Study of the resonant phonon scattering in KCl : Li using the spin-phonon interaction

CONFERENCE ON LOCALIZED EXCITATIONS IN SOLIDS

xli

where the frequency of bocal vibration ex-

modes and one p-like localized mode,

ceeds considerably the maximum frequency

whose energies may lie above or within

of crystal

THE RELAXATION OF THE LOCAL VIBRONIC EX-

the spinwave band depending upon the magnitude of the impurity spin and its coupling to the host. We have calculated

CITATION IN SOLIDS E.D. Trifonov (Department of Physics,Len— ingrad State University, Leningrad,USSR)

the eigenvalues of the p—like modes when two such impurities are present. In the

A local mode having unharmonic coup— ling with the crystal modes is consider-

case where the single impurity mode lies outside the spinwave band we now find two

ed, The Hamiltonian of the unharmonic int~raction is chosen to have the form

modes symmetrically located with respect to this original mode. This mode split—

H’=~!~a a a’~ + C.C. where a ,a are an— V nihilation operators for the crystal nodes

ting defines an effective impurity—im— purity interaction which we find is pro—

and a~ is the creation operator for the local mode, It is shown that in the case

portional to the overlap at the localized mode wavefunctions, Since the modes be—

T~Othe muster equation for the local

come more localized

mode can be easily solved. Tile decay of a given energy state “n” is descri bed by

from the spinwave band this implies that the interaction is very short range un—

the binomial distribution. The probabil— ity that at the time “t” we shall have the local mode in the quantum state ‘rn” is 6 (~)=C~’(l_e”~’t)m e_’~’tth_m), where mm ~“ n 2 ~ IBVI 6(ui~+w~-w, 6),~ are frequencies of the crystal and local nodes

less the modes are very close to the band. When the single impurity mode lies with— in the band it is characterized by a re— distribution of the density of states, ~We have investigated this redistribution for the case of two impurities.

correspondingly. In particular, we see that the lifetime of arbitrary energy st— ate of the local mode is inverse to its quantum number. In conclusion, a quantum-

STUDY OF THE RESONANT PHONON SCATTERING IN KC1:Li USING THE SPIN—PHONON INTER— ACTION* D. Walton (Solid State Division, Oak Ridge National Laboratory, Oak Ridge,

vibrations,

as they move away

mechanical perturbation method which is equivalent to the muster equation approx— imation is developed.

Tennessee) In a magnetic field, a crystal which

THE INTERACTION BETWEEN LOCALIZED SPINWAVE MODES

conductivity. This effect may be described as an effective removal of heat

Robert M. White and C. Michael Hogan(Department of Physics, Stanford University, Stanford, California)

carriers

The pesence of an impurity spin in a one-dimension Eeisenberg ferromagnet can give rise to two s—hike localized

contains magnetic ions will exhibit a field—dependent decrease in the thermal

from a narrow band in the phon-

Spectrum which is centered about the Larmor frequency for the spins. The

Ofl

spectrum of heat carriers and hence the frequency dependence of the total phonon

xlii

CONFERENCE ON LOCALIZED EXCITATIONS IN SOLIDS

scattering cross section for the crystal can be determined from the field depend-

LOCALIZED MAGNONS IN IMPURE HEISENBERG ANTIFERROMAGNETS Laurence R. Walker (Bell Telephone Lab-

ence of the thermal conductivity,

oratories, Murray Hill. New Jersey)and Daniel Hone and Herbert Callen (Physics Department, University of Pennsylvania, Philadelphia, Pennsylvania)

The total scattering cross—section which is seen is that at zero xield: in a sense the role of the magnetic defect

We have extended previous work on the

is to provide a probe which yields, by subtraction, the total zero field scat—

thermodynamics of a spin impurity in a Heisenberg ferromagnet to impure anti—

tering cross—section of a narrow band of phonons. Therefore, if the crystal con— tains nonmagnetic defects their scatter— ing cross—section may be obtained by in—

ferromagnetic systems. In the former case localized magnons appear only for impurities coupled sufficiently strongly to their neighbors (relative to the pure

troducing a magnetic ion and measuring the field dependence of the thermal con— ductivity. The thermal conduction of irradiated

host exchange coupling), the correspond— ing energy then clearly lying above the continuum of the spin wave band of the host crystal. Because of their high en—

KC1 exhibits a magnetic field dependence, and the radiation—produced defect which is responsible appears to be the R center,

ergies, such modes do not importantly affect the thermodynamic behavior of the system. Even the introduction of ex—

Thus, a technique becomes available for studying phonon scattering by defects in-

change anisotropy so as to produce an energy gap cannot split of f a mode be-

troduced prior to irradiation. By irradiating Li doped KC1 we have been able to identify the resonant scat—

low the spin wave band - at least, if the anisotropy energies for host and inpurity spins are equal — for the lowest

tering of phonons due to transitions be— tween tunneling states of the Li ion. We

energy excitation will still be the uni— form (k = 0) spin wave mode.

have observed three resonances, one at 1, another at 1.4 cm”’1, and anoth— 0.7 cm”’ er at 2.3 cm1.

These considerations are not, however, applicable to the impure antiferro— magnet. Furthermore, there is experiment-

Theory predicts that the tunneling states for the Li+ion in an isotropic well should consist of four equally sp— aced levels. Other work indicates that

ally available a variety of insulating antiferromagnets, so that we anticipate little difficulty in observing the effects of low—lying localized magnons in these

the separation of the levels in KC1 sh— ould be 0.75 cm””. Our observations are

systems. We have taken as a not unreal— istic model of a substance like MnF 2, a

consistent with this picture since our experimental error is about i 0.1 cm—l ‘

Heisenberg Hamiltonian with uniaxial an— isotropy: H= 2

j

~ where the

S~,’S—~ sums are over lattice

sites,