• Volume 28, Issue 5

May 1987,   pages  433-605

• Foreword

• High pressure techniques at low temperatures

The article reviews the experimental techniques used in high pressure-low temperature investigations to study a variety of physico-chemical phenomena. The general principles of producing high pressures at low temperatures, the methods of measuring P and T, the materials used for construction and the diamond anvil cell (DAC) are briefly given first. Specific pieces of apparatus to measure the mechanical properties, phase equilibria, thermal properties, electrical properties, magnetic phenomena, optical and Raman/IR spectroscopic behaviour as well as Mössbauer spectra are then discussed. While instrumentation is the main emphasis of the article, a few illustrative examples of interesting observations are also indicated. Over 250 current papers are cited.

• Low temperature elastic behaviour of As-Sb-Se and Ge-Sb-Se glasses

The ternary glasses of arsenic and germanium with antimony and selenium can be prepared in large sizes for optical purposes. The elastic behaviour of eight compositions of each glass has been studied down to 4.2 K using a 10 MHz ultrasonic pulse echo interferometer. The glasses have a normal elastic behaviour, with the velocities gradually increasing as the temperature is lowered. An anharmonic solid model of Lakkad satisfactorily explains the temperature variations. The elastic moduli of GexSb10Se90−x glasses increase linearly as the Ge content is increased up to 25 at. % and beyond this the increase is nonlinear. (AsSb)40Se60 glasses show a linear increase in elastic moduli with increasing Sb content. The elastic moduli of AsxSb15Se85−x glasses exhibit a drastic change near the stoichiometric composition As25Sb15Se60. These behaviours have been qualitatively explained on the basis of the structural changes in glasses.

• Electromagnetic generation of ultrasound in metals at low temperatures

Excitation of longitudinal and transverse ultrasound by electromagnetic waves incident on the metal surface is the subject of the present work. This is a simple and convenient experimental technique. The reason for this approach is to overcome the primary difficulty during precise measurements of the frequency or temperature dependences of the velocity and attenuation of ultrasound in pure metals by the conventional methods where it is difficult to achieve reliable acoustic contact between the transducer and the sample. The reasons are (i) the creation of this contact unavoidably results in a deformation of a surface layer of the metal affecting the experimental results, (ii) as the temperature is varied over a broad range, the properties of the acoustic contact itself change resulting in non-reproducible experimental results.

• Phonon drag effect in three- and two-dimensional electron systems

The nonequilibrium phonon flow drags the electrons, and depending upon experimental conditions manifests itself in the acoustoelectric current, acoustomagnetic field or acoustoelectric field. The results of these phenomena in Sn, Al, Ga, Ag measured with SQUID technique are discussed.

In the two-dimensional (2D) case the phonon drag is studied on the interface of bicrystals and on the cleavage (111) surface of Ge and on the inversion layer on (111) (100) planes of Si. In all these cases the phonon drag is about two orders of magnitude larger than in metals with the same charge density. This is due to the drag of surface electrons by nonequilibrium phonon of the whole specimen.

The Kohn resonance of phonons with Fermi surface and topological transitions on Fermi surface of 2D electrons produced sharp singularities of phonon drag effect in 2D cases.

• Low-temperature resistance fluctuation in disordered conductors

At low temperatures the electron elastic mean free path in a disordered conductor can become much smaller than the inelastic mean free path (or more precisely the Thouless length) which in turn may be comparable with, or even larger than the sample size. In this quantum regime, the electrical resistance is dominated by the coherence effects that eventually lead to the now well-known weak or strong localization. Yet another remarkable manifestation of the quantum coherence is that it makes the resistance non-additive in series and, more importantly, non-self averaging, thus replacing the classical Ohm’s law with a quantum Ohm’s law describing statistical fluctuations. In this paper, we report on some of our recent work on the statistics of these “Sinai” fluctuations of residual resistance for one and higher space dimensions (d). In particular we show that the physics at the mobility edge may be dominated by these fluctuations. We also show that an external electric field tends to harness these fluctuations. Some observational consequences such as 1/f-noise at low temperatures are discussed. Our approach is based on invariant imbedding extended by us for this purpose.

• Resistivity of metallic systems with a strong dynamic disorder

If the static disorder in a system is increased the conductivity and the electron mean free path decreases to the limit where it reaches the Ioffe-Regal criterion. In this paper experimental results are presented which show that dynamic disorder (produced by electronphonon interaction) can produce similar effects as static disorder. In certain metallic glasses it has been found that when the resistivity as a function of temperature reaches a critical value (almost equal to the maximum metallic resistivity value) the TCR changes from positive to negative values.

