from bulk to nano. the many sides of magnetism, 2008, p.188

[...]... sources of the atomic magnetic moment: currents associated with the orbital motion of the electrons, and the electron spin [13] 1.2 Origins of Magnetism on an Atomic Scale 7 1.2.1 The Importance of Angular Momentum For an n-electron atom, these 2n angular momenta couple together to give a total angular momentum whose exact properties depend on the details of the coupling parameters [16] The individual atomic... momenta couple together to give a total orbital angular momentum L, and the individual atomic spin angular momenta couple together to give a total spin angular momentum S Finally, L and S couple together, to give a total atomic angular momentum [16] J The orbital and spin angular momenta each have a magnetic moment associated with them µL = −βL, µS = −2βS, (1.8) where β is the Bohr magneton The total magnetic... Introduction 1.2.2 Magnetic Moment of a Sample of N Atoms In a simple paramagnet, the atoms do not interact with each other, and the ˆ only contributions to the Hamiltonian H come from their interaction with the applied magnetic field H 0 As the atoms are identical, only the Hamiltonian for a single atom needs to be considered [15–17] ˆ H = −µJ · H 0 (1.13) Choosing H 0 to be along the z-axis, we can write... direction of the magnetic field H and the direction of the magnetization M of the bar magnet [11] The product pl is the magnetization M of the bar [13] The work done by the torque gives rise to a potential energy U in the absence of frictional forces [11, 13] U = −M H cos θ (1.6) This equation is particularly important in the discussion of magnetic domains and the realignment of their magnetization when an external... splitting factor is given by∗ e g =1+ J(J + 1) + S(S + 1) − L(L + 1) 2J(J + 1) (1.12) Nevertheless, the Land´ g-factor results from the calculation of the first-order e perturbation of the energy of an atom when a weak external magnetic field acts on the sample [15,16] Normally, the quantum states of electrons in atomic orbitals are degenerate in energy, thereby the degenerate states all share the same... decreasing the exchange energy [11] The width of the transition layer is determined, and thereby limited by the magnetocrystalline energy, which in order to maintain a minimum, tends to keep atomic magnetic moments aligned along one of the easy directions of the crystal axes [11] 1.3.3 Types of Domain Walls The transition layer known as a domain wall can be of two types: Bloch wall [24] where the atomic... typically of the order of 0.1 β, because the orbital motion of electrons is “quenched” by something called the crystal field [17] Each atomic moment is acted on by the crystal field, proportional to the magnetization of its environment [12] If an atomic moment were to be removed from its environment, it would leave behind a magnetic field The field is produced by the surrounding spins, and is a manifestation of. .. momentum However, if the atom is placed in a weak magnetic field, the degeneracy is lifted [17] Furthermore, this dimensionless g-factor relates the observed magnetic moment µJz of an atom to the angular momentum quantum number mj and the fundamental quantum unit of magnetism, that is the Bohr magneton [15, 16] ∗ For a rigorous derivation of above results, please see any introduction to quantum mechanics... Until then, these techniques are confined to the laboratory In the following chapters, a closer look will also be taken at other types of nanostructures, and their feasibility examined The present book examines the fascinating realm of magnetic phenomena from a variety of angles, emphasizing current interests, as well as emerging trends in the ever-progressing technological miniaturization Of course, the. .. with respect to the direction of the applied magnetic field, opposing the latter according to Lenz’s law Thus, the magnetization of a diamagnetic material is proportional to the applied magnetic field as seen in Fig 1.1 Diamagnets have a negative and very weak relative susceptibility, of the order 10−5 [12] Consequently, if a few magnetic atoms exist in the material, their influence overshadows the diamagnetism . D. De 117 From Bulk to Nano The Many Sides of Magnetism By C G. Stefanita Volumes 50–98 are listed at the end of the book. Carmen-Gabriela Stefanita From Bulk to Nano The Many Sides of Magnetism With. broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationor parts thereof is permitted only under the provisions of the German Copyright Law of September. work has attempted to clarify the nature of macroscopic magnetic phenomena and how, in some cases, they can be traced back to a nanoscale. These days, the Preface IX popularity of nanotechnology