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1

Pavlov, Rossen L., Yavor I. Delchev, Alexander I. Kuleff, and Jean Maruani. "Théorie de la fonctionnelle de la densité avec spin. VIII. Équation d'Euler-Lagrange pour f(r)." Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy 325, no. 12 (1997): 719–26. http://dx.doi.org/10.1016/s1251-8069(97)82337-8.

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2

Gaha, Mehdi, Abdullah Abu Jamea, Fahad Albader, and Hamdy Hassan. "Amélioration de la détection des lésions médullaires de sclérose en plaques par l’utilisation des images de fusion des séquences densité protonique/T2 Dual Echo Fast Spin Echo." Journal of Neuroradiology 44, no. 2 (2017): 94. http://dx.doi.org/10.1016/j.neurad.2017.01.052.

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3

Pang, Xiaoyan, Chen Feng, and Xinying Zhao. "Evolution of spin density vectors in a strongly focused composite field." Chinese Optics Letters 19, no. 2 (2021): 022601. http://dx.doi.org/10.3788/col202119.022601.

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4

Bruno, Giovanna, Giovanni Macetti, Leonardo Lo Presti, and Carlo Gatti. "Spin Density Topology." Molecules 25, no. 15 (2020): 3537. http://dx.doi.org/10.3390/molecules25153537.

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Despite its role in spin density functional theory and it being the basic observable for describing and understanding magnetic phenomena, few studies have appeared on the electron spin density subtleties thus far. A systematic full topological analysis of this function is lacking, seemingly in contrast to the blossoming in the last 20 years of many studies on the topological features of other scalar fields of chemical interest. We aim to fill this gap by unveiling the kind of information hidden in the spin density distribution that only its topology can disclose. The significance of the spin d
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5

Aly, Abeer E., and D. P. Rai. "Spin Density for Intermetallic Compounds." International Journal of Computational Physics Series 1, no. 1 (2018): 97–101. http://dx.doi.org/10.29167/a1i1p97-101.

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We first performed a pure spin-polarized calculation on Nd2Fe14B using the self-consistent Full Potential Linearized Augmented Plane Wave (FPLAPW). The total charge density and the spin density calculated by taking the sum or the difference of spin-up and spin-down charge densities, respectively. In this paper, we present the spin and charge density contours for rare-earth transition metal compounds e.g. Nd2Fe14B in the (001) and (110) planes using spin-polarized only. The charge density map and the spin density map on the (001) and (110) plane of the tetragonal cell show the evidence for cova
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6

Lee, Jounghun, and Ue‐Li Pen. "Galaxy Spin Statistics and Spin‐Density Correlation." Astrophysical Journal 555, no. 1 (2001): 106–24. http://dx.doi.org/10.1086/321472.

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7

Soncini, A., and P. Lazzeretti. "Nuclear spin-spin coupling density in molecules." Journal of Chemical Physics 118, no. 16 (2003): 7165. http://dx.doi.org/10.1063/1.1561871.

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8

Becker, Ch, J. Hafner, and R. Lorenz. "Local spin-density theory of spin-glasses." Journal of Magnetism and Magnetic Materials 157-158 (May 1996): 619–21. http://dx.doi.org/10.1016/0304-8853(95)01021-1.

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9

Maki, Kazumi, and Attila Virosztek. "Fröhlich conduction in spin density waves and field induced spin density waves." Journal of Magnetism and Magnetic Materials 90-91 (December 1990): 758–62. http://dx.doi.org/10.1016/s0304-8853(10)80276-8.

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10

Fuentealba, P., and Junia Melin. "Atomic spin-density polarization index and atomic spin-density information entropy distance." International Journal of Quantum Chemistry 90, no. 1 (2002): 334–41. http://dx.doi.org/10.1002/qua.994.

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11

Gearhart, C. C., and J. C. Hicks. "Self-consistent spin-spin and density-density correlations in the Hubbard model." Physical Review B 52, no. 11 (1995): 7787–90. http://dx.doi.org/10.1103/physrevb.52.7787.

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12

Capelle, K., and L. N. Oliveira. "Density-functional approach to spin-density waves." Europhysics Letters (EPL) 49, no. 3 (2000): 376–82. http://dx.doi.org/10.1209/epl/i2000-00159-8.

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13

Long, M. W., and W. Yeung. "Spin waves in multiple-spin-density-wave systems." Journal of Physics C: Solid State Physics 19, no. 9 (1986): 1409–29. http://dx.doi.org/10.1088/0022-3719/19/9/012.

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14

Chen, X. M., and A. W. Overhauser. "Anisotropic spin susceptibility of spin-density-wave states." Physical Review B 42, no. 16 (1990): 10601–9. http://dx.doi.org/10.1103/physrevb.42.10601.

