Lower Spin Research Articles

Black hole mergers as tracers of spinning massive black hole and galaxy populations in the OBELISK simulation

Massive black hole (BH) mergers will be key targets of future gravitational wave and electromagnetic observational facilities. In order to constrain BH evolution with the information extracted from BH mergers, one must take into account the complex relationship between the population of merging BHs and the global BH population. We analysed the high-resolution cosmological radiation-hydrodynamics simulation OBELISK, run to redshift z = 3.5, to study the properties of the merging BH population, and its differences with the underlying global BH population in terms of BH and galaxy properties. In post-processing, we calculated dynamical delays between the merger in the simulation at the resolution limit and the actual coalescence well below the resolution scale. We find that merging BHs are hosted in relatively massive galaxies with stellar mass M* ≳ 109 M⊙. Given that galaxy mass is correlated with other BH and galaxy properties, BH mergers tend to also have a higher total BH mass and higher BH accretion rates than the global population of main BHs. These differences generally disappear if the merger population is compared with a BH population sampled with the same galaxy mass distribution as merger hosts. Galaxy mergers can temporarily boost the BH accretion rate and the host’s star formation rate, which can remain active at the BH merger if sub-resolution delays are not taken into account. When dynamical delays are taken into account, the burst has generally faded by the time the BHs merge. BH spins are followed self-consistently in the simulation under the effect of accretion and BH mergers. We find that merging BHs have higher spins than the global population, but similar or somewhat lower spins compared to a mass-matched sample. For our sample, mergers tend to decrease the spin of the final BH remnant.

Non‐planar Nest‐like [Fe2S2] Cluster Sites for Efficient Oxygen Reduction Catalysis

AbstractMetal‐nitrogen‐carbon catalysts, as promising alternative to platinum‐based catalysts for oxygen reduction reaction (ORR), are still highly expected to achieve better performance by modulating the composition and spatial structure of active site. Herein, we constructed the non‐planar nest‐like [Fe2S2] cluster sites in N‐doped carbon plane. Adjacent double Fe atoms effectively weaken the O−O bond by forming a peroxide bridge‐like adsorption configuration, and the introduction of S atoms breaks the planar coordination of Fe resulting in greater structural deformation tension, lower spin state, and downward shifted Fe d‐band center, which together facilitate the release of OH* intermediate. Hence, the non‐planar [Fe2S2] cluster catalyst, with a half‐wave potential of 0.92 V, displays superior ORR activity than that of planar [FeN4] or [Fe2N6]. This work provides insights into the co‐regulation of atomic composition and spatial configuration for efficient oxygen reduction catalysis.

Non-planar Nest-like [Fe2 S2 ] Cluster Sites for Efficient Oxygen Reduction Catalysis.

Metal-nitrogen-carbon catalysts, as promising alternative to platinum-based catalysts for oxygen reduction reaction (ORR), are still highly expected to achieve better performance by modulating the composition and spatial structure of active site. Herein, we constructed the non-planar nest-like [Fe2 S2 ] cluster sites in N-doped carbon plane. Adjacent double Fe atoms effectively weaken the O-O bond by forming a peroxide bridge-like adsorption configuration, and the introduction of S atoms breaks the planar coordination of Fe resulting in greater structural deformation tension, lower spin state, and downward shifted Fe d-band center, which together facilitate the release of OH* intermediate. Hence, the non-planar [Fe2 S2 ] cluster catalyst, with a half-wave potential of 0.92 V, displays superior ORR activity than that of planar [FeN4 ] or [Fe2 N6 ]. This work provides insights into the co-regulation of atomic composition and spatial configuration for efficient oxygen reduction catalysis.

Operator fusion from wave-function overlap: Universal finite-size corrections and application to the Haagerup model

Given a critical quantum spin chain described by a conformal field theory (CFT) at long distances, it is crucial to understand the universal conformal data. One most important ingredient is the operator product expansion (OPE) coefficients, which describe how operators fuse into each other. It has been proposed in [Zou, Vidal, Phys. Rev. B 105, 125125] that the OPE coefficients can be computed from overlaps of low-energy wavefunctions of the spin chain. In this work, we establish that all conformal data including central charge, conformal dimensions, and OPE coefficients are encoded in the wavefunction overlaps, with universal finite-size corrections that depend on the operator content of the cyclic orbifold CFT. Thus this method allows us to numerically compute all the conformal data based solely on the low-energy eigenstates. The predictions are verified in the Ising and XXZ model. As an application, we study the recently proposed Haagerup model built from the Haagerup fusion category. We find that the CFT has central charge $c \approx 2.1$ and the lowest spin-$1$ operator in the twisted sector has scaling dimension $1 < \Delta_J \leq 1.4$.

