Studying Small Oscillations of Spin Vector of The Ferromagnetic With Spin S=1

ziad Rustum, Amir TFIHA

Abstract


يهدف البحث إلى دراسة الأمواج السبينيّة في المغانط الحديدية ذات سبين  S=1 في جملة الإحداثيات المركبة, ويقسم البحث إلى ثلاثة محاور:

يتلخّص  المحور الأول في إيجاد جملة نقل تمكننا من دراسة ظاهرة مجهريّة (ميكروسكوبيّة) , وهي الأمواج السبينيّة بطريقة كلاسيكية ، والخطوة الأولى تكمن في إيجاد التابع الموجي المناسب في الإحداثيات المختارة ثم الهاملتوني واللاغرانجي ثم المعادلات الديناميكية بالشكل العام, واختبار صحة تلك الجملة من خلال التأكد من أنها تحقق شروط المسألة .

المحور الثاني هو استخدام تلك المنظومة (تسمّى الطريقة شبه الكلاسيكية) لدراسة الأمواج السبينيّة , واستنتاج علاقات التشتّت والسويّات الطاقيّة , ثم مناقشة تلك النتائج من مختلف الجوانب والتأثيرات.

ويتضمّن المحور الثالث:

1-إيجاد السويّة الأساسية , نظراً لأنّ تحديدها يعطي فكرة عن طاقة الجملة.

2-إيجاد معادلات الحركة المرتبطة بالزمان والمكان(المعادلات الزمكانيّة) . وتكمن أهميتها في أنّها تمكّننا من جهة من معرفة تغيّر إحداثيات السبين بتابعية الزمن , ومن جهة أخرى معرفة سرعة انتشار الأمواج وفق المحور المختار, وارتباط تغيّر حدود القطاعات المغناطيسية بانتشار الأمواج السبينيّة وسرعتها.

The aim of this paper is to study spin waves in ferromagnetic with spin (S=1/2) in complex coordinates system, the paper is divided into three sections:

The First section is about finding a transportation system that enables us to study a microscopic phenomenon ,its the spin waves in a classical way. The first step in this transportation system lies in finding the suitable wave function in the chosen coordinates, then the Hamiltonian and the Lagrangian then after that the dynamic equations in the general form, and testing the credibility of the system by making sure that it follow the rules of the study.

The Second section is about the use of that system, which is called the Simi classic way of studying the spin waves, and finding the dispersing equations and energetic levels then discussing the resultes from different ways and effects.

The Third section includes 1- Finding the ground state (basic) and the importance of finding the energy of the ground state lies in its direct effect on the system's energy.2- Finding the movement equations connected with time and place (the time-place equations). Its importance lies in two points; the first one is that it enables us to find the variance in the coordinates of the spin according to time. The second point is to know the spread speed of spin waves according to the chosen axle and the connection of the variation of domains (the magnetic sectors) with the spreading of spin waves and its speed.


References


Landau L.Q – LEAVSHETS E.M. – NON RELATIVITY THEORY ON QUANTOM MECHANICS, Tom3, Moscow, 1989.

Ziead Rostom, SPIN WAVES IN FERROMAGNETIC WITH SPIN S=1/2 IN THE REAL COORDINATES, Tishreen University Journal of science, Folder 33 issue, no.1, 2010.

Kittel ch. – INTRODUCTION TO SOLID STATE PHYSICS, seventh edition, Printed USA, John Wiley 8 sons, inc. 1996.

Davidov A.C. SOLID STATE THEORY, Nauka Moscow 1976.

Kh. O. Abdulloev and Kh. Kh. Muminov, “COHERENT STATES OF SU(4) GROUP IN REAL PARAMETERIZATION AND HAMILTONIAN EQUATIONS OF MOTION,” Reports of Tajikistan Academy of science, vol. 36, no. 6, I993 (Russian).

Davidov A.C – QUANTUM MECHANICS, Nauka Moscow 1972.

FEYNMAN . R.P – Leighton . R.B – Matthew Sands – THE FEYNMAN LECTURES ON PHYSICS, printed Mer. Moscow 1978.

Y. Yousefi, et.al, Semi classical modeling of isotropic Non-Heisenberg magnets for spin S=1 and linear quadrupole excitation dynamics,arXiv:1304.0245,2013.

Ziead Rostom, THE SEMI CLASSIC DESCRIPTION AND DYNAMIC EQUATIONS OF SPIN WAVES IN FERROMAGNETIC WITH SPIN S-1/2 COMPLEX COORDINATES SYSTEM. Al – baas University journal of science, 2013.

Akuezer A. – Daria kmek V.G- SPIN WAVES, Nauaka Moscow, 1976 [360- 368].

Krenchic .G.C – PHYSICS OF MAGNETICAL PHENOMENA Moscow University, 1985.

SB Doma, UNITARY SCHEME MODEL STUDY OF HE-4 WITH THE GOGNY, PIRES AND DETOURREIL INTERACTION. Helvetica Physica Acta 58 (6), 1985,1072-1077‏.

