Muon Spin Rotation and Relaxation Experiments on Thin Films

The recent development at the Paul Scherrer Institute of a beam of low energy muons allows depth dependent muon spin rotation and relaxation investigations in thin samples, multilayers and near surface regions (low energy SR, LE-SR). After a brief overview of the LE-SR method, some representative experiments performed with this technique will be presented. The first direct determination of the field profile just below the surface of a high-temperature superconductor in the Meissner phase illustrates the power and sensitivity of low energy muons as near-surface probe and is an example of general application to depth profiling of magnetic fields. The evolution of the flux line lattice distribution across the surface of a YBa₂Cu₃O₇ film in the vortex phase has been investigated by implanting muons on both sides of a normal-superconducting boundary. A determination of the relaxation time and energy barrier to thermal activation in iron nanoclusters, embedded in a silver thin film matrix (500nm), demonstrates the use of slow muons to measure the properties of samples that cannot be made thick enough for the use of conventional SR. Other experiments investigated the magnetic properties of thin Cr(001) layers at thicknesses above and below the collapse of the spin density wave.     

L'Étude de la Structure Électronique des Métaux des Terres Rares

In rare earth metals, one can neglect interactions between 4f shells centred on neighbouring sites. The conduction band is occupied by three sd electrons (eventually two in europium and ytterbium). These sd electrons are coupled to the f electrons through an interaction of the form where s _e is the spin of a conduction electron and Sf _i the spin of the ith f electron of a given ion. It is therefore possible to consider two groups of properties:

1. The ones, related to the nature of the conduction electrons, change very little through the series: this is the case of the crystalline structure, of the atomic volume.

2. The others, such as the magnetic properties, are related to the internal shells and vary with the filling of the 4f shell. Experiment shows a correlation between those two groups of properties. De Gennes formalism, essentially valid in the hypothesis of tightly bound 4f electrons, gives a satisfactory picture of the properties of the metals in the second half of the series, but it does not give as good a picture for the first rare earth metals, especially for cerium. In the cerium free atom, the 4f, 5d, 6s states have comparable energies and one might think that, in the trivalent metal, the 4f states are broadened in energy by resonances with the extended sd states, but still do not overlap from one atom to the other. They would then occupy virtual bound states analogous to the virtual bound states described by Blandin and Friedel for the transition impurities in noble metals.

An identical situation seems to occur in ytterbium under pressure: one observes a huge increase of the electrical resistivity which goes back to low values at very high pressures. This might also be the case of the actinide metals, especially of Plutonium, in which the 5f states begin to stabilize. So we have to consider two cases:

1. The 4f electrons occupy bound states.

2. The 4f electrons occupy virtual bound states.

In the first part (§ 2), we use de Gennes formalism for 4f bound states. The energy related to magnetic interactions is computed making the assumption of a spherical Fermi surface. A correlation between the crystalline structure and the magnetic properties shows up. In the second half of the series, one can neglect the crystalline field effects and the total energy is the sum of the magnetic term and of the elastic term due to the contribution of the conduction electrons. For every state of magnetic order, the crystalline structure is well defined, corresponding to the minimum of the total energy, and conversely. It is possible to explain in this manner:

1. The b.c.c. structure of europium, which is unusual for a divalent transition metal.

2. The variation of the c/a ratio of the h.c.p. structure both through the series and with temperature.

3. The anomalies in the thermal expansion coefficient observed below the magnetic order-disorder transitions.

4. The helix pitch of the magnetic configurations of this type.

The anomalies of the thermoelectric power observed at the transition points are related to the different dependences of the spin correlations above and below the transition temperatures. The agreement between theory and experiment is satisfactory. Some discrepancy can be attributed to the rather crude approximation of a spherical Fermi surface.