• Josephson voltage standard at National Physical Laboratory, New Delhi

A C Josephson effect is now used by several countries as the reference standard for the unit of d.c. voltage. This paper describes the work done at the National Physical Laboratory (NPL), New Delhi in the realization of the unit of volt based on the a.c Josephson effect. A voltage standard at 1 mV level using a Nb-Nb point contact junction has been established and the as-maintained volt based on a bank of standard cells has been intercompared against it using a 1:1000 voltage divider. The experimental set-up used in this comparison and the results of recent measurements are described. The overall uncertainty in assigning the value of emf to a standard cell is about 1 ppm. The as-maintained volt has been found to agree with the Josephson voltage within overall uncertainty.

• Transformation kinetics of A-15 superconductors formed by solid state reactions

Various fabrication processes devised for making multifilamentary A-15 super-conductors are all based on solid state reactions, transforming the host metal into the binary A-15 phase. The kinetics of the growth process involved in the compound formation form the theme of this paper.

• Disorder in superconductors—a study on Cu2Mo6S8

Some of the recent work on disorder-induced changes inTc is reviewed. Shock-pressures induce a disorder uncomplicated by antisite disorder typical of particle irradiation, and have generated interest because of the shock-synthesis of A-15 Nb3Si. In this paper we present our results on laser-induced shock-damage, and compare it with the results on V3Si and the results on particle irradiation of Chevrel phase superconductors.

• Structural instability and superconductivity in niobium-titanium alloys

Niobium-titanium is the most widely used technical superconductor. Titaniumrich transition metal alloys, quenched from high temperatures, can generally be retained in the bccβ phase. This phase is metastable and the instability is relieved by a variety of low temperature structural transformations. This aspect has been investigated using x-ray, TEM, low temperature resistivity,Tc and dHc2/dT studies, in a series of Nb-Ti alloys. The instability has been characterized by the normal state resistivityρn and dρ/dT.

The commercially used Nb-Ti alloys are Ti rich per atom-wise. This stems basically from the anomalous increase in the normal state resistivityρn as the Ti concentration is increased. This is a consequence of a dynamical process through which theβ phase instability tends to be relieved leading to athermal ω precipitation. The resulting anomalous resistivity behaviour can be understood in terms of a ‘two-level system’ model generally invoked for amorphous materials. It has also been possible to induce instability towards athermal ω precipitation in a system spontaneously undergoing a martensitic transformation to become stable. Thus in an alloy of Nb-83 at % Ti, addition of 1% nitrogen has suppressed the martensitic transformation, giving a three-fold increase inρn (about 150µΘ cm), the highest known in Nb-Ti so far.

The increase in the normal state resistivity has beneficial effects on the upper critical field. From studies on several Nb-Ti alloys, it is inferred that a peak inHc2(0) occurs at 17–18 tesla at aρn value of 100µΘ cm. It is pointed out that in the present commercial alloys, the sequence of thermo-mechanical treatments given to optimizeJc, restrictsρn, perhaps owing to the partial relieving of the metastability of theβ phase. They are therefore non-optimized with respect toHc2.

• Theoretical studies on magnetic superconductors

The discovery of magnetic superconductors has posed the problem of the coexistence of two kinds of orders (magnetic and superconducting) in some temperature intervals in these systems. New microscopic mechanisms developed by us to explain the coexistence and reentrant behaviour are reported. The mechanism for antiferromagnetic superconductors which shows enhancement of superconductivity below the magnetic transition is found relevant for rare-earth systems having less than half-filled f-atomic shells. The theory will be compared with the experimental results of SmRh4B4 system. A phenomenological treatment based on a generalized Ginzburg-Landau approach will also be presented to explain the anomalous behaviour of the second critical field in some antiferromagnetic superconductors.

These magnetic superconductors provide two kinds of Bose fields, namely, phonons and magnons which interact with each other and also with the conduction electrons. Theoretical studies of the effects of the excitations of these modes on superconducting pairing and magnetic ordering in these systems will be discussed.

• Phase transition studies of paramagnetic crystals at low temperatures

Magnetic, thermal, electrical and optical properties of a series of paramagnetic compounds of general formula ABF6, 6H2/6D2O and A(ClO4)2, 6H2O where A=Co, Na, Zn, Hg and B=Si, Ti, Zr, showing structural transition from room temperature hexagonal with one molecule in the unit cell to low temperature monoclinic with two molecules in the unit cell, are reviewed.

