Rare earth paramagnetism,as studied by μSR

Some recent result of muon spin relaxation measurements in rare earth metals and intermetallic compounds are reviewed. Special emphasis is put on measurements that relate to the properties of correlated regions of spins existing relatively far above the ordering temperature in the rare earth ions. As far as comparable data from paramagnetic neutron scattering exist, they will be discussed in the same framework. For each temperature the correlated regions (or short-lived magnetic clusters) are characterized by their size, possible anisotropy with respect to the crystalline axes and their lifetime. The actual form of the interaction between the rare earth spins themselves and with the crystal fields determine the temperature dependence of these properties; a strong dipole interaction can, for instance, be expected to change the critical behaviour nearT _c . Much of the time will be devoted to experiments on Gd-metal where there are experimental indications that several interesting phenomena occur: (1) a strong effect of a cross-over from a non-conserved dynamics (dipolar) regime to a conserved (exchange dominated) regime some 10 K aboveT _c , (2) an anisotropy of the magnetic clusters with respect to the hexagonalc-axis, and (3), a persistence of spin correlations far aboveT _c . Some attempts to correlate the rare earth spin relaxation times measured in this region with cluster lifetimes deduced from neutron scattering will be reviewed, as well as a model for understanding these lifetimes in terms of temperature dependent cluster wall motion, which is determined by exchange and magnetic anisotropy parameters. Effects of possible quantum correlations originating from the “spin system+bath” interaction will be mentioned.     

Low-frequency electrical resistance of iron,cobalt, and nickel in the vicinity of their Curie temperatures

Alternating-current electrical resistance measurements between 17 Hz and 100 kHz were made on high purity Fe, Co, and Ni wires in the vicinity of their Curie temperatures (T _c). The electrical resistance was independent of frequency for temperatures (T) aboveT _c. As the temperature was lowered, however, there was an abrupt jump in the electrical resistance atT _c followed by a gradual decrease toward its dc value. The magnitude of the electrical resistance jump atT _c increased as the square root of the frequency. The enhancement of the electrical resistance forT≦T _c is produced by an abrupt decrease of the skin depth atT _c which, in turn, is due to the sudden increase in the initial magnetic permeability atT _c. Measurements of the ac electrical resistance in the vicinity of the Curie temperature of certain ferromagnetic metals can be utilized to 1) accurately determine the Curie temperature using frequencies as low as 17 Hz, and 2) quantitatively determine the initial magnetic permeability as a function of temperature and heat treatment.     

Spin fluctuations in both the ordered and paramagnetic phases of MnSi! MnSi a heavy Fermi liquid?

Polarised neutrons and polarisation analysis have been used to determine the diffuse magnetic scattering from MnSi as a function of temperature. Measurements at 50 K (1.72T _c) and 100 K (3.45T _c) in the paramagnetic phase confirmed the presence of strong spatial correlations previously reported at 300 K (10T _c) and 580 K (20T _c). The spatial correlations between regions of spin density separated by 12 Å are of a ferromagnetic nature and determine the static susceptibility. Integration of the paramagnetic response over an inverse atomic volume yields a moment per manganese atom of 1.2 _B , a value considerably larger than the 0.4 _B observed in Bragg scattering and magnetisation measurements at 4.2 K. Measurements made at 11 K in the ordered magnetic phase reveal strong diffuse scattering corresponding to 0.8 _B per Mn atom. The increase in the diffuse scattering observed in the paramagnetic phase corresponds to the passage of the Bragg component into the background.The presence of significant scattering in the ordered phase and the very unusual wave vector dependence of the diffuse scattering observed at 11 K has been interpreted assuming MnSi to be a heavy Fermi liquid. Furthermore we believe these measurements give the first direct observation of the exchange hole.     

Scaling assumption for lattice animals in percolation theory

A scaling assumption for the numberg _ns of different cluster configurations with perimeters and sizen leads to the desired cluster numbers near the percolation threshold. The perimeter distribution function has a mean square width proportional ton for largen. The relation between the average perimeter and the cluster sizen for percolation has three different forms atp _c, belowp _c, and abovep _c and is closely related to the shape of the cluster size distribution.     

