Acoustic Paramagnetic Resonance Research Articles

The properties of (3d)4ions in corundum. I. APR spectra and their interpretation

Measurements have been made of the acoustic paramagnetic resonance spectra of both Cr2+ and Mn3+ in Al2O3 at frequencies between 8.4 and 9.5 GHz. Results have been obtained as the direction of the magnetic field H is verified in the ac plane, the bc plane and in a cone around the c axis. Two types of lines are in evidence: type 1 lines have an edge and type 2 lines a peak. The shapes are explained by assuming that random internal strains and electric fields of E type symmetry exist in the crystal. The variations of the positions of the peak or edge as H is varied are readily explained. This analysis shows that (3d)4 ions in Al2O3 are at a site which has predominantly trigonal symmetry and that the superimposed random tetragonal components are small.

Influence of Strains on Paramagnetic-Resonance Spectrum for Strongly Coupled Ions—Application toV3+in MgO

We develop a Monte Carlo method to study the influence of static random strains on EPR and acoustic-paramagnetic-resonance (APR) spectra. The method consists of calculating the line shape using random numbers which represent the random strains. We have applied this method to the particular case of a $S=1$ system in cubic symmetry in the presence of ${\ensuremath{\Gamma}}_{3g}$-type strains. The important parameter is the product of the strain-ion coupling coefficient and the width of the distribution function of the strains. When this parameter is small compared to the Zeeman term, we find the known results obtained using perturbation theory. When this parameter is of the order of the Zeeman term, the line shape is profoundly modified and the spectrum has great similarity to an axial spectrum. The comparison between calculated and experimental spectra obtained with MgO: ${\mathrm{V}}^{3+}$ confirms the previously proposed interpretation. The strain-ion coupling coefficient is deduced from this comparison. We also discuss the possibility of deducing the Jahn-Teller energy and covalency from our recent experimental results interpreted within the model developed here. The values obtained show that Jahn-Teller coupling is only slightly greater than spin-orbit coupling. Thus, the MgO: ${\mathrm{V}}^{3+}$ system appears to be near the limit where the Jahn-Teller effect is stabilized by spin-orbit coupling.

An investigation of the ground state of Cr2+in MgO based on thermal conductivity measurements

Measurements of the thermal conductivity of MgO doped with chromium in the temperature range 0.4 to 300 K indicate the existence of resonant scattering by Cr2+ions at 5.2 and 21 cm-1. These measurements confirm that the ion cannot be described by simple crystal field theory or by static Jahn-Teller theory, but they are consistent with the dynamic Jahn-Teller theory of Fletcher & Stevens (1969) with the parameters 8 (tunnelling frequency) = 16 cm-1andD(spin-orbit splitting) = 4 cm-1. It is not possible to determine the sign of the anharmonic term,B, from the measurements. These parameters differ significantly from those determined by Fletcher & Stevens and those determined by Ham (1971) from acoustic paramagnetic resonance data for Cr2+in MgO. The data also appear to confirm earlier indications that strong coupled mode effects are present. The scattering in a Ni-doped specimen was found to be largely due to the difference in mass between the Ni and Mg ions, whereas that in Fe-doped specimens was largely due to a process resonant atca. 100 cm-1.

Observation of Higher-Order Acoustic Paramagnetic-Resonance Transitions in MgO:Fe2+

The higher-order $\ensuremath{\Delta}m=3$ and $\ensuremath{\Delta}m=4$ transitions in MgO: ${\mathrm{Fe}}^{2+}$ (effective spin = 1) have been observed directly by acoustic paramagnetic resonance. The angular dependence and temperature dependence are found to differ significantly from the normally "allowed" $\ensuremath{\Delta}m=1$ and $\ensuremath{\Delta}m=2$ transitions. A theory due to Fedders and Myles agrees well with the observed behavior of the $\ensuremath{\Delta}m=4$ line.

Ferrous ions in ruby crystals. (Cross relaxation processes)

Acoustic paramagnetic resonance measurements have been made on a ruby crystal doped with iron and silicon. The presence of Fe2+ ions is confirmed but no other fast relaxing ions were found. The results are discussed particularly in relation to previous measurements of T1 of the Cr3+ ions in ruby.

Acoustic paramagnetic resonance of V 4+ ions in Al 2O 3

A.P.R. spectra of V 4+ ions were observed at 8975 MHz. From intensity measurements, an estimate of some dipolar spinphonon coupling constants was made: | F 11| = | F 12| ≈ 200 and | F 41| ≲ 20.