• Nuclear magnetic resonance studies in rare earth ternary phosphides

The results of31P Knight shift (KS) and spin-lattice relaxation time (T1) measurements in the temperature interval 4.2–300 K are reported for the compounds RENi2P2(RE=Ce, Eu, Yb) in order to understand the nature of the ground state in these compounds. KS results conclusively establish that all these compounds exhibit non-magnetic ground states. The temperature dependence of spin-fluctuation temperature (Tsf) in each case is estimated from the measured data. For EuNi2P2 the values ofTsf above 77 K qualitatively agree with those obtained from Mössbauer and susceptibility data employing ionic interconfigurational fluctuation model, but disagree at lower temperatures.

• Layered structure of superfluid4He at supercritical motion

Landau’s criterion plays an important role in the theory of superfluidity. According to this criterion, superfluid motion is possible if$$\tilde \varepsilon \left( p \right) \equiv \varepsilon \left( p \right) + pV &gt; 0$$ along the curve of the spectrumɛ(p) of excitations. For4He it means thatv&lt;vc,vc≈60 m/sec.vs is equal to the tangent of the slope to the roton part of the spectrum. The question of what happens to the liquid when this velocity is exceeded, as far as we know, remains unclear. We shall show that for small excesses abovevc a one-dimensional periodic structure appears in the helium. A wave vector of this structure oriented opposite to the flow and equal toρc/h whereρc is the momentum at the tangent point. The quantity$$\tilde \varepsilon \left( p \right)$$ is the energy of excitation in the liquid moving with velocity v. Inequality of Landau ensures that$$\tilde \varepsilon$$ is positive. If$$\tilde \varepsilon$$ becomes negative, then the boson distribution function$$n\left( {\tilde \varepsilon } \right)$$ becomes negative, indicating the impossibility of thermodynamic equilibrium of the ideal gas of rotons; therefore the interaction between them must be taken into account. The final form of the energy operator is$$\hat H = \int {\left\{ {\hat \psi + \tilde \varepsilon \left( p \right)\hat \psi + \tfrac{g}{2}\hat \psi + \hat \psi + \hat \psi \hat \psi } \right\}} d^3 x, g \sim 2 \cdot 10^{ - 38} erg.cm.$$ Then we can seek the rotonψ-operator in the formψ=ηexp(ipcr/h), determiningη from the condition that the energy is minimized. The result is (η)2=(vvc)ρc/g, forv&gt;vc. The plane waveψ corresponds to a uniform distribution of rotons. It leads, however, to a spatial modulation of the density of the helium, since the density operator$$\hat n$$ contains a term which is linear in the operator$$\psi :\hat n = n_0 + \left( {n_0 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} {A \mathord{\left/ {\vphantom {A {\hat \psi \to \hat \psi ^ + }}} \right. \kern-\nulldelimiterspace} {\hat \psi \to \hat \psi ^ + }}$$), where |A|2ρc2/2(ρc). Finally we find that the density of helium is modulated according to the law$$\frac{{n - n_0 }}{{n_0 }} = \left[ {\frac{{\left| A \right|^2 \left( {\nu - \nu _c } \right)\rho _c }}{{n_0 g}}} \right]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \sin \rho _c x \approx 2,6\left[ {\frac{{\nu - \nu _c }}{{\nu _c }}} \right]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \sin \rho _c x$$. This phenomenon can be observed, in principle, in the experiments on scattering ofx-rays in moving helium.

• Study of the two-domain processing structure in the superfluid3He-B

The systematic experimental and theoretical investigation of the longlived induction signal, known to exist in the3He-B, has shown that even very small nonuniformity of a steady magnetic fieldH0 changes qualitatively the precession pattern arising in the pulsed NMR experiments after tipping of the magnetization. The spin supercurrents redistribute magnetization within the experimental cell to produce the precessing structure, consisting of two domains. In one-domain, situated in the higher field region, magnetizationM has its equilibrium value and is parallel toH0. In the other domain the angle betweenM andH0 is slightly larger thanϑ0=arc cos (−1/4). The structure precesses with frequency, equal to the Larmor frequency at the site of the wall, separating the domains. The relaxation of this structure goes via the growth of the equilibrium domain at the expense of the precessing domain; therefore in the course of the relaxation the frequency of the precession has to decrease with time. The calculated rate decrease agrees with the observed value. Experiments were carried out directly demonstrating the existence of the two-domain structure.

After the formation of the two-domain structure, as well as after a perturbation of the structure by short r.f. pulses, low frequency (≈200 Hz) modulation of the induction signal is observed due to vibration of the structure. These vibrations are the standing spin waves in the precessing domain, their frequency being proportional to the size of the domain. The observed dependence of the frequency on other parameters is in agreement with theoretical calculations.

The analysis of the data on the vibration and relaxation of the two-domain structure enables us to find the spin wave velocity and the spin diffusion coefficient in3He-B.

Further investigation of the two-domain structure enables the study of spin supercurrents in3He-B.