Origin of the Distinctive Electronic Structure of Co- and Fe-Porphyrin-Nitrene and Its Effect on Their Nitrene Transfer Reactivity

Metal-bound nitrene species are the crucial intermediate in catalytic nitrene transfer reactions exhibited by engineered enzymes and molecular catalysts. The electronic structure of such species and its correlation with nitrene transfer reactivity have not been fully understood yet. This work presents an in-depth electronic structure analysis and nitrene transfer reactivity of two prototypical metal-nitrene species derived from CoII(TPP) and FeII(TPP) (TPP = meso-tetraphenylporphyrin) complexes and tosyl azide nitrene precursor. Parallel to the well-known "cobalt(III)-imidyl" electronic structure of the Co-porphyrin-nitrene species, the formation mechanism and electronic structure of the elusive Fe-porphyrin-nitrene have been established using density functional theory (DFT) and multiconfigurational complete active-space self-consistent field (CASSCF) calculations. Electronic structure evolution analysis for the metal-nitrene formation step and CASSCF-derived natural orbitals advocates that the electronic nature of the metal-nitrene (M-N) core of Fe(TPP) is strikingly different from that of the Co(TPP). Specifically, the "imidyl" nature of the Co-porphyrin-nitrene [(TPP)CoIII-•NTos] (Tos = tosyl) (I1Co) is contrasted by the "imido-like" character of the Fe-porphyrin-nitrene [(TPP)FeIV[Formula: see text]NTos] (I1Fe). This difference between Co- and Fe-nitrene has been attributed to the additional interactions between Fe-dπ and N-pπ orbitals in Fe-nitrene, which is further complemented by the shortened Fe-N bond length of 1.71 Å. This stronger M-N bond in Fe-nitrene compared to the Co-nitrene is also reflected in the higher exothermicity (ΔΔH = 16 kcal/mol) of the Fe-nitrene formation step. The "imido-like" character renders a relatively lower spin population on the nitrene nitrogen (+0.42) in the Fe-nitrene complex I1Fe, which undergoes the nitrene transfer to the C═C bond of styrene with a considerably higher enthalpy barrier (ΔH‡ = 10.0 kcal/mol) compared to the Co congener I1Co (ΔH‡ = 5.6 kcal/mol) possessing a higher nitrogen spin population (+0.88) and a relatively weaker M-N bond (Co-N = 1.80 Å).

Unitarity cuts of the worldsheet

We compute the imaginary parts of genus-one string scattering amplitudes. Following Witten’s i\varepsiloniε prescription for the integration contour on the moduli space of worldsheets, we give a general algorithm for computing unitarity cuts of the annulus, Möbius strip, and torus topologies exactly in \alpha'α′. With the help of tropical analysis, we show how the intricate pattern of thresholds (normal and anomalous) opening up arises from the worldsheet computation. The result is a manifestly-convergent representation of the imaginary parts of amplitudes, which has the analytic form expected from Cutkosky rules in field theory, but bypasses the need for performing laborious sums over the intermediate states. We use this representation to study various physical aspects of string amplitudes, including their behavior in the (s,t)(s,t) plane, exponential suppression, decay widths of massive strings, total cross section, and low-energy expansions. We find that planar annulus amplitudes exhibit a version of low-spin dominance: at any finite energy, only a finite number of low partial-wave spins give an appreciable contribution to the imaginary part.

