THE SCATTERING OF HEAT PULSES BY RESONANT SPINS IN MgO : Fe2+

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THE SCATTERING OF HEAT PULSES BY RESONANT SPINS IN MgO : Fe2+

J. Wigmore

To cite this version:

J. Wigmore. THE SCATTERING OF HEAT PULSES BY RESONANT SPINS IN MgO : Fe2+.

Journal de Physique Colloques, 1971, 32 (C1), pp.C1-766-C1-768. �10.1051/jphyscol:19711267�. �jpa- 00214098�

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JOURNAL DE PHYSIQUE Colloque C 1, supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1

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766

THE SCATTERING OF HEAT PULSES BY RESONANT SPINS IN MgO : Fez+

J. K. WIGMORE (*)

Department of Physics, The University, Lancaster

RCsumC. - Le couplage entre les pulses thermiques et les spins rksonnants dans MgO : Fez+ a kt6 6tudi8 a 1.7 OK en fonction du champ magnktique jusqu'a 2,8 Teslas, et en fonction de la tempkrature du pulse thermique entre 13 et 20 OK. Les rksultats ont kt6 interprktes en utilisant un modCle acoustique courant de la propagation des pulses de chaleur.

On deduit un coefficient d'attenuation intrinskque a(v) ⁼1,45 x 10-47 ^{v 4}qui suggkre un mecanisme de diffusion des phonons par les impuretts par effet de difference de masse.

Abstract. - The interaction of ballistic heat pulses with resonant spins in MgO : Fez+ has been studied at 1.7 OK, as a function of magnetic field up to 2.8 Teslas, and of heat pulse temperature between 13 and 20 OK. The data were interpreted using an acoustic flow model of heat pulse propagation. An intrinsic attenuation coefficient of a(v) ⁼1.45 x 10-47 v 4

was inferred, suggesting mass difference scattering by impurities.

I. The heat pulse technique. - We have observed the scattering of ballistic heat pulses by resonant spins in MgO : Fez+ at helium temperatures. The heat pulse technique provides a means of studying the interaction of spin systems with phonons up to two orders of magnitude more energetic than those generated in ultrasonic experiments [I]. The phonons comprising the heat pulse are incoherent, and have a frequency spectrum p(v) cc vZ/{ exp(hvlk6) - 1 } where 8 is the excitation temperature of the heater. For the experiments reported here this parameter was typi- cally 17 OK so that the majority of the emitted phonons had frequencies around 10'' Hz.

In the presence of a magnetic field, those heat pulse phonons that have energies equal to the splittings of the paramagnetic spins can induce transitions and be absorbed. As a result, the ballistic part of the bolometer signal, which is due to phonons that travel directly from heater to bolometer without being scattered, decreases in magnitude. Scattering of thermal phonons by a resonant spin system has also been observed in steady state thermal conductivity experiments [2]. Interpretation of such data is complicated, however, because phonons of all polarisations and wavevectors are involved. With ballistic heat pulses, a narrow cone of phonon wavevectors is iiolated and the different polarisations, which travel with different velocities, are separated by time resolution of the bolometer response.

11. Experimental details.

-

The experiments were carried out a t 1.7 OK using a semiconducting avalan- che bolometer as the heat pulse detector. Technical details of this device have been published elsewhere [3].

Of fundamental importance is the fact that it is able to function in a large magnetic field. The heat pulses propagated along a

<

100

>

axis in the MgO, which was cut as a cylinder 6.0 mm in diameter and 6.7 mm long. The detector was a wafer of silicon doped with approximately loi6 cm-3 of phosphorus, and bonded

(*) Formerly at IBM T. J. Watson Research Center, York- town Heights, New York, where part of this work was carried out.

to the specimen with epoxy resin. The magnetic field was applied parallel to the direction of heat pulse propagation.