• Roughening (faceting) transitions on the helium crystal-superfluid interface

The concept of roughening transitions (RT) was first introduced into theory by Burton and Cabrera (1949). RT, which manifests itself in disappearance of smooth facets in equilibrium shape of the crystal (faceting transition), has been under intensive theoretical study in the last few years (Andreev 1981; Rottman and Wortis 1984). Current interest in this field is connected mainly with the problems of “quantum roughening’ and critical behaviour of the surface stiffness. Experimental studies of RT in usual classical crystals meet with serious difficulties due to very long crystal shape relaxation times. In this respect, helium crystals seem to be the best candidates because of their extremely fast growth kinetics which ensures sufficiently short shape relaxation times (Keshishevet al 1982).

We have recently investigated the equilibrium shape of large4He crystals in the vicinities of the two different RT (TR=1.2 K and 0.9 K) by a simple optical technique which provides the temperature and angular dependences of the surface stiffness (Babkinet al 1958, 1984, 1985). The data obtained by this method show, in accord with theory, that both studied RT being continuous phase transitions. However, the measured critical behaviour of the surface stiffness cannot be explained satisfactorily by current theories, either by the phenomenological “mean field” theory (Andreev 1981) or by the lattice model calculation (Rottman and Wortis 1984).

• Quantum interference of electrons in disordered metals

Investigation of the galvanomagnetic properties of disordered metals in weak magnetic fields [r(H)≫l, wherer(H) is the electron trajectory radius andl, the electron free path], proved to be one of the effective experimental methods of studying disordered metals. The phase difference between the interfering electron waves is affected by the presence of magnetic flux in the sample. One of the observable effects is the oscillatory magnetoresistanceK(H) of multiconnected samples predicted by Altshuleret al (1981). The period ofK(H) oscillations for the hollow cylinders, networks or chains with orifices cross-sections areasS isΔH=φ0/2S [whereφ0=hc/e]. The amplitude and the phase of the oscillations depend on the spin orbit interaction, the intensity of superconductive fluctuation etc.

It should be noted that in small “mesoscopic” single loops the oscillations with the periodΔHφ0/S were also observed recently (see also Altshuleret al 1987 included in this issue).

• Residual conductance fluctuations of tiny disordered conductors

Conductances of the equivalent samples differ randomly (Stone 1985). At zero temperature these fluctuations were found to be of the order ofe2/h for samples of arbitrary size and form (Altshuler 1985; Lee and Stone 1985). Experimentally such fluctuations manifest themselves as e.g. the reproducible aperiodic oscillations of the given sample conductance in magnetic field (Webbet al 1985; Stone 1985). These oscillations can be understood in terms of the correlation function (Lee and Stone 1985; Altshuler and Khmel’nitskii 1985) of the conductances in different fields. The characteristic field scale of the aperiodic oscillations corresponds to the unit magnetic flux through the sample.

Conductance fluctuations decrease with the growth of temperature if the sample size is larger than the diffusion length within the timeh/T (Stone 1985; Lee and Stone 1985; Webbet al 1984, 1985; Altshuler and Khmel’nitskii 1985). These fluctuations are proportional toT−1/4,T−1/2 logT, andT−1/2 in the 3-d, 2-d and 1-d cases, respectively (Altshuler and Khmel’nitskii 1985) (the experiments of Webbet al 1984, 1985 correspond to the latter case).

Random potential in tiny samples breaks all space symmetries. All effects which are forbidden in the average by these symmetries should manifest themselves by (i) conductance anisotropy, (ii) its dependence on the electric field direction and (iii) giant generation of the second harmonic in the granular sample under light radiation (Altshuler and Khmel’nitskii 1985).

Conductance changes aperiodically with variation of the chemical potential (Lee and Stone 1985). Because of this thermopower fluctuations are much larger than its average value (Altshuler and Khmel’nitskii 1985).

Conductance fluctuations are very sensitive to the random impurity potential variations (Altshuler and Spivak 1985). For instance, the change of the film conductance due to the shift ofone impurity isfinite for any film size. This effect can be used for the super flow impurity diffusion investigations. Variations of the localized spins realization in spin glasses change the conductance. This can explain (Altshuler and Spivak 1985) the conductance dependence on the magnetic field direction observed by Webbet al (1984, 1985).

• Experimental study of resistivity of metallic materials with dynamic disorder

As a result of strong electron-phonon interaction, the enhancement of scattering with increasing temperature may decrease the mean free pathl in crystals down to interatomic distances:la. This means that with respect to the electron wave the degree of the atomic disorder in these crystals is approximately the same as in amorphous metal. Because of a high electron velocity the dynamic character of the disorder seems to be unimportant. At the same time, the degree of disorder can be easily changed by varying the temperature. This makes it possible to simulate and study the transport properties of the disordered media on highquality crystals with strong phonon scattering. The sign that indicates the fitness of a crystalline metallic material for such studies is the saturation of its resistivityρ that ceases to grow as the temperature is increased.