X-ray polarimetry as a tool to measure the black hole spin in microquasars: simulations of IXPE capabilities

ABSTRACT Measurements of the angular momentum (spin) of astrophysical black holes are extremely important, as they provide information on the black hole formation and evolution. We present simulated observations of an X-ray binary system with the Imaging X-ray Polarimetry Explorer (IXPE), with the aim to study the robustness of black hole spin and geometry measurements using X-ray polarimetry. As a representative example, we used the parameters of GRS 1915+105 in its former unobscured, soft state. In order to simulate the polarization properties, we modelled the source emission with a multicolour blackbody accounting for thermal radiation from the accretion disc, including returning radiation. Our analysis shows that the polarimetric observations in the X-ray waveband will be able to estimate both spin and inclination of the system with a good precision [without returning radiation we obtained for the lowest spin Δa ≤ 0.4 (0.4/0.998 ∼ 40 per cent) for spin and Δi ≤ 30° (30°/70$^\circ \, \sim$ 43 per cent) for inclination, while for the higher spin values we obtained Δa ≤ 0.12 (∼12 per cent) for spin and Δi ≤ 20° (∼29 per cent) for inclination, within 1σ errors]. When focusing on the case of returning radiation and treating inclination as a known parameter, we were able to successfully reconstruct spin and disc albedo in Δa ≤ 0.15 (∼15 per cent) interval and Δ albedo ≤0.45 (45 per cent) intervals within 1σ errors. We conclude that X-ray polarimetry will be a useful tool to constrain black hole spins, in addition to timing and spectral-fitting methods.

Unsaturated single-atom CoN3 sites for improved fenton-like reaction towards high-valent metal species

High-valent metal species hold promise for selective removal of organic pollutants in wastewater, which necessitate two or more electrons transfer to allow intensive electron from catalysts to PMS. Herein, we design undercoordinated single-atom CoN3 catalyst for boosted generation of high-valent Co species in peroxymonosulfate activation process, to be carefully distinguished from the traditional saturated CoN4 configuration. Enabled by temperature-dependent magnetization measurements, in-situ Raman spectra and electrochemical tests, we found that the unsaturated Co sites in CoN3 with higher spin state can afford enhanced electron-donating ability and intensive electron flow to drive the valence transformation from Co(II) to Co(IV), while the saturated ones in CoN4 with lower spin state only trigger Co(II)/ Co(III) conversion and subsequently produce free radicals. This work highlights the pivotal role of coordination environment for electron flow regulation in Fenton-like catalysts to alleviate water pollution dilemma and advance environmental remediation technologies.

Electronic Spin Qubit Candidates Arrayed within Layered Two-Dimensional Polymers

Molecular electronic spin qubits are promising candidates for quantum information science applications because they can be reliably produced and engineered via chemical design. Embedding electronic spin qubits within two-dimensional polymers (2DPs) offers the possibility to systematically engineer inter-qubit interactions while maintaining long coherence times, both of which are prerequisites to their technological utility. Here, we introduce electronic spin qubits into a diamagnetic 2DP by n-doping naphthalene diimide subunits with varying amounts of CoCp2 and analyze their spin densities by quantitative electronic paramagnetic resonance spectroscopy. Low spin densities (e.g., 6.0 × 1012 spins mm-3) enable lengthy spin-lattice (T1) and spin-spin relaxation (T2) times across a range of temperatures, ranging from T1 values of 164 ms at 10 K to 30.2 μs at 296 K and T2 values of 2.36 μs at 10 K to 0.49 μs at 296 K for the lowest spin density sample examined. Higher spin densities and temperatures were both found to diminish T1 times, which we attribute to detrimental cross-relaxation from spin-spin dipolar interactions and spin-phonon coupling, respectively. Higher spin densities decreased T2 times and modulated the T2 temperature dependence. We attribute these differences to the competition between hyperfine and dipolar interactions for electron spin decoherence, with the dominant interaction transitioning from the former to the latter as spin density and temperature increase. Overall, this investigation demonstrates that dispersing electronic spin qubits within layered 2DPs enables chemical control of their inter-qubit interactions and spin decoherence times.

The description of nuclear superdeformed rotational bands in A∼190 region with pq formula

The nuclear superdeformed (SD) rotational bands in [Formula: see text] mass region were systematically analyzed with the two-parameter [Formula: see text] formula. The study of the observed transition energies by using the best-fitting method shows that the [Formula: see text] formula can provide excellent descriptions of the SD bands. The analysis of two types of moments of inertia ([Formula: see text] and [Formula: see text]) and bandhead moment of inertia ([Formula: see text]) also demonstrates the reliability of the [Formula: see text] formula in describing the SD bands. Finally, by using the [Formula: see text] formula, the unobserved transition energies for the lower and higher spin regions were predicted herein.