MgO : Fez+ was chosen for this investigation because it has a large spin-phonon coupling which is particularly well understood as a result of acoustic paramagnetic resonance and stressed electron spin resonance measurements [4], [5]. I t is a non-Kramers ion having an isotropic effective spin Hamiltonian X = go, H.S with g = 3.43 and S = 1. In general, lattice waves may cause both AM = f 1 and

transitions, but in the present study of transverse phonons propagating along a

<

100

>

axis parallel to the magnetic field, only AM = $- 1 transitions were allowed.

The response of the bolometer following exc.itation of the heater by 15 watts 0.1 microsecond pulses is shown in figures l a and l b for magnetic fields of 0 and 2.8 Teslas, respectively. The onset time of 1.05 microsecond corresponded to the arrival of the transverse modes, which are degenerate for this cut of MgO. For reasons that are not fully understood, no longitudinal mode was seen. The ^(<tail >> of the heat pulse consisted of phonons that reached the detector after being scattered either by intrinsic processes or by the surfaces of the specimen. Figure 1 shows clearly the decrease of the ballistic heat pulse caused by the increased spin-phonon scattering in a magnetic field. The magnitude of the heat pulse was sampled with a box-car integrator a t a time 0.1 n~icrosecond after the arrival of the first ballistic phonons and plot- ted as a function of magnetic field (Fig. 2). It is note- worthy that the curve does not pass through a mini- mum. This would occur when the energy splitting of the AM =

+

1 transitions was equal t o the energy of the majority of the heat pulse phonons, that is when gA H ^N3 kg, where 8 is the characteristic temperature of the heat pulse frequency spectrum. For 8 = 17 OK, a magnetic field of about 22 Teslas would therefore be required to obtain the maximum heat pulse absorption. In the present experiments we could

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711267

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THE SCATTERING OF HEAT PULSES BY RESONANT SPINS IN MgO : Fen+ C 1 767

FIG. 1. - Response of the bolometer to heat pulses following excitation of the heater by 0.1 microsecond, 15 watts pulses, (a) in zero magnetic field, and (b) in a magnetic field of 2.8 Teslas.

Bolometer current (vertical) in arbitrary units ; time (horizontal, increasing from left to right) 0.5 microsecond per larges cale division.

vary 8 only between 13 and 20 ^OK,varying the power dissipated in the heater, and a turning point was never observed. Figure 3 illustrates the change in parama- gnetic scattering of the heat pulse as a function of heat pulse temperature.

FIG. 2. - The variation with magnetic field, H, of the bolo- meter current S(H, 17) monitored at a time 0.1 microsecond after the onset of the ballistic mode, for a constant heat pulse temperature of 17 OK. The current is normalised to S(0.17), the value in zero magnetic field, in order to eliminate the sensitivity parameter of the bolometer. The theoretical curve (solid line) has been calculated assuming an intrinsic attenuation

coefficient, ~ ( v ) = 1.45 x 10-47 v4.

111. Interpretation of results. - The data summa- rised in figures 2 and 3 was analysed using an acoustic flow model. The bolometer signal S(H, 0) as a func- tion of magnetic field H, and heat pulse temperature, 8, was given by

where c is the sensitivity parameter of the bolometer eliminated by normalisation to S(0, 8). p(v) is the frequency spectrum of the heat pulses, a(v) is the phonon attenuation coefficient for intrinsic (that is, inde- pendent of magnetic field) processes, and P(v, H ) is

FIG. 3. - The variation with heat pulse temperature, 8, of the relative change in bolometer current between zero and maximum fields, S(2.8, B)/S(O, 8). The theoretical curve (solid line) has been calculated assuming an intrinsic attenuation

coefficient, GC(V) = 1.45 x 10-41 v4.

