Molecular Field Constants Research Articles

Exchange-striction of rare earth-Al 2 laves phase compounds

The exchange-striction of the cubic Laves phase compounds R-Al 2 ( R =Gd, Tb, Dy, and Ho) has been determined at 0 K from measurements of thermal expansion. The results are interpreted in terms of rare earth sublattice ( R- R) interactions, using the molecular field approximation. It is found that the signs of the strain derivatives of the molecular field constants are positive for Dy-Al 2 and Ho-Al 2 and negative for Gd-Al 2 and Tb-Al 2 compounds.

Magnetic Torque of Ferrimagnetic Materials Near the Compensation Point

The behavior of uniaxial magnetic torque is studied for ferrimagnetic materials consisting of nearly compensated sublattice moments. The magnetic anisotropy is assumed to originate from the (pseudo) dipolar interaction of atom pairs. In the calculation of the magnetic torque, some approximations are used considering the material constant of Gd–Co and Gd–Fe amorphous alloys. The behavior of the torque curve is characterized by the parameter r=Ku/λM2, where Ku is the anisotropy constant, and λ is the molecular field constant for the sublattice interaction. The parameter r can be estimated from the magnetization curve in the hard direction. If r<0.5, the anisotropy is shown to be determined by the amplitude of the torque curve by applying a field of appropriate magnitude.

Magnetic ordering in ternary rare earth iron aluminium compounds (RFe4Al8)

The magnetic properties of the tetragonal ternary compounds RFe4Al8(R=La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Y and Th) were investigated. An analysis of the data is given in terms of a molecular field model involving three magnetic sublattices: the R sublattice and two antiparallel-coupled Fe sublattices. It was found that in RFe4Al8 the iron moments are coupled antiparallel to the rare earth spin moments. Estimates are given of the molecular field constants associated with the R-Fe interaction and the Fe intrasublattice interaction. Most of these compounds were also investigated by 57Fe Mossbauer spectroscopy. Values are given for the effective hyperfine fields and the isomer shifts. This technique also made possible an accurate determination of the magnetic ordering temperatures, which were difficult to detect by magnetic measurements, even though the Fe moment is about 0.7 mu B/Fe in the magnetically ordered state. The magnetic ordering temperatures range from 140 to 200K. The effective moment of the Fe atom in the paramagnetic regime is about 3.8 mu B/Fe. The magnetic properties of GdMn4Al8 and YMn4Al8 were also determined.

Thermal and Magnetic Study of CoBr2·6H2O

The measurements of specific heats, isentropic curves and isothermal susceptibilities under an external field are carried out for single crystals of CoBr 2 ·6H 2 O. The hysteresis is observed at the phase boundary between antiferromagnetic (AF) and spin-flopping (SF) states. The molecular field constants are calculated from the magnetic specific heat and the magnetic phase diagram. The two kinds of path in exchange interaction at the ab plane, so called J 1 and J 2 are estimated as 1.75 k B and 1.13 k B respectively. The other path of exchange interaction J 3 along the c axis, is determined as 0.57 k B . The critical exponents of specific heat near the Neel point are shown as α=0.6±0.1 and α'=-0.1±0.1 at zero magnetic field.

High field magnetization of NdAl 2 single crystals interpreted with crystal field theory

The magnetization of NdAl 2 single crystals was measured at 4.2, 20.3 and 77 K, in magnetic fields up to 35 tesla applied in the 〈100〉, 〈110〉 and 〈111〉 directions. The magnetization in these directions may be described theoretically, without any fitting, in terms of two cubic crystalline electric field parameters and one molecular field constant which have been taken from inelastic neutron scattering data. 5

The effect that finite lattice spacing has upon the ESR Bloch equations

The ESR Bloch equations are rederived within a model which allows for finite lattice spacing. It is found this causes the usual Bloch equations to be modified. The internal field as seen by the local moments is changed from Hext+ lambda Me to Hext+ lambda Me+ alpha Me where alpha = lambda 2( Sigma i not=jF1(Rij)- chi e0) and where Hext is the total external field, lambda is the molecular field constant, F1(R) is the usual RKKY range function, chi e0 the static conduction electron susceptibility and Rij is the distance between the sites i and j. The effect this change has upon various limits of physical interest is investigated, compared with the previous results and the experimental data for Mg-Gd is discussed. Finally, the effect of short range correlations in dilute alloys is discussed and a set of generalized Bloch equations are proposed to account for the effects of such correlations in systems which exhibit structured resonances.

