Collinear Spins Research Articles

Collinear-spin machine learned interatomic potential for Fe7Cr2Ni alloy

We have developed a machine learned interatomic potential for the prototypical austenitic steel Fe7Cr2Ni, using the Gaussian approximation potential (GAP) framework. This GAP can model the alloy's properties with close to density functional theory (DFT) accuracy, while at the same time allowing us to access larger length and time scales than expensive first-principles methods. We also extended the GAP input descriptors to approximate the effects of collinear spins (spin GAP), and demonstrate how this extended model successfully predicts structural distortions due to antiferromagnetic and paramagnetic spin states. We demonstrate the application of the spin GAP model for bulk properties and vacancies and validate against DFT. These results are a step towards modeling the atomistic origins of ageing in austenitic steels with higher accuracy. Published by the American Physical Society 2024

Coexistence of tetragonal and cubic phase induced complex magnetic behaviour in CoMn2O4 nanoparticles

CoMn2O4, known for its extensive range of applications, has been subject to limited investigations regarding its structure dependent magnetic properties. Here, we have examined the structure dependent magnetic properties of CoMn2O4 nanoparticles synthesized through a facile coprecipitation technique and are characterized using x-ray diffractometer, x-ray photoelectron spectroscopy (XPS), RAMAN spectroscopy, transmission electron microscopy and magnetic measurements. Rietveld refinement of the x-ray diffraction pattern reveals the coexistence of 91.84% of tetragonal and 8.16% of cubic phase. The cation distribution for tetragonal and cubic phases are (Co0.94Mn0.06)[Co0.06Mn1.94]O4 and (Co0.04Mn0.96)[Co0.96Mn1.04]O4, respectively. While Raman spectra and selected area electron diffraction pattern confirm the spinel structure, both +2 and +3 oxidation states for Co and Mn confirmed by XPS further corroborate the cation distribution. Magnetic measurement shows two magnetic transitions, Tc1 at 165 K and Tc2 at 93 K corresponding to paramagnetic to a lower magnetically ordered ferrimagnetic state followed by a higher magnetically ordered ferrimagnetic state, respectively. While Tc1 is attributed to the cubic phase having inverse spinel structure, Tc2 corresponds to the tetragonal phase with normal spinel. In contrast to general temperature dependent H C observed in ferrimagnetic material, an unusual temperature dependent H C with high spontaneous exchange bias of 2.971 kOe and conventional exchange bias of 3.316 kOe at 50 K are observed. Interestingly, a high vertical magnetization shift (VMS) of 2.5 emu g−1 is observed at 5 K, attributed to the Yafet–Kittel spin structure of Mn3+ in the octahedral site. Such unusual results are discussed on the basis of competition between the non-collinear triangular spin canting configuration of Mn3+ cations of octahedral sites and collinear spins of tetrahedral site. The observed VMS has the potential to revolutionize the future of ultrahigh density magnetic recording technology.

Noncollinear density functional theory

An approach to generalize any kind of collinear functional in density functional theory to noncollinear functionals is proposed. This approach satisfies the correct collinear limit for any kind of functional, guaranteeing that the exact collinear functional after generalization is still exact for collinear spins. Besides, it has well-defined and numerically stable functional derivatives, a desired feature for noncollinear and spin-flip time-dependent density functional theory. Furthermore, it provides local torque, hinting at its applications in spin dynamics.

Double frustration and magnetoelectroelastic excitations in collinear multiferroic materials

We discuss a model scenario for multiferroic systems of type II (collinear spins) where the electric dipolar order competes with a frustrated magnetic order in determining the elastic distortions of the lattice ion positions. High magnetic frustration due to second-neighbors exchange and small spin easy-axis anisotropy lead to the appearance of the so-called quantum magnetic plateau states. Increasing the magnetic field above the plateau border produces composite excitations, where fractionalized spin tertions arise together with spontaneous dipolar flips (in the form of domain walls) and enhanced localized elastic distortions. This peculiar magnetoelectric effect may be described by magneto-electric-elastic quasiparticles that could be detected by x-ray and neutron diffraction techniques. Our results are supported by extensive DMRG computations on the spin sector and self-consistent equations for the lattice distortions.