Interacting one dimensional Ising spin chains as a model of the layered antiferroelectric squaric acid

Starting from the structure of the layered antiferroelectric squaric acid and assuming an ice rule type interaction mechanism of the protons it is shown that aboveT _c the molecular layers may be considered as a system of parallel and orthogonal nearly independent linear Ising spin chains with strong intrachain and comparatively weak interchain interactions. Whereas the former are treated exactly as nearest neighbour interactions the interchain interactions are taken into account either by the molecular field approximation or, in computer simulations, by nearest neighbour interactions. The parameters of the model are related to the unusually small transition entropy, to the high and nearly temperature independent dielectric constant aboveT _c ,and to neutron scattering data.     

Method of analysis of neutron polarization using noncentrosymmetric cubic helicoidal magnets

A new way of analyzing the polarization of thermal and cold neutron beams, based on the dependence of the neutron-scattering cross section on the neutron polarization upon diffraction from a magnetic spiral, is proposed. In this method, the working element of the neutron-polarization analyzer is a single-crystal noncentrosymmetric cubic helicoidal MnSi magnet, the spin spiral in which is formed at T < T _c (T _c = 29 K) in the magnetic-field range H < H _C2 ～ 500 mT. Since the spiral period d in MnSi is 180 Å, thermal and cold neutrons with wavelengths λ ≤ 2d diffract from this structure. It is established that the efficiency of neutron-polarization analysis is as high as 100% with the experimental geometry when the polarization vector P is parallel to the scattering vector Q.     

Magnetic correlations in Eu x Sr1−x S and the ferromagnet-spin glass transition

Neutron (Bragg and small angle) scattering and susceptibility measurements are used to study magnetic ordering in Eu _x Sr_1–x S with ferromagnetic nearest neighbor exchangeJ ₁ and antiferromagnetic next-nearest neighbor exchangeJ ₂. We present data for 0.50x0.70 which cannot be analyzed within the merely geometrical treatments of percolation theory. Breakdown of ferromagnetism occurs atx _c =0.51, far above the percolation thresholdx _p =0.136, and a spin-glass phase is observed in the intermediate concentration regime. Close tox _c , the ferromagnetic state is also displaced by the spinglass phase at lower temperatures. Both properties are a general characteristic of diluted systems with competing interactions. An effective decoupling of finite magnetic clusters from the ferromagnetic net arises from frustration, which enhances the ground-state entropy. Anomalous properties below the Curie temperatureT _c as well as atT _c support this microscopic picture.     

Generalized bethe approximation in lattice models of long polymers

The phase transition behavior of a self-avoiding linear polymer model on a three-dimensional lattice is studied. An approximate procedure is proposed which gives the exact divergence of the specific heat aboveT _c for the two-dimensional case. In three dimensions our method predicts a finite value forC atT _c and demonstrates clearly what neglected contributions to the partition function lead to such a behavior of the model.     

Spin correlations in REAl2 compounds aboveT c

Transverse fieldSR measurements in the paramagnetic region on polycrystalline samples of CeAl₂, NdAl₂, PrAl₂, GdAl₂, ErAl₂, HoAl₂, DyAl₂ and TmAl₂ are reported. We have observed increased damping rate and frequency shifts of the muon precession signal asT _c is approached from above. The shifts are linear in applied magnetic field, while the damping rates are more complicated functions of magnetic field strength and temperature.We interpret the damping as being partly due to inhomogeneous broadening proportional to the magnetic susceptibility, and partly due to apparent slowing down of RE spin fluctuations. These slow fluctuations are ascribed to the existence of correlations between the RE spins also at temperatures well aboveT _c. The variations of shifts and damping rates within the series of REAl₂ compounds will be discussed.     

