Weiss Field Research Articles

NMR Study of Antiferromagnetic Spinel CoCo2O4 in Paramagnetic and Ordered State

Nuclear magnetic resonance of 59 Co at both the tetrahedral A-site and octahedral B-site in an older generation spinel compound of antiferromagnetic CoCo 2 O 4 ( T N =34 K) was carried out between T =1.4 and 300 K to provide additional information on the importance of the local crystal field parameters and electron-electron correlations. From an analysis of the T -independent relaxation rate of 59 Co at the A-site in the paramagnetic state, the super-exchange interaction J between the Co 2+ ions at the A-site through intervening O 2- and Co 3+ ions is estimated to be 0.050 cm -1 with an exchange frequency ω e =5.9×10 10 sec -1 , which can not simply be explained within the framework of the Weiss field. A small experimental value of the spin hyperfine field at the A-site, A s =1.63×10 -4 cm -1 , is well understood when the second-order orbital moment due to the spin-orbit interaction is taken into consideration. The energy difference Δ between t 2 g and e g orbitals at the A- and B-site in CoCo 2 O 4 is found to be 3.3×10 3 cm -1 and 17.7×10 3 cm -1 , respectively.

Compositional short-range ordering in metallic alloys: Band-filling, charge-transfer, and size effects from a first-principles all-electron Landau-type theory.

Using a mean-field statistical description, we derive a general formalism to investigate atomic short-range order in alloys based on a density-functional description of the finite-temperature, grand potential of the random alloy. This ``first-principles,'' Landau-type approach attempts to treat several contributions (electronic structure, Fermi surface, electrostatics, magnetism, etc.) to the electronic energy on an equal footing. An important ingredient for the statistical averaging is the replacement of the molecular mean fields (Weiss fields) with Onsager cavity fields, which forces the diagonal part of the fluctuation-dissipation theorem to be obeyed. To show its general applicability and usefulness, we apply the theory to three fcc alloy systems. In ${\mathrm{Cu}}_{0.75}$${\mathrm{Pd}}_{0.25}$, the incommensurate atomic short-range order is driven by a Fermi-surface effect, in agreement with earlier work. In contrast, ${\mathrm{Pd}}_{0.5}$${\mathrm{Rh}}_{0.5}$ exhibits clustering tendencies, with both band-filling and charge-rearrangement effects being important in setting the spinodal temperature at 1150 K, in good agreement with experiment. In the final examples of three nickel-rich NiCr alloys, previously ignored electrostatic effects are found to play a significant role in determining the atomic short-range order.

Magnetic properties of the crystals of p-(1-oxyl-3-oxido-4,4,5,5-tetramethyl-2-imidazolin-2-yl)benzoic acid and its alkali metal salts

The crystals of p-(1-oxyl-3-oxido-4,4,5,5-tetramethyl-2-imidazolin-2-yl)benzoic acid and its alkali metal (Li, Na, and K) salts were prepared. Dimer structures were found in the crystals of the free acid 1 and the lithium salt 1·Li· 1 2 MeOH by X-ray crystal structure studies. A dimer model was fitted to the observed magnetic susceptibility data of 1 and 1·Li· 1 2 MeOH in the whole temperature range studied. The optimized exchange coupling parameters 2 J/ k B in the dimers were −6.0 and +31.8 K in 1 and 1·Li· 1 2 MeOH, respectively. The sodium and potassium salts were paramagnetic and analyzed in terms of the Curie-Weiss relation to have weak Weiss fields of θ = −0.4 and −1.0 K, respectively.