In the second part (§ 3), we deal with a situation where the 4f electrons occupy virtual bound states. These levels are very narrow, about 10^?2 ev wide, and separated in energy by the correlations between electrons. Using Blandin's formalism we calculate the electrical and magnetic properties associated with such a situation. Calculations lead to very strong magnetic coupling; the indirect interaction between magnetic ions is antiferromagnetic for first nearest neighbours, whereas in the case of 4f bound states it is ferromagnetic. Finally, it is possible to explain the properties of cerium and ytterbium.

1. In Cerium, the two first levels overlap at the Fermi level, in such a way that the f electron be almost entirely distributed in the first level.

2. In ytterbium, under pressure, the fourteenth level comes across and above the Fermi level. The maximum resistivity is obtained for a half filling of this level.

In the third part (§ 4), we attempt to apply this model of virtual bound states to plutonium, although in this metal, the 5f shells have a larger spatial extension than the 4f orbitals in rare earths. Anomalies in several physical properties of plutonium seem to indicate a magnetic transition at about 65° K, but no anomaly shows up in the magnetic susceptibility. Using a virtual bound state model associated with a very small polarization of the 5f states, it is possible to explain all the physical properties of plutonium. This model leads to a very small magnetic moment, that cannot be detected by experiment.     

A new mechanism for the anomalous hall coefficient with application to liquid metals

The effect of spin-orbit coupling of conduction electrons on the Hall coefficient of liquid metals is studied and a new mechanism for the anomalous Hall coefficient is suggested. S.O. coupling causes asymmetric scattering and a current, perpendicular to the magnetic field and to the electric field, is set up. This leads to an additional Hall coefficient , as was first calculated by Luttinger. But S.O. coupling also causes a dipole to appear near each ion, leading to an electrical polarization and an additional Hall coefficient,R _so.R _so is calculated for liquid normal metals and transition metals to first order in S.O. coupling. In normal metals,R _so and are proportional to the Pauli susceptibility. Both are positive for electron-like charge carriers. S.O. coupling leads to a maximum deviation from nearly free electron value in the Hall coefficient of a heavy, four or five-valent liquid metal with short mean free path. In transition metals, different expressions are obtained forR _so depending whether localized moments are present (magnetic model) or not (non-magnetic model). The sign ofR _so is determined by the value of thed-phase shift alone.R _so is proportional to the susceptibility ofd-electrons and can be large, leading to a positive Hall coefficient in the liquid transition metal.     

Zur Lage des Maximums der Ausbeutekurve bei der Sekundärelektronenemission

There exists a quantitative connection between penetration depth of primary electrons, the maximum escape depth of secondary electrons and the position of the maximum of the yield curve if one assumes: (1) the maximum of the yield curve is determined by an energyE _p ^max of the primary electrons where the maximum penetration depth of primary electrons equals the maximum escape depth of the secondary electrons; and (2) the maximum escape depth of secondary electrons is given by 10 atomic layers for all metals investigated as it has been found earlier by Mayer and Hölzl for potassium. These assumptions are confirmed experimentally by measurements of yield curves and energy distributions at defined conditions and by variation of several parameters as temperature, contamination of the surface, surface roughness, evaporation conditions, and angle of incidence of the primary electrons.     

Untersuchung der Zustandsdichte und der charakteristischen Energieverluste von Ir,Rh, Pt und Pd mit Isochromatenmessungen

X-ray isochromats of the above metals measured with high resolution are presented. Assuming a rigid band model for the four metals they give — with some usual approximations — the qualitative form of the density of states. It turns out that the densities of statesZ(ε) at the Fermi limits decrease in the succession Ir, Rh, Pt, Pd. This is in contradiction to low temperature measurements of the electronic specific heatc _e which for the same succession give an appreciable raising inZ(ε). It is assumed that this discrepancy is caused by a special coupling of the electrons to the transverse phonons. In consequence of this,Z(ε) of the renormalized electron system measured byc _e can be very different from that of the bare electrons measured by the isochromats. Assuming that the transition temperature of elemental superconductors is related according to BCS-theory to the latter density of states the absence of superconductivity of Rh, Pt and Pd can be understood. In addition the isochromats give values for the characteristic energy losses of the four metals.     

