Volume 37, Issue 3, 01 March 1966
 GARNETS


aāc Exchange in the Garnets
View Description Hide DescriptionIn the ferrimagneticgarnets the aād (octahedralātetrahedral) exchange is the dominant one and reasonable values of the other exchange values are difficult to obtain. Thus, direct measurement of some of the smaller exchange constants is of interest because of the ambiguity of the values obtained by molecular field analysis. In this paper an optical technique is used to measure the aāc exchange of Cr^{3+}āGd^{3+} in the garnet Gd_{3}Ga_{2}(GaO_{4})_{3}. The 16a site is octahedrally coordinated and the rare earth is on the 24c site. The structure on sharp redline fluorescence from the Cr^{3+}ions is measured. The fluorescence transitions are from the excited ^{2} E state to the ground ^{4} A _{2} state; thus the exchange constant in both states can, in principle, be determined. The analysis of the aāc interaction was done by assuming a Heisenberg Hamiltonianwhere the sum is over the six nearestāneighbor Gd^{3+}ions each with a span . The most probable value ofis 8. The Cr^{3+}āGd^{3+} exchange splitting in the ^{2} E state of Cr^{3+} is just resolvable. A detailed fitting of the lines gives J=0.32 cm^{ā1} (0.46Ā°K). The Cr^{3+}āCd^{3+} exchange splitting of the Cr^{3+}ground state is not resolvable. However, the lowātemperature linewidth is much too wide to be due to anything except an exchange splitting. Fitting the line one obtains an exchange value in the ground state approximately half the excited state.

Influence of JahnāTeller Ions on the Acoustic and Magnetic Properties of YIG
View Description Hide DescriptionThe presence of Mn^{3+} ions in YIG leads to a large lowātemperature acoustic loss and to a reduction in soundvelocity. In the range of 1 to 15 Mc/sec, these effects increase rapidly with decreasing temperature. In addition, the presence of Mn^{3+} also gives rise to a large microwave loss which peaks at 37Ā°K for 15 kMc/sec and at 58Ā°K for 56 kMc/sec. In the range of 0 to 1 wt % Mn additions, both acoustic and microwave losses increase monotonically with Mn content. The observed effects are attributed to relaxation between the three possible directions of the JahnāTeller distortion. At high temperatures the relaxation time becomes characteristic of thermal activation over a potential barrier. At low temperatures the relaxation time becomes independent of temperature which is characteristic of quantumāmechanical tunneling. A simple model gives a reasonable description of the observed results in YIG, and a comparison with Mn^{3+} in YAG or Ni^{3+} in corundum indicates that the remaining discrepancies may be attributed to the exchange field and magnetostrictive effects. The latter are substantially enhanced by the presence of Mn.

IronāIron Exchange Resonance in GaāSubstituted EuIG
View Description Hide DescriptionThe ironāiron exchange resonance in the garnet system Eu_{3}Fe_{5āx }Ga_{ x }O_{12} has been studied as a function of x at 4.2Ā°K. In zero field, v=200 cm^{ā1} at x=0 and decreases to zero near the angular momentum compensation point x=1.2. It then rises to a maximum of 9 cm^{ā1} at x=1.35 and falls for larger x. Measurements in a magnetic field indicate a spin flop at the magnetic moment compensation point x=0.75, and an anomalous dispersion in the g factor near x=1.2. These results are in good agreement with a two sublattice model of EuIG for x<1. The tetrahedralāoctahedral iron exchange molecular field constant Ī»=500 kOe/Ī¼_{B}.

Crystal Field Effects for Ce^{3+} and Yb^{3+} in the Garnets
View Description Hide DescriptionWe show that the methods used by Hutchings and Wolf for fitting the Yb^{3+}spectra in the garnets can be employed, with suitably modified spināorbit and crystalāfield parameters, to calculate the energy levels and wave functions of the electronically similar ion Ce^{3+}. The results are in sufficient agreement with infrared data to verify our interpretation of the Ce^{3+}spectrum and at the same time to support strongly the Hutchings and Wolf results for Yb^{3+}.