Magnetic Phase Transition in the Two-Dimensional Heisenberg Antiferromagnet Mn(HCOO)2·2(NH2)2CO

The development of the short-range ordering in Mn(HCOO) 2 ·2(NH 2 ) 2 CO has been observed by the measurements of magnetic heat capacity and susceptibility. The experimental results are well reproduced by the high-temperature series expansion for the two-dimensional Heisenberg antiferromagnet with the exchange constant J / k B =-0.34±0.02 K in the temperature region T >1.2 T SK ( T SK ; the Stanley-Kaplan temperature). The critical temperature T N =3.77±0.02 K≃1.1 T SK nearly coincides with that of Mn(HCOO) 2 ·2H 2 O. It is suggested that the long-range ordering is responsible for the small Ising-like anisotropy in the exchange interaction. A two-dimensional spin structure with the canceled Weiss field from the adjacent layers, as in K 2 NiF 4 , is conjectured.

A Simple Model of Re‐Entrant Magnetism in Amorphous Alloys

AbstractA phenomenological model involving two kinds of self‐consistent interaction fields is shown to simulate the “re‐entrant” magnetic behaviour (i.e., mixed ferromagnetic and spin glass‐like ordering). Besides the Weiss field, it postulates fields of random directions and magnitude proportional to the mean absolute value of the local magnetic moment. Simple qualitative results are discussed and numerical results are compared with recent experiments on amorphous Fe8Ni72P10B10 alloys.

Rotating transverse nuclear helimagnetism in CaF2. II. Theoretical approximations

For pt.I see ibid., vol.19, p.2275 (1986). The authors describe two approximate methods for the study of rotating transverse helimagnetism in high field in CaF2: the random phase approximation (RPA) and a physical model based on the fact that the Weiss field at any nuclear site is produced by distant spins. Both methods predict the helical structure to be stable in zero effective field, and the physical model predicts the occurrence of a mixed longitudinal and transverse phase in non-zero effective field. The rate of thermal mixing upon irradiation of the rare 43Ca spins with the 19F spins is analysed through RPA, and the shape of the NMR line of the ordered 19F spins is analysed through the physical model.

New Point of View on Metastability in Spin-Glasses

It is shown that the Onsager theory, which distinguishes the Weiss field, the cavity field, and the reaction field, must be used in spin-glasses as the reaction field can be large. Along this line a simple mean-field theory permits one to recover results similar to those of Thouless, Anderson, and Palmer. Moreover the anisotropy of the reaction field explains the two-level systems introduced in these materials in order to explain the low-temperature properties such as hysteresis, remanence, etc.

SURFACE AND INTERFACE MAGNETISM BY MÖSSBAUER SPECTROSCOPY

SURFACE AND INTERFACE MAGNETISM BY MÖSSBAUER SPECTROSCOPY

Flux quantization in ordered ferromagnetic substances?

The Weiss field of eight well investigated ferromagnetic materials is shown to be numerically equivalent to roughly 0.14 to 0.3 of a London flux per atom for the ferromagnetic elements and 0.6 of a London flux per molecule for the ferrites.

NUCLEAR MAGNETIC ORDERING

Because of the smallness of dipolar interactions between nuclear spins in diamagnetic solids, temperatures of the order of 6 K or less are required to produce nuclear magnetic ordering. In our study, we cool only the nuclear spins in a two-step process. The spins are first polarized in high field by the 'solid effect' to an equivalent temperature of a few mdeg and then demagnetized in the rotating frame, which lowers their temperature below 1O6K. Experiments have been so far mostly limited to magnetic resonance measurements on the 19F spins in CaF2. The parallel and perpendicular susceptibilities exhibit a behaviour characteristic of antiferromagnetism. Results on perpendicular susceptibility and critical field are in qualititative agreement with an extension of the Weiss field theory. Neutron diffraction experiments on CaF2 and magnetic ordering studies on LiF are in progress.

Molecular field theory, the Onsager reaction field and the spherical model

We have examined the physical and formal aspects of the Onsager method [1] of solution of the many dipole problem. Our principal conclusion is: the Onsager prescription of subtracting out the reaction field from the mean molecular field (e.g. Weiss field in ferromagnets, Lorentz field in dielectrics, van der Waals field in fluids) is the necessary modification of molecular field theory which guarantees the fluctuation theorem of statistical mechanics (equality of the mean fluctuation of a coordinate to its susceptibility in response to an external field to which it is coupled).We develop the theory in detail for the Ising model. In the paramagnetic phase, we show that the Onsager method reduces to the spherical model. This reduction is somewhat incidental, and does not occur in the magnetized phase. On the contrary, the Onsager method then leads to a system of simultaneous differential equations for the magnetization, which is in general intractable. We introduce a scheme of successive approximations, and recover the Weiss theory and the generalized spherical model after the first and second iterations, respectively.Finally, we indicate how to apply these ideas in the liquid-vapor system.