Dynamical Jahn-Teller Effects for aV3+Ion in a MgO Crystal

A theory of the acoustic paramagnetic resonance APR for ${\mathrm{V}}^{3+}$ ions in MgO is developed to explain the results of Brabin-Smith and Rampton which shows the importance of the second-order spin-orbit interaction resulting from Jahn-Teller interactions, i.e., from the excited vibronic levels. Essentially, it is this interaction which is responsible for lifting the degeneracy of the spin-orbit ground states ${E}_{g}+{T}_{2g}$ of the ${\mathrm{V}}^{3+}$ ions in the cubic state. Straightforward APR experiments give the $g$ value within the excited triplet ${T}_{2g}$ and the magnitude of the zero-field separation ($D$) between the ${T}_{2g}$ and ${E}_{g}$ levels is deduced from the study of the dependence of the APR spectra on temperature. The magnitudes of the Jahn-Teller energy ${E}_{\mathrm{J}\mathrm{T}}$ and the frequency ${\ensuremath{\omega}}_{E}$ of the ${E}_{g}$ mode of vibration of the molecular cluster formed around a ${\mathrm{V}}^{3+}$ ion, which give the best fit with the experimentally observed parameters $g$ and $D$, are in good agreement with the estimate of ${E}_{\mathrm{J}\mathrm{T}}$ in an effective point-charge model and with the results on phonon sidebands in MgO crystals doped with different paramagnetic impurities, respectively. The strongly asymmetric nature of the line shape is explained by taking into account the presence of small random strain fields of tetragonal and orthorhombic nature about the cubic site. The experimentally determined hyperfine parameter $A$ is fitted in this theory, assuming the magnitude of the contact term $k$ to be 0.2.

Theory of Acoustic Paramagnetic Resonance in Dense Magnetic Insulators

Several mechanisms which describe the interaction between spins and phonons in a dense paramagnetic insulator are theoretically explored in order to estimate their resonant contribution to the ultrasonic attenuation at high temperatures. In particular, one mechanism provides a quasiresonant contribution to the attenuation which is roughly proportional to the square root of the difference of the frequency and certain multiples of the Larmor frequency. Other mechanisms may lead to the same type of line shape.

Acoustic Paramagnetic Resonance Spectrum ofCr2+in MgO

The theory of acoustic paramagnetic resonance (APR) for the ${\mathrm{Cr}}^{2+}(3{d}^{4})$ ion at cubic crystal sites with octahedral coordination is developed for comparison with data by Marshall and Rampton for ${\mathrm{Cr}}^{2+}$ in MgO. An analytic model that takes explicit account of random strain is obtained and shown to predict in a simple way both the angular dependence of the resonance lines and the asymmetric line shape found experimentally. Although most ${\mathrm{Cr}}^{2+}$ ions experience distortions of effectively orthorhombic symmetry, the apparent presence of a tetragonal distortion at the site of the relatively few acoustically active ions is shown to result from the conditions of the experiments, in which the random strain splitting of the ${\mathrm{Cr}}^{2+}$ levels is typically larger than the acoustic energy quantum. Using this model, we show that the data for ${\mathrm{Cr}}^{2+}$ in MgO may be accounted for quantitatively if the ${\mathrm{Cr}}^{2+}$ is subject to a dynamic Jahn-Teller effect for which the tunneling splitting $3\ensuremath{\Gamma}$ is large compared with the spin-orbit splitting of the $^{5}E$ state. This interpretation differs from one proposed previously by Fletcher and Stevens, in which a much smaller value for $3\ensuremath{\Gamma}$ was obtained. It is shown that from presently available data one cannot yet determine $3\ensuremath{\Gamma}$ or other Jahn-Teller parameters of the system with any certainty. The theory of a dynamic Jahn-Teller effect for a $^{5}E$ state is developed in a general way to encompass the regime of weak Jahn-Teller coupling, which would be applicable to APR experiments on ${\mathrm{Fe}}^{2+}$ in tetrahedral coordination, while also including the limit of strong coupling in which the adiabatic approximation used by Fletcher and Stevens is applicable.

Acoustic Paramagnetic Resonance in a Dense Magnetic Insulator

The first observation of acoustic paramagnetic resonance in a dense magnetic system (RbMnF3) is reported and a theory proposed which correctly predicts the shape of the observed line.Received 27 August 1971DOI:https://doi.org/10.1103/PhysRevLett.27.1063©1971 American Physical Society

New results on the acoustic paramagnetic resonance of V 3+ in MgO

New experimental results of acoustic paramagnetic resonance of V 3+ in MgO are presented, which

Dynamical Jahn-Teller effects in V 3+ ion in a MgO crystal

The observed acoustic paramagnetic resonance spectra of V 3+ in MgO are shown to be due to the effects of the excited vibronic levels on the low lying spin-orbit states of V 3+ ion at the cubic site.

