Index of content:
Volume 34, Issue 4, 01 April 1963
- MAGNETOELASTIC AND MAGNETO‐OPTIC EFFECTS
34(1963); http://dx.doi.org/10.1063/1.1729446View Description Hide Description
Well‐defined exchange splittings of the R lines of Cr3+ in Cr2O3 have been observed in absorption at low temperatures. The majority of the transitions originate on the lowest component of the 4 A 2 (ground) state and terminate on the four (exchange split) components of the two 2 E levels. The lines show strong polarization effects, the outer two components of the four line group appearing in the perpendicular spectrum and the inner two components appearing in the parallel spectrum. From the observed polarizations and from relative intensity measurements the identity of each of the components has been deduced. On the basis of the identifications made, the exchange splitting of the R 1 doublet is approximately 183 cm−1 and that of the R 2 doublet is approximately 139 cm−1. A ground‐state splitting of 245±20 cm−1 is obtained from a weak line originating on the level. The trigonal field (plus spin orbit) splitting of the 2 E levels can also be deduced from the spectrum. The splitting would appear to be very small (of the order of 1 cm−1) compared with that of Cr3+ in ruby (29.6 cm−1) and of the opposite sign.
34(1963); http://dx.doi.org/10.1063/1.1729447View Description Hide Description
It is shown in detail how the magnetoelectric effect depends quadratically on the spin‐orbit interaction. The effect is discussed in Cr2O3 using the spin Hamiltonian for the cases of an applied field parallel and perpendicular to the crystalline c axis.
34(1963); http://dx.doi.org/10.1063/1.1729448View Description Hide Description
A marked variation of contrast over the field of view has been discovered in apparatus for displaying domains by means of the Kerr longitudinal magneto‐optic effect when convergent light is used to illuminate the sample. One of the effects seen is a rather dark central band parallel to the mean plane of incidence when polarizer and analyzer are crossed and one polarizes in the mean plane of incidence. Within this band there is no contrast between antiparallel domains, but on either side there is a region of strong contrast, and if a domain pattern is moved from one of these to the other its contrast reverses. The band of zero contrast moves at right angles to the mean plane of incidence if the polarizer is rotated, and tilting the sample gives a similar effect. Simple classical explanations of the effects are given, taking into account both metallic and Kerr ellipticities.
34(1963); http://dx.doi.org/10.1063/1.1729449View Description Hide Description
The operation of an optical modulator based on the time‐varying optical Faraday rotation produced by the precessing magnetization in a magnetic material is analyzed, and experimental results given for an X‐band modulator using a thin disk of yttrium iron garnet. The analysis is valid for both lumped and traveling‐wave magneto‐optical interactions, and leads to a figure of merit on the basis of which some presently available ferrimagneticmaterials are compared.
34(1963); http://dx.doi.org/10.1063/1.1729450View Description Hide Description
We have investigated the Zeeman effect of the R lines at 4.2°K in fields up to 88 kOe. The magnetic field has been applied both parallel and perpendicular to the C 3 axis. When the external field is applied along the C 3 axis, all of the lines split into two components. No splitting is observed in the perpendicular orientation. As the Kramer's degeneracy has already been lifted by the exchange field, the splitting is attributed to the removal of a sublattice degeneracy. It is well known that the spin system of Cr2O3 will flip when a critical field of about 59 kOe is applied along the C 3 axis at 4.2°K. The spin‐flop phenomenon has been seen in the optical spectra. From the splitting above the critical field there is tentative evidence of an anisotropicexchange interaction.
34(1963); http://dx.doi.org/10.1063/1.1729451View Description Hide Description
The optical properties of magnetic materials are studied using symmetry considerations. It is found that in addition to birefringence,Faraday rotation, and optical activity there should exist another effect, namely gyrotropic birefringence. This birefringence is of opposite sign for magnetic domains related to each other by time reversal, and can, therefore, in principle be used for observation of antiferromagnetic domains so related. The dependence of the optical properties on external agents such as electric and magnetic fields and stress is also considered.
34(1963); http://dx.doi.org/10.1063/1.1729452View Description Hide Description
Far‐infrared (10–100 cm−1) spectroscopic transmission measurements have been made on sintered powder samples of ferrimagnetic holmium, samarium, and gadolinium iron garnets. Both single‐ion transitions and also the Kaplan—Kittel exchange resonances have been observed in HoIG and SmIG. A breakdown of selection rules permits the observation of the single‐ion transitions, in which the effective angular momentum of a single rare‐earth ion changes in the presence of the crystalline electric and iron exchange fields. Because no magnetic absorption is observed in GdIG, single‐ion transition probabilities appear to be governed by the effect of the local crystalline electric field on the rare‐earth ion, as expected theoretically. Experimentally, one can distinguish the collective modes because their resonant frequencies are more temperature dependent than those of the single‐ion transitions.
