MODELS OF HAMILTONIAN AND LOW-FREQUENCY SPECTRA OF COLLECTIVE EXCITATIONS IN SPIN S = 1 MAGNETICS
Keywords:
SU(3) symmetry, magnet, spin, exchange interaction, Casimir invariant, spectra
Abstract
The paper studies the dynamic description of non-equilibrium processes in single-sublattice and multisublattice magnets with the spin s=1. In case of magnets with the spin s=1 and SU(3) symmetry of the exchange interaction, there are eight magnetic integrals of motion: the spin and the quadrupole matrix. If there are multiple sublattices, the number of additional magnetic quantities characterizing the state increases to sixteen. The presence of the Casimir invariants makes it possible to reduce the number of independent degrees of freedom. Exchange energy models are presented in terms of Casimir invariants corresponding to SO(3) or SU(3) symmetry groups for all four types of magnetic degrees of freedom. For the homogeneous part of the exchange energy, we have found conditions for the existence of local minima, which correspond to equilibrium values of the magnet. Along with the known waves (quadrupole and Goldstone – for the spin nematic), spectra of collective excitations that take into account ferro-quadrupole excitation, quadro-nematic, quadro- antiferromagnetic, and antiferro-nematic waves excitation, are also obtained. In the case of many-sublattice magnetic systems, we have shown that the selected form of the homogeneous energy model allows us to find possible magnetic orderings and to investigate them for stability.Downloads
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References
1. Demishev S.V. et al. Antiferro-quadrupole resonance in CeB 6 // Physica B: Condensed Matter. – 2006. – Vol. 378. – P. 602-603.
2. Takeya H. et al. Spin dynamics and spin freezing behavior in the two-dimensional antiferromagnet NiGa2S4 revealed by Ga-NMR, NQR and μSR measurements // Physical Review B. – 2008. – Vol. 77. – No. 5. – P. 054429.
3. Santini P. et al. Multipolar interactions in f-electron systems: The paradigm of actinide dioxides // Reviews of Modern Physics. – 2009. – Vol. 81. – No. 2. – P. 807.
4. Zibold T. et al. Spin-nematic order in antiferromagnetic spinor condensates // Physical Review A. – 2016.–Vol. 93. – No. 2. – P. 023614.
5. Tsunetsugu H., Arikawa M. Spin nematic phase in S=1 triangular antiferromagnets // Journal of the Physical Society of Japan. – 2006. – Vol. 75. – No. 8. – P. 083701-083701.
6. Fridman Yu.A., Matyunin D.A. Phase states of a 2D non-Heisenberg ferromagnet // Pis'ma v ZHTF. – 2007. – Vol. 33. – No. 22.
7. Kosmachev O.A., Krivtsova A.V., Fridman Y.A. Effect of interionic anisotropy on the phase states and spectra of a non-Heisenberg magnet with S= 1 //Journal of Experimental and Theoretical Physics. – 2016. – Vol. 122. – No. 2. – P. 318-327.
8. Bar'yakhtar V.G. et al. Dynamics and relaxation in spin nematics // Physical Review B. – 2013. – Vol. 87. – No. 22. – P. 224407.
9. Papanicolaou N. Unusual phases in quantum spin-1 systems // Nuclear Physics B. – 1988.–Vol. 305. – No. 3. – P. 367-395.
10. Li P., Shen S.Q. Two-dimensional gapless spin liquids in frustrated SU(N) quantum magnets // New Journal of Physics. – 2004. – Vol. 6. – No. 1. – P. 160.
11. Bernatska J., Holod P. A generalized Landau–Lifshitz equation for an isotropic SU(3) magnet // Journal of Physics A: Mathematical and Theoretical. – 2009. – Vol. 42. – No. 7. – P. 075401.
12. Kovalevsky M. Y. Dynamics of normal and degenerate nonequilibrium states of magnets with spin S=1 // Low Temperature Physics. – 2010. – Vol. 36. – No. 802. – P. 1006-1012.
13. Kovalevsky M. Y. Unitary symmetry and generalization of the Landau–Lifshitz equation for high-spinmagnets // Low Temperature Physics. – 2015. – Vol. 41. – No. 9. – P. 917-937.
14. Bogolyubov N.N. Izbrannyje trudy, Vol. 3. – Kiyev: Naukova dumka, 1971. – Vol. 19. – No. 1.
15. Halperin B.I., Hohenberg P.C. Hydrodynamic theory of spin waves // Physical Review. – 1969. – Vol. 188. – No. 2. – P. 898.
16. Volkov D.V., Zheltukhin A.A., BliokhYu.P. Phenomenological Lagrangian of spin waves // FTT. – 1971. – P. 1668-1678.
17. Andreev A.F., Marchenko V.I. Symmetry and macroscopic dynamics of magnets // Uspekhi Fizicheskikh Nauk. – 1980. - Vol. 130. - No. 1. - P. 39-63.
18. Dzyaloshinskii I.E., Volovick G.E. Poisson brackets in condensed matter physics // Annals of Physics. – 1980. – Vol. 125. – No. 1. – P. 67-97.
19. Landau L., Lifshitz E. On the theory of the dispersion of magnetic permeability in ferromagnetic bodies // Phys. Z. Sowjetunion. – 1935. – Vol. 8. – No. 153. – P. 101-114.
20. Turov E.A. et al. Symmetry and Physical Properties of Antiferromagnets. – Moscow: Fizmatlit, 2001. – Vol. 560.
21. Kovalevsky M.Y., Glushchenko A.V. Quantum states, symmetry and dynamics in degenerate spin s= 1 magnets // Journal of Magnetism and Magnetic Materials. – 2014. – Vol. 355. – P. 192-196.