Modulated and monotonic monolayer-magnetism in hetero-epitaxial Fe on Cu(001)

We have combined two complementary techniques, element sensitive ex situ X-ray magnetic circular dichroism (XMCD) and in situ polarized neutron reflectivity (i-PNR), to determine the values of evolving magnetic moments obtained from a low symmetry system of hetero-epitaxial Fe monolayers (MLs), as a function of thickness. The samples were grown by magnetron sputtering on face-centered-cubic (fcc) Cu(001)/Si(001). Within experimental errors, we found a corroboration of the modulated moments from the XMCD and of the magnetic anisotropies from magnetization measurements with those obtained earlier from layer-by-layer i-PNR measurements. The modulation was attributed to initial island-like growth morphology assisted monolayer-magnetism during sputtering. Furthermore, analyzing the depth sensitive i-PNR profile of a bulk-like film, we developed a model characterized by monotonic magnetism involving collinear spins. The model is further described by a higher magnetization for the deeper layers, which decreases gradually for the upper layers before attaining saturation at its bulk value within a few MLs. This model contradicts the earlier proposed non-collinear model involving antiferromagnetic units, thus clarifying the long standing ambiguity in the coverage regime. The results have been compared with those existing, following the theoretical parameterized tight-binding model with satisfactory agreement. This study distinguishes the variation of monolayer-magnetism owing to the growth morphology from the layer-by-layer investigation vis-à-vis depth-profiling of bulk-like film. At the same time, it also promises the general possibility of depth-profiling using i-PNR in other complex multilayered systems on high flux neutron sources.

Spin-reorientation transitions in the Cairo pentagonal magnet Bi4Fe5O13F

We show that interlayer spins play a dual role in the Cairo pentagonal magnet Bi$_4$Fe$_5$O$_{13}$F, on one hand mediating the three-dimensional (3D) magnetic order and on the other driving spin-reorientation transitions both within and between the planes. The corresponding sequence of magnetic orders unraveled by neutron diffraction and M\"ossbauer spectroscopy features two orthogonal magnetic structures described by opposite local vector chiralities, and an intermediate, partly disordered phase with nearly collinear spins. A similar collinear phase has been predicted theoretically to be stabilized by quantum fluctuations, but Bi$_4$Fe$_5$O$_{13}$F is very far from the relevant parameter regime. While the observed in-plane reorientation cannot be explained by any standard frustration mechanism, our ab initio band-structure calculations reveal strong single-ion anisotropy of the interlayer Fe$^{3+}$ spins that turns out to be instrumental in controlling the local vector chirality and the associated interlayer order.

On Why the Two Polymorphs of NaFePO4 Exhibit Widely Different Magnetic Structures: Density Functional Analysis.

Triphylite-NaFePO4 is a cathode material for Na(+)-ion batteries, whereas its alternative polymorph maricite-NaFePO4 is not. These two different polymorphs exhibit widely different magnetic structures; the ordered magnetic structure of triphylite-NaFePO4 below ∼50 K is described by the propagation vector q1 = (0, 0, 0) with collinear spins, and that of maricite-NaFePO4 below ∼13 K is described by q2 = (1/2, 0, 1/2) with noncollinear spins. We probed the causes for these differences by calculating the spin exchange interactions of the two polymorphs and determining the preferred orientations of their high-spin Fe(2+) (d(6), S = 2) ions on the basis of density functional calculations. Our study shows that maricite-NaFePO4 is not spin-frustrated, which is also the case for triphylite-NaFePO4, that the ordered magnetic structure of triphylite-NaFePO4 is determined mainly by spin exchange, whereas that of maricite-NaFePO4 is determined by both spin exchange and magnetic anisotropy, and that the preferred spin orientations in the two polymorphs can be explained by perturbation theory using spin-orbit coupling as the perturbation.

Microscopic description of twisted magnet Cu2OSeO3

Twisted structures of chiral cubic ferromagnets MnSi and Cu2OSeO3 can be described both in the frame of the phenomenological Ginzburg–Landau theory and using the microscopical Heisenberg formalism with a chirality arising from the Dzyaloshinskii–Moriya (DM) interaction. Recent progress in quantum first-principal methods allows us to calculate interatomic bond parameters of the Heisenberg model, namely isotropic exchange constants Jij and DM vectors Dij, which can be used for simulations of observed magnetic textures and comparison of their calculated characteristics, such as magnetic helix sense and pitch, with an experimental data. In the present work, it is found that unaveraged microscopical details of the spin structures (local canting) have a strong impact on the global twist and can significantly change the helix propagation number. Coefficients J and D of the phenomenological theory and helix propagation number k=D/2J are derived from interatomic parameters Jij and Dij of individual bonds for MnSi and Cu2OSeO3 crystals and similar cubic magnets with almost collinear spins.