Quantum critical phenomena, entanglement entropy and Hubbard model in 1d with the boundary site with a negative chemical potential −p and the Hubbard coupling U positive

Recently the ground state and some excited states of the half-filled case of the 1d Hubbard model were discussed exactly for an open chain with L sites. The case when the boundary site has the chemical potential −p and the Hubbard coupling U is positive was considered. We model CeAl₂ nanoparticles, in which a valence of 4f electron number changes on surface Ce atoms, by this Hubbard model. A surface phase transition exists at some critical value pc3 of chemical potential (its absolute value) p in the model; when p<pc3 all the charge excitations have the gap, while there exists a massless charge mode when p>pc3. The aim of this Letter is to find whether this surface phase transition is of the first order or of the second order. We have found that the entanglement entropy and its derivative has a discontinuity at pc3 in general and thus this transition is of the first order (with exception of two points for the probability w₂ of occurrence of two electrons with opposites spins on the same site). There is a divergence in the difference of entanglement entropy for points w₂=0 and . The first point w₂=0 corresponds to ferro- (antiferro-) magnetic state at half-filled case. The second point does not correspond to any state for halffilled case. In the first case there is present the surface phase transition of the second order type.     

Magnetic and transport properties of UPd2Sb

A new compound UPd₂Sb was prepared and studied by means of X-ray diffraction, magnetization, electrical resistivity, magnetoresistivity, thermoelectric power and specific heat measurements. The phase crystallizes with a cubic structure of the MnCu₂Al-type (s.g. ). It orders antiferromagnetically at T_N=55 K and exhibits a modified Curie-Weiss behaviour with reduced effective magnetic moment at higher temperatures. The electrical resistivity behaves in a manner characteristic of systems with strong electronic correlations, showing Kondo effect in the paramagnetic region and Kondo-like response to the applied magnetic field. The Seebeck coefficient exhibits a behaviour expected for scattering of conduction electrons on a narrow quasiparticle band near the Fermi energy. The low-temperature electronic specific heat in UPd₂Sb is moderately enhanced being about 81 mJ/mol K².     

Ab initio calculations of generalized-stacking-fault energy surfaces and surface energies for FCC metals

The ab initio calculations have been used to study the generalized-stacking-fault energy (GSFE) surfaces and surface energies for the closed-packed (1 1 1) plane in FCC metals Cu, Ag, Au, Ni, Al, Rh, Ir, Pd, Pt, and Pb. The GSFE curves along (1 1 1) direction and (1 1 1) direction, and surface energies have been calculated from first principles. Based on the translational symmetry of the GSFE surfaces, the fitted expressions have been obtained from the Fourier series. Our results of the GSFEs and surface energies agree better with experimental results. The metals Al, Pd, and Pt have low γ_us/γ_I value, so full dislocation will be observed easily; while Cu, Ag, Au, and Ni have large γ_us/γ_I value, so it is preferred to create partial dislocation. From the calculations of surface energies, it is confirmed that the VIII column elements Ni, Rh, Ir, Pd, and Pt have higher surface energies than other metals.     

Stopping of slow ions in electron gas with magnetic interaction

The electronic stopping and straggling of low velocity point charge in the electron gas subjected to magnetic ordering is analysed within the linear response theory. The electrons were described by the Lindhard dielectric function ?(k,ω)$\mathrm{?}(\mathbf{k},\omega )$. The magnetic interactions were included in the model along the Stoner treatment of itinerant electrons. The effect caused by phase transition was shown to be negligible comparing to the experimental result.     

