Phonon spectroscopy

A versatile method of phonon spectroscopy in which frequency crossing effects are utilized. A heat current is passed through a composite structure incorporating two bodies respectively containing different types of resonant phonon-scattering center. A varying external perturbation, suitably a magnetic field, is applied to the structure so as to affect the resonant frequency for only one of these types. The temperature difference between two points on the structure is monitored as the perturbation varies, this temperature difference exhibiting an excursion when the resonant frequencies for the two types of center coincide.

This invention relates to phonon spectroscopy and is concerned in 
particular with methods in which frequency crossing effects are utilised. 
By way of background reference may be made to an article published in 
Spectrum No. 149 (1977) pages 9-11, which gives a brief review of the 
subject of phonon spectroscopy, and to a series of three papers published 
in Journal of Physics C: Solid State Physics, Vol. 8 (1975) pages 
1475-1505, in which frequency crossing effects are discussed in some 
detail. 
In known methods of phonon spectroscopy utilising frequency crossing 
effects, the properties of resonant phonon-scattering centres in a solid 
body are investigated by passing through the body a heat current of 
phonons of broad spectral width while subjecting the body to a varying 
external perturbation which affects the resonant frequency of at least one 
scattering process associated with the relevant centres; the external 
perturbation is commonly a magnetic field, but could instead be an 
electric field or a mechanical stress. The variation of the external 
perturbation gives rise to a variation in the thermal conductivity of the 
solid body, which exhibits a sharp maximum or minimum when a frequency 
crossing occurs, i.e. when the size of the perturbation is such as to 
bring into coincidence the resonant frequencies of two scattering 
processes associated with the relevant centres; the variation in thermal 
conductivity can conveniently be observed by monitoring the temperature 
gradient along the body in the direction of flow of the heat current. It 
should be noted that the two scattering processes involved in the 
frequency crossing may be associated with scattering centres of the same 
type, or respectively with scattering centres of two different types. 
While valuable results can be obtained with such known methods, their range 
of application is severely limited by the necessity for all the relevant 
scattering centres to be incorporated in a single body; this is 
particularly inhibiting in cases where it would be desirable to 
investigate the properties of a specific type of scattering centre in a 
specific host material by reference to the known properties of a different 
type of scattering centre. It is accordingly an object of the present 
invention to provide a method employing similar principles but of 
considerably enhanced versatility. 
A method according to the invention comprises passing a heat current of 
phonons of broad spectral width through a composite solid structure 
incorporating two solid bodies respectively containing resonant 
phonon-scattering centres of different types, said bodies being so 
arranged that the occurrence of a frequency crossing involving two 
scattering processes respectively associated with said different types of 
centre will give rise to an excursion in the temperature difference 
between a pair of given locations on said structure spaced apart in the 
direction of flow of the heat current, subjecting said structure to a 
varying external perturbation so as to affect the resonant frequency of 
only one of said scattering processes, and monitoring the changes of said 
temperature difference caused by the variation of said perturbation.