Response functions, superconductivity and ferromagnetism in the many fermion system

At the phase transition, the anomalies of thermodynamic and static response functions coincide due to the fact that the free energy, expressed in terms of response functions at imaginary frequency including zero, has its pole at zero frequency. Previous work has considered the singularities which arise from the polarisation of the medium. In this paper, a study is made of the divergences arising from the modification of the vertex function. The diamagnetic current is related to the free energy via the Ward Identity so that the specific heat anomaly inevitably gives rise to the Meissner effect. Below the transition the system adjusts to the singularity by going into the BCS condensed state. The similarity between BCS theory and ferromagnetism is shown both through a Weiss field approach and diagrammatically by including special correlations between k and - k. Its importance for an understanding of the broken symmetry problem is discussed. Finally, the parallel behaviour of the susceptibility and specific heat of a Bloch ferromagnet is demonstrated.

Interactions in Various Magnetic Compounds

Susceptibility measurements on single crystals of KFe11O17 show an anomalous antiferromagnetic behavior, which we propose to call antiferrimagnetism. The behavior follows from Weiss field theory on a simplified (i.e., two-sublattice) model. The magnetic structure of K2NiF4 has been determined by neutron diffraction by Legrand and Plumier at C.E.N., Mol (Belgium). Measurements on their single crystal show that χ∥ and χ⊥ become nearly equal at ≈100°K, i.e., far below the temperature where χ is maximum. This is believed to be due to a gradual breaking up of the long-range order in the basal layers. Results obtained on powders of La0.5Sr1.5MnO4 and La1.5Sr0.5CoO4 are also given. Pure polycrystalline samples of EuS, EuSe, and EuTe with rocksalt structure show θ values of +16, +6, and −7°K; EuTe has a Néel temperature at +11°K. The ferromagnetism of EuO, EuS, and EuSe is due to a predominant direct positive exchange interaction Eu-Eu, the antiferromagnetism of EuTe to a predominant next-nearest neighbor superexchange interaction Eu-X-Eu. Neither interaction is believed to change sign in the series. Measurements of M vs T at various field strengths are in very good agreement with Weiss field theory. Oxidic spinels with diamagnetic ions in A sites have so far shown negative θ values. The substances Ge[Fe2]O4, Ge[Co2]O4, and Ge[Ni2]O4 have θ values of −15, +90, and 0°K, respectively. The materials Ge[Ni2−2δLiδFeδIII]O4 have positive θ values, increasing linearly with δ to 180°K for δ=0.5. Here the Ni2+–Fe3+ interaction must be positive and this interaction is thought to be a direct one, as is discussed.

Superconductivity and ferromagnetism

Superconductivity and ferromagnetism were considered exclusive phenomena for many decades. Ever since Kamerlingh Onnes' discovery that strong magnetic fields will destroy superconductivity it had been assumed that the large internal, or Weiss field, in a ferromagnet would never permit the occurrence of superconductivity. In the case of the magnetic elements, chromium, manganese, iron, cobalt, and nickel, this point of view certainly seems justified, as none of them has as yet been shown to be superconducting. And yet, whenever two phenomena seem to exclude one another so entirely, it is frequently because similar, if not identical, mechanisms are responsible.

Diffusion in Cobalt-Nickel Alloys

The self-diffusivities of Co60 and Ni63 in cobalt-nickel solid solutions exhibit a greater activation energy below the Curie temperature (Tc) than above. Values of ΔQ=Q (ferromagnetic) —Q (paramagnetic) are approximately equal to RTc. This is interpreted to indicate that the increment in activation energy arises from an increase in the formation energy of a vacancy in the ferromagnetic lattice, with the additional binding energy arising from the interaction of a spin with the Weiss field.