Anisotropy of the RareāEarthāIron Exchange Interaction in Garnets
View Description Hide DescriptionWe have evaluated the exchange splittings of the lowest ^{2} F _{5/2} and ^{2} F _{7/2} doublets of Yb^{3+} in YbIG, in terms of the exchange potential parameters given by us in a previous article, by using the wave functions of Yb^{3+} in YGaG. As there are ten exchange potential parameters and only six experimental splittings, it was necessary to reduce the number of unknowns by assuming: (1) that the REāFe exchange interaction takes place through the neighboring eight oxygen ions, and (2) that the rareāearthāoxygen (REāO) exchange potential is axial about the REāO axis. Defining A (m_{l} ) by:we find a good fourāparameter fit of the experimental exchange splittings by assigning the values A (m_{l} =0) = 6.41 cm^{ā1}, A (m_{l} =Ā±1) = 6.52 cm^{ā1}, A (m_{l} =Ā±2) = ā29.6 cm^{ā1}, A (m_{l} =Ā±3) = 6.17 cm^{ā1} to the REāFe exchange interactions that take place through the nextānearest oxygen ions, and by adopting essentially zero values for the REāFe exchange iuteractions that take place through the nearest oxygen ions. This result corroborates qualitative conjectures based on superexchange bonding anglcs.

Magnetization of Holmium Iron Garnet at 4.2Ā°K
View Description Hide DescriptionMagnetic measurements have been made on a spherical single crystal of holmiumirongarnet at 4.2Ā°K, in fields of up to 44 kOe. The sample was mounted in such a way that, by rotation about a ć110ć direction, any direction lying in the plane perpendicular to the axis of rotation could be brought parallel to the applied field and held there. An extraction method was used for these measurements.
In any direction, domain movement is observable only below 6 kOe; above this the magnetization varies linearly: M (H) = M (0)+ĻH. M (0) has a flat maximum about the direction of easy magnetization ć111ć. The directions ć110ć and ć100ć are directions of difficult magnetization where M (0) exhibits very sharp minima. We find that M (0) varies proportionally with the cosine of the angle between the ć111ć axis and the direction of the field. This is in conformity with the results of neutron diffraction experiments. The maximum value of M (0) gives a value for the resultant magnetic moment of 13.6 Ī¼_{B} per formula unit Fe_{5}Ho_{3}O_{12}. The differential susceptibility in this direction is equal to 0.02 Ī¼_{B}/kOe=1.27Ć10^{ā4}/g, and is larger in the other directions. The canted arrangement of the moments of the holmium ions is thus sensitive to the field in this temperature range.

FrequencyāDependent Anisotropy in Siā and CaāDoped YIG and LuIG
View Description Hide DescriptionThe magnetic anisotropy of small spherical samples of Siā and Caādoped singleācrystal yttrium and lutetiumirongarnets has been studied at 10 and 25 kMc/sec over the temperature range from 4.2Ā° to 300Ā°K. The experimental results have been compared with similar data from static torque measurements. There is a considerable difference between the microwave and static magnetic anisotropy in dopedgarnets, while for pure garnets the agreement between the microwave and static data is very good. In particular, the microwave firstāorder anisotropy constant in Siā and Caādoped garnets is less negative than the static anisotropy constant, which is independent of doping, and the difference between the two types of measurements is linearly proportional to the doping density. In Caādoped garnets the microwaveanisotropy constant becomes zero at about 5.5% doping density, and for larger Ca concentrations changes sign and becomes positive. The same effect, although of lesser magnitude, is observed in Siādoped garnets. The frequency dependence of the microwaveanisotropy is confirmed by measurements at two different wavelengths. As expected, the deviation of the microwaveanisotropy constant from the static one is larger at 25 than at 10 kMc/sec.