SB Doma, FN El-Gammal‏,Application of variational Monte Carlo method to the confined helium atom‏. Journal of Theoretical and Applied Physics 6 (1), 2012,28.‏

SB Doma, FN El-Gammal‏, Atomic Properties of the Two-Electron System using Variational Monte Carlo Technique.‏Acta Physica Polonica, A. 122 (1)‏ 2012.

SB Doma, MM Amin‏.The single particle Schroedinger fluid and moments of inertia of the nuclei 24 Mg, 25 Al, 27 Al, 183 W and 238 Pu‏.International Journal of Modern Physics E 11 (05), 2002,455-461‏.

SB Doma, NA El-Nohy, KK Gharib, The ground-state characteristics of deuteron using Gaussian potentials‏.Helvetica Physica Acta 69 (2), 1996,90-104‏.

TI Kopalejshvili, IZ Machabeli, SB Doma‏,Study on the A= 6 nuclei in basis of the unitarity scheme model‏. Yadernaya Fizika 21 (4), 1975,720-729‏.

SB Doma, HS El-Gendy‏, Some deformation properties of the even–even ytterbium, hafnium and tungsten nuclei‏. International Journal of Modern Physics E 21 (09), 2012, 1250077‏.

SB Doma , Ground state characteristics of the light nuclei with A≤ 6 on the basis of the translation invariant shell model by using nucleon-nucleon interaction‏. High Energy Physics and Nuclear Physics 26 (9), 2002, 941-948‏.

SB Doma, Study of Nuclei with A= 5 on the Basis of the Unitary Scheme Model‏ International Journal of Modern Physics E 12 (03), 2003,421-429‏.

SB Domaa, MO Shakerb, M Faragb, FN El-Gammalc , Ground States of Helium Atom and Hydrogen Negative Ion in the Presence of Magnetic Field Using Variational Monte Carlo Technique‏. trial 50 (1), 2014.

SB Doma, FN El-Gammal, Applications of the variational Monte Carlo method to the two-electron atom‏. Appl. Math. Inf. Sci 5, 2011, 315S-325S‏.

SB Doma, AFM El-Zebidy, MA Abdel-Khalik‏, The mean lifetime of the β-decay and the nuclear magnetic dipole moment for nuclei with A= 7‏. Journal of Physics G: Nuclear and Particle Physics 34 (1), 2006,27‏.

SB Doma, Unitary scheme model calculations of a= 6 nuclei with realistic interactions‏. Ukrayins' kij Fyizichnij Zhurnal 42 (3),1997, 279-287‏.

SB Doma, IH El-Sirafy, AH El-Sharif‏, Two-Dimensional Fluid Flow Past a Rectangular Plate with Variable Initial Velocity‏.Alexandria Journal of Mathematics 1 (2), 2010,36-57‏.

SB Doma, MM Amin‏, Single Particle Schrödinger Fluid and Moments of Inertia of the Even-Even Uranium Isotopes‏. The Open Applied Mathematics Journal 3 (1)‏ ,2009.

SB Doma, AFM El-Zebidy , CLUSTER–CLUSTER POTENTIALS FOR THE LITHIUM NUCLEI‏. International Journal of Modern Physics E 14 (02), 2005, 189-195‏.

SB Doma‏, Unitary scheme model study of triton with the Hu and Massey potential‏. Indian Journal of Pure and Applied Mathematics 13 (12), 1982,1455-1459‏.

SM Salem, SB Doma‏,The binding energy for S-state wave function for triton.‏ Bull. Fac. Sci. Alexandria 11, 17, 1971.

SB Doma, M Abu-Shady, FN El-Gammal, AA Amer‏, Ground states of the hydrogen molecule and its molecular ion in the presence of a magnetic field using the variational Monte Carlo method‏. Molecular Physics 114 (11), 2016,1787-1793‏.

SB Doma, MM Hammad, Classification, selection rules, and symmetry properties of the Clebsch-Gordan coefficients of symmetric group‏. Journal of Mathematical Physics 53 (3), 2012,033511‏.

SB Doma, KA Kharroube, AD Tefiha, HS El-Gendy‏, The Deformation Structure of the Even-Even p-and sd Shell Nuclei‏. Alexandria Journal of Physics 1, 2011, 1-13‏.

SB Doma, IS Ismail , Calculations of the Binding States In Deformed Nuclei‏. ‏Bulletin of the Faculty of Science 25 (1), 1985,69‏.

SB Doma, Salman, H, Tfiha, A D. ,The octupole correlations in the 209 Bi, 209 Pb nuclei, Tishreen University Journal for Studies and Scientific Research 25 (13), 2003,237-245‏.

SB Doma, H.A. Salman, A.D. Tfiha‏, The quadrupole moments of the deformed nuclei in the P-Shell‏. Tishreen University Journal for Studies and Scientific Research 25 (13), 2003, 237-245‏


Full Text: PDF

Refbacks

  • There are currently no refbacks.


رئيس التحرير: الأستاذ الدكتور هاني محمود شعبان

هيئة التحرير , أمين التحرير: د.أمير درويش تفيحة