The saturation of resistivity was investigated experimentally on (i) Cu-Zr alloys in the crystalline state, (ii) single crystals of WO2, which is a metal with well-defined Fermi surface.

The samples of Cu-Zr were produced by the recrystallization of amorphous ribbon. Some of these samples reveal resistivity saturation. With further increase ofT a maximum in theρ(T) dependence was observed at those compositions which slightly decreased theirρ value under recrystallization. This unusual dependence can be explained in terms of the two-band model assuming that thed-electrons reach the minimal free path,la, while thes-electrons do not.

The WO2 crystals were used to study the anisotropy of (T). In the directions, whereρ is high, there is a tendency to saturation. Whereρ is low, no tendency to saturation is observed. The quantitative analysis of the curves has shown that not only the absolute value but also the relative value of the deviation from the Boltzmann lawρT decreases down as the resistivity decreases.

• Nonstationary phenomena in Si MOSFETs in the quantum hall effects regime

We report the observation of nonstationary hysteresis phenomena in charging of Si MOSFET at a quantizing magnetic field. In these experiments (Pudalovet al 1984; Pudalov and Semenchinsky 1985) the charging currentJg of the capacitance gate-2D-layer was measured while sweeping of the magnetic fieldH or a gate voltageVg at a constant rate. The numerical integration of the measured valuesJg with respect to time gave the dependences of change inQs vsVg or vsH.

At low temperatureT&lt;1 K there arise deviations from the linear dependenceQs(Vg) near those integer values of Landau level fillingν=ns/nH=2, 4, 6, 8, 12, which correspond to the most deep minima inρxx and flat plateaux inρxy. Herens is the 2D electron density,nH being Landau level degeneracy number,ρxx andρxy —the resistivity tensor components. The inherent feature of the curveQs(Vg) is the hysteresis: at increasingVg the chargeQs is less than the equilibrium value, while at decreasingVg the charge exceeds the equilibrium one.

The maximum difference of charges at an increase and decrease ofVg grows-rapidly at loweringT and atT=0.42 K amounts to ∼10% of the full charge confined by one Landau level (nH.e.S). It is worth to note that such behaviour ofQs(Vg) does not influence the values ofρxy (with accuracy of ∼ 10−5) and the shape ofρxy plateaux andρxx-minima.

Measurements at various sweep rates dVg/dt demonstrated that if the sweep rate is lower, the hysteresis region is narrower and the deviation of chargesQs from its equilibrium value is smaller. By extrapolating the dependence of hysteresis loop width on dVg/dt, the ultimate sweep rate may be estimated, for which a hysteresis will completely disappear. Thus, for instance, atT=0.42 K andν=4 it will occur when the time interval of one Landau level fillingτH will be equal to 100 years.

A similar hysteresis in 2D-layer charge occurs in varying magnetic field also, when the gate voltage is disconnected with the battery and hence the charge in MOSFET is maintained constant. This hysteresis loop rapidly vanishes at temperatures &gt;1 K.

The long relaxation time of a nonequilibrium charge in 2D-layer can be connected phenomenologically with small drift velocities of electrons along the potential gradient due to a small value of conductivityσxx. This relaxation time may be estimated asτC/σxx whereC is the electrical capacitance of MOSFET area with a nonequilibrium charge. The value ofτ∼109 s givesσxx&lt;10a−18 Ohm−1/□, i.e.ρxx&lt;10−11 Ohm/□. Simultaneously with nonequilibrium charge relaxation in 2D-layer there arise circular Hall currents decaying with the same rate.

In conclusion, we observed and investigated nonequilibrium charging of 2D-layer in quantum Hall effect regime. To explain the phenomenon we supposed that circular Hall currents is comparable to the eddy currents excited in a superconducting ring.

• Electron fluid and quasiparticles in the quantum Hall effect

To explain fractional quantum Hall effect, it is necessary to take into account both the interaction between electrons and their interaction with impurities. We propose a simple model, where the Coulomb repulsion is replaced by a short range potential. For this model we are able to find many-body wave functions of the electron system interacting with impurities and calculate the Hall conductivityσxy. A simple physical picture, arising in the framework of this model, provides the understanding of a general reason for both fractional and integral quantum Hall effect.