Ein experimenteller Beitrag zu der durch langsame Primärelektronen ausgelösten Sekundärelektronenemission

The energy distribution of secondary electrons emitted from a highly degassed polycristalline Pt surface was investigated as a function of low energy (V _p ) primary electrons 5<V _p <150eV. The measurements were carried out in an UHV of better than 10^?10 mm Hg. The dependence of the numberN _S ^(Ev) of secondary electrons of a fixed energyE _v (3<E _v <12eV) on the energyV _p of the primaries (=isochromates) is studied. A lot of observations can be detected:

1. I.
   The exit depth of true secondary electrons is strongly dependent of their energy.     
   
   

Electronic structure and magnetism in 4d-transition metal clusters

We analyze the stability of magnetic states obtained within the tight-binding model for cubooctahedral (O_h) and icosahedral (I_h) clusters of early 4d (Y, Zr, Nb, Mo, and Tc) transition metals. Several metastable magnetic clusters are identified which suggests the existence of multiple magnetic solutions in realistic systems. A bulk-like parabolic behavior is observed for the binding energy of O_h and I_h clusters as a function of the atomic number along the 4 d-series. The charge transfer on the central atom changes sign, while the average magnetic moments present an oscillatory behavior as a function of the number of d electrons in the cluster. Our results are in agreement with other theoretical calculations. Received: 20 November 1997 / Received in final form: 9 March 1998 / Accepted: 30 March 1998     

Optical bistability produced by resonant Joule's heating of semiconductors

The thermal hysteresis of Joule's absorption of infrared radiation in then-type semiconductor magnetoplasma is analysed. Such bistability is connected with the temperature dependence of the relaxation time of free electrons, their density being constant. The resonant Joule's absorption bistability of the pumping infrared wave near a Langmuir resonance of free electrons is discussed as well as the hysteresis cross-modulation of an infrared probing wave by means of a pumping microwave. The possibilities of smooth detuning of the hysteresis regime due to a magnetic-field control and low energy thresholds of these regimes are illustrated for InSb thin films in relatively weak magnetic fieldsH1–2 kG.     

Analysis of electronic structures of 3d transition metal-doped TiO2 based on band calculations

The electronic structures of titanium dioxide (TiO₂) doped with 3d transition metals (V, Cr, Mn, Fe, Co and Ni) have been analyzed by ab initio band calculations based on the density functional theory with the full-potential linearized-augmented-plane-wave method. When TiO₂ is doped with V, Cr, Mn, Fe, or Co, an electron occupied level occurs and the electrons are localized around each dopant. As the atomic number of the dopant increases the localized level shifts to lower energy. The energy of the localized level due to Co is sufficiently low to lie at the top of the valence band while the other metals produce midgap states. In contrast, the electrons from the Ni dopant are somewhat delocalized, thus significantly contributing to the formation of the valence band with the O p and Ti 3d electrons. Based on a comparison with the absorption and photoconductivity data previously reported, we show that the t_2g state of the dopant plays a significant role in the photoresponse of TiO₂ under visible light irradiation.     

Structure and electronic properties of monoclinic Nb12O29

Monoclinic Nb₁₂O₂₉ is metallic and antiferromagnet despite possessing a low number of unpaired electrons. The origin of its magnetic ordering is described, which is due to a charge ordering transition, localising half of the unpaired electrons onto a specific crystallographic site within its (4×3) block structure, causing the formation of a one-dimensional chain of spins.     

Zur Änderung der übergangstemperatur verschiedener Supraleiter durch Elektronenentzug

The growing of oxid layers on pure metal films at low temperatures may be explained by acceptor levels at the oxid-oxygen interface. These surface states produce an electrical field of high strength by extracting about 10¹⁵ electrons per cm² out of the metal film. As had been shown in earlier experiments, this capturing process shifts the superconducting transition temperature to higher values for the 3-valent metals Al, In and Tl and to lower values for the 4-valent metals Sn and Pb. Extended studies on Tl show that this change in transition temperature is proportional to the relative decrease of the electron density in the metal film. The constant of proportionality has the valuek _Tl=?4.4 deg. With reasonable assumptions, this constant could be determined for Sn too:k _Sn=7.9 deg. These values agree quantitatively with the results ofGlover andSherill who investigated the charge effect on superconductors by a condenser method. They also fit the data calculated byGinsberg from experimental results on superconducting compounds with his extension of the theory ofMarkowitz andKadanoff.     