Molecular Field and Exchange Constants of Gd3+- Substituted Ferrimagnetic Garnets

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Magnetic Resonance of ZnCr2Se4 with Screw Spin Structure

Magnetic resonance of a ZnCr 2 Se 4 single crystal with screw spin structure was observed in the frequency range of 38∼83 GHz at above 4.2 K , mainly at 5.5 K . Frequency and angular dependences of the resonance field were successfully explained by a theory of first order perturbation due to uniaxial anisotropy. Data of the resonance, together with the results of static magnetization measurements, give two isotropic molecular field constants in k space: E (0)- E ( k 0 )=2.15 and E (0)- E (2 k 0 )=-0.01 (mole) and three anisotropy constants: K (0)=0.01 5 , K ( k 0 )=0.10 and K (2 k 0 )=-0.06 (mole). It is demonstrated conclusively that superexchange interaction through more than two Se ions is important in this substance.

Molecular Field Coefficients of Substituted Yttrium Iron Garnets

By fitting the Néel theory of ferrimagnetism to previously reported magnetic moment-temperature data for several {Y3}[RxFe2−x](QyFe3−y)O12compositions, where R and Q represent diamagnetic octahedral and tetrahedral substitutions, i.e., Sc3+, In3+, Ga3+, and Al3+, the molecular field coefficients were determined to have the following linear relations with the levels of substitution: Ndd=−30.4(1−043x),Naa=−65.0(1−042y),Nad=97.0(1−0.125x−0.127y) mole/cm3,for x≤0.70 and y≤1.95. Since both intrasublattice coefficients are affected only by substitutions in the opposite sublattice, a strong similarity to Geller's random canting concepts is apparent. Below the antiferromagnetic transitions it is demonstrated that a clear correlation exists between the decrease in sublattice moment from canting and the reduction in magnitude of the molecular field constant. For both sublattices, the antiferromagnetic transition occurs when Ndd, Naa∼−20 mole/cm3. This observation lends further credence to the notion that canting sets in immediately upon substitution. To demonstrate the applicability of the above results, magnetic moment-temperature curves are computed for compositions of {Y3} [Mgx2+Fe2−x] (Six4+Fe3−x) O12 and are shown to compare very favorably with experiment, thus providing a method for predicting the behavior of a wide variety of substituted garnet compositions.

Magnetic Investigation of Single Crystal of Ni(NH3)2·Ni(CN)4·2C6H6

The magnetic susceptibility of single crystal of Ni(NH 3 ) 2 ·Ni(CN) 4 ·2C 6 H 6 has been measured in liquid hydrogen and liquid helium temperature regions. The Neel temperature was found to be 2.37°K from the experimental results of proton resonance and specific heat measurements. The uniaxial anisotropy constant and the molecular field constant which are obtained from the present research, are respectively D / k =3.6°K and A / k =4.5°K and they are the same order of magnitude. The values of perpendicular susceptibility and spin-flopping field in antiferromagnetic state are well described using the values of uniaxial anisotropy constant and exchange interaction constant obtained in the molecular field approximation. The temperature dependence of parallel susceptibility χ // in antiferromagnetic state is in good agreement with the theoretical result calculated by the spin wave method, over the temperature range 0∼2.2°K. The preferred direction of sublattice magnetization is the c -axis of this crystal.

The pressure effect on the Curie temperature of the collective-electron ferromagnet: The origin of the invar effects

The pressure effect on the Curie temperature of the invar alloy is calculated by the molecular field theory for the collective-electron ferromagnet. The bandwidth ( W) is assumed to depend on R, the atomic-distance, in such a way that W ∝ R −5. Kanamori's effective correlation energy is employed as the molecular-field constant. The large negative pressure effect, which is observed in the invar alloy is obtained for a parabolic band and a more realistic band.