In the model, electrons forming a two-dimensional system, is supposed to occupy the first Landau level. The interaction of electrons is regarded as being small compared with the distance between the Landau levels. The radius of interaction is much less than the magnetic length. The following statements have been proved (Pokrovsky and Talapov 1985a,b; Trugman and Kivelson 1985). For the fillingν=1/m of the first Landau level the ground state is nondegenerate and has the wave functionΩw, proposed by Laughlin (1983). Forν, which is slightly less than 1/m the ground state is highly degenerate in the absence of impurities. It can be described as a system of noninteracting quasiholes as proposed by Laughlin (1983). These quasiholes float in the uniform incompressible fluid. Each quasihole has the charge |e|/m. The total number of quasiholes isq=SmN, whereS is a number of states on the Landau level,N is the number of electrons. The impurities capture quasiholes. If the number of quasiholesq is less than the number of impuritiesNi, then the ground state becomes nondegenerate. This fact permits us to calculateσxy (Pokrovsky and Talapov 1985b). Let there be a small electric fieldE in the system. In the absence of impurities the electron fluid is at rest in the frame of reference, moving with velocityν=cE/H. In this frame of reference the impurities move with the velocity −v, carrying captured quasiholes. Therefore, the quasihole currents isjq=(−ν)(|e|/m)q. Hence, in the initial frame of reference the total current isj=Nev+jq=Sev/m. This means thatσxy=(1/m)e2/2πħ).

• Unusual superconductivity and its physical properties

Physical properties are discussed, which, in principle, would allow us to distinguish between nontrivial superconductivity and superconductivity of the ordinary type thus establishing its superconducting class. These properties are: the anisotropy of the upper and low critical fields, the magnetization curve, some peculiarities of the penetration depth, the impedance behaviour etc. It is pointed out that these superconductors could possess some magnetic properties. The role of defects is investigated and, in particular, the possibility of the magnetization in these superconductors which originates from the presence of ordinary defects.

The problem of nontrivial superconductivity is discussed in connection with available experimental data concerning new materials with the so-called “heavy fermions”.

• Superconductivity of the twinning plane

Lately superconductivity of a new object, twinning plane (TP) of metal crystals, has been discovered and investigated (Shaikin and Khlustikov 1981; Khlustikov and Khaikin 1982; Buzdin and Khlustikov 1984; Khlustikov and Moskvin 1985). The only one monolayer of atoms of the samples is in crystallographically shaped position, which proves TP to be unique. The monolayer of atoms generating TP is a two-dimensional crystal. The two-dimensional crystal is supposed to have its own two-dimensional electrons and phonons (Khaikin and Khlustikov 1981). Superconductivity of twinning plane (STP) is the first effect discovered which demonstrates unusual properties in such two-dimensional systems.

STP is essentially different from three-dimensional superconductivity and is observed in a number of metals, such as In, Nb, Re, Sn and Tl. The fact that STP emerges at higher temperatures than three-dimensional superconductivity is a case of special interest to this problem. Superconductors of first type (Sn) and of second type (Nb) have been studied in detail. The measurements of phase (H, T) diagram STP in these metals have been carried out. STP is shown to appear in Sn by the first type phase transition (Khlustikov and Khaikin 1982; Buzdin and Khlustikov 1984), and in Nb, most likely, by the second type phase transition. Topological phase transition of Berezinsky-Kosterlitz-Thouless (Khlustikov and Moskvin 1985) transition type was discovered in twins of Nb.

• Investigations of UBe13 of other compounds of Be and U in normal and superconductive states

During the last few years superconductive systems of heavy fermions with highly large values ofm* and electronic heat capacityγT have been thoroughly investigated.

The following compounds viz CeCu2Si2 (Tc=0.6 K;γ=1100*), UBe13(Tc=0.95 K;γ=1000) and UPt3 (Tc=0.5 K;γ=450)(I) may be referred to such systems as well as the U and Ce compounds: U2Pt C2 (Tc=1.47 K;γ=75), U6Fe (Tc=3.86 K;γ=25), U6Co (Tc=2.3 K;γ=21), URu2Si2 (Tc=0.68 K,γ=17.6), as well asα-U (Tc=2.1;γ=12), CeRu3Si2 (Tc=1 K;γ=39), CeOs2 (Tc=1,1 K;γ=22), CeRu2 (Tc=6 K;γ=23.3) and α-Ce (Tc≲2K;γ=14) (Alekseevskii and Homskiy 1985).

It should be noted that there exists a class of U and Ce compounds with a similar structure as those given above, which undergo transition to superconductive state, but are not characterized by abnormal values ofm* (Alekseevskii 1984).