Domino-Style Spin–Orbit Torque-Based Spin Logic

We propose a new spin–orbit torque-based domino-style spin logic (SOT-DSL) that operates in a sequence of preset and evaluation modes of operation. During the preset mode, the output magnet is clocked to its hard axis using spin-Hall effect. In the evaluation mode, the clocked output magnet is switched by a spin current from the preceding stage. The nanomagnets in SOT-DSL are always driven by orthogonal spins rather than collinear spins, which in turn eliminates the incubation delay and allows fast magnetization switching. Based on our simulation results, SOT-DSL shows up to 50% improvement in energy consumption compared to all-spin logic. Moreover, SOT-DSL relaxes the requirement for buffer insertion between long spin channels and significantly lowers the design complexity.

The Spiral Spin State in LiCu2O2

We studied the spiral spin state of LiCu2O2. Our calculation is based on the physical picture of classical spiral spins and their quantum fluctuation. Comparison with the spectra of the electron spin resonance (ESR) shows that the excitations come from the spin waves. If the magnetic field is applied along the b-axis of the crystal, there are two branches of excitations. The resonance frequency \(\nu _{1} \sim 30\) GHz corresponds to the spin wave states of wave vectors k = ±Q where Q is the wave vector of spiral spins. However, when the magnetic field is parallel to c-axis, there is only one branch and it comes from the spin wave state of wave vectors k = 0. Our calculation also shows that the former come from the spin waves in spiral spin configuration and the latter from the collinear spins. We have also analyzed the data of dM/dH. Our calculation shows that the spiral spin axis is parallel to b-axis if there is no applied field. When magnetic field is applied along a- or c-axis the spiral axis remains more or less the same until a critical field is reached. When the field strength reaches the second critical field, all the spins become collinear. These results confirm the assumption that there are two critical fields, Hc1 and Hc2. We further discuss the roles played by anisotropy exchange interaction and Dzyaloshinskii–Moriya interaction and how the spiral spin state in LiCu2O2.

Where angular momentum goes in a precessing black-hole binary

We evolve a set of 32 equal-mass black-hole binaries with collinear spins (with intrinsic spin magnitudes $|{\stackrel{P\vec}{S}}_{1,2}/{m}_{1,2}^{2}|=0.8$) to study the effects of precession in the highly nonlinear plunge and merger regimes. We compare the direction of the instantaneous radiated angular momentum, ${\stackrel{^}{\ensuremath{\delta}J}}_{\mathrm{rad}}(t)$, to the directions of the total angular momentum, $\stackrel{^}{J}(t)$, and the orbital angular momentum, $\stackrel{^}{L}(t)$. We find that ${\stackrel{^}{\ensuremath{\delta}J}}_{\mathrm{rad}}(t)$ approximately follows $\stackrel{^}{L}$ throughout the evolution. During the orbital evolution and merger, we observe that the angle between $\stackrel{P\vec}{L}$ and total spin $\stackrel{P\vec}{S}$ is approximately conserved to within 1\ifmmode^\circ\else\textdegree\fi{}, which allows us to propose and test models for the merger remnant's mass and spin. For instance, we verify that the hang-up effect is the dominant effect and largely explains the observed total energy and angular momentum radiated by these precessing systems. We also verify that the total angular momentum, which significantly decreases in magnitude during the inspiral, varies in direction by less than $\ensuremath{\sim}{5}^{\ifmmode^\circ\else\textdegree\fi{}}$. The maximum variation in the direction of $\stackrel{P\vec}{J}$ occurs when the spins are nearly antialigned with the orbital angular momentum. Based on our results, we conjecture that transitional precession, which would lead to large variations in the direction of $\stackrel{P\vec}{J}$, is not possible for similar-mass binaries and would require a mass ratio ${m}_{1}/{m}_{2}\ensuremath{\lesssim}1/4$.

Structural, Magnetic, and Optical Characterization of ${\rm MnFe}_{2}{\rm O}_{4}$ Nanoparticles Synthesized Via Sol-Gel Method