Thermal Expansion, Electrical Resistance and the Effect of Hydrostatic Pressure on the Néel Temperature in Fe-Mn Alloys

Thermal expansion, temperature change of electrical resistance and its change due to hydrostatic pressure, and magnetic susceptibility were measured with some antiferromagnetic Fe-Mn alloys containing 30 to 40 at% Mn. It was found that an additional magnetic volume expansivity, δ V / V , due to an antiferromagnetic spin ordering is as large as 10 -3 ∼10 -4 , and the change of the Neel temperature with pressure, ∂ T N /∂ P , is about -2.5×10 -3 deg·Kg -1 ·cm 2 in 30 at% Mn alloy. With these values, the volume dependence of the molecular field constant, ∂ A /∂ω, is estimated to be positive by the molecular field theory with the localized moment model. The results are discussed in comparison with Bethe-Slater's and Weiss' theories and with the similar behavior in some ferromagnetic invar-type alloys.

Molecular Force Field and Centrifugal Distortion Constants of Nitrosyl Fluoride

The microwave spectrum of nitrosyl fluoride, NOF, has been reinvestigated in the microwave region and extended into the millimeter wave region. Some 80 transitions, consisting of both ``a''- and ``b''-type transitions, have been measured and assigned. These data provide the information required for a centrifugal distortion analysis which yields the following ground-state rotational parameters (megacycles per second): A=95 189.77,B=11 844.12,C=10 508.31,τxxxx=−0.099630,τzzzz=−15.586926,τxxzz=0.418629,τxzxz=−0.289581,HJK=2.339×10−6andHKJ=−4.946×10−5. Combination of infrared data and microwave data yields the following quadratic potential constants millidynes per angstron, fr1=2.09, fr2=15.08, fα/d2=1.08, fr1r2=1.85, fr1α/d=0.17. Here fr1 and fr2 are the N-F and N-O bond force constants, respectively, and fα is the bond-bending force constant.

Low-Temperature Magnetic Susceptibilities of the Hydrated Nickel Nitrates

The zero-field magnetic susceptibilities of Ni(NO3)22H2O, Ni(NO3)24H2O, and Ni(NO3)26H2O have been measured in the liquid-hydrogen and liquid-helium ranges. The dihydrate is obtained by evaporation of a solution at 105°C.1 Its powder susceptibility has a large, sharp, peak at 4.20°K, where it reaches 0.74 cgs/mole, then drops down to 0.2 cgs/mole below 2°K. When measured along the a axis, the susceptibility of monoclinic single crystals of the dihydrate shows a similar peak. It reaches 1.5 cgs/mole, but drops to vanishing values at lower temperatures. The susceptibility in the bc plane reaches only 0.3 cgs/mole, and is nearly isotropic. It drops little below 4.20°K. This behavior is similar2-5 to that of FeCl2 or FeCO3, and suggests the existence of two magnetic sublattices, with strong ferromagnetic interactions within each sublattice, and weaker antiferromagnetic interactions between one sublattice and the other (metamagnetism). Direct evidence for such a layer structure is also provided by a recent x-ray structural work.6 A spin Hamiltonian with S=1 and uniaxial one-ion anisotropy gives results in fair agreement with the experimental data if the exchange interactions are described in the molecular field approximation. The best fit corresponds to g=2.25, D/k=−6.50°K, n1=+0.32 mole/cgs, n2=−2.12 mole/cgs, where n1 and n2 are, respectively, the antiferromagnetic and the ferromagnetic molecular field constants. In the case of the tetrahydrate1 and of the hexahydrate, the powder susceptibility approaches a constant value of 0.35 cgs/mole below 2°K; the data can be fitted to the spin Hamiltonian7 for a nickel ion in a rhombic field, without exchange, with E/k=−2.66°K, D/k=−8.67°K, and g=2.25. A detailed account of this work has been published elsewhere.8

