UDC
537.874; 537.624
THE INFLUENCE OF EXCHANGE
INTERACTION AND DYNAMIC DEMAGNETIZING FIELD ON DISPERSION PROPERTIES OF
DAMON-ESHBACH SURFACE WAVE
PART 1. DISPERSION
RELATION
V. I. Shcheglov
Kotelnikov Institute of
Radioengineering and Electronics of RAS,
Mokhovaya 11-7, Moscow 125009, Russia
The
paper is received on August 6, 2019
Abstract. The propagation of
magnetostatic wave in classic geometry of Damon-Eshbach task which is
established as ferrite plate magnetized by external field in its plane is
investigated. The investigation is made in connection with dynamic demagnetization
and nonuniform exchange interaction. It is found the tensor of magnetic
permeability in consideration with the periodic character of propagating wave.
It is found the mixed symmetrical-anti-symmetrical character of permeability
tensor which is connected with the consideration of dynamic demagnetization. It
is found the conditions of frequency divergence of tensor components wish are
supplemented to the influence of direct field also by the nonuniform exchange
action. It is investigated the whole organization of task about propagation of
magnetostatic surface wave. It is established that the equality to zero of
circle from dynamic magnetic field of wave allows to introduce the potential of
this field. Also the equality to zero of divergence from magnetic induction of
the same wave allows to found the Walker equation which is analog with the Laplace equation for magnetic medium. It is found the existence of mixed second derivation
by coordinated in Walker excitation which is brought by the influence of
demagnetization and exchange. It is shown that the mixed character of
derivation leads to the ambivalent character of transverse wave number. For the
geometry of Damon-Eshbach task the equations for potential in magnetic plate
and surrounding its form both sides free half-spaces. It is described the
boundary conditions on the surfaces between the material of plate and free
spaces. As a result from the decision of established boundary task by variation
division method the dispersion relation for surface wave propagating in plate
plane in direction perpendicular to constant field is found. In details it is
investigated the double character of transversal wave number which is connected
with the mixed derivation in Walker equation. It is found the analytical
expressions for both meanings of wave number which determined only the demagnetization
without the exchange. It is shown that the founding of both components of wave
number when exchange interaction is present require with the decision of eight
degree algebraic equation which may be decided only by numerical method. It is
described the general scheme of dispersion law founding as a functional
dependence of wave frequency from the its longitudinal wave number. It is
proposed the algorithm of calculation which consist of step by step assignment
of longitudinal wave number with the determination of frequency value on each
step by zero searching method. It is described the schemes of calculation
algorithms of both paths of dispersion relation and also the real and imaginary
paths of relation as a whole. It is demonstrated that described algorithm
allows to found the functional dependence of wave propagating frequency from
the longitudinal wave number which is the unknown dispersion law. It is
described the results of calculation magnetostatic surfaces wave dispersion on
the basis of received dispersion relation. As a point for comparison it is
described the classic dispersion dependence for exchange wave in infinite space
and its generalization for the case of thin plate. On the basis of founded
dispersion relation are constructed the dispersion curves with the
consideration of demagnetization and exchange interaction. The investigations
are performed in the interval of longitudinal wave number from zero to
4x104 cm-1, which is
more than traditionally realized range in experiments of dipole magnetostatic
waves about of two orders. It is made the comparison of founded curves with the
same for classic Damon-Eshbach task and also for classic exchange wave in
infinite space and thin plate. It is shown that the consideration with demagnetization
direct to the increasing of dispersion curves in the region of wave numbers
having values more the inverse value of plate thickness. It is shown that the
exchange interaction leads to the quadratic exchange of dispersion curves which
is more increased from dispersion curves for surface waves founded in frames of
classic Damon-Eshbach task. On the basis of founded dispersion relation with
the consideration of demagnetization and exchange it is investigated the
dependence of dispersion law for surface wave from the plate thickness. It is
found that the dispersion curves for any thickness when the wave number is
increased also increase by the law near to quadratic. In this case in region
near the wave number values which are less from inverse value of plate
thickness the steepness of dispersion curves increases when the thickness is
decreases. In the region of wave number which are more than inverse value of
plate thickness the steepness of dispersion curves when the thickness is decreases
asymptotically try to attain the value which is determined by dispersion law
when the demagnetization is absent. On the basis of founded dispersion relation
with the consideration of demagnetization and exchange it is investigated the
dependence of dispersion law for surface wave from the constant of exchange
interaction. The investigation is made when the thickness of plate is equal to
1 micrometer. This choice ensures the visible influence of demagnetization
about the middle of investigated range of wave number (so as
2x104 cm-1). As the
standard it was established the value of exchange constant equal to the same in
yttrium iron garnet. It is found the dispersion curves having different values
of exchange constant in the region from unit to hundred standard values. It is
shown that when constant value exchanged from unit near the standard value the
dispersion curve positioned less higher from classic Damon-Eshbach curve but
its quadratic character is in visible not maintained. It is founded that for
visible manifestation of quadratic character it is necessary the increasing of
exchange constant more than one order in comparison with standard value. In
this case the exceeding of constant above standard to two orders brings to the
whole predomination of quadratic law over the classic. It is mentioned the connected
with numerical character of task decision technical reason of limitation of
longitudinal wave number by the value of
4x104 cm-1. Its
reasons is founded and the way of its overcoming is proposed. As a most important task for
further investigation it is established the necessity of expansion of investigated
region of longitudinal wave number no less than two orders of value.
Key words: magnetostatic wave,
demagnetizing field, exchange interaction, wave dispersion, nanoscale.
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For citation:
V.I.Shcheglov. The influence of exchange
interaction and dynamic demagnetizing field on dispersion properties of Damon-Eshbach
surface wave. Part 2. Dispersion relation. Zhurnal
Radioelektroniki - Journal of Radio Electronics. 2019. No. 9. Available at http://jre.cplire.ru/jre/sep19/8/text.pdf
DOI 10.30898/1684-1719.2019.9.8