A correlation between accreted stellar kinematics and dark-matter halo spin in the artemis simulations

ABSTRACT We report a correlation between the presence of a Gaia-Sausage-Enceladus (GSE) analogue and dark-matter (DM) halo spin in the artemis simulations of Milky Way-like galaxies. The haloes which contain a large population of accreted stars on highly radial orbits (like the GSE) have lower spin on average than their counterparts with more isotropic stellar velocity distributions. The median modified spin parameters λ′ differ by a factor of ∼1.7 at the present day, with a similar value when the haloes far from virial equilibrium are removed. We also show that accreted stars make up a smaller proportion of the stellar populations in haloes containing a GSE analogue, and are stripped from satellites with stellar masses typically ∼4 times smaller. Our findings suggest that the higher spin of DM haloes without a GSE-like feature is due to mergers with large satellites of stellar mass ∼1010 M⊙, which do not result in prominent radially anisotropic features like the GSE.

Black hole–neutron star mergers: The first mass gap and kilonovae

Observations of X-ray binaries indicate a dearth of compact objects in the mass range from ∼2 − 5 M⊙. The existence of this (first mass) gap has been used to discriminate between proposed engines behind core-collapse supernovae. From LIGO/Virgo observations of binary compact remnant masses, several candidate first mass gap objects, either neutron stars (NSs) or black holes (BHs), were identified during the O3 science run. Motivated by these new observations, we study the formation of BH-NS mergers in the framework of isolated classical binary evolution, using population synthesis methods to evolve large populations of binary stars (Population I and II) across cosmic time. We present results on the NS to BH mass ratios (q = MNS/MBH ) in merging systems, showing that although systems with a mass ratio as low as q = 0.02 can exist, typically BH-NS systems form with moderate mass ratios q = 0.1 − 0.2. If we adopt a delayed supernova engine, we conclude that ∼30% of BH-NS mergers may host at least one compact object in the first mass gap (FMG). Even allowing for uncertainties in the processes behind compact object formation, we expect the fraction of BH-NS systems ejecting mass during the merger to be small (from ∼0.6 − 9%). In our reference model, we assume: (i) the formation of compact objects within the FMG, (ii) natal NS/BH kicks decreased by fallback, (iii) low BH spins due to Tayler-Spruit angular momentum transport in massive stars. We find that ≲1% of BH-NS mergers will have any mass ejection and about the same percentage will produce kilonova bright enough to have a chance of being detected with a large (Subaru-class) 8 m telescope. Interestingly, all these mergers will have both a BH and an NS in the FMG.

Routes for the topological surface state energy gap modulation in antiferromagnetic MnBi2Te4

We have analyzed different factors responsible for changes in the Dirac gap in MnBi2Te4 and the routes that determine the possibilities of the purposeful gap modulation. It was shown that upon changing the surface van der Waals interval and surface spin–orbit coupling strength the topological surface states localization shifts between the surface septuple layers with opposite magnetizations, which leads to a nonmonotonic change in the Dirac gap size. The minimum in the Dirac gap corresponds to the point of changing the sign of the emerging exchange field. Moreover, we have shown that the Dirac gap can be effectively modulated by replacing magnetic Mn atoms in the surface layer with nonmagnetic ones or Bi and Te atoms with atoms of elements with a lower spin–orbit coupling that makes it possible to create synthetic layered topological systems with purposeful modification of the surface properties.

Computational Study of Very High Spin Actinyl Peroxide Matryoshka Nanoclusters

AbstractGeneralised gradient approximation and hybrid density functional theory is used to study the geometries, electronic structures and spin state energetics of a series of high symmetry multi‐layer “Matryoshka” actinyl peroxide manganese nanoclusters “E@Mn12@An20n+” (An=U, Np, Pu; E=S, Se, Te, n=2; E=Br, n=3; E=Xe, n=4). These systems are all highly open shell, with up to 100 unpaired electrons in the case of the highest spin state plutonyl complexes. Very strong linear correlations are found in all cases between the number of unpaired electrons and the energies of the complexes, with the highest spin states being much the most stable. We confirm a key conclusion from our previous work in this area (Chemistry, A European Journal 24 (2018) 347) i. e. that the highest spin states of the chalcogen‐centred systems are the ground states only when the chalcogen is present; removal of the central group 16 element causes lower spin states to become the most stable. The compositions of the molecular orbitals associated with the changing spin states are studied in detail, and the relative energies of the highest and next highest spin states of the E‐free uranyl and plutonyl clusters rationalized on the basis of the characters of the orbitals whose occupation changes between the different spin states.

