This paper is a comprehensive review of almost twenty years of research on nuclear magnetic ordering, first in copper and later in silver and rhodium metals. The basic principles of nuclear magnetism and the measurement of positive and negative spin temperatures are discussed first. Cascade nuclear refrigeration techniques, susceptibility and nuclear-magnetic-resonance (NMR) measurements, and arrangements for neutron-diffraction experiments at nanokelvin and picokelvin temperatures are described next. Comprehensive magnetic-susceptibility and neutron-diffraction measurements on copper, which led to the discovery of at least three antiferromagnetic phases, one displaying the novel (0 ) spin structure and the other two showing the type-I order of the fcc system, are then described in detail. NMR data on silver, at Tg0 and T0, are presented next leading to the observation that silver orders antiferromagnetically at positive spin temperatures and ferromagnetically at negative spin temperatures. The authors discuss recent neutron-diffraction measurements that show that the antiferromagnetic structure at Tg0 is in a single-k type-I state. NMR data on rhodium at Tg0 and T0 are also described. Results obtained on Tl, Sc, ${\mathrm{AuIn}}_{2}$, and metallic Pr compounds and on insulators like ${\mathrm{CaF}}_{2}$ are then discussed briefly. The paper is concluded by an extensive theoretical section. Calculations of conduction-electron mediated exchange interactions are described, and the mean-field theory of nuclear magnetic ordering is presented. The role of thermal and quantum fluctuations is then discussed, particularly in the selection of the antiferromagnetic ground state. Finally, theoretically calculated magnetic phase diagrams and ordered spin structures of copper and silver are presented in detail and compared with experimental results. The overall agreement is good, affirming the value of nuclear magnets in Cu and Ag as realizations of simple physical models.

Nuclear magnetic ordering in simple metals at positive and negative nanokelvin temperatures

Until recently the properties of nuclear matter at high densities ϱ > ϱ 0 = 015 fm-3 and/or temperatures T > B 0 = 16 MeV have been inaccessible for study experimentally This is because normal nuclei saturate at one density, ϱ ≈ ϱ 0, with a unique volume energy per nucleon, —B 0 In the past, nuclear properties have been studied either with elementary probes such as electrons, pions, and protons, or with low-energy nuclear probes Such probes, however, cannot compress entire nuclei nor heat them up to T > B 0 Thus, these probes have been unable to shed light on this aspect of nuclear matter In nature gravity can crush nuclear matter to high densities in the hearts of neutron stars Also, supernova collapse may involve high densities and temperatures before exploding However, it is clear that the properties of dense nuclear matter are very difficult to extract from the limited observations of such objects

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High-energy nuclear collisions

We report magnetic susceptibility and electrical resistivity measurements under hydrostatic pressure up to 2 GPa on single-crystalline $\mathrm{Pr}{\mathrm{Cu}}_{2}$, which exhibits the pressure-induced Van Vleck paramagnet-to-antiferromagnet transition at 1.2 GPa. The measured anisotropy in the susceptibility shows that the ordered $4f$ moments lie in the ac plane in the pressure-induced magnetic state. We propose that remarkable pressure effects on the susceptibility and resistivity are due to changes in the quadrupolar state of ${O}_{2}^{2}$ and/or ${O}_{2}^{0}$ under pressure. We present a simple analysis in terms of the singlet-singlet model.

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Ordered magnetic and quadrupolar states under hydrostatic pressure in orthorhombic PrCu2

Publisher Summary This chapter reviews a reasonable accounting of the magnetic and transport properties of rare earth metals and their alloys The rare earths, or lanthanides, are the trivalent 4f shell transition metals Their magnetic properties stem from unpaired electrons in the 4f shell 4f electron wave functions are confined close to the nucleus and that wave function overlap with neighboring atoms in a lattice is vanishingly small To account for the observed magnetic order in the rare earths, an indirect exchange mechanism via three 5d–6s conduction electrons is invoked Strong evidence to support this view comes from the observed spin polarization of the conduction electrons A wide variety of magnetic structures are displayed by the rare earth metals and their alloys These range from simple ferromagnetism to complex sinusoidal or helical ordering; the magnetic structure sometimes involves sublattices Because of the low magnetic moments of the light rare earths it is possible for electric crystal field effects to dominate the magnetic exchange interaction