Many authors considered superconductivity of heavy fermion systems as unusually anisotropic where charge carrier coupling occurs in P-state (Stewart 1984). On the other hand such a view does not agree with many experimental results, e.g. lack of anisotropy Hc2 for UBe13 (Alekseevskiiet al 1985) as predicted by Gorkov (1984) and the results of investigation of the Josephson effect. The Hall-effect investigations for UBe13 in a wide range of fields and temperatures (Alekseevskii 1984) make it possible to consider systems with two types of carriers—heavy and light. The unique properties of the above systems in a number of cases are possibly caused by these two types of carriers and the peculiarity of interaction between them.

• Disordered magnets

The physics of strongly-disordered magnets and especially that of spin glass is an example of a scientific problem whose ideas and results are widely used in different and sometimes rather distant areas (up to biology, for example). This is the consequence of the paradoxical nature of the main question of this problem: how does ordering occur in systems which do not possess any apparent order at all? In other words, how can one find genuine (but hidden) internal variables which determine dynamics (and thermodynamics) of the system having no macroscopic order parameter.

From the theoretical point of view the “generic model” for such a system is the well-studied model of spin glass with infinite-range interaction. The next necessary step is to understand the degree of applicability of the results of infinite-range models to real systems. Further there are a number of phenomena which are completely beyond the frame of this model and are governed by fluctuation effects. The theory of fluctuation phenomena in strongly disordered magnets is at the very beginning of its development. In this report we discuss some relevant problems which have been well studied. In the case of genuine spin glasses the problems are as follows: whether there exists a thermodynamic phase transition to the spin glass phase and how does it occur? What is the physics of non-exponential relaxation far above the transition point? Further there are a number of systems belonging to the spin glass universality class (in the sense of phase-transition theory) but possessing the same sort of short-range order. We consider the following spin glasses with local helical order (for example, the diluted yttriumbased alloys YEr, YDy); amorphous magnets with strong random-axis anisotropy; disordered magnets with strong dipolar interaction. We discuss mainly the structures of low-temperature phases in these systems.

• Spin waves in paramagnetic Boltzmann gases

As the temperature is lowered we get an interesting temperature regionɛdTħ2/mr02(whereɛd is the quantum degeneracy temperature,m the mass of a gas molecule,r0 the radius of interparticle interaction) in which the thermal de Broglie wavelength Λ of a particle is considerably greater than its sizer0 though Λ turns out to be less than the mean interparticle distanceN−1/3≫Λ≫r0. Although the gas molecules obey the classical Boltzmann-Maxwell statistics the system as a whole begins to exhibit a larger number of essentially quantum macroscopic collective features. One of the most interesting and dramatic features is the possibility of propagation of weakly damped spin oscillations in spin-polarized gases (external magnetic field, optical pumping). Such oscillations can propagate both in the low-frequencyθτ≪1 regime and the high frequencyθτ≫1. The last case is highly non-trivial for a Boltzmann gas with a short range interaction between particles. The weakness of relaxation damping of spin modes implies that the degree of polarization is high enough 1&gt;/|α|≫|a|/Λ, whereα=(N+N)N,a is the two-particles-wave scattering length. Under these conditions the spectrum of magnons has the form (Bashkin 1981, 1984; Lhuillier and Laloe 1982)$$\omega = \Omega _H + \left( {{{K^2 \nu _{\rm T}^2 } \mathord{\left/ {\vphantom {{K^2 \nu _{\rm T}^2 } {\Omega _{int} }}} \right. \kern-\nulldelimiterspace} {\Omega _{int} }}} \right)\left( {{{1 - i} \mathord{\left/ {\vphantom {{1 - i} {\Omega _{int} }}} \right. \kern-\nulldelimiterspace} {\Omega _{int} }}\tau } \right), \Omega _{int} = {{ - 4\pi ahN\alpha } \mathord{\left/ {\vphantom {{ - 4\pi ahN\alpha } m}} \right. \kern-\nulldelimiterspace} m}, \nu _{\rm T}^2 = {T \mathord{\left/ {\vphantom {T m}} \right. \kern-\nulldelimiterspace} m}$$ where ΩH is the Larmor precession frequency for spins in the magnetic fieldH. Collisionless Landau damping restricts the region of applicability of (1) with not too large wave vectorsKvT≪|Ωint|. The existence of collective spin waves has been experimentally confirmed in NMR-experiments with gaseous atomic hydrogen H↑ (Johnsonet al 1984). The presence of undamped spin oscillations means automatically the existence of long range correlations for transverse magnetization. Such correlations decrease with the distance according to the power law$$\delta _{ik} \left( r \right) = 2\left| a \right|\frac{{\left( {\beta N\alpha } \right)^2 }}{\gamma }\delta _{ik}$$. Hereβ is the molecule magnetic moment. Spin waves being even damped can nevertheless reveal themselves atTħ2/mr02 or when |α|≲r0/Λ. The first experimental discovery or damped spin waves in gaseous3He↑ has been done in Nacheret al 1984. Oscillations of magnetization can also propagate in some condensed media such as liquid3He-4He solutions, semimagnetic semiconductors etc.