Statistical Mechanical Theory of Ferromagnetism. High Density Behavior

The partition function of the Ising model of ferromagnetism is examined in the limit of high density in the anticipation that in the limit of infinite density one recovers the Weiss molecular field. The formal parameter of expansion is $\frac{1}{z}$ where $z$ is the number of spins in the range of the exchange potential (not restricted to nearest neighbor interactions). In the absence of long-range order, only ring diagrams in the cluster expansion contribute. These give a divergence in the specific heat at $k{T}_{c}=\ensuremath{\Sigma}{j\ensuremath{\ne}i}^{}{v}_{\mathrm{ij}}$ where ${v}_{\mathrm{ij}}$ is the exchange potential. This is the molecular field value for the Curie point ${T}_{c}$. In the presence of a magnetic field the partition function is evaluated for fixed magnetic moment $M$ in the same approximation, $M$ being determined by minimization. This results in a susceptibility differing from the molecular field theory and hence an inconsistency in the theory.The inconsistency is traced back to the observation that the acceptance of ring diagrams is equivalent to the gaussian model of Kac and Berlin which violates the sum rule ${{\ensuremath{\Sigma}}_{i=1}}^{N}{{\ensuremath{\mu}}_{i}}^{2}=N$. Here ${\ensuremath{\mu}}_{i}$ is the "spin" per particle and $N$ is the total number of particles. This condition is reinstated by insuring the sum rule. The result leads to the spherical model. Thus, a consistent high density approximation to the Ising model is the spherical model. Below the Curie point or for fixed magnetic field, $M$ is again held fixed and only the Fourier components of the spin density with nonvanishing wave vector are "sphericalized." The result leads to a physically acceptable model which becomes the molecular field theory at low temperatures or high fields and deviates in $O(\frac{1}{z})$ in general. Formally, the results are simply expressed in terms of a temperature dependent Weiss field. These results differ from the ordinary spherical model which is physically unacceptable below the Curie point. However, a molecular field modification of the spherical model due to M. Lax yields the same result when properly interpreted.It is shown that the above results are also valid (to the same approximation) in the quantum mechanical Heisenberg model, for temperatures above the Curie point.

Molecular Field Treatment of Ferromagnetism and Antiferromagnetism

A modified Weiss treatment of magnetism in crystals which considers both first and second nearest neighbor interactions with all four combinations of signs has been carried out. The usual results for ferromagnetism are obtained for both interactions positive. For the other cases, various types of magnetic ordering below the Curie temperature are predicted, the exact kind depending on the signs and magnitudes of ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{2}$, the Weiss field coefficients for first and second nearest neighbor interactions, respectively. Explicit results are given for the kind of ordering as functions of $\frac{\ensuremath{\theta}}{{T}_{c}}$ for bcc and fcc lattices. Expressions are derived for the susceptibility of an antiferromagnet above and below the Curie temperature, the latter calculation being given for only a single axis of spontaneous magnetization only. The theory gives a good qualitative description of the behavior of an antiferromagnet for all temperatures, although some of the detailed results are in disagreement with experiment.

A Note on the statistics of the weiss field

A Note on the statistics of the weiss field

Technical Publications by Bell System Authors Other Than in The Bell System Technical Journal

A Weiss field calculation has been carried out for antiferromagnetism in more complicated structures than the usual calculation allows and has been shown to give results more detailed and more consistent with experimental evidence on the magnetic properties of such structures than does the simpler theory.

Generalizations of the Weiss Molecular Field Theory of Antiferromagnetism

A Weiss field calculation has been carried out for antiferromagnetism in more complicated structures than the usual calculation allows, and has been shown to give results more detailed and more consistent with experimental evidence on the magnetic properties of such structures than does the simpler theory.