Chapter 3 Rare earth metals and alloys

We have observed the magnetoelectric (ME) response at room temperature and above in high-resistive ceramics made of multiferroic Pb(Fe1/2Nb1/2)O3 (PFN) and PFN-based solid solution 0.91PFN-0.09PbTiO3 (PFN-PT). The value of the paramagnetoelectric (PME) coefficient shows a pronounced maximum near the ferroelectric-to-paraelectric phase transition temperature, T
 C, and then decreases sharply to zero for T > T
 C. The maximal PME coefficient in PFN is about 4 × 10−18 s/A. The theoretical description of the PME effect, within the framework of a Landau theory of phase transitions allowing for realistic temperature dependences of spontaneous polarization, dielectric and magnetic susceptibilities, qualitatively reproduces well the temperature dependence of the PME coefficient. In particular, the Landau theory predicts the significant increase of the PME effect at low temperatures and near the temperature of the paraelectric-to-ferroelectric phase transition, since the PME coefficient is equal to the product of the spontaneous polarization, dielectric permittivity, square of magnetic susceptibility, and the coefficient quantifying the strength of the biquadratic ME coupling. An atomistic technique is further developed and used to further demonstrate that the PME effect can also be sensitive to the frequency of the applied magnetic field (when this frequency is of the order of GHz).

Room-temperature paramagnetoelectric effect in magnetoelectric multiferroics Pb(Fe1/2Nb1/2)O3 and its solid solution with PbTiO3

Nuclear magnetism is discussed for a system in which each nuclear spin interacts only with electrons on the same atom by the hyperfine interaction, the electrons having the singlet ground state and interacting with an appreciable exchange interaction. As the exchange interaction approaches to the threshold value to induce a spontaneous electron spin ordering, the Curie temperature of the “ nuclear spin ordering ” and the “ nuclear contribution ” to the paramagnetic susceptibility are both raised by the electron exchange enhancement factor and an appreciable electron spin polarization is also induced. There is collective mode of mainly electron spin nature and of mainly nuclear spin nature. The energy gaps at q =0 in their dispersions are obtained in some typical cases.

Magnetism of a “Nuclei Plus Electrons” System

The ferromagnetic spin wave is investigated for the system with the uniaxial anisotropy energy which is not necessarily small compared with the exchange energy. The double time green functions ≪ A : B ≫ are used with the spin and the quadrupole moment operators of single ion for A and B , and the decoupling procedure is made in the RPA both for these operators. Two types of the excitation spectrum are involved in the interested group of the Green functions. The derived expressions for thermodynamic quantities show the behavior characteristic of the magnon mode at low temperatures with some new correction terms, while they always reduce to the results of the Weiss approximation if the despersion in the two spectra is neglected. In some general cases with the anisotropy energy, numerical computations are made for T c , , , χ // , and χ ⊥ , and some significant deviations from the Weiss approximation are found.

A Green Function Approach to a Uniaxial Ferromagnet

Here is presented a model for one-dimensional metallic systems which is based on the pseudopotential theory. Each metallic chain has a finite size cross-section and has the band energy as well as the electrostatic energy, while the interaction between chains is assumed to be only electrostatic. When vibrational states of the atomic (Einstein) type are restricted to the zero- and one-quantum states, the phonon Hamiltonian in the 1-D case is equal to the “Ising model with a transverse field” and existing exact solutions for this model can be used to discuss the structural phase transition. The temperature-dependence of the Peierls instability arises both from the vibrational and the electronic freedoms, and a numerical calculation is made for the latter.

A Theory of Structural Phase Transition in One-Dimensional Metallic Systems

The results of the preceding paper on a combined system of nuclear spins and electron spins are analyzed numerically in the Weiss approximation at the “electronic region” (2\bar J / D >1) as well as the “nuclear region” (2\bar J / D <1). The Curie temperature and the electron spin polarization at T =0 K are smoothly continuous against 2\bar J / D , but change steeply across threshold condition 2\bar J / D =1. Some peculiar features are found in temperature dependence of the electron spin and of the nuclear spin polarizations and in the “nuclear” specific heat, particularly when 2\bar J / D is close to unity.

Magnetism of a nuclei plus electrons system. ii. numerical analyses.

In certain crystal classes, besides the intrinsic optical activity of the individual molecule, optical activity is caused by the exciton dispersion which shows the linear dependence on wave vector near zone center. The expression for the optical rotation and ellipticity caused by exciton dispersion is derived. New term which gives rise to the antisymmetric optical rotation about the center of the absorption band is obtained in addition to the ordinary symmetric term. The relative magnitude of the optical rotation caused by exciton dispersion to that of the individual molecule is found to be proportional to the ratio of the electric dipole to magnetic dipole transition moment of the molecule, and to the matrix element of excitation transfer along optic axis.

Tsuyoshi Murao

Papers

Magnetism of a “Nuclei Plus Electrons” System

A Green Function Approach to a Uniaxial Ferromagnet

A Theory of Structural Phase Transition in One-Dimensional Metallic Systems

Magnetism of a nuclei plus electrons system. ii. numerical analyses.

Optical Activity Caused by Exciton Dispersion