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15

Shurigin, V. J., and R. M. Yulmetyev. "Spin relaxation of spin density fluctuations in liquids." Physics Letters A 141, no. 3-4 (1989): 196–200. http://dx.doi.org/10.1016/0375-9601(89)90788-3.

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16

Di Fabrizio, E., G. Mazzone, C. Petrillo, and F. Sacchetti. "Spin density of ordered FeCo: A failure of the local-spin-density approximation." Physical Review B 40, no. 14 (1989): 9502–7. http://dx.doi.org/10.1103/physrevb.40.9502.

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17

SABLIKOV, V. A., and S. V. POLYAKOV. "SPIN-CHARGE STRUCTURE OF QUANTUM WIRES COUPLED TO ELECTRON RESERVOIRS." International Journal of Nanoscience 02, no. 06 (2003): 487–94. http://dx.doi.org/10.1142/s0219581x03001590.

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We report the correlated charge and spin density distributions in a quantum wire coupled to electron reservoirs. It is found that charging the wire because of the electron density redistribution between the wire and reservoirs results in the increase of the critical electron density, below which the spontaneous spin polarization appears. The distributions of the electron densities with spin up and spin down along the wire have components oscillating in opposite phases with the wave vector 2kF, kF being the Fermi wave vector. As a result the antiferromagnetic spin order appears, with one of the
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18

Wang, Jiahu, and Vedene H. Smith, Jr. "Ab initio Study of the Spin Density of Nitroxide Radicals." Zeitschrift für Naturforschung A 48, no. 1-2 (1993): 109–16. http://dx.doi.org/10.1515/zna-1993-1-225.

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Abstract The spin densities of the nitroxides H2NO, (CH3)HNO and (CH3)2 NO have been studied by iterative CI methods. Calculations at different geometries with various basis sets were performed. It is found that the spin distribution is delocalized within the N-O group, and substitution of the hydrogen atoms on the nitroxyl group by methyl groups changes the spin distribution significantly. Electron correlation, as well as the basis-set quality, plays an important role for the fluctuation of spin populations in the nitroxide radicals. It has been found that the spin density map can be predicte
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19

Yamanaka, S., D. Yamaki, Y. Shigeta, H. Nagao, and K. Yamaguchi. "Noncollinear spin density functional theory for spin-frustrated and spin-degenerate systems." International Journal of Quantum Chemistry 84, no. 6 (2001): 670–76. http://dx.doi.org/10.1002/qua.1422.

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20

Yamase, Hiroyuki, and Roland Zeyher. "Spin nematic fluctuations near a spin-density-wave phase." New Journal of Physics 17, no. 7 (2015): 073030. http://dx.doi.org/10.1088/1367-2630/17/7/073030.

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21

Kaneshita, Eiji, Masanori Ichioka, and Kazushige Machida. "Spin and Charge Excitations in Incommensurate Spin Density Waves." Journal of the Physical Society of Japan 70, no. 3 (2001): 866–76. http://dx.doi.org/10.1143/jpsj.70.866.

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22

Tsunoda, Y., N. Hiruma, J. L. Robertson, and J. W. Cable. "Spin-density-wave clusters in PdMn spin-glass alloys." Physical Review B 56, no. 17 (1997): 11051–55. http://dx.doi.org/10.1103/physrevb.56.11051.

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23

Kaiser, A. B., A. M. Oleś, and J. Major. "Chromium: Spin-split state versus spin-density-wave state." Physical Review B 45, no. 13 (1992): 7477–80. http://dx.doi.org/10.1103/physrevb.45.7477.

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24

F̊ak, B., and Henry R. Glyde. "Density and spin-density excitations in normal-liquidHe3." Physical Review B 55, no. 9 (1997): 5651–54. http://dx.doi.org/10.1103/physrevb.55.5651.

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25

Gillon, B., and Y. Ellinger. "Theoretical spin density in nitroxides." Molecular Physics 63, no. 6 (1988): 967–79. http://dx.doi.org/10.1080/00268978800100711.

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26

Daemen, L. L., and A. W. Overhauser. "Superconductivity and spin-density waves." Physical Review B 39, no. 10 (1989): 6431–40. http://dx.doi.org/10.1103/physrevb.39.6431.

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27

Maki, Kazumi. "Magnetotransport in spin-density waves." Physical Review B 47, no. 17 (1993): 11506–9. http://dx.doi.org/10.1103/physrevb.47.11506.

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28

Brown, Stuart, and George Grüner. "Charge and Spin Density Waves." Scientific American 270, no. 4 (1994): 50–56. http://dx.doi.org/10.1038/scientificamerican0494-50.

