AUTHORS: Rafał Michalski, Jakub Zygadło, Marek Karaś
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ABSTRACT: We present main algorithms of new software application developed to calculate magnetic, spectral and calorimetric properties of materials under Crystal Electric Field (CEF) and Mean Field Approximation paradigm. The novelty of our approach lies in the automatic construction of Hamiltonian matrices and computation of true 3-dimensional properties of the material in wide range of temperatures also around the phase transition temperature. User defined calculation rules as real or complex matrices and two calculation spaces (|JJz> or |LSLzSz>) to define interactions, utilize single diagonalization procedure in all cases. Our software predicts thermal dependent properties of materials in isostructural series of compounds, such as: magnetic moment in ordered state, paramagnetic susceptibility, specific heat, entropy and absorption spectra. Calculated properties are closely related to local symmetry of crystal surrounding of paramagnetic ion. Obtained angular momentum coordinates of paramagnetic ions makes it possible to calculate anisotropy coefficients as a result of dynamic calculations using Mean Field Approximation scheme.
KEYWORDS: Crystal Electric Field, Spin-Orbit coupling, Hamiltonian diagonalization, Mean Field Approximation, CEF, MFA, Atomic Matters
REFERENCES:
[1] R. Michalski, J. Zygadło, Proc. 18th Int. Conf. on Physics, Mathematics and Computer Science – Dubai(2016) http://waset.org/publications/10004653/pdf
[2] Software website: www.atomicmatters.eu
[3] H. A. Bethe, Ann. Phys. Lpz. 3 (1929) 133.
[4] J. Elliot, K. W. H. Stevens, Proc. Roy. Soc. A 215 (1953) 437.
[5] J. Elliot, K. W. H. Stevens, Proc. Roy. Soc. A 218 (1953) 553.
[6] M. T. Hutchings, Solid State Phys. 16, New York (1964) 227.
[7] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Clarendon Press, Oxford (1970).
[8] B. G. Wybourne, Symmetry Principles and Atomic Spectroscopy, J. Wiley and Sons, New York (1970).
[9] R. J. Radwański, Acta Phys. Pol. B 31 (2000) 3079.
[10] P. O. Ribeiro et al. J. Magn. Magn. Mater. 379 (2015) 112.
[11] B. Szpunart, P.-A. Lindgard, J. Phys. F: Metal Phys. 9, No. 3. (1979).
[12] J. J. M. Franse, R. J. Radwanski; Magnetic properties of binary rare-earth… in Handbook of Magnetic Materials Vol 7. Edited K. H. J. Bushow (1993) 307.
[13] C. Min, S. Lee, S.-G. Kim, J. Korean Soc. Math. Educ. B: Pure Appl. Math. 18, No. 3 (2011) 185.
[14] D. Kincaid, W. Cheney, Numerical analysis, American Mathematical Society, Providence (2002).
[15] H. Park, V. Hari, BIT Num. Math. 33 (1993) 158.
[16] V. K. Pecharsky, K. A. Gschneidner, A. O. Pecharsky, A. M. Tishin, Phys. Rev. B 64, (2001) 144406.
[17] P. J. von Ranke et al., Journal Of Applied Physics 104 (2008) 093906.
[18] L. A. Gil, J.C.P. Campoy, E.J.R. Plaza, M.V. de Souza, Journal of Magnetism and Magnetic Materials 409 (2016) 45.
[19] M. Patra, S. Majumdar and S. Giri, Y. Xiao, T. Chatterji, Magnetic and magnetoresistive properties of cubic Laves phase HoAl2 single crystal (2011) arXiv:1107.1975
[20] R. M. Sternheimer, Phys. Rev. 146 (1966) 140.
[21] S. Edvardsson, M. Klintenberg, Journal of Alloys and Compounds 275-277 (1998) 230.