22. Sheynman O.K. Krichever-Novikov algebras, their representations and applications in geometry and mathematical physics // Sovremennye problemy matematiki. – 2007. – Vol. 10. – P. 3-140.
23. Kovalevsky M.Y., Glushchenko A.V. symmetry and nonlinear dynamics of high spin magnets // Annals of physics. – 2014. – Vol. 349. – P. 55-72.
24. Smerald A., Shannon N. Theory of spin excitations in a quantum spin-nematic state // Physical Review B. – 2013.–Vol. 88. – No. 18. – P. 184430.
2. Takeya H. et al. Spin dynamics and spin freezing behavior in the two-dimensional antiferromagnet NiGa2S4 revealed by Ga-NMR, NQR and μSR measurements // Physical Review B. – 2008. – Vol. 77. – No. 5. – P. 054429.
3. Santini P. et al. Multipolar interactions in f-electron systems: The paradigm of actinide dioxides // Reviews of Modern Physics. – 2009. – Vol. 81. – No. 2. – P. 807.
4. Zibold T. et al. Spin-nematic order in antiferromagnetic spinor condensates // Physical Review A. – 2016.–Vol. 93. – No. 2. – P. 023614.
5. Tsunetsugu H., Arikawa M. Spin nematic phase in S=1 triangular antiferromagnets // Journal of the Physical Society of Japan. – 2006. – Vol. 75. – No. 8. – P. 083701-083701.
6. Fridman Yu.A., Matyunin D.A. Phase states of a 2D non-Heisenberg ferromagnet // Pis'ma v ZHTF. – 2007. – Vol. 33. – No. 22.
7. Kosmachev O.A., Krivtsova A.V., Fridman Y.A. Effect of interionic anisotropy on the phase states and spectra of a non-Heisenberg magnet with S= 1 //Journal of Experimental and Theoretical Physics. – 2016. – Vol. 122. – No. 2. – P. 318-327.
8. Bar'yakhtar V.G. et al. Dynamics and relaxation in spin nematics // Physical Review B. – 2013. – Vol. 87. – No. 22. – P. 224407.
9. Papanicolaou N. Unusual phases in quantum spin-1 systems // Nuclear Physics B. – 1988.–Vol. 305. – No. 3. – P. 367-395.
10. Li P., Shen S.Q. Two-dimensional gapless spin liquids in frustrated SU(N) quantum magnets // New Journal of Physics. – 2004. – Vol. 6. – No. 1. – P. 160.
11. Bernatska J., Holod P. A generalized Landau–Lifshitz equation for an isotropic SU(3) magnet // Journal of Physics A: Mathematical and Theoretical. – 2009. – Vol. 42. – No. 7. – P. 075401.
12. Kovalevsky M. Y. Dynamics of normal and degenerate nonequilibrium states of magnets with spin S=1 // Low Temperature Physics. – 2010. – Vol. 36. – No. 802. – P. 1006-1012.
13. Kovalevsky M. Y. Unitary symmetry and generalization of the Landau–Lifshitz equation for high-spinmagnets // Low Temperature Physics. – 2015. – Vol. 41. – No. 9. – P. 917-937.
14. Bogolyubov N.N. Izbrannyje trudy, Vol. 3. – Kiyev: Naukova dumka, 1971. – Vol. 19. – No. 1.
15. Halperin B.I., Hohenberg P.C. Hydrodynamic theory of spin waves // Physical Review. – 1969. – Vol. 188. – No. 2. – P. 898.
16. Volkov D.V., Zheltukhin A.A., BliokhYu.P. Phenomenological Lagrangian of spin waves // FTT. – 1971. – P. 1668-1678.
17. Andreev A.F., Marchenko V.I. Symmetry and macroscopic dynamics of magnets // Uspekhi Fizicheskikh Nauk. – 1980. - Vol. 130. - No. 1. - P. 39-63.
18. Dzyaloshinskii I.E., Volovick G.E. Poisson brackets in condensed matter physics // Annals of Physics. – 1980. – Vol. 125. – No. 1. – P. 67-97.
19. Landau L., Lifshitz E. On the theory of the dispersion of magnetic permeability in ferromagnetic bodies // Phys. Z. Sowjetunion. – 1935. – Vol. 8. – No. 153. – P. 101-114.
20. Turov E.A. et al. Symmetry and Physical Properties of Antiferromagnets. – Moscow: Fizmatlit, 2001. – Vol. 560.
21. Kovalevsky M.Y., Glushchenko A.V. Quantum states, symmetry and dynamics in degenerate spin s= 1 magnets // Journal of Magnetism and Magnetic Materials. – 2014. – Vol. 355. – P. 192-196.
22. Sheynman O.K. Krichever-Novikov algebras, their representations and applications in geometry and mathematical physics // Sovremennye problemy matematiki. – 2007. – Vol. 10. – P. 3-140.
23. Kovalevsky M.Y., Glushchenko A.V. symmetry and nonlinear dynamics of high spin magnets // Annals of physics. – 2014. – Vol. 349. – P. 55-72.
24. Smerald A., Shannon N. Theory of spin excitations in a quantum spin-nematic state // Physical Review B. – 2013.–Vol. 88. – No. 18. – P. 184430.
Published
2017-08-01
Cited
How to Cite
Glushchenko, A. V., & Kovalevsky, M. Y. (2017). MODELS OF HAMILTONIAN AND LOW-FREQUENCY SPECTRA OF COLLECTIVE EXCITATIONS IN SPIN S = 1 MAGNETICS. East European Journal of Physics, 4(2), 4-10. https://doi.org/10.26565/2312-4334-2017-2-01
Section
Original Papers
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