Manifestations of hyperfine interaction in plasticity

Abstract

A mechanism is proposed of how the hyperfine interaction of the electron and nuclear spins in the paramagnetic obstacle‐dislocation system may influence the plastic properties of crystals in a magnetic field. It is shown that the hyperfine interaction leads to a threshold-type behavior of the magnetic-field dependence of various plasticity-related quantities. A strong influence of the hyperfine interaction on the behavior of the internal friction of dislocations in weak magnetic fields is predicted. @S0163-1829~97!01142-9# The theory of mechanical properties of crystals usually considers nuclei as point charges disregarding their internal structure. A similar approximation has been widely used in the theory of electronic structure of molecules. This approximation is justified as long as various characteristics of nuclei, such as mass, spin, size, and shape, do not appreciably influence static properties of molecules or crystals. However, it is known that the role of nuclear magnetic moments may appear to be of importance for chemical reaction rates in a magnetic field. 1,2 This leads to the phenomenon called the magnetic isotope effect in chemical reactions in which the hyperfine interaction of the electron and nuclear spins changes populations of various electronic states of radical pairs thereby changing their chemical reactivity. When addressing plasticity-related phenomena we have to consider the motion of dislocations and their pinning by point defects—obstacles. The dynamics of formation of the obstacle‐dislocation bonds in a magnetic field was recently discussed in Ref. 3 ~see also Refs. 4‐7 discussing various plasticity-related phenomena!. It is assumed that the dangling bond of a paramagnetic obstacle forms a radical pair with a dangling bond of the dislocation core. The magnetic field influences the transitions between different spin states of such pairs, which are characterized by different binding energies, and thus changes the depinning probability. This is a mechanism of how the plastic properties of crystals ~both metals and dielectrics! may be influenced by a magnetic field in a broad temperature range. In pure undeformed metals at low temperatures there is also a large contribution from the Kravchenko mechanism, 8 in which the magnetic field increases the electron component of the dislocation viscous drag. An analogy with chemical reaction theory suggests that a hyperfine interaction in the obstacle‐dislocation system also may play an important role in plasticity of crystals in a magnetic field. This may also lead to a magnetic isotope effect in plasticity. This paper discusses the part played by the hyperfine interaction in the dynamics of obstacle‐dislocation radical pairs in a magnetic field and presents results for several experimentally measurable quantities. The influence of hyperfine interactions on the plasticity will be considered within the framework of the model outlined in Ref. 3, which considers the dislocation motion at low stresses, not exceeding the Peierls stress, which occurs by means of depinning of dislocation kinks from paramagnetic obstacles. Unsaturated electron states in the kink and the obstacle form a radical pair whose binding energy depends strongly on the total spin of the pair. This energy is usually much higher in the singlet S state than in a triplet T state. The pair in a T state allows the kink to pass the obstacle freely and the dislocation depins. This model allows one to explain various effects related to a change of plasticity in a magnetic field. 3 Now we modify this model by introducing an interaction between the spins of electrons forming the radical pair and the spins of nuclei of the obstacle or/and dislocation core. The simple, but still rather general, situation is considered here when only one nucleus in the kink-obstacle radical pair has a nonzero spin I51/2. Then the spin Hamiltonian of the system can be written in the form