Contribution Of Spin Fluctuations Research Articles

Spin fluctuation contributions to the specific heat of CuNi alloys

The electronic and magnetic specific heat of CuNi alloys has been determined in the temperature range 1.5-240K for Ni concentrations between 25 and 70 at.%. For concentrations up to 58 at.% Ni the specific heat at 240K is close to the unenhanced electronic value deduced from a recent CPA band-structure calculation for paramagnetic CuNi. At lower temperatures the electronic specific heat is strongly enhanced in the critical concentration region. Arguments are presented against a superparamagnetic cluster explanation, and it is concluded that the results may best be understood in terms of an electron effective mass enhancement due to their coupling to spin fluctuations localised in regions of high Ni density.

Specific heat, magnetic susceptibility, and resistivity of anU0.85La0.15Al2alloy

The compound U${\mathrm{Al}}_{2}$ exhibits ferromagnetic spin fluctuations at low temperatures. When 15 at.% La is substituted for U in U${\mathrm{Al}}_{2}$, we find the low-temperature magnetic susceptibility increases by more than a factor of 2. We have also measured specific heat on this sample at low temperatures. We find that the electronic density of states has increased by 60% and the spin-fluctuation contribution has increased by a factor of 2. We conclude from these measurements that the Stoner enhancement factor has increased by \ensuremath{\sim}30% and the spin-fluctuation temperature has increased by \ensuremath{\sim}50% as compared with U${\mathrm{Al}}_{2}$. In addition, we have measured the electrical resistivity of ${\mathrm{U}}_{0.85}$${\mathrm{La}}_{0.15}$${\mathrm{Al}}_{2}$. We find the residual resistivity to be approximately an order of magnitude larger than that of U${\mathrm{Al}}_{2}$. We attribute this effect to the breaking of U---U bonds by the La atoms.

Spin-fluctuation contribution to the high-frequency electrical conductivity of nearly magnetic transition metals

The high-frequency limit of the electrical conductivity of nonmagnetic transition metals is calculated. The conduction electrons are assumed to be scattered by the spin fluctuations in the partially filled $d$ bands. The frequency-dependent conductivity has a Drude-type form, in which the scattering rate is itself frequency dependent. The scattering rate is increased as the magnetic susceptibility is enhanced by the spin fluctuations. The scattering rate exhibits a complicated frequency and temperature dependence. However, in the dc limit it does follow the low-temperature ${T}^{2}$ law of electron-electron collisions followed at higher temperatures by a linear dependence on $T$. On the other hand, at $T=0$, the scattering rate is proportional to ${\ensuremath{\omega}}^{2}$ for low frequency.

NMR Study of Spin Fluctuations in Antiferromagnetic Cr1-xVx Alloys

Nuclear spin relaxation for 51 V in both the paramagnetic and ordered states of incommensurate antiferromagnetic Cr 1- x V x ( x =0.01, 0.02, 0.03 and 0.038) alloys have been investigated in a temperature range between 1.3 and 300 K. The experimental results of the temperature dependence of the relaxation rate ( T 1 T ) -1 are interpreted in terms of the contribution of spin fluctuations, which behaves as ( T 1 T ) sf -1 ∝( T - T N ) -1/2 for T - T N , and the Korringa rate.

Influence of high magnetic fields on the low temperature heat capacity of the itinerant electron ferromagnet Sc 3In

The low temperature (1.3–20 K) heat capacity of the weak itinerant electron ferromagnet Sc 3In was measured in magnetic fields up to 10 T. The measurements were made on three different samples containing 24.1, 24.3 and 24.4 at.% In with Curie temperatures at H = 0 of 5.5, 6.0 and 6.3 K, respectively. The heat capacity peak at T c becomes smaller with increasing fields and at 9.98 T the magnetic entropies are only 11 to 19% of the zero field value. Above T c the spin fluctuation contribution to heat capacity, which is enhanced by the magnetic field at low fields (<≈ 5 T), is quenched at high fields (⩾ ≈ 5 T). Our results show that the spin fluctuations in Sc 3In are almost completely quenched by the magnetic fields of ≈ 10 T, and that the characteristics spin fluctuation temperature, T s , of this itinerant electron ferromagnet is about the same as T c .