Nanoparticles of MnFe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> were synthesized via sol-gel method, with calcination processes at 400 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C and 500 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C in air. The effects of the different calcinations in the formation of the crystal structure and magnetic and optical properties were studied with X-ray diffraction (XRD), electron microscopy, SQUID magnetometer, and optical absorption. The XRD studies reveal the formation of a phase corresponding to cubic spinel structure in both samples and the presence of a second phase identified as Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , in the case of the sample with higher temperature treatment. The TEM images of the first sample show small nonuniform nanoparticles with a mean size of 7.8 nm, with a strong tendency to form agglomerates. Magnetization studies as a function of temperature were carried following field-cooled (FC)-Zero-field-cooled (ZFC) routines, where the ZFC curves exhibit blocking temperatures close to 250 K in both cases, and the behavior of the samples below this temperature suggests strong interaction between the particles. In the magnetization as a function of magnetic field studies, the curves display a tendency to saturate at low temperatures and the system shows superparamagnetic behavior above the blocking temperature. Saturation magnetization values (at low temperatures) are low compared to the expected ones, according to the Néel model of collinear spins, this can be attributed to canting effects or the presence of a second antiferromagnetic phase, specifically in the sample treated at 500 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C. No significant differences were observed in the magnetic behavior of the samples. Semiconducting characteristics of the ferrites were confirmed by optical absorption measurements, obtaining an energy gap value close to 2.23 eV at room temperature.

Coexisting Order and Disorder Hidden in a Quasi-Two-Dimensional Frustrated Magnet

Frustrated magnetic interactions in a quasi-two-dimensional [111] slab of pyrochlore lattice were studied. For uniform nearest neighbor (NN) interactions, we show that the complex magnetic problem can be mapped onto a model with two independent degrees of freedom, tricolor and binary sign. This provides a systematic way to construct the complex classical spin ground states with collinear and coplanar bipyramid spins. We also identify "partial but extended" zero-energy excitations amongst the ground states. For nonuniform NN interactions, the coplanar ground state can be obtained from the collinear bipyramid spin state by collectively rotating two spins of each tetrahedron with an angle α in an opposite direction. The latter model with α~30° fits the experimental neutron data from SrCr(9p)Ga(12-9p)O(19) well.

Crystal and magnetic structure and cation distribution of Mn 2− xV 1+ xO 4 spinels ( x = 0, 1/3 and 1)

We synthesized the spinel-type compounds belonging to the Mn 2− x V 1+ x O 4 series with x = 0, 1/3 and 1 as polycrystalline powders. Crystal and magnetic structures were refined using synchrotron X-ray and neutron powder diffraction. At 300 K all members crystallize in the cubic system, space group F d 3 ¯ m , and show a structural transition at low temperature, changing to a tetragonal symmetry (space group I4 1/ amd). Cations distributions between octahedral and tetrahedral sites were refined from neutrons diffraction (ND) data and explained based on crystal field stabilization energies (CFSE) and ionic radii. The magnetic unit cell is the same as the crystallographic one, having identical symmetry relations. The magnetic structure was refined as an arrangement of collinear spins, antiferromagnetically ordered, parallel to the c-axis of the unit cell. The refined site magnetic moments are smaller than those obtained from hysteresis cycles of the M vs. H measurements, indicating that some non-collinear disordered component coexists with the ordered component along the c-axis.

Ab initiotheory of excitons and optical properties for spin-polarized systems: Application to antiferromagnetic MnO

We study quasiparticle and electron-hole pair excitations in the presence of spin polarization within the framework of many-body perturbation theory. The influence of magnetic ordering on linear optical response is examined in detail for collinear spins. Whereas Hedin's expression for the exchange-correlation self-energy in the $GW$ approximation remains diagonal with respect to the one-particle spin quantum number, the Bethe-Salpeter equation becomes more complex: The separation between triplet and singlet excitons no longer holds. The submatrices of the two-particle Hamiltonian are coupled by the matrix elements of the bare Coulomb potential which account for local-field effects. Therefore, the rank of the corresponding eigenvalue problem doubles. Numerical results are computed from first principles for the antiferromagnetic insulator MnO starting from electronic states obtained with nonlocal exchange-correlation potentials. The calculated electronic structure and optical absorption spectra including excitonic and local-field effects are compared with experimental data. The dominance of interatomic transitions between Mn atoms in the interband region of the optical absorption is revealed.

Spin dynamics near the critical doping in weakly superconducting underdopedYBa2Cu3O6.35(Tc=18K)