NMR Study of Iron Sublattice Magnetization in YIG and GdIG
View Description Hide DescriptionThe ^{57}Fe NMR frequencies in the two iron sublattices of YIG and GdIG have been measured accurately at 5Ā° to 15Ā°K intervals from 4.2Ā° to 500Ā°K. We have also measured the pressure dependence of the ^{57}Fe NMR frequencies in YIG to 10 kbar at 196Ā°, 273Ā°, 299Ā°, and 346Ā°K. In YIG, we find the pressure dependence of the critical temperature to be āT_{c} /āP = 0.69Ā°Ā±0.02Ā°K/kbar. The results of the pressure measurements have been used to correct the NMR frequencies for thermal expansion. From these data the temperature dependence at constant volume of each sublattice magnetization has been determined to about 0.01% precision. A spināwave analysis of the lowātemperature data gives the dispersion constant for the acoustic spināwave mode as D=31.8Ā±1 cm^{ā1}. Our NMRmeasurements of the iron sublattice magnetizations in GdIG have been combined with total magnetization data to obtain the Gd sublattice magnetization up to 0.9 T_{c} . The Gd magnetization can be fit quite well by a molecular field calculation and yields estimates of the exchange constants to be J_{cd} =ā3.46 cm^{ā1}, J_{ca} =ā0.22 cm^{ā1}, and J_{cc} =ā0.13 cm^{ā1}.

Sublattice Magnetization in Several RareāEarth and Yttrium Iron Garnets by Means of ^{57}Fe NMR
View Description Hide DescriptionWe have observed the NMR of ^{57}Fe on the a and d sublattices of YIG, GdIG, and LuIG between 4Ā° and 200Ā°K. Using the spināecho technique the frequencies could be determined to within a few kHz. For LuIG the determination of the frequency was less accurate due to the presence of the lutetiumresonances which overlay the ironresonances. Assuming the frequency is proportional to the sublattice magnetization, the data were fitted to the equation derived from spināwave theory. For YIG and LuIG inclusion of the T ^{7/2} term was necessary to represent the data above 40Ā°K. Using the theory of noninteracting spin waves we have derived expressions for the sublattice magnetizations in terms of the exchange integrals J_{aa}, J_{ad}, J_{dd} , and Jā²_{ad} , where Jā²_{ad} describes interactions between nextānearestāneighboring pairs of spins on the a and d sublattices. Our experimental results indicate that J_{aa} and J_{dd} are not negligible. The coefficients were found to be about 15% larger for LuIG than for YIG. Our value of the exchange stiffness constant of YIG is 10% larger than those determined calorimetrically and hence agrees with values determined by microwave instability measurements. For LuIG our value of this constant agrees with the specific heat value.

Magnetostriction of Dysprosium, Holmium, and Erbium Iron Garnets
View Description Hide DescriptionThe temperature and field dependences of the anisotropic magnetostriction coefficients of Dy, Ho, and Er iron garnets were measured from 78Ā°K to room temperature. At the compensation points there is a reversal in the fieldādependent magnetostriction (anisotropic forced magnetostriction) and a sharp dip in the apparent saturation magnetostriction. At high temperatures, the magnetostriction coefficients approach the values measured previously for YIG (ā 10^{ā6}). At low temperatures, large strains arise because of the large magnetoelastic coupling of the rareāearth ion: Ī»_{100} (0Ā°K) _{REIG}/Ī»_{100} (0Ā°K) _{YIG}ā 10^{3}; Ī»_{111} (0Ā°K) _{REIG}/Ī»_{111} (0Ā°K) _{YIG}ā 50. Estimates of the 0Ā°K magnetostrictions based upon the singleāion theory of magnetoelastic coupling are ā1400, ā930, and 420Ć10^{ā6} for Ī»_{100}, and ā550, ā220, and ā300Ć10^{ā6} for Ī»_{111} of Dy, Ho, and Er iron garnets, respectively. These values, although 50 to 1000 times larger than YIG, are one order of magnitude smaller than the enormous strains observed in the heavy rareāearth metals. This difference can be accounted for by the difference in elastic moduli and density of rareāearth ions. In both the metal and garnet the magnetoelastic coupling coefficient of the rareāearth ion is approximately 10^{3} cm^{ā1}.