Low-Temperature Magnetic Susceptibilities of the Hydrated Nickel Nitrates

The zero-field magnetic susceptibilities of Ni${(\mathrm{N}{\mathrm{O}}_{3})}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O, Ni${(\mathrm{N}{\mathrm{O}}_{3})}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}4${\mathrm{H}}_{2}$O, and Ni${(\mathrm{N}{\mathrm{O}}_{3})}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}6${\mathrm{H}}_{2}$O have been measured in the liquid-hydrogen and liquid-helium ranges. The dihydrate is obtained by evaporation of a solution at 105\ifmmode^\circ\else\textdegree\fi{}C. Its powder susceptibility has a large, sharp, peak at 4.20\ifmmode^\circ\else\textdegree\fi{}K, where it reaches 0.74 cgs/mole, then drops down to 0.2 cgs/mole below 2\ifmmode^\circ\else\textdegree\fi{}K. When measured along the $a$ axis, the susceptibility of monoclinic single crystals of the dihydrate shows a similar peak. It reaches 1.5 cgs/mole, but drops to vanishing values at lower temperatures. The susceptibility in the bc plane reaches only 0.3 cgs/mole, and is nearly isotropic. It drops little below 4.20\ifmmode^\circ\else\textdegree\fi{}K. This behavior is similar to that of Fe${\mathrm{Cl}}_{2}$, or FeC${\mathrm{O}}_{3}$, and suggests the existence of two magnetic sublattices, with strong ferromagnetic interactions within each sublattice, and weaker antiferromagnetic interactions between one sublattice and the other (metamagnetism). A spin Hamiltonian with $S=1$ and uniaxial one-ion anisotropy gives results in fair agreement with the experimental data if the exchange interactions are described in the molecular-field approximation. The best fit corresponds to $g=2.25$, $\frac{D}{k}=\ensuremath{-}6.50\ifmmode^\circ\else\textdegree\fi{}$K, ${n}_{1}=+0.32$ mole/cgs, ${n}_{2}=\ensuremath{-}2.12$ mole/cgs, where ${n}_{1}$ and ${n}_{2}$ are, respectively, the antiferromagnetic and the ferromagnetic molecular-field constants. In the case of the tetrahydrate and of the hexahydrate, the powder susceptibility approaches a constant value of 0.35 cgs/mole below 2\ifmmode^\circ\else\textdegree\fi{}K; the data can be fitted to the spin Hamiltonian for a nickel ion in a rhombic field, without exchange, with $\frac{E}{k}=\ensuremath{-}2.66\ifmmode^\circ\else\textdegree\fi{}$K, $\frac{D}{k}=\ensuremath{-}8.67\ifmmode^\circ\else\textdegree\fi{}$K, and $g=2.25$.

Antiferromagnetic Resonance in CoCl26H2O

Antiferromagnetic resonance experiment was performed on a single crystal of CoCl 2 6H 2 O in the frequency range of 9.5 to 47 kMc/sec at liquid helium temperature. The result can be understood by the theory of antiferromagnetic resonance developed by Nagamiya and Yosida and also by Ubbink et al., except for certain systematic deviations from the theory. These deviations can be removed by introducing a large anisotropic exchange interaction of the symmetric tensor form in place of the ordinary small anisotropy energy. Thus, the effective fields acting on sublattice magnetizations, M + and M - , are assumed to be of the form \begin{aligned} {H_{E}}^{\pm}{=}-AM^{\mp}-\varGamma M^{\pm}-A'M^{\mp}-\varGamma'M^{\pm}, \end{aligned} where A and \(\varGamma\) are the isotropic molecular field constants and A ' and \(\varGamma'\) are newly introduced anisotropic molecular field tensors. It was found that the symmetry axes of A ' and \(\varGamma'\) coincide with those of the g -tensor and their components are given by

Spin-Wave Spectrum of Yttrium Iron Garnet

The spin-wave spectrum of yttrium iron garnet is treated using a Hamiltonian involving nearest-neighbor $a\ensuremath{-}a$, $d\ensuremath{-}d$, and $a\ensuremath{-}d$ isotropic exchange interactions. Values of the exchange constants are estimated from the molecular field constants of Pauthenet. Anisotropy and magnetic dipole-dipole interactions are neglected. Twenty spin-wave modes are found, and their energies calculated at points of cubic symmetry in k space. The dispersion relation of the single "acoustical" spin-wave mode is found to agree with the value previously reported by Meyer and Harris.

The influence of the interaction of more than two molecules on the molecular distribution-function in compressed gases

Starting from the usual expression for the molecular distribution function g(r), a series expansion into powers of 1/ν is given. The second approximation has been evaluated numerically for a Lennard-Jones potential field in the revised form V(r) = 4ε(R−12 — R−6) (where R = r/σ), which allows the results to be applied to all gases, for which the molecular field constants are known. The results obtained are compared with the experimental curves for liquid Hg, Ga and K and the general behaviour is interpreted, using the relations between g(r) and the potential of the mean force acting between two molecules. Finally, using the virial-theorem and the calculated g(r)-values, the third virial-coefficient has been evaluated theoretically, the results being compared with the experimental figures for nitrogen and argon.