The SAMI Galaxy Survey: physical drivers of stellar-gas kinematic misalignments in the nearby Universe

ABSTRACT Misalignments between the rotation axis of stars and gas are an indication of external processes shaping galaxies throughout their evolution. Using observations of 3068 galaxies from the SAMI Galaxy Survey, we compute global kinematic position angles for 1445 objects with reliable kinematics and identify 169 (12 per cent) galaxies which show stellar-gas misalignments. Kinematically decoupled features are more prevalent in early-type/passive galaxies compared to late-type/star-forming systems. Star formation is the main source of gas ionization in only 22 per cent of misaligned galaxies; 17 per cent are Seyfert objects, while 61 per cent show Low-Ionization Nuclear Emission-line Region features. We identify the most probable physical cause of the kinematic decoupling and find that, while accretion-driven cases are dominant, for up to 8 per cent of our sample, the misalignment may be tracing outflowing gas. When considering only misalignments driven by accretion, the acquired gas is feeding active star formation in only ∼1/4 of cases. As a population, misaligned galaxies have higher Sérsic indices and lower stellar spin and specific star formation rates than appropriately matched samples of aligned systems. These results suggest that both morphology and star formation/gas content are significantly correlated with the prevalence and timescales of misalignments. Specifically, torques on misaligned gas discs are smaller for more centrally concentrated galaxies, while the newly accreted gas feels lower viscous drag forces in more gas-poor objects. Marginal evidence of star formation not being correlated with misalignment likelihood for late-type galaxies suggests that such morphologies in the nearby Universe might be the result of preferentially aligned accretion at higher redshifts.

Spin excitations of individual magnetic dopants in an ionic thin film

Individual magnetic transition metal dopants in a solid host usually exhibit relatively small spin excitation energies of a few meV. Using scanning tunneling microscopy and inelastic electron tunneling spectroscopy (IETS) techniques, we have observed a high spin excitation energy around 36 meV for an individual Co substitutional dopant in ultrathin NaCl films. In contrast, the Cr dopant in the NaCl film shows much lower spin excitation energy around 2.5 meV. Electronic multiplet calculations combined with first-principles calculations confirm the spin excitation induced IETS, and quantitatively reveal the out-of-plane magnetic anisotropies for both Co and Cr. They also allow reproducing the experimentally observed redshift in the spin excitations of Co dimers and ascribe it to a charge and geometry redistribution.

Elucidating the Impact of Hydrophilic Segments on 19F MRI Sensitivity of Fluorinated Block Copolymers.

A major challenge in the preparation of polymeric 19F magnetic resonance imaging (MRI) contrast agents (CAs) is signal attenuation caused by reduced segmental mobility of partly fluorinated polymers possessing large numbers of fluorine atoms. Previous studies have thus mainly focused on the development of fluorinated segments for improved 19F MRI; however, detailed investigations of the role of hydrophilic segments on imaging performance remain scarce. In this study, three hydrophilic and biocompatible monomers, i.e., 2-(methylsulfinyl)ethyl acrylate (MSEA), oligo(ethylene glycol) methyl ether acrylate (OEGA), and oligo(2-methyl-2-oxazoline) acrylate (OMOXA), were used to prepare perfluoropolyether (PFPE)-containing amphiphilic block polymers through reversible addition-fragmentation chain-transfer (RAFT) polymerization. The effect of the different hydrophilic segments on 19F imaging performance was explored. The three polymers could be readily dissolved in aqueous solutions, forming assemblies with the hydrophobic PFPE as the core and the hydrophilic chains as the shell. Molecular dynamics simulations demonstrate that the POMOXA chains adopt a rigid, extended conformation, leading to a relatively short 19F NMR spin-spin relaxation time (T2), lower NMR detectable 19F spins (i.e., visibility), and the least intense 19F MRI signal. In contrast, although PMSEA-PFPE has a shorter 19F NMR T2 than POEGA-PFPE, the much higher 19F spin visibility enhances its MRI signal intensity. The result confirms the importance of maintaining both high fluorine visibility and long T2 relaxation time to prepare effective CAs and highlight the key role of the nonfluorinated hydrophilic segments in determining these parameters.