Magnetic neutron scattering and crystal-field states in CeCu2Si2

The energy-loss spectra of Ce${\mathrm{Cu}}_{2}$${\mathrm{Si}}_{2}$ and La${\mathrm{Cu}}_{2}$${\mathrm{Si}}_{2}$ have been determined using neutrons of high incident energy. The magnetic part of the low-temperature spectra of Ce${\mathrm{Cu}}_{2}$${\mathrm{Si}}_{2}$ consists of a quasielastic line and two inelastic lines at 12.5 and 31 meV resulting from transitions between the Kramers ground state and two excited crystal-field doublets of ${\mathrm{Ce}}^{3+}$ in tetragonal symmetry. When positions as well as intensities of the inelastic lines are used, the crystal-field level scheme can be derived. The temperature dependence and magnitude of the quasielastic linewidth suggest that the contribution of Kondo-type spin fluctuations to the spin dynamics of Ce${\mathrm{Cu}}_{2}$${\mathrm{Si}}_{2}$ predominates over that of valence fluctuations. No indication of any magnetic ordering in Ce${\mathrm{Cu}}_{2}$${\mathrm{Si}}_{2}$ was found by neutron diffraction down to the mK range.

Local-density-functional approach to the isostructualγ−αtransition in cerium using the self-consistent linearized-augmented-plane-wave method

The isostructural $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\alpha}$ phase transition of Ce which occurs at 8 kbar has been studied by means of fully self-consistent (non-muffin-tin potential) linearized-augmented-plane-wave energy band calculations carried out for five different values of the lattice constant. In contradiction to the $4f$ electron promotional model of the transition, the results yield essentially one $4f$ electron to be occupied in each phase but with the $4f$ wave function somewhat less localized, and therefore more bandlike, in the collapsed $\ensuremath{\alpha}$ phase. A singly occupied $4f$ state is shown to be consistent with the available experimental data. These results strongly support the picture of a $4f$ localized \ensuremath{\leftrightarrow} itinerant transition at the $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\alpha}$ transition and conflict with the promotional model in which some fraction of $4f$ electrons are transferred to the $\mathrm{sd}$ conduction bands. The weaker bonding of the $4f$ electrons, compared to that of the $6s\ensuremath{-}5d$ valence electrons, accounts for $\ensuremath{\alpha}$-Ce appearing to have 3.5-3.7 bonding electrons in some respects. Calculation of the superconducting transition temperature ${T}_{c}$ suggests that a small spin-fluctuation contribution detrimental to superconductivity is necessary to account for the very low value of ${T}_{c}$ in $\ensuremath{\alpha}$-Ce. Comparison with specific-heat data also suggests a spin-fluctuation contribution to the effective mass; susceptibility data point to a moderate exchange enhancement in $\ensuremath{\alpha}$-Ce. We calculate a spin-susceptibility (\ifmmode \acute{S}\else \'{S}\fi{}toner) enhancement that increases with temperature, in agreement with experiment up to 150 K, and which tends to diverge at higher temperatures. Certain experiments are suggested which could help greatly in understanding further some important characteristics of the $\ensuremath{\alpha}$ phase.

Disappearance of the heat capacity peak of Sc 3In around the curie temperature in high magnetic fields

The low temperature (1.3–20.0 K) heat capacity of the weak itinerant electron ferromagnet Sc 3In was measured in magnetic fields up to ∼ 10 T. The heat capacity peak observed around T c = 6.0 K in zero field becomes smaller with increasing fields and at 9.98 T its magnetic entropy is ≈ 18% of the zero field value. Above T c, the spin fluctuation contribution to the heat capacity, which is enhanced by the magnetic field at lower fields (⪅5 T), is quenched at higher fields (⪆5 T). This depression of the spin fluctuation contibution to the heat capacity by the high magnetic fields occurs at lower magnetic fields than had been considered possible heretofore. Our results suggest that the itinerant ferromagnetism is Sc 3In is completely quenched at 12 T.

Effect of magnetic fields on spin fluctuations in metals: Electronic specific heat and electrical resistivity

The spin-fluctuation contribution to the electronic specific-heat enhancement and to the resistivity is calculated in the presence of a magnetic field using the random-phase approximation. The result is a depression of these contributions in the presence of the field thus providing a test of the paramagnon theory. A comparison with experiments on U${\mathrm{Al}}_{2}$ is presented and a measurable effect of several percent is predicted in very high magnetic fields of the order of 100 kG.