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29

Lu, S. T., Qiang Jiang, and Haruo Kojima. "Spin-density relaxation in superfluidA13." Physical Review Letters 62, no. 14 (1989): 1639–42. http://dx.doi.org/10.1103/physrevlett.62.1639.

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30

Chaikin, P. M. "Field Induced Spin Density Waves." Journal de Physique I 6, no. 12 (1996): 1875–7898. http://dx.doi.org/10.1051/jp1:1996169.

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31

Paciaroni, A., C. Petrillo, and F. Sacchetti. "Spin density distribution in Ni95Mn5." Solid State Communications 103, no. 2 (1997): 97–101. http://dx.doi.org/10.1016/s0038-1098(97)00148-8.

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32

Gonzalez-Jimenez, F., E. Jaimes, A. Rivas, L. D'Onofrio, J. Gonzalez, and M. Quintero. "New spin-density waves systems:." Physica B: Condensed Matter 259-261 (January 1999): 987–89. http://dx.doi.org/10.1016/s0921-4526(98)00930-2.

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33

Jacob, Christoph R., and Markus Reiher. "Spin in density-functional theory." International Journal of Quantum Chemistry 112, no. 23 (2012): 3661–84. http://dx.doi.org/10.1002/qua.24309.

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34

Bai, Yujoung, Chang-Mo Ryu, Chul Koo Kim, Sang Koo You, and Kyun Nahm. "Spin-density fluctuation in paramagnets." Physical Review B 54, no. 1 (1996): 33–36. http://dx.doi.org/10.1103/physrevb.54.33.

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35

Fenton, E. W., and H. Chu. "Superconductivity and spin density waves." Phase Transitions 28, no. 1-4 (1990): 27–31. http://dx.doi.org/10.1080/01411599008207929.

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36

Worsnop, S. Kent, Russell J. Boyd, Cecilia Sarasola, and Jesus M. Ugalde. "A spin-density polarization index." Journal of Chemical Physics 108, no. 7 (1998): 2824–30. http://dx.doi.org/10.1063/1.475673.

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37

Syromyatnikov, A. G. "Electro-gravity spin density waves." International Journal of Geometric Methods in Modern Physics 14, no. 10 (2017): 1750146. http://dx.doi.org/10.1142/s0219887817501468.

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It is known that some string models predict that strong bursts of gravitational radiation which should be detectable by LIGO, VIRGO and LISA detectors are accompanied by cosmologic gamma-ray bursts (GRBs). GRBs of low-energy gamma ray are associated with core-collapse supernovae (SN). However, measurements of the X-ray afterglow of very intense GRBs (allow a critical test of GRB theories) disagree with that predicted by widely accepted fireball internal–external shocks models of GRBs. It is also known that in a system of a large number of fermions, pairs of gravitational interaction occur on s
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38

Petrillo, C., and F. Sacchetti. "Spin density in Co65Pd35 alloy." Il Nuovo Cimento D 7, no. 1 (1986): 46–54. http://dx.doi.org/10.1007/bf02452394.

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39

Campi, Gaetano, Nicola Poccia, Boby Joseph, et al. "Direct Visualization of Spatial Inhomogeneity of Spin Stripes Order in La1.72Sr0.28NiO4." Condensed Matter 4, no. 3 (2019): 77. http://dx.doi.org/10.3390/condmat4030077.

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In several strongly correlated electron systems, the short range ordering of defects, charge and local lattice distortions are found to show complex inhomogeneous spatial distributions. There is growing evidence that such inhomogeneity plays a fundamental role in unique functionality of quantum complex materials. La1.72Sr0.28NiO4 is a prototypical strongly correlated perovskite showing spin stripes order. In this work we present the spatial distribution of the spin order inhomogeneity by applying micro X-ray diffraction to La1.72Sr0.28NiO4, mapping the spin-density-wave order below the 120 K o
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40

Gatti, Carlo, Ahmed Orlando, and Leonardo Lo Presti. "Insights on spin-polarization via the spin density Source Function." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C281. http://dx.doi.org/10.1107/s2053273314097186.

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The Source Function (SF) [1-3], enables one to view chemical bonding and other chemical paradigms from a new perspective and using only information from the electron density observable and its derivatives. We show how this tool may be straightforwardly applied to another important observable, the electron spin density, which analogously to the electron density may be locally interpreted in terms of a cause-effect relationship of contributions from the atoms of a molecular or crystalline system. Application of the spin density SF to molecules in vacuo and to slab or crystals, is made possible t
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41

Deutsch, Maxime, Béatrice Gillon, Nicolas Claiser, Jean-Michel Gillet, Claude Lecomte, and Mohamed Souhassou. "First spin-resolved electron distributions in crystals from combined polarized neutron and X-ray diffraction experiments." IUCrJ 1, no. 3 (2014): 194–99. http://dx.doi.org/10.1107/s2052252514007283.