Spin of information and inconsistency between abstract and full text in RCTs investigating upper limb rehabilitation after stroke: An overview study.

Researchers may be tempted to favorably distort the interpretation of their findings when reporting the abstract (i.e., spin). Spin bias overemphasizes the beneficial effects of the intervention compared with the results shown in the full text. To assess the occurrence of spin bias and incompleteness in reporting abstracts in post-stroke upper limb (UL) rehabilitation randomized clinical trials (RCTs). A sample of 120 post-stroke UL rehabilitation RCTs (indexed in PEDro database), published in English between 2012 and 2020, was included. The completeness of reporting and spin were assessed using the Consolidated Standards of Reporting Trials for Abstracts (CONSORT-A) and the spin checklist. The relationship between CONSORT-A and spin checklist scores with RCT and journal characteristics was assessed. CONSORT-A and spin checklist scored 5.3±2.4 (max 15-points, higher scores indicating better reporting) and 5.5±2.0 (max 7-points, higher scores indicating presence of spin), respectively; Significant differences were detected between abstract and full-text scores in the CONSORT-A checklist (p < 0.01) and the spin checklist (p < 0.01). Items of the CONSORT-A checklist in the abstracts and full text showed a fair agreement (k = 0.31), while a moderate agreement (k = 0.59) for the spin checklist was detected. Completeness of abstract was associated (R2 = 0.46) with journal Impact Factor (p < 0.01), CONSORT Guideline endorsement (p = 0.04), and abstract word number (p = 0.02). A lower spin was associated with a higher journal Impact Factor (p = 0.01) and CONSORT Guideline endorsement (p = 0.01). Post-stroke UL rehabilitation RCTs abstracts were largely incomplete showing spin. Authors, reviewers, publishers, and stakeholders should be aware of this phenomenon. Publishers should consider allowing more words in abstracts to improve the completeness of reporting abstracts. Although we have investigated only stroke rehabilitation, our results suggest that health care professionals of all disciplines should avoid clinical decision-making based solely upon abstracts.

On the three lowest spin states of Na13+: Hybrid Density Functional Theory and benchmark CASSCF(12,12)+CASPT2 studies

AbstractThe three lowest spin states (S = 0,1,2) of 12 representative isomers have been estudied using both, KS‐DFT via three hybrid density functionals, and benchmark multireference CASSCF and CASPT2 methods with a couple of Dunning's correlation consistent basis sets. CASSCF(12,12) geometry optimizations were carried out. Since 12 electrons in 12 active orbitals span the chemically‐significant complete valence space, the results of the present study provide benchmarks for . The CASPT2(12,12)/cc‐pVTZ* lowest energy structures are three nearly degenerate singlets (S = 0): an isomer formed from two pentagonal bipyramids fused together (PBPb), a capped centered‐squared antiprism [CSAP‐(1,3)] and an optimum tetrahedral OPTET(II) structure, the last two lying 0.88 and 1.63 kcal/mol above the first, respectively. The lowest triplet (S = 1) and quintet (S = 2) states lie 4.33 and 3.77 kcal/mol above the singlet global minimum, respectively. The latter is a deformed icosahedron while the former is a CSAP‐(1,3). The flatness of the potential energy surface of this cluster suggests a rather strong dynamical character at finite temperature. Prediction of the lowest energy structures and electronic properties is crucially sensitive both to non‐dynamical and dynamical electron correlation treatment. The CASPT2 vertical ionization energy is 3.66 eV, in excellent agreement with the 3.6 ± 0.1 eV experimental figure. All the isomers are found to have a strong multireference character, thus making KS density functional theory fundamentally inappropriate for these systems. Only large multiconfigurational CASSCF wavefunctions provide a reliable zeroth‐order description; then the dynamic correlation effects must be properly taken into account for a truly accurate account of the structural and energetic features of alkali‐metal clusters.

The 2PM Hamiltonian for binary Kerr to quartic in spin

From the S-matrix of spinning particles, we extract the 2 PM conservative potential for binary spinning black holes up to quartic order in spin operators. An important ingredient is the exponentiated gravitational Compton amplitude in the classical spin-limit for all graviton helicity sectors. The validity of the resulting Hamiltonian is verified by matching to known lower spin order results, as well as direct computation of the 2PM impulse and spin kicks from the eikonal phase and that from the test black hole scattering based on Mathisson-Papapetrou-Dixon equations.