Saturation intensity for ultrashort-pulse X-ray laser schemes

Analytic expressions are obtained for the saturation intensity in X-ray laser schemes based on short-pulse high-intensity drivers. For field-ionized plasma schemes, the specific mean saturation intensityJ _sat is time independent and depends only on atomic transition probabilities, level degeneracies, and transition energies. The analytic expression is found to be in good agreement with a detailed numerical calculation. Integrating over space and frequency gives a saturation intensityI _sat of order 2 × 10¹¹ W/cm² for lasing in Li-like Ne at 98 . The low input energy requirements for this scheme (< 1 J), associated with using a confocal geometry, give energy efficiencies of order 10^–6 and greater. For inner-shell photo-ionization schemes, an accurate expression for a time-dependent saturation intensity is obtained. This scheme is calculated to have high saturation intensities,I _sat 10¹³ W/cm², at short wavelengths (5–15 ). The requirement of a line focus geometry leads to higher input energies (5 J) and the short duration of lasing (50 fs) results in lower energy efficiencies ( 10^–7). Repetition rates are important in determining appropriate applications for both schemes.     

Theory of electron escape from the surface of liquid helium

We have studied the properties of an electron bubble close to the surface of liquid³ He, by using a Density Functional approach. We find that up to an electron-surface distanced ₀ 23 Åthe bubble is stable, while at smaller distances it becomes unstable and bursts. A potential energy barrier /K _B 38°K for the thermal emission of electrons is obtained from our results, in agreement with experiments. Even when the electron-surface distance is larger thand ₀, however, tunneling through the surface layer dominates the electron escape probability. Large deviations of the electron potential energy from its ideal value are found close to the surface. These deviations have a profound effect on the calculated decay rates of the tunneling curent, which are much smaller than those obtained previously and in semi-quantitative agreement with experiments.     

Effect of Ta<Superscript>5+</Superscript> substitution for Mn on the ground state of La<Subscript>0.67</Subscript>Ca<Subscript>0.33</Subscript>MnO<Subscript>3</Subscript>

We report the charge state modification effects at the Mn site on the ground state properties of colossal magnetoresistive manganites. Ta⁵⁺ substitution results in an appreciable increase in the lattice parameters and unit cell volume due to increased Mn³⁺ concentration. The ferromagnetic-metallic ground state modifies to a cluster glass insulator for . The reduction in the transition temperatures with increasing x is ∼39 K/at.%. Besides the modification of majority carrier concentration due to increased Mn³⁺ concentration and enhanced local structural effects, the local electrostatic potential of the substituent seems to contribute to the unusually strong reduction of the transition temperatures of the compounds. Thermo magnetic irreversibility just below Curie temperature (T_c), non-saturation of magnetization, two distinct magnetic transitions in ac susceptibility in an appropriate static field: close to T_c and other at low temperature (the spin freezing temperature (T_g)) and non-stationary dynamics with a characteristic maximum in the magnetic viscosity close to T_g confirm a cluster glass state for . These results find additional support from a linear low temperature magnetic specific heat of x = 0.10 with a characteristic broad maximum close to T_g.     

Spin dynamics of the intermediate-valence compound EuCu<Subscript>2</Subscript>Si<Subscript>2</Subscript>

The dynamic magnetic response of the intermediate-valence compound EuCu₂Si₂ has been studied using inelastic neutron scattering. At low temperatures, strong renormalization of the ⁷ F ₀ → ⁷ F ₁ spin-orbit transition energy is detected; it is likely to be related to partial delocalization of the f electrons of Eu. An increase in the temperature increases the valence instability of europium and results in further changes in the magnetic excitation spectrum parameters and the appearance of an intense quasi-elastic component.