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SQUID ACOUSTOMAGNETIC PARAMAGNETIC
RELAXATION STUDIES OF MgO : Fe2 +
R. Sundfors, M. Holland
To cite this version:
R. Sundfors, M. Holland.
SQUID ACOUSTOMAGNETIC PARAMAGNETIC RELAXATION
JOURNAL DE PHYSIQUE
Colloque C10, suppl6ment au n012, Tome 46, dbcembre 1985 page C10-783
SQUID ACOUSTOMAGNETIC PARAMAGNETIC RELAXATION STUDIES OF M ~ o : F ~ ~ +
R.K. SUNDFORS AND M.R. HOLLAND
Physics Department, Washington University, St. Louis, Missouri 63130. U.S.A.
Abstract
-
A
Superconducting Quantum Interferometer Device (SQUID) which is part of a SQUID acoustomagnetic spectrometer has measured a magnetization change in MgO:Fe2+ which corresponds t o a non-resonant acoustic phonon-electron spin coupling t o the paramagnetic spin system.I. INTRODUCTION
With the use of a high sensitivity SQUID (Superconducting Quantum Interference Device) acoustomagnetic spectrometer, it has been possible t o observe at 4.2
K
the non-resonant ( A m = 0) absorption of acoustic energy coupled t o the dilute paramagnetic ion Fe2+ in MgO as a change in magnetization (AM,) along a n external magnetic field in the 2 direction. An earlier investigation [I] has also investigated the non-resonant absorption in M ~ O : F ~ ~ + using ultrasonic attenuation and dispersion measurements. The ultrasonic frequencies chosen in both experiments are much less than the resonant frequencies for the paramagnetic spin system in the applied magnetic fields but are comparable t o spin-lattice relaxation rates. T h e non- resonant acoustomagnetic experiments are very similar t o Paramagnetic Relaxation experiments except t h a t the time varying external magnetic field along the 2 direction in a Paramagnetic elaxation experiment is replaced by a time varying effective magnetic field due t o the spin-k1
phonon interaction.
In M 0:Fe2+, the lowest lying energy state is a triplet 100 cm-' below t h e next highest energy level IS]. A t magnetic fields less than 1
T,
the Zeeman splittings of t h e triplet state are less than 1 cm-' and t h e Fe2+ impurity can be described by a n effective spin of S = 1. In a n exter- nal magnetic field, the spin energy levels will be described by the quantum numbers m = +1, 0, and -1 and the equilibrium population of electronic spins in these states is described by t h e Boltzman distribution for t h e magnetic fieldH
and the lattice temperatureT .
If a spin- phonon coupling is present giving rise t o a n effective field in the direction of H , the energy lev- els will vary in spacing at the frequency of t h e acoustic wave. If the frequency of the acoustic wave is much less than t h e relaxation rate r , relaxation occurs within the period of the acoustic wave and a n isothermal situation occurs with no net absorption of acoustic energy and no mag- netization change. If t h e frequency of the acoustic wave is much greater than the relaxation rater,
then a n adiabatic, s i - x t i m occurs and a ain there is no net magnetization change or acoustic absorption. Using tbe theory of Feddersf4,
Yuhas e t al. (11 have shown when w r~ I.t h a t there is a net acoustic absorption for longitu inal acoustic waves propagating in a 11001
.
direction of this cubic crystal given byd
where
N
is the number of Fe2+ ~ m - . ~ ,G
the magneto-elastic coupling constant,kB
the Boltz- man constant, p the mass density, v the phase velocity of the acoustic waves, and 0 the angle in t h e (010 plane between the direction of propagation and the direction of the magnetic field.d
The relate spin-phonon transition probability is
where e is the elastic strain amplitude. A t 4.2K, the dominant contribution t o the relaxation rate
r
is the direct process. In this case [I]C10-784 JOURNAL DE PHYSIQUE
where
ro
and C are field and temperature independent. 11. EXPERIMENT&From previous experimentation with the
SQUID
acoustomagnetic spectrometer, AM, have been found for direct nuclear spin-phonon coupling [5,6 as well as for the mechanical resonancesL
within the fundamental and odd harmonics of t e transducer responses, transmission line responses, sample cavity resonances, and whenever t h e acoustic power in the sample is changed. We have measured the radial distribution of acoustic energy for acoustic standing longitudinal waves in a ciyslai with' Rat and parallel faces whose dimensions are larger than t h e piezoelectric transducer radiating area (r R 2 ) . The acoustic energy falls rapidly from a maximum value near the center t o approximately 25% of the maximum value a t R and is near zero a t 1.3 R .