34(1963); http://dx.doi.org/10.1063/1.1729453View Description Hide Description
The far‐infrared transmission spectra of a variety of magnetic insulators have been measured using the techniques of Fourier‐transformation interferometry.Antiferromagnetic resonance has been observed for the first time in CoF2, NiF2, and KNiF3, and the ferrimagneticresonance in YbIG has been found near 0°K. The temperature dependences of these resonances have been measured and, in the case of the iron‐group fluorides, the results are compared with the Zener theory for the temperature dependence of the anisotropy energy. Resonances previously found by other investigators in YbIG, MnF2, MnO, and NiO have been observed with (in most cases) improved precision.
34(1963); http://dx.doi.org/10.1063/1.1729454View Description Hide Description
The ground state of the free Co2+ ion, 4F(3d 7), splits into an orbital triplet 4 T 1, another triplet 4 T 2, and a singlet 4 A 2 in a cubic field. Among these states, the 4 T 1 state has the lowest energy. The degeneracy of the ground state4 T 1 is further lifted by the spin‐orbit interaction and the crystalline field with rhombic symmetry and thus the fine structure multiplet consists of six Kramers' doublets.
Newman and Chrenko1 observed several absorption peaks in the 0.15 to 0.20 eV range both above and below the Néel temperature (TN =38°K). These peaks correspond to transitions within the ground state multiplet. Changes in the spectrum below TN appear in the number of the peaks and their intensities. Recently, Dietz2 has found out that these are magnetic dipole transitions.
The explanation of these experimental facts by the crystal field theory is reported. Nakamura and Taketa3 pointed out an important role of the rhombic crystal field in understanding the anomalous behavior of the temperature dependence of the magnetic anisotropy. We show that the rhombic component of the crystal field is also important in explaining the number of peaks and their relative intensities.
The numerical values of the axial crystal field Δ, the rhombic crystal field Γ, the over‐all spin‐orbit coupling constant λ, effective Lande factors −ρ and −η, and the exchange integral J are determined from the experimental data of peak positions above TN and the temperature dependence of the magnetic anisotropy For this purpose the expressions for and are derived, taking the effect of the unquenched orbital angular momentum into account. Better agreement with observed anisotropy are obtained by our theory than by Nakamura and Taketa's. The values of parameters thus obtained are: Δ = −707 cm−1, Γ = −183 cm−1, λ = −157 cm−1, ρ = 1.125, η = 1.59, and J = 2.6 cm−1. By using these values, g values are calculated. The result is gx = 6.18, gy = 4.07, and gz = 2.03, where y and z axes are taken along the c axis and the line connecting two nearest neighbor F− ions, respectively. These values are very close to the observed ones.5 And further, we predict the energy separation of the lowest two Kramers' doublets to be 175 cm−1 (255°K). This is in good agreement with the observed value of 240°K determined from the Shottky‐type anomaly in the specific heat measurement, although the observed value is rather uncertain.6
The magnitude of the splitting of each peak by the molecular field, intensities of the split peaks, and the dichroic behavior for polarized light are also calculated. The comparison with the observed spectrum below TN shows that the number of peaks in the observed spectrum exceeds that given by the theory and that observed intensities below TN are not explained by the theory. The former disagreement is expected to be resolved by taking into account a simultaneous excitation to different excited states of two adjacent Co ions coupled by the exchange interaction, instead of molecular field approximation. Finally, the expression for the antiferromagnetic resonance frequency is derived. The contribution from the anisotropy due to the crystal field is quite large. The frequency is estimated to be 21 cm−1.
34(1963); http://dx.doi.org/10.1063/1.1729455View Description Hide Description
Chromium tribromide is one of the few ionic ferromagnetic crystals known. It has a hexagonal layer structure, and its Curie point is at about 36°K. Thin sections are transparent from the near infrared up to a strong sharp band edge at about 20 000 cm−1. Below this band edge a number of broad bands and sharp lines are observed. Linearly polarized light passing through a magnetically saturated crystal experiences a rotation of the axis of polarization which varies with wavelength and is proportional to the magnetization component along the line of sight. Exceedingly large magnetic rotations are associated with the band edge near 20 000 cm−1 where values of over 500 000° / cm were measured. The detailed structure of the 2 T 2 absorption at about 19 000 cm−1 seems to involve the ferromagnetic exchange coupling. An assignment is given for the band edge. Microwave‐optical experiments have been performed in which ferromagnetic resonance has been observed visually and light has been amplitude modulated at 23 and 46 kMc.
34(1963); http://dx.doi.org/10.1063/1.1729456View Description Hide Description
Magnetic field induced magnetoelectric (ME) effects in Cr2O3 and (Cr2O3)0.8·(Al2O3)0.2 have been examined with an ac method as a function of temperature and magnetic field. The ME effect parallel to the c axis reverses in sign at low temperatures for both materials, and is linear in H for all temperatures up to the spin‐flop field HC after which the ME effect approaches zero. The temperature dependence of the extrema of (dE/dH) vs H leads to a measure of HC vs T which agrees with earlier antiferromagnetic resonance and magnetic moment data in similar materials. Complete reversibility of the ME effect is observed when the magnetic field exceeds HC and then returns to lower values, thus demonstrating a stable memory of the domain distribution introduced during magnetic annealing. Brief remarks are made on the angular dependence of the ME effect, and indications of nondiagonal contributions in the vicinity of HC are mentioned.