stancil - spin waves - theory and applications (springer, 2009)

[...]... configurations illustrated in Figure 1.1 are the most common, helical and complex-canted configurations are also possible Further details on magnetic materials are found in [1–4] and in standard texts on solid-state physics such as Ashcroft and Mermin [5] and Kittel [6] D.D Stancil, A Prabhakar, Spin Waves, DOI 10.1007/97 8-0 -3 8 7-7 786 5-5 1 c Springer Science+Business Media, LLC 2009 1 2 1 Introduction... Note that J1 and J2 do not have definite projections along z This is an illustration of the result that J1z and J2z are not good quantum numbers for the state ψj1 j2 jm Goudsmit and Uhlenbeck correctly interpreted the results of the Stern– Gerlach experiment and introduced the possibility of half-integer spin z Jz J J1 J2 Fig 1.8 Vector model for visualizing the random precession of J, J1 , and J2 22... Contents XV 10 Novel Applications 309 10.1 Nano-Contact Spin- Wave Excitations 309 10.1.1 Current-Induced Spin Torque 310 10.1.2 Magnetic Precession 315 10.2 Magnetic Precession in Patterned Structures 322 10.3 Inverse Doppler Effect in Backward Volume Waves 325... Uniform Precession Mode Frequencies 344 C.3 Spin Wave Resonance Frequencies 344 C.4 General Magnetostatic Field Relations 344 C.5 Forward Volume Spin Waves 345 C.6 Backward Volume Spin Waves 346 C.7 Surface Spin Waves 347 Appendix D: Mathematical... Backward Volume Waves 158 5.6 Tangentially Magnetized Film: Surface Waves 162 Problems 166 References 167 6 Propagation Characteristics and Excitation of Dipolar Spin Waves 169 6.1 Energy Velocities for Dipolar Spin Waves ... parallel or antiparallel when both L and S contribute to J (cf Eq (1.20)) However, it can be shown that only the component of μ parallel to J has a well-defined measurable value Because of this, it is possible to write μ = γJ, (1.29) where q (1.30) 2mq and g is called the Land´ g factor It has the value 2 for pure spin and 1 for e pure orbital angular momenta For mixtures of L and S, it takes on other values... operator for a given system As an example, consider two operators, A and B, such that Aψ = αψ (1.49) and Bψ = βψ + ϕ, (1.50) where α and β are scalars and ψ and ϕ are linearly independent functions For ψ to simultaneously be an eigenfunction of A and B, we need to determine the conditions under which ϕ vanishes The difference in the result when A and B are applied in opposite order is given by ABψ − BAψ = A(βψ... 171 6.2.2 Surface Waves 173 6.2.3 Volume Waves 174 6.2.4 Summary of the Phenomenological Loss Theory 176 6.3 Mode Orthogonality and Normalization 178 6.3.1 Forward Volume Waves 178 6.3.2 Backward Volume Waves 180 6.3.3 Surface Waves ... exhibiting long-range magnetic order As the temperature is increased, these fluctuations become larger and larger until the magnetic order is destroyed The transition temperature above which magnetic order is destroyed is called the Curie temperature for ferromagnets and the N´el e temperature for ferri- and antiferromagnets Above this transition temperature, ferromagnets, ferrimagnets, and antiferromagnets... importance for microwave device applications are magnetic oxides known as ferrites and magnetic garnets Principal among these for dipolar spin wave applications is single-crystal yttrium iron garnet (YIG), Y3 Fe5 O12 , which is a ferrimagnet with two sublattices The five iron ions per formula unit are the only magnetic constituents Three of these ions are on one magnetic sublattice and two are on the other . Technology Pittsburgh, PA Chennai USA India stancil@ cmu.edu anilpr@iitm.ac.in ISBN 97 8-0 -3 8 7-7 786 4-8 e-ISBN 97 8-0 -3 8 7-7 786 5-5 DOI 10.1007/97 8-0 -3 8 7-7 786 5-5 Library of Congress Control Number: 2008936559 c . found in [1–4] and in standard texts on solid-state physics such as Ashcroft and Mermin [5] and Kittel [6]. D.D. Stancil, A. Prabhakar, Spin Waves, DOI 10.1007/97 8-0 -3 8 7-7 786 5-5 11 c  Springer. angular momentum, exchange, and spin waves; nonlinear phenom- ena such as solitons and chaos; and applications such as the generation of spin waves using current-induced spin torques. This book has