• Magnetic properties and peculiarity of magnetic states in dilute antiferromagnets Mn1−xZnxF2

The dependence of magnetic moment and susceptibility on temperature, magnetic field and frequency of some single crystals Mn1−xZnxF2 (xxe=0.75—percolation limit) were experimentally investigated. Our experiments show that (Bazhan and Petrov 1984; Cowleyet al 1984; Villain 1984) in these crystals the nonequilibrium magnetic state of spinglass type with finite correlation length appears as temperature decreasesT&lt;T in weak magnetic fields. This state is determined by fluctuation magnetic moments √ (wheren is the number of magnetic ions, corresponding to finite correlation length andμ the magnetic moment Mn+1).

In the experiments in low magnetic fields and frequencies there are no peculiarities in the magnetic susceptibility temperature dependence atTTf. At temperaturesT&gt;Tf andT&lt;Tf magnetic susceptibility is determined by$$\chi \left( {T &gt; T_f } \right) = \frac{{N\left\langle \mu \right\rangle ^2 }}{{3k\left( {T + \theta } \right)}} = \frac{N}{n}\frac{{\left\langle {\sqrt n \mu } \right\rangle ^2 }}{{3k\left( {T + \theta } \right)}} = \chi \left( {T&lt; T_f } \right)$$. In strong magnetic fields and large frequencies there are peculiarities in thex(T) dependence atT=Tf. AtT&lt;Tf and strong magnetic fieldsX(T)=x0 andT&lt;Tf and at large frequenciesx(T)=x0+α/T.

The dependences of magnetic susceptibility on the frequency are determined by the magnetic system relaxation. Calculations and comparison with experiments show that the relaxation of the investigated magnetic systems atT&lt;Tf follows the relaxation lawM(t)=M(0) exp[−(t/τ)r], suggested in Palmeret al (1984) for spin-glasses relaxation taking into account the time relaxation distributionτ0....τmax in the system and its ‘hierarchically’ dynamics.

• Periodic density redistribution of parametrically excited spin waves in an antiferromagnet

A nonuniform distribution of the density of parametrically excited magnons is observed experimentally in an antiferromagnetic CsMnF3 sample. The nonuniform distribution occurs at a high pumping power when oscillations of the high frequency susceptibility occur. These oscillations were observed earlier and their nature was not clear. It is found that during the increase of the absorbed power on the occurrence of the oscillation, the spin wave condenses near the middle of the sample. The condensation occurs as a result of a nonlinear shift of the magnon spectrum and is similar to self-focusing of light in nonlinear media. The electromagnetic radiation of parametrically excited spin waves is studied. It is found that the periodic redistribution of the density exerts an additional restrictive effect on the amplitude of the parametrically excited magnons.

• Frozen photoconductivity in PbTe films

We have studied PbTe films of thicknessd=200/10000 A made with telluride vapour deposition on glass substrate at room temperature. The estimate of the donor concentration ∼1019 cm−3 of the fresh-deposited film compared with the impurity content in the bulk raw material ∼1017 cm−3 shows that the donors were mainly film defects or nonstoichiometric Pb atoms. Electrical conductivity of the freshly deposited film increased with lowering of the temperature. After deposition the donors were compensated with an oxidation in the laboratory air. Transition to the thermally activated conductivity resulted from oxidation. At temperatures belowT≈100 K the resistance of the compensated films followed Mott’s ruleR=R0 exp(T0/T)1/3. The square film value 1 Mohm andT0≈100 K ford=1000 A.

At low temperatures an exposure to light resulted in sharp decrease of the film resistance. At liquid helium temperatures the resistance dropped 103–106 times and stayed at the low value for an indeterminate time. The heating of the film aboveT=100 K gave rise to an initial high resistive state. The critical temperatureTc, when the frozen photoconductivity became negligible, varied with samples in the temperature region 90–120 K. Near the critical temperature we could measure the time dependence of the film resistance after the light exposure, which followed the equationR=A+B.lnt fort&gt;1 sec with the empirical constantsA andB. After a time intervalτ the resistance gained the initial “dark” value and remained stationary. The value lnτα.(TcT), where the factorα approximately wasα≈0.5 K−1.

Some results of these experiments were published earlier (Krylov and Nadgorny 1982; Krylov and Pojarkov 1984).

• Erratum

• # Pramana – Journal of Physics

Current Issue
Volume 93 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019