From neutron inelastic and elastic scattering we have determined the magnetic structure and fluctuations in the $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.35}$ (YBCO) superconductor $({T}_{c}=18\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ near the boundary of the superconducting phase. The long-range ordered collinear spins of the insulating antiferromagnet are replaced by a commensurate central mode arising from slow, isotropically polarized, short-range spin correlations extending over four planar unit cells. The inelastic spectrum up to $30\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ is also broad in wave vector and commensurate. In contrast to the resonance peak of higher-${T}_{c}$ superconductors, the spins exhibit a single overdamped spectrum whose rate of relaxation $\ensuremath{\Gamma}$ decreases on cooling and saturates at $2\ensuremath{\Gamma}=5\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ below $\ensuremath{\sim}50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. As the relaxation rate saturates, the quasistatic spin correlations grow and become resolution limited in energy. The spin susceptibility above $\ensuremath{\sim}50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ follows the same $\ensuremath{\omega}∕T$ scaling relation found for the monolayer ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ system, indicating that the dominant energy scale is set by the temperature. Below $50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ the scale length is geometric and not linked by velocity to dynamic widths. Despite the large differences from an antiferromagnet, we show that integrated intensity conserves the total moment sum rule, and that on cooling the spectral weight transfers from the inelastic spin relaxation to the elastic central peak. There is no observable suppression of the spin fluctuations or central mode upon the onset of superconductivity. The spins respond not to coherent charge pairs but to hole doping, allowing coexistence of glassy short-range spin order with superconductivity. Since the physics of the weakly superconducting system ${\mathrm{YBCO}}_{6.35}$ must connect continuously with that in more strongly superconducting ${\mathrm{YBCO}}_{6.5}$, we find that neither incommensurate stripe-like spin modulations nor a well-defined neutron spin resonance are essential for the onset with doping of pairing in a high-temperature cuprate superconductor.

Semiclassical degeneracies and ordering for highly frustrated magnets in a field

We discuss ground state selection by quantum fluctuations in frustrated magnets in a strong magnetic field. We show that there exist dynamical symmetries -- one a generalisation of Henley's gauge-like symmetry for collinear spins, the other the quantum relict of non-collinear weathervane modes -- which ensure a partial survival of the classical degeneracies. We illustrate these for the case of the kagome magnet, where we find zero-point energy differences to be rather small everywhere except near the collinear `up-up-down` configurations, where there is rotational but not translational symmetry breaking. In the effective Hamiltonian, we demonstrate the presence of a term sensitive to a topological `flux'. We discuss the connection of such problems to gauge theories by casting the frustrated lattices as medial lattices of appropriately chosen simplex lattices, and in particular we show how the magnetic field can be used to tune the physical sector of the resulting gauge theories.

Preparation, crystal and magnetic structure of the double perovskite Ba 2 FeWO 6

Single-phase polycrystalline material of the double perovskite Ba2FeWO6 was prepared and characterized by X-ray and neutron powder diffraction (NPD). The crystal structure was tetragonal with lattice parameters a=b=5.7479(4) A and c=8.1444(9) A at room temperature (295 K). NPD data at 10 K shows the evidence of an antiferromagnetic ordering of the Fe atoms. The reverse Monte Carlo powder (RMCPOW) technique was used to find the magnetic structure, which showed that it is based on a unit cell related to that of the nuclear structure by the propagation vector 0\(\frac\Box1\Box\Box2\Box\)\(\frac\Box1\Box\Box2\Box\) . An ordering of collinear spins was found with alternate layers in the c-direction or in the a-b plane. The model was checked by Rietveld refinement and the magnetic moment of iron was found to be 3.39(2)μB at 10 K.

Evidence of antiferromagnetic ordering of Cu 2+ spins in non-superconducting Bi-2212

Using neutron scattering we have investigated the magnetic correlations in single crystals with the nominal composition Bi 2 Sr 2 PrCu 2 O 8+ δ . We have shown that while the Pr moment remains paramagnetic down to 1.3K, a long-range, three-dimensional, antiferromagnetic ordering of the Cu +2 spins occurs below a Néel temperature T N ∼ 350K. Assuming collinear spins, the experimental data are well accounted for by a model consisting of two antiferromagnetic, Y Ba 2 Cu 3 O 6+ δ -type CuO 2 bilayers, having a three-dimensional coupling of the La 2 CuO 4 -type, i.e. the spins are parallel to the [100] direction and the magnetic propagation vector is q=(0,1,0) . The resulting ordered moment per Cu ion measured at 10K is found to be m Cu =(0.7±0.1) μ B , compatible with a system of lightly doped CuO 2 layers.

Spin structures of tetragonal lamellar copper oxides.

The spin Hamiltonian of tetragonal lamellar antiferromagnets is shown to contain several novel anisotropies. Symmetry allows bond-dependent anisotropic exchange interactions, which lead to (a) interplane mean-field coupling and (b) an in-plane anisotropy which vanishes classically but arises from quantum zero point energy (QZPE). A similar QZPE involving the interplane isotropic interaction prefers collinear spins. Adding also diploar anisotropy, the competition between all these effects explains for the first time the spin structures of many cuprates.