ factor. In thin planar nanoplatelets (NPLs) with infinite or large lateral sizes, the dependence of the heavy-hole $g$ factor on NPL thickness is relatively weak. It is drastically enhanced and may become nonmonotonic in NPLs with finite in-plane sizes due to the additional hole states mixing. We discuss our results in comparison with published experimental data for CdSe- and InP-based spherical NCs and NPLs and point out the specificity of extracting hole $g$ factor from the data measured on excitons.

Relativistic effects in confined helium-like atoms

The first-order relativistic effects such as relativistic correction to the kinetic energy, spin-orbit interaction and one-and two-body Darwin terms for the ground and excited states of confined H−,He,Li+ and Be++ atoms have been investigated. The results reveal that impurity charge and dot radius have a strong influence on the relativistic effects. In the strong confinement region, when the dot radius is further decreased, the magnitude of relativistic effects increases rapidly. Similarly, as the impurity charge increases, the relativistic effects increase substantially. In the electronic configuration 1,3S (1s2s), spin-orbit interaction energy and total Darwin energy for the case of triplet are lower than the singlet case. In addition, when the dot radius is large enough, the results for the relativistic effects approach to the corresponding values of free atom.