Effect of spin fluctuations in induced moment systems

The effects of spin fluctuations on the magnetism of induced moment systems are examined using the method of Moriya and Kawabata for the itinerant-electron model. The contribution of spin fluctuations to the free energy is expressed in terms of the longitudinal and transverse dynamic susceptibilities and used, in a self-consistent way, to obtain an expression for the static susceptibility. This expression enables the authors to calculate the critical criterion for ferromagnetic ordering, the Curie temperature and the static susceptibility as a function of temperature in the singlet-singlet model. It is found that a higher value of the exchange interaction is needed to induce ferromagnetic order than in the molecular field theory. All results are found to depend on the lattice structure.

Nuclear spin relaxation and the Knight shift of61Ni metal in the paramagnetic solid and liquid phases

Nuclear spin-lattice and spin-spin relaxation measurements of 61Ni metal in the paramagnetic solid phase, and Knight shift measurements extended into the liquid phase are reported. It is shown that the spin-lattice relaxation rate is the sum of an electronic contribution of the form (T,1T)-1=(4.6+or-0.2)(sK)-1, which is mainly orbital in origin, and a spin fluctuation contribution in the vicinity of the Curie temperature. From 820K to 1000K, the Knight shift varies linearly with the susceptibility, yielding a d spin hyperfine field of -(113+or-5)kG mu B-1. From 1000K to the melting point (1726K) a departure from this linearity is observed and analysed in terms of the change in the orbital susceptibility due to volume thermal expansion in the solid. Upon melting a further change Delta K=(0.26+or-0.03)% is observed. It is also attributed to the effect of a volume change on the orbital susceptibility.

Spin-fluctuation theory of strong coupling corrections to the free energy in superfluid 3He

Previous spin-fluctuation theories yielding the strong coupling corrections ..delta..beta-bar/sub i/ to the five coefficients of the fourth-order invariants in the free energy functional are extended. First, the superfluid part of the susceptibility is calculated up to order ..delta../sup 4/for all momenta and frequencies and the contribution arising from p-wave fluctuations of the order parameter is included. Then the frequency sums yielding the ..delta..beta-bar/sub i/ are calculated by taking into account the full momentum and frequency dependence of the superfluid susceptibility and the spin fluctuation propagator. The results for the ..delta..beta-bar/sub i/ are plotted vs. a cutoff q/sub c/ on the momentum integration for spin-fluctuation parameters IequivalentN(0)I=0.75 and I=0.95. The cutoff takes into account in a rough way the effect of additional terms in the free energy functional which were neglected in previous theories. These additional terms are due to the implicit dependence of the superfluid susceptibility on the spin-fluctuation parameter I via the gap parameter ..delta... The gap equation providing the relation between ..delta.. and I is derived in the weak coupling approximation. The cutoffs obtained by fitting the experimental values of the three combinations of ..delta..beta-bar/sub i/(arising from the measured specific heat discontinuities on the melting curve) are comparablemore » to the cutoff obtained from the spin-fluctuation contribution to the weak coupling free energy (q/sub c/=0.3(2k/sub F/) for I=0.75). The corrections due to the momentum and frequency dependence of the superfluid susceptibility and the spinfluctuation propagator are large and point in the direction of better agreement with experiment: The ratio R/sub 1/ =..delta..beta-bar/sub 5//(..delta..beta-bar/sub 2/+..delta..beta-bar/sub 4/) decreases from 2 to about 1.2. It is concluded that spin-fluctuation theory in its present form cannot account quantitatively for the measured specific heat discontinuities on the melting curve.« less

Possibility of triplet pairing in palladium

The spin-fluctuation contribution to the $p$-state pairing interaction in Pd is calculated. The resulting transition temperature, due to spin fluctuations alone, is only of order ${10}^{\ensuremath{-}5}$ K indicating that the occurrence of an observable $p$-state transition depends strongly on the phonon interaction. Recent calculations of the $p$-wave phonon interaction are briefly discussed but do not yet allow a reliable prediction of ${T}_{c}$.