HighāTemperature Electronic Relaxation at the RareāEarth Ions in Garnets
View Description Hide DescriptionThe electronic relaxation times at Tb^{3+}, Sm^{3+}, and Tm^{3+}ions in magnetic iron and nonmagnetic gallium and aluminumgarnets have been studied by gammaāgamma angular correlation experiments. The relaxation time of Tb^{3+} in irongarnets reaches a minimum value of ā¼10^{ā11} sec at higher temperatures, considerably larger than similar values for the Sm^{3+} and Tb^{3+}ions in irongarnets. The Tb^{3+} ion relaxation time in irongarnet was independent of temperature from below room temperature to 1100Ā°K. This result suggests that the transitions which determine the relaxation time occur between closely spaced levels. In Sm^{3+} in irongarnets the relaxation time Ļ_{ s }ā¼[exp(Ī/KT)ā1] with Ī/K=250Ā°K, while in Tm^{3+} Ļ_{ s }ā¼T ^{ā1}. No significant differences were observed between the relaxation times in magnetic iron and nonmagnetic gallium or aluminumgarnets at room temperature. In the case of Sm^{3+} and Tm^{3+} where no temperature saturation effects have been observed this result seems to indicate that processes involving spin magnoninteractions and phonon modulation of the exchange field do not play a dominant role in the rareāearth ion relaxation process in rareāearth irongarnets at room temperature.

Anisotropic Magnetic Resonance and Relaxation in SiliconāSubstituted YIG
View Description Hide DescriptionThe magnetic resonance behavior of siliconāsubstituted yttriumirongarnet (YIG) crystals having the average ionic composition {Y_{3} ^{3+}} [Fe_{1.95} ^{3+}Fe_{0.05} ^{2+}] (Fe_{2.95} ^{3+}Si_{0.05} ^{4+})O_{12} has been investigated as a function of temperature and orientation at 9 Gc/sec. Unexpectedly, four extrema were observed in the resonance field H _{res} at low temperatures. For example, the values of H _{res}(100)=1575 Oe, H _{res}(111)=1985 Oe, and H _{res} (110)=2175 Oe were measured at 77Ā°K. Further measurements at 24 Gc/sec indicated that g=2Ā±0.02 from 300Ā° to 77Ā°K. This inverted anisotropy can be described phenomenologically by an isotropic downward shift of 1260 Oe and the cubic anisotropy fields K _{1}/M _{0}=200 Oe and K _{2}/M _{0}=ā540 Oe. These K _{1}>0 and K _{2}<0 values are attributed to the Si^{4+}āinduced Fe^{2+}ions. The enormous isotropic depression of H _{res} is shown to be predicted by an extended formulation of the ``slow'' relaxation theory. A peak was observed in the resonancelinewidth ĪH(100) of 60 Oe at about 350Ā°K corresponding to ĻĻ(100)=1. Because of the appearance of multiple absorption modes due possibly to nonuniform Si substitution, the second predicted peak in ĪH could not be observed. Since the activation energy of both the resistivity and relaxation time constant Ļ(100) was 0.30 eV, it is suggested that the quasiāfree valence electrons of the induced Fe^{2+}ions constitute the slowārelaxing system in YIG (Si_{0.05}).

Induced Anisotropy of SiliconāDoped YIG
View Description Hide DescriptionThe induced anisotropy of singleācrystal siliconādoped YIG (Y_{3}Fe_{5āĪ“}Si_{Ī“}O_{12}; 0ā¤Ī“ā¤0.18) was studied by means of a torque magnetometer. It was found that the annealed component of the torque could be adequately described by a free energy of the formwhere Ī±_{ i } and Ī²_{ i }, respectively, specify the direction cosines of M during measurement and anneal.
A model consistent with these observations was formulated. Specifically, it was assumed that the annealedanisotropy was caused by an ordering of the Fe^{2+}ions over the four types of magnetically inequivalent octahedral sites. Taking into account the interaction of crystal field, spināorbit, and exchange interaction, a calculation of the energy levels of the octahedrally coordinated Fe^{2+} ion provides an eigenvalue spectra compatible with the symmetry and magnitude of A ^{an}.