The acoustic paramagnetic resonance of x-irradiated ruby

The results of an acoustic paramagnetic resonance study of x-irradiated ruby using longitudinal ultrasonic waves at 9.1-9.6 ghz are presented. Most resonances are attributed to the cr2+ ion which is very strongly coupled to the lattice and is subject to a dynamic jahn-teller effect. Four principal resonances are observed with the magnetic field along the c axis at approximately 6.3 kg, 7.7 kg, 11.4 kg and 15.8 kg. These split up into several components as the field is turned away from the c axis. The results are in broad agreement with the theory of bates and dixon (1969). Lines due to other centres are observed.

Self-Induced Transparency in Acoustic Paramagnetic Resonance

Experiments on the propagation of microwave ultrasonic pulses through a resonant absorber are described. The principal features of self-induced transparency as described by McCall and Hahn for light pulses are observed. Quantitative measurements of pulse delay, output pulse width, energy, and area are in fair agreement with a calculation by Hopf which accounts approximately for the effect of the single reflection present in most of the experiments. Multiply reflected pulses exhibited linearly cumulative delay times, indicating constant reduced velocity during successive traversals through the absorber. Coherence-induced pulse breakup is shown to be a possible explanation of the pulse distortion and modulation observed in acoustic-paramagnetic-resonance experiments on ${\mathrm{Fe}}^{2+}$.

Saturation and instability in acoustic paramagnetic resonance

The saturation behaviour of an acoustic paramagnetic resonance experiment is derived in the steady state for a variety of lineshapes, using a semiclassical phenological model. Above a critical acoustic power instability appears and oscillations of acoustic power grow as they propagate through the system. Conditions are given for the appearance of the instability. The oscillations should be observable in acoustic paramagnetic response experiments.

Ultrasonic Study of the Properties of the Ferrous and Ferric Ions in Corundum

Ferrous and ferric ions properties in corundum from observing acoustic paramagnetic resonance

The thermal conductivity of Ni 2 + doped KMgF 3 in a magnetic field at low temperatures: the effect of single ions and coupled pairs

The thermal conductivity between 0.4 and 4.2 K and in magnetic fields up to 50 kOe of KMgF 3 doped with Ni 2+ has been measured. The results are analysed to give values of the average spin-lattice coupling constants ( x Sl ) for the Ni 2+ ion. These are in agreement with values calculated using the magneto-elastic constants (GX1 and 6r44) derived from acoustic paramagnetic resonance (a.p.r.) experiments. Below IK the thermal resistivity as a function of magnetic field shows a number of anomalies, for which possible causes are discussed; it is concluded that they result from phonon interactions with exchange-coupled pairs of Ni 2+ ions. Such pairs are also observed in a.p.r. experiments.

The spin-phonon interaction of Ni 2+ ion pairs in KMgF 3

Unexpected lines in the acoustic paramagnetic resonance spectrum of KMgF 3 :Ni 2+ are assigned to second nearest neighbour and more distant Ni 2+ ion pairs. Exchange parameters are deduced for the pairs, and the mechanism for their spin-phonon interaction is inferred to be the single-ion, ( S 1 . d . S 1 ) + ( S 2 - d . S 2 ) process.

Acoustic paramagnetic resonance investigation

Acoustic paramagnetic resonance investigation

Phonon and Photon Paramagnetic-Response Line Shapes in Ruby

Acoustic-paramagnetic-resonance (APR) and electron-paramagnetic-resonance (EPR) line shapes have been measured in ruby for various ${\mathrm{Cr}}^{3+}$ concentrations. The second-moment theory of Pryce and Stevens is shown to be applicable to APR as well as EPR, predicting the same second moments $〈\ensuremath{\Delta}{\ensuremath{\nu}}^{2}〉$ for both APR and EPR transitions. Experimentally, the APR and EPR line shapes are indeed identical for the same transition; however, the theory predicts a larger $〈\ensuremath{\Delta}{\ensuremath{\nu}}^{2}〉$ than measured, because the larger Cr-Cr interactions do not appear in the observed line. A qualitative calculation of $〈\ensuremath{\Delta}{\ensuremath{\nu}}^{2}〉$ from the known interactions supports this conclusion.