NMR Studies of the Effect of Spin Fluctuations in Itinerant Electron Ferromagnet ZrZn2

Effects of external magnetic field and orbital degeneracy on the spin fluctuations in weakly ferromagnetic metals are studied based on the recent self-consistently renormalized spin fluctuation theory to obtain expressions for the spin fluctuation contributions to the nuclear magnetic relaxation rate 1/ T 1 and the specific heat. By using these expressions and taking account of the orbital relaxation contribution, our experimental data of the temperature and magnetic field dependences of 1/ T 1 for 91 Zr in ZrZn 2 are well interpreted and are analysed semi-quantitatively yielding useful informations on the electronic structure of ZrZn 2 . The spin fluctuation contribution to the specific heat at low temperatures in ZrZn 2 is also estimated.

Energy of formation for dilute alloys with transitional impurities

The authors determine the electronic contribution to the energy of formation Delta E in completely disordered dilute alloys from an expansion in successive powers of the impurity concentration; a similar analysis can be used for the magnetic (spin fluctuation) contribution to the energy of formation. Numerical results are presented and discussed, for alloys of transition impurities in noble (copper) or transition (first series) metals, using a realistic band structure and aluminium-based alloys. For transitional alloys a simple sum rule is used which relates Delta E to the host density of states.

Contribution of Spin Fluctuations to the Electrical and Thermal Resistivities of Weakly and Nearly Ferromagnetic Metals

The electrical and thermal resistivities due to the spin fluctuations in weakly and nearly ferromagnetic metals are studied by using the s-d band model and the self-consistently renormalized spin fluctuation theory for the d-band electrons. The resistivities are calculated in the whole temperature range of interest and their temperature dependences are discussed in detail. The resistivities are shown to be suppressed significantly by the renormalization from those calculated by using the RPA results for the spin fluctuations. Particularly the electrical resistivity can have a tendency towards saturation with increasing temperature.

Spin Fluctuation Depressed Superconductivity in Nb‐V Alloys

AbstractThe electrical resistivity of Nb‐V alloys has been measured around 250°C. Together with published values of the susceptibility and the electronic part of the specific heat the contribution of spin fluctuations t o the depression of the superconducting transition temperature, Tc has been estimated. A calculation of Tc based on experimental resistivity, susceptibility, and specific heat and with one adjustable parameter shows qualitative agreement with the observed Tc over the whole alloy system and reasonable quantitative agreement in the dilute B V region. Further evidence for the existence of spin fluctuations in Nb‐V and an enhanced electron‐phonon coupling constant γ in V is derived from the observed rate of depression of Tc with V concentration, published band structure calculations for V, and published Knight shift relaxation times.

Spin fluctuation resistivity of [formula omitted]RhNi alloys

Spin fluctuation resistivities ϱ SF in the range 1.5–35°K have been measured for dilute alloys of Pd with 1–7 nominal at.% Rh and up to 1 nominal at.% Ni. The presence of Rh reduces the host spin fluctuation contribution of Pd by a factor of at least five for all Rh concentrations. The experimental results on the Pd RhNi alloys are discussed in terms of the Lederer and Mills spin fluctuation theory and its extension to high temperature by Kaiser and Doniach. For a fixed Ni concentration the characteristic parameters T s and ϱ 0 increase with the Pd Rh host susceptibility.

Spin-Fluctuation Contributions to the Specific Heat

The specific heat is calculated for weakly ferromagnetic and nearly ferromagnetic metals. These systems are characterized by an enhanced susceptibility indicating large spin fluctuations. An expression for the mass enhancement on both sides of the ferromagnetic instability is presented. The specific heat just above the Curie temperature is investigated. In this region, the terms which lead to the large low-temperature mass enhancements are greatly reduced, and a new term contributes a singular specific heat at the Curie temperature. Spin-fluctuation contributions to the low-temperature specific heat are calculated for both phases, and numerical results are presented. Very large magnetic fields are shown to be effective in reducing the strongly enhanced specific heat. Calculations of the temperature dependence of the specific heat due to spin fluctuations in the paramagnetic phase are compared with the experimental results on ${\mathrm{He}}^{3}$.

On the specific heat of fermi liquids

The spin fluctuation contribution to theT 3 logT term in the specific heat of nearly ferromagnetic Fermi liquids is evaluted again. A result different from1,2 is found, which in the case of liquid Helium agrees better with experiment.