UDC 537.874; 537.624
THE INFLUENCE OF EXCHANGE
INTERACTION AND DYNAMIC DEMAGNETIZING FIELD ON
DISPERSION PROPERTIES OF DAMON-ESHBACH SURFACE WAVE
PART 1. TRANSVERSE WAVE
NUMBER
V. I. Shcheglov
Kotelnikov Institute of Radioengineering and Electronics of Russian Academy
of Sciences,
Mokhovaya 11-7, Moscow 125009, Russia
The paper is received on July 9, 2019
Abstract. The influence of
demagnetizing field and nonuniform exchange interaction on dispersion properties
of Damon-Eshbach surface wave is investigated. On the basis of short review of
to-day works level by investigation of magnetostatic waves it is found the
necessity of the investigation waves which long is about some nanometers and
less. It is established that for investigation of so short waves it is
necessary to take into account the dynamic demagnetizing and exchange fields.
The quantity description of demagnetizing field is made in the form of
hyperbolic tangent which argument is the multiplication of wave number on plate
thickness. In the linear approximation it is decided the equation of motion for
magnetization with the consideration of demagnetizing and exchange fields. It
is found the magnetic sensibility tensor which components have resonance character.
In the geometry of Damon-Eshbach task for potential of propagating wave field
it is found the Walker equation which considers the influence of
demagnetization and exchange. The most difference of this equation from its
classic variant is the existence of mixed second order derivative by
coordinates which are normal to constant field direction. It if found the Walker equation solution be division of variable quantity method. It is shown that the
mixed second order derivative lead to complex character of wave number
component which is perpendicular to the plane of magnetic plate. It is found
the double character of transverse wave number which is caused by two possible
decisions of Walker equation for the wave component which propagates
perpendicular to plane of magnetic plate to its depth. For the case of exchange
absence the transverse wave number is presented as a sum of real and imaginary
parts. It is found the dependencies of real and imaginary transverse wave
number components from longitudinal wave number by different values of
demagnetization parameter. It is investigated the possibility of presentation
of transverse wave number as a sum of real and imaginary parts in the case of exchange
interaction presence. It is found that in this case the transverse wave number
having complex character is defined by the decision of algebraic equation
having eight degree. The whole complex equation is reduced to the system of two
eight degree equations which roots are real. It is proposed the algorithm of
this system the step by step decision which consist of variation of first
variable value and founding on the each step two meaning of other value and
with the following minimization of difference between its. With the assistance
of this algorithm it is found the dependencies of real and imaginary transverse
wave number components from the value of longitudinal wave number. It is shown
that the exchange interaction leads to raising of both components transverse
wave number dependencies from longitudinal wave number value relatively to same
dependencies when exchange is absent. It is established three fundamental
affirmations which determine the character of observed phenomena: 1) the
influence of demagnetization causes the formation of imaginary part of transverse
wave number; 2) when the demagnetization is increased the absolute value of
imaginary part of transverse wave number is increased; 3) when the exchange
interaction is increased the absolute value of imaginary part of transverse
wave number is increased. For the quality interpretation of these affirmations
it is proposed the model which considers the propagating wave as progressive
moving of periodic flat planes having maximum deflection of magnetization. When
these planes crops out of magnetic plate surface near this surface are forms
the fields which are “get out” of the plate boundaries. It is voiced the
supposition that in the process of wave propagation owing to these “getting
out” fields the plates of maximum deflection acquires the inclined areas which
falls behind the main part of moving surface. These inclined areas ensure the
formation of transverse component of whole wave number. When the demagnetization
is increased the deflection of inclined areas from the normal to the plane of
magnetic plate the length of wave in these areas directed along the normal to
plane of plate is decreased. The exchange interaction causes to difficulty of
distortion of maximum deflections and so the wave length in inclined areas also
is decreased. On the basis of mechanics it is voiced supposition that the increasing
as demagnetization so exchange increases the hardness of system and this
increasing causes the increasing of wave length. It is proposed the conclusion
that the variation of transverse wave number by the variation of
demagnetization and exchange is subjected to influence of two factors: the
variation of maximum deflections plate form and variation of system hardness
which both acts in opposite directions. So the resulted alteration of wave
number may be determined by the compromises between these two factors. It is
established that the more detailed investigation of question about mutual
alignment both factors also on the model level may be established as a object
for new separate task.
Key words: magnetostatic wave,
demagnetizing field, exchange interaction, wave dispersion, nanoscale.
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