Mode dependent scattering of phonons by domain walls in ferroelectric KDP

Thermal conductivity and ballistic phonon imaging measurements in KH₂PO₄ (KDP) at low temperature (T<3K) indicate that scattering from domain walls has a large effect on phonon transport. kDP has a ferroelectric phase transition from tetragonal to orthorhombic structure atT _c =122 K. BelowT _c domains of opposite electric polarization and crystal orientation form unless the sample is colled in an electric field. Thermal conductivity measured along the [100] (tetragonal) axis drops 30% when domain walls are present, which is independent of sample size and temperature. We attribute this decrease to phonon polarization-dependent scattering at the domain boundaries. This is verified by measurements of ballistic transport, using phonon imaging techniques, which reveal the phonon polarization and mode dependence of the scattering. The scattering is successfully modelled using continuum acoustics with simple acoustic mismatch at the domainwall. The interface scattering is found to be mode dependent: Caustic structures in the phonon images due to slow transverse phonons are most affected by the domain wall scattering, which channels these phonons along parallel planes by multiple reflections without mode conversion. Mode conversion scattering, though possible for a number of phonons, has little effect on the overall phonon transmission.     

Superconducting and electronic properties of the metallic glass system La75Si25−x M x (M=Cr,Mn, Fe,Co, Ni,Cu, B,Al, Ga,In)

A new ternary metallic glass system, La₇₅Si_25–x M _x (where M is a 3d or a IIIA element) has been prepared by melt spinning. The superconducting transition temperature,T _c , is depressed by the magnetic 3d elements. For low Fe concentrations (less than 5 at.%) the depression is about 0.3 K/at.%. Part of the depression may be explained by a decreased density of states atE _F as determined by UPS measurements. The strongest depression is associated with the magnetic pair breaking due to spin scattering. In the IIIA additions we correlateT _c with the atomic radius of the additive.     

Magnetic properties of the weak ferromagnet NiCO3 in the paramagnetic range

Detailed magnetization measurements up toH=6T have been performed on a powdered specimen of the weak ferromagnet NiCO₃ in the temperature rangeT _c <T<4T _c . Starting atT=1.15T _c , an excellent agreement is found at all temperatures between the experimental values of the magnetization and those calculated up toH ³ terms in an extension ofDzyaloshinsky's theory of weak ferromagnetism. Both isotropic and antisymmetrical exchange constants are determined and found in good agreement with previous low temperature magnetization results. These results indicate that at allT>1.15T _c , the molecular field approximation satisfactorily describes the magnetic properties of NiCO₃.     

Muon spin relaxation studies in frustrated and/or low-dimensional spin systems

An overview is given on muon spin relaxation (SR) measurements in frustrated and/or low dimensional spin systems. In the frustrated Kagomé lattice system SrCr₈Ga₄O₁₉, we observed dynamic spin fluctuations of 30 GHz, without any static frozen component even atT=0.1 K, much below the susceptibility-cusp temperatureT _g=3.5 K. This is in clear contrast with the case in dilute-alloy spin glassesCuMn andAuFe, where static order develops belowT _g. We also present the dimensionality dependence of the sub-lattice magnetization curves in 2-d Heisenberg systems, the remarkable suppression of the ordering temperature in a 1-d system Sr₂CuO₃, the observation of activation type spin dynamics in a 1-d Ising ferromagnet (DMeFc)(TCNE) aboveT _c, slow spin fluctuations ( 60 MHz) in Haldane-gap systems at low temperatures, and some results from organic 1-d and 2-d magnetic systems.     

Electronic states of boron in superconducting MgB2 studied by11B NMR

Nuclear magnetic resonance (NMR) spectra and nuclear spin-lattice relaxation rateT ₁⁻¹ of¹¹B have been measured in superconducting polycrystalline MgB₂ with 7_c^ons = 39.5 K. It is shown that (T ₁T⁻¹ and the Knight shiftK _s are independent of temperature and nearly isotropic aboveT _c. Both of these quantities are decreased gradually in going to the superconducting state. According to NMR data the density of states near the Fermi level is flat at the scale of about 500 K. Some conclusions on the orbital content of the density of states at the Fermi level were drawn and compared with the results of the band structure calculations.     

Magnetic phases in UNi<Subscript>2</Subscript>Si<Subscript>2</Subscript>

The tetragonal compound UNi₂Si₂ exhibits in zero magnetic field three different antiferromagnetic phases belowT _N =124 K. They are formed by ferromagnetic basal planes, which are antiferromagnetically coupled along thec-axis with the propagation vectorq=(0, 0, q _z ). Two additional order-order magnetic phase transitions are observed below T _N , namely atT ₁=108 K and T ₂=40 K in zero magnetic field. All three phases exhibit strong uniaxial anisotropy confining the U moments to a direction parallel to the c-axis. UNi₂Si₂ single crystals were studied in detail by measuring bulk thermodynamic properties, such as thermal expansion, resistivity, susceptibility, and specific heat. A microscopic study using neutron diffraction was performed in magnetic fields up to 14.5 T parallel to the c-axis, and a complex magnetic phase diagram has been determined. Here, we present the analysis of specific-heat data measured in magnetic fields up to 14 T compared with the results of the neutron-diffraction study and with other thermodynamic properties of UNi₂Si₂.     