the spin-phonon attenuation coefficient due to the Fez+ ions. For the experimental conditions of figure 2, the heat pulse temperature 0, which determined p(v), was calculated from a knowledge of the power dissipated in the heater film, to be 17 f 1 OK. P(v, H) is given by the standard acoustic paramagnetic resonance expression [6]

where the suffices

+

^and- refer to the (1,O) ^t^,(1,

+

¹⁾

and (1, 0) * (I, - 1) transitions respectively. M+ is

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C 1

-

⁷⁶⁸ ^J.K. WIGMORE the matrix element of the spin-lattice Hamiltonian

between the appropriate eigenstates, p, the popula- tion difference, and g+(v, H ) the lineshape. Other symbols appearing in (2), are I, the length of the specimen, p the specimen density, v the acoustic velocity,

E the magnitude of the acoustic strain and h, Planck's constant. The concentration of ~ e ' + in the MgO crystal and the resonance lineshapes were determined in a separate acoustic paramagnetic resonance experi- ment. Because of the large magnetic fields, both the quadrupolar and the dipolar terms in the spin-lattice Hamiltonian made significant contributions t o the spin-phonon matrix elements. In our experimental configuration (M+/E)' = (112)

(pm

HF,,

+

^G,,)' ^and

( M -I&)' = (112) (P, - G4,l2 where

Dm

is the Bohr magneton and G,, and F4, the magnetoelastic coefficients. In the determination of the population differences p , and p-, we took account, after the method of McClintock et al. [7] of Iinewidths being of the order of kT in magnitude, and we included both the resonant and antiresonant contributions to the scattering cross-section. Finally, it was assumed that no saturation of the spin system took place, and that normal phonon processes could be neglected.

In the absence of any other information on the form of the intrinsic attenuation coefficient a(v), we used the expression a(v) = AvN and assumed N to be an integer.

Since A and N were then the only unknowns in the calculation, we made a least squares fit to the data

of figures 2 and 3 in order to find values of these para- mkters. By this procedure, we obtained N = 4, and A = 1.45 x The exponent of 4 clearly suggests that the intrinsic attenuation is due to mass-difference scattering by impurities in the MgO [8]. If we take the impurity to be Fez+, with an atomic concentration'of 5.7 x we can estimate a value of 0.20 x for the constant, A. Although this is rather less than the measured figure, an electron spin resonance ana- lysis of the crystal indicated the presence of other impurities, notably MnZf and CoZt, both of wich would contribute to a(v) but not to P(v, H>.

IV. Conclusions. - Paramagnetic scattering of ballistic heat pulses has been measured. No unknown parameters are involved in calculating the spin-phonon interaction of MgO : Fez', and good agreement with the experimental data has been obtained. The measurements are sensitive, however, to other interac- tions involving the very high frequency phonons that comprise the heat pulse, in the present case, to mass- difference scattering by impurities. This type of expe- riment should therefore prove a valuable means of studying such processes.

The author is grateful to Dr. N. S. Shiren for suggesting these investigations, and to Drs. M. Pomerantz and R. J. von Gutfeld for many helpful discussions.

The work is being supported by a research grant from the Science Research Council.

References

Tll VON GUTFELD (R. J.). Phvsical Acoustics (Academic r61 ROSENBERG (H. M.) and WIGMORE (J. K.). Proc. ROV.

. - -

^- ^,^,

Press ; ~di'tor W. P. ason on) 1969, V 133. SOC., 1967, 3 0 2 ~ , 69.

121 WALTON (D.), Phys. Rev., 1970, lB, 1234. [7] MCCLINTOCK (P. V. E.), MORTON (I. P.), ORBACH (R.) [3] WIGMORE (J. K.), J. Appl. Phys., 1970, 41, 1996. and ROSENBERG (H. M.), Proc. Roy. SOC., 1967, 141 SHIREN (N. S.), Phys. Rev., 1962, 128, 2103. 298A, 359.

151 LEWIS (M. F.) and STONEHAM (A. M.), Phys. Rev., [8] KLEMENS (P. G.), P ~ o c . Phys. Soc., 1955, 68A, 1113.

1967, 164, 271.