When this distribution of acoustic energy is present, i t raises the temperature of the sample within the volume of t h e acoustic energy distribution, where A T is the spatial average of the temperature increase above t h e sample boundary and the surrounding sample holder.
In MgO, t h e time domain response when the acoustic frequency is changed from the center of a mechanical resonance t o a n off-resonance position in a p-sec, the decay of the of AM, has a
time constant of seconds. This long decay suggests t h a t mechanism by which AM, decays is due t o thermal conduction of acoustic power from t h e acoustic radial distribution discussed above radially outward t o the sample boundary and the sample holder. This "indirect cou- pling" magnetization change is related t o
A T
through Curie's Lawwhere ,yo is the paramagnetic susceptibility.
If
P
is the acoustic power supplied t o the sample when the acoustic frequency is adjusted t o a mechanical resonance, then steady s t a t e relationship between incident power and power transferred by thermal conduction radially iswhere j is the transducer response a t t h e fundamental or odd harmonic,
a a
f
I =( w o n
12
'
(6)( a a
)'+
( v / a
l2
K
is a constant including the thermal conductivity and geometrical factors ibelated t o the ther- mal conduction, cu is t h e total acoustic attenuation a t the frequency w and fieldH
a is twice t h e sample length, won in the position of the n t h mechanical resonance in the t r a n s ducer response, and a b is the "background" attenuation. T h e insertion of (5) into ( 4 ) gives
AM, ic = -P xoHf s f 1
K T
When there is a direct spin-phonon coupling, the magnetization change, AM,, from Abragam
[?I
is- -
AM, = -Wap T1xoH
l+W,, T1
If a mechanical resonance is observed a t the position of a direct spin-phonon coupling resc- nance, then the observed AM, in t h e above equation is multiplied by j
f
2.In t h e experiment described in this paper, what is actually measured is the fractional change at the center of a mechanical resonance when the angle B = 0 and for Wap T I < < l for two different, but close magnetic field values which is given by
and
Experimentally, we measured
F
a t the center of a mechanical resonances a t the third through fifteenth transducer harmonics a t the magnetic fields of 194.4, 402.3, 817.0, 2085.9, 4627.1, 6539.0, and 7670.1 G. Widths of mechanical resonances were also determined t o provide a measure of a,,.Values of AM, are proportional to H and F=O up to H=817.OC. For H>817.0 and increasing F becomes increasingly more negative indicating the presence of an additional absorption of acoustic energy in the sample which causes a decrease in the magnitude of A M , .
With the use of the Yuhas determined values [8] for
C
and r o , the average of the two measured values of GI> [9], and the measured value of the thermal conductivity inMgO
a t 4.2K
[lo], we have determined a computed value of F .Table I
--
Comparison of the experimental, Fdata,
and computed Fmode[, fractional changes in magnetization. The precision of Fdata is f 0.01 and the uncertainty in Fmodel is f 0.02.SONCLUSION
We have reported observation of acoustic properties, such a s mechanical resonances, in MgO as a AM, due to the heating of the sample and therefore the paramagnetic Fe2+ ions by the
acoustic wave. A physical model has been developed which allows calculation of the fractional change
F
from acoustic coupling t o AM, from both thermally heating the lattice and a directspin-phonon coupling. In Table I, the computed values of
F
generally agree in ma nitude and sign with the experimental values which (i) supports the two couplings t o AM, and fii) confirmsthe direct relaxation rate in
M ~ o : F ~ ~ +
as having a constant term(ro)
and a second term( C )
multiplying H 2 as shown in (3), and (iii) is in general agreement with the values ofro
andC
measured by Yuhas [8].REFERENCES
[I] Yuhas, M. P., Fedders, P. A., Miller, J. G., and Bolef,
D.
I., Phys. Rev. Lett.a
(1975) 1028.121 Gorter, C. J., Physica
2
(1936) 503.31 Low, W., Solid State Phys., Supplement 2, ed. by F. Seitz and D. Turball (Academic Press,
b
ew York) 1960.[4] Fedders, P. A., Phys. Rev.
12
(1975) 2045./5] Pickens, K. S., Mozurkewich, G., Bolef,
D.
I.,
and Sundfors, R. K., Phys. Rev. Lett. 1984) 156.161 Pickens, K. S., Bolef, D. I., Holland, M. R., and Sundfors, R. K., Phys. Rev. B
a
(1984) 3644.(71 Abragam, A., The Principles of Nuclear Magnetism (Clarendon Press, Oxford) 1961. [8] Yuhas,
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