Low temperature electrical conductivity and magnetoconductivity of Fe39Ni39Mo4Si6B12 and Co58Ni10Fe5Si11B16 metallic glass alloys

A detailed study on the weak localization phenomenon vis-a-vis electron-electron interaction effects in magnetic metallic glasses has been carried out. We measured the electrical conductivity and magnetoconductivity within the temperature range 1.8≤T≤300K. A maximum on the conductivity versus temperature curve exists atT=T _m. The conductivity was observed to follow aT ^1/2 law forT<T _m andT ² law forT>T _m. Magnetoconductivity data of these alloys indicate the prominence of electron-electron interaction at low temperatures. The authors have determined the inelastic scattering field and spin-orbit scattering field from the magnetoconductivity data. The inelastic scattering field obeys aT ^p law (p=2) at low temperatures.     

Low-temperature properties of CePd2In

We report measurements of the specific heatC _p(T), electrical resistivity ϱ(T) and magnetic susceptibility ξ(T) of hexagonal CePd₂In, at low temperatures. Anomalies inC _p(T), χ(T) and ϱ(T) atT=1.23 K, indicate a phase transition, most likely to an antiferromagnetically-ordered phase. The electronic entropy reachesR ln2 per mole Ce at 9.2K, suggesting that the phase transition involves a doublet state. The ordered phase coexists with moderately correlated itinerant electrons.     

Richtungseffekte der Lichtausbeute von Anthrazen bei Beschü\ mit Protonen im Energiebereich 200–600 keV

The results of the three-dimensional liquid droplet model are compared with experiment and other phenomenological theories. The homogeneity assumption of the scaling laws holds both above and belowT _c , and various series expansions can be derived. But there is a nonanalyticity near the critical isotherm aboveT _c for fixed “field” μ?μ(p _c ,T); and liquid and gas are not symmetric about the critical isochore aboveT _c . Both results contradict the usual scaling assumptions and experiment. The equation of state is fixed if the density on the coexistence curve and the critical pressure are known. Therefore we can derive various relations between critical quantities. They are compared with experiment and the corresponding relations in the Vicentini-Missoni ansatz, the parametric representation, and the generalized Landau ansatz. The disagreement ranges from about 20% to one order of magnitude.     

The onset of deconfinement inSU(2) lattice gauge theory

InSU(2) lattice gauge theory, we study deviations from ideal gas behaviour near the deconfinement point. On lattices of sizeN _σ ³ ×4,N _σ=8, 12, 18 and 26, we calculate the quantityΔ≡(ε?3P)/T ⁴. It increases sharply just aboveT _c , peaks atT/T _c =1.15 ±0.05 and then drops quickly. This form of behaviour is shown to be the consequence of a second order phase transition. Dynamically it could arise because just aboveT _c , the low momentum states of the system are remnant massive modes rather than deconfined massless gluons.     

μSR studies of heavy fermion systems

We have performed both zero field and high transverse field measurements at dilution refrigerator temperatures on a number of heavy electron systems, examining the superconducting and magnetic properties of these interesting materials. Among the materials studied to date are UBe₁₃, URu₂Si₂ and U₆Fe. The magnetic field penetration depth in the superconducting state of UBe₁₃ is greater than 10000 Å, as no increase in the transverse field relaxation rate is observed belowT _c . A sharp increase in the precession frequency is seen, starting atT _c . This frequency shift shows little temperature dependence at low temperature; we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we have observed relaxation in high transverse field due to the formation of a flux lattice in U₆Fe, a material where the electron effective mass is rather lighter than in other heavy fermion systems. The relaxation exhibits a sharp onset atT _c=3.9 K, and is flat at low temperatures as expected for a conventional superconductor.