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Since the 1980s it has been possible to probe crystallized matter, thanks to X-ray or neutron scattering techniques, to obtain an accurate charge density or spin distribution at the atomic scale. Despite the description of the same physical quantity (electron density) and tremendous development of sources, detectors, data treatment softwareetc., these different techniques evolved separately with one model per experiment. However, a breakthrough was recently made by the development of a common model in order to combine information coming from all these different experiments. Here we report the
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42

Sharma, Prachi, Jie J. Bao, Donald G. Truhlar, and Laura Gagliardi. "Multiconfiguration Pair-Density Functional Theory." Annual Review of Physical Chemistry 72, no. 1 (2021): 541–64. http://dx.doi.org/10.1146/annurev-physchem-090419-043839.

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Kohn-Sham density functional theory with the available exchange–correlation functionals is less accurate for strongly correlated systems, which require a multiconfigurational description as a zero-order function, than for weakly correlated systems, and available functionals of the spin densities do not accurately predict energies for many strongly correlated systems when one uses multiconfigurational wave functions with spin symmetry. Furthermore, adding a correlation functional to a multiconfigurational reference energy can lead to double counting of electron correlation. Multiconfiguration p
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43

Najdi, M. A., J. M. AL-Mukh, and H. A. Jassem. "Theoretical Investigation in Coherent Manipulation throughout the Calculation of the Local Density of States in FM-DQD-FM Device." Materials Science Forum 1039 (July 20, 2021): 451–69. http://dx.doi.org/10.4028/www.scientific.net/msf.1039.451.

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In this work, theoretical investigation in coherent manipulation throughout local density of states calculation for serially coupled double quantum dots embedded between ferromagnetic leads (FM-QD1-QD2-FM) by using the non-equilibrium Green's function approach. Since the local density of states are formulated incorporating the spin polarization and the type of spin configuration on the leads. Our model incorporates the inter-dot hopping, the intra-dot Coulomb correlation, the spin exchange energy and the coupling interactions between the quantum dots and leads. The results concerned to the par
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44

Wei, Huihui, Jiatian Guo, Xiaobo Yuan, and Junfeng Ren. "Spin Polarization Properties of Two Dimensional GaP3 Induced by 3d Transition-Metal Doping." Micromachines 12, no. 7 (2021): 743. http://dx.doi.org/10.3390/mi12070743.

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The electronic structure and spin polarization properties of monolayer GaP3 induced by transition metal (TM) doping were investigated through a first-principles calculation based on density functional theory. The calculation results show that all the doped systems perform spin polarization properties, and the Fe–doped system shows the greatest spin polarization property with the biggest magnetic moment. Based on the analysis from the projected density of states, it was found that the new spin electronic states originated from the p–d orbital couplings between TM atoms and GaP3 lead to spin pol
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45

Glaser, Rainer, and Godwin Sik Cheung Choy. "Electron and spin density analysis of spin-projected unrestricted Hartree-Fock density matrixes of radicals." Journal of Physical Chemistry 97, no. 13 (1993): 3188–98. http://dx.doi.org/10.1021/j100115a022.

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46

Iyetomi, Hiroshi, and Setsuo Ichimaru. "Density-functional study of antiferromagnetic spin correlations in layered electrons: Conductive spin-density-wave states." Physical Review B 49, no. 17 (1994): 11900–11909. http://dx.doi.org/10.1103/physrevb.49.11900.

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47

Galkin, Vladimir Yu, Wilson A. Ortiz, and Naushad Ali. "Spin glass-like behavior in spin-density-wave CrCoMn alloys." Journal of Magnetism and Magnetic Materials 258-259 (March 2003): 413–15. http://dx.doi.org/10.1016/s0304-8853(02)01076-4.

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48

López-Sandoval, R., and G. M. Pastor. "Spin dependence of density functionals that respect spin-rotational invariance." Journal of Magnetism and Magnetic Materials 294, no. 2 (2005): e17-e20. http://dx.doi.org/10.1016/j.jmmm.2005.03.046.

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49

Malkin, Vladimir G., Olga L. Malkina, and Dennis R. Salahub. "Calculation of spin—spin coupling constants using density functional theory." Chemical Physics Letters 221, no. 1-2 (1994): 91–99. http://dx.doi.org/10.1016/0009-2614(94)87023-3.

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50

Lantto, Perttu, Juha Vaara, and Trygve Helgaker. "Spin–spin coupling tensors by density-functional linear response theory." Journal of Chemical Physics 117, no. 13 (2002): 5998–6009. http://dx.doi.org/10.1063/1.1502243.

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