In each of these arrangements a heat current is arranged to pass from a 
heater to a heat sink constituted by a bath of liquid helium, through a 
composite solid structure incorporating a monocrystalline body of alumina 
doped with vanadium at a concentration of about 100 p.p.m. and a sample of 
a dielectric material containing resonant phonon-scattering centres which 
are to be investigated, the structure being maintained at a constant mean 
temperature of a few .degree.K. by means of a suitable cryostat. The 
heater is constituted by a film or wire of a normal metal which is 
maintained in contact with an appropriate part of the composite structure 
and through which is passed a constant electric current. The heat current 
consequently consists of phonons whose frequency spectrum is similar to 
that of a black body radiator and has a width of several tens of GHz. 
The arrangements illustrated in FIGS. 1 and 2 are suitable for the 
investigation of non-magnetic scattering centres in the sample, for 
example molecular defects with motional levels and possibly chain motion 
in polymers. In these arrangements the composite structure effectively 
consists of only the alumina crystal 1 and the sample 2, and is subjected 
to a magnetic field B directed perpendicular to the general direction of 
flow of the heat current Q, the crystal 1 being oriented so that its 
c-axis is parallel to the magnetic field B. 
In the FIG. 1 arrangement, the sample 2 is in the form of a self-supporting 
body and the whole heat current Q is arranged to flow in succession 
through the crystal 1 and the sample 2. In the crystal 1 strong scattering 
will occur of phonons whose frequency corresponds to that of the sharp 
.DELTA.M=2 transition of trivalent vanadium ions, so that the phonon 
current passing into the sample 2 is `labelled` by an absorption line at 
this frequency, whose value is proportional to the magnetic flux density 
(with a numerical relationship of approximately 80 GHz/tesla). In carrying 
out an investigation with the FIG. 1 arrangement, the temperature 
difference between two points 3 and 4, spaced apart on the sample 2 in the 
direction of flow of the heat current Q, is continuously monitored while 
the frequency of the absorption line referred to above is swept through an 
appropriate range of values by variation of the magnetic field B. The 
consequent variation of the temperature difference will exhibit a minimum 
whenever the frequency of the absorption line referred to above is brought 
into coincidence with the frequency of an absorption line due to resonant 
phonon-scattering centres in the sample 2. 
In certain cases it may be convenient to modify the arrangement shown in 
FIG. 1 by reversing the order of the crystal 1 and sample 2 in the heat 
current path. In such cases, it is of course necessary for the monitored 
temperature difference to be that between two points on the crystal 1 
instead of on the sample 2. 
In the FIG. 2 arrangement the crystal 1 is of generally cylindrical shape 
and the heat current Q is arranged to flow through it from end to end. The 
sample 2 is in the form of a film deposited in a groove cut in the crystal 
1 so as to extend perpendicular to the cylindrical axis, the base of the 
groove being planar and being highly polished. As with the FIG. 1 
arrangement, there will be strong scattering of the phonons by the 
trivalent vanadium ions in the crystal 1; there will also be significant 
scattering of the phonons at the interface between the crystal 1 and the 
sample 2, and the reflectivity at this interface will be substantially 
affected if there is a coincidence between the frequency of the absorption 
line due to the vanadium ions and the frequency of an absorption line due 
to resonant phonon-scattering centres in the sample 2. In this case, 
therefore, in carrying out an investigation the temperature difference 
between two points 5 and 6, located on the crystal 1 on either side of the 
sample 2, is continuously monitored while the frequency of the absorption 
line due to the vanadium ions is appropriately swept by variation of the 
magnetic field B. 
FIG. 3 illustrates a variation of the FIG. 1 arrangement which may be 
adopted where it is desired to investigate magnetic phonon-scattering 
centres in the sample, for example donors or acceptors in a semiconductor. 
In this case the composite structure includes a further body 7 
constituting a `phonon guide`, interposed between the crystal 1 and the 
sample 2; the body 7 may for example be a rod of very pure silicon having 
a highly polished surface. The magnetic field B in this case is confined 
to a limited region, indicated by the line 8; the crystal 1 is located 
within this region but the sample 2 is located outside it, so that the 
properties of the centres under investigation will not be affected by the 
presence of the magnetic field. With the FIG. 3 arrangement, an 
investigation is carried out in the same way as for the FIG. 1 
arrangement. 
In both the FIG. 1 and FIG. 3 arrangements, the individual bodies 
constituting the composite structure may in some cases be held together 
simply by mechanical pressure, but in other cases it may be desirable for 
these bodies to be bonded together. It appears desirable to avoid the use 
for this purpose of conventional glues, which are amorphous and contain 
tunnelling defects which are strongly coupled to phonons; it is thought 
that such defects would absorb the phonons and re-emit the `labelled` 
spectrum as a black body spectrum. Accordingly it is considered preferable 
to use crystalline glues if it is required to bond the individual bodies 
together. 
With all these arrangements, the monitoring of the relevant temperature 
difference may conveniently be effected by utilising a pair of 
thermometers of the semiconductor resistance type respectively located at 
the appropriate points, these thermometers being connected in a bridge 
circuit energised from an a.c. source (suitably having a frequency of 
about one kHz) and the out-of-balance signal from the bridge circuit being 
detected by means of a phase-sensitive detector to which a control signal 
is fed from the a.c. source. If desired, the signal/noise ratio for a 
given experiment can be improved by the employment of conventional signal 
averaging techniques involving a series of sweeps of the magnetic field. 
Sensitivity can also be improved by employing a differential technique 
involving modulation of the magnetic field as it is swept (the modulation 
suitably being at a frequency of a few Hz); in this case the output of the 
detector referred to above is fed to a second phase-sensitive detector 
supplied with a control signal corresponding to the field modulation. The 
resultant output is of a form which enables frequency crossing effects to 
be more readily distinguished from background effects. 
It will be appreciated that the use in the illustrated arrangements of an 
alumina crystal doped with vanadium is referred to merely by way of 
example, and that in alternative embodiments of the invention there could 
be employed other types of body containing resonant phonon-scattering 
centres whose resonant frequency can be varied by the application of an 
external perturbation; as is the case with the known methods referred to 
above, this perturbation could be an electric field or a mechanical stress 
instead of a magnetic field.