Specific heat measurements in scandium-rare earth anisotropic spin glasses

We report on specific heat measurements at low temperature of the anisotropic spin glass alloys $\text{Sc}$Dy 3 at%, $\text{Sc}$Er 4.25 at% and $\text{Sc}$Er 10 at%. We find that at the lowest temperature range the data indicate the occurrence of an anisotropy induced gap around zero frequency in the density of states of the magnetic excitations. Moreover, some of our specific heat curves present a maximum coinciding with T_g, raising thus the question of thermal signs for a spin glass phase transition in anisotropic systems.     

Electric-magnetic duality in non-abelian gauge theories

The duality transformation of the vacuum expectation value of the operator which creates magnetic vortices (the 't Hooft loop operator in the Higgs phase), is performed in the radial gauge (x_uA_u^a(x) = 0). It is found that in the weak coupling region (small g) of a pure Yang-Mills theory the dual operator creates electric vortices whose strength is $\text{1}\text{g}$. The theory is self-dual in this region, and the effective coupling of the dual Lagrangian is $\text{1}\text{g}$. (It is self-dual also in the extreme strong coupling region.) Thus the above duality transformation reduces to electric-magnetic duality where the electric field in the 't Hooft loop operators transforms into a magnetic field in the dual operator. In a spontaneously broken gauge theory these results are valid only within the region where the vortices (or the monopoles) are concentrated, or in directions of the algebra space of unbroken symmetry, as self-duality holds only for this subset of fields. Noting that the 't Hooft loop operator project into the subspace of these field configurations we find that it is an electric-magnetic duality for the spontaneously broken theory as well. In the strong coupling region a strong coupling expansion in powers $\text{1}\text{g}$ is suggested.     

Dynamics of the infinite-range ising spin glass

The Glauber dynamics of an Ising spin glass with infinite-range interactions and additional static field, h, is investigated near the freezing temperature, T_f. We obtain critical slowing down at and below the de Almeida-Thouless instability line, h_c(T), to order (1?T/T_f)³ with algebraic decay of the spin correlations ～t^?ν, where $\text{ν=}\text{1}\text{2}$ at T_f and $\text{ν≤}\text{1}\text{2}$ for T<T_f.     

Tetravalent vanadium in CaF2 and SrF2 crystals: An EPR study

An EPR study of tetravalent vanadium centers created by room temperature X-irradiation in CaF₂ and SrF₂ is presented. The production efficiency of these centers is enhanced by previous annealing of the samples at 1000 K in air. The symmetry of V⁴⁺ ions is tetragonal and its EPR spectrum can be described by an axial spin Hamiltonian including a Zeeman and hyperfine term with $\text{S =}\text{1}\text{2}$ and $\text{I =}\text{7}\text{2}$ (corresponding to ⁵¹V nuclei). The following values for the spin Hamiltonian parameters are obtained g_∥ = 1.947 ± 0.002, g_⊥ = 1.935 ± 0.005, A_∥ = 500 ± 5 MHz, A_⊥ = 150 ± 10 MHz in the case of SrF₂ and g_∥ = 1.945 ± 0.002, A_∥ = 505 ± 5 MHz and A_⊥ < 200 MHz, in the case of CaF₂. A model for the center including an interstitial O^2? ion is tentatively proposed.     

The magnetic dipole moment of 55Co

The ground state g-factor for ⁵⁵Co has been measured as $\text{¦g¦= 1.378±0.001}$ by the technique of nuclear magnetic resonance on oriented nuclei. The temperature dependence of γ-ray anisotropy in the ⁵⁵Fe daughter decay determines both the 1408 keV level spin and the ⁵⁵Co ground state spin to be $\text{7}\text{2}$, and yields values of mixing ratios in the 1037 keV β-transition and the 477 keV γ-transition. The configuration mixing model is used to discuss 1f_{$\text{7}\text{2}$} moment systematics.     

The ground-state rotational band in 159Tb

162 MeV ⁴⁰Ca ions have been used to Coulomb excite the ground-state band of ¹⁵⁹Tb up to spin $\text{25}\text{2}$. Lifetimes for levels up to spin $\text{25}\text{2}$ have been determined with DSA and recoil distance methods. Multipole mixing ratios for several cascade transitions were extracted from an analysis of γ-ray angular correlation data. Reduced transition probabilities thus deduced in a model-independent way were found to be in agreement with the rotational model with Q₀ = 7.41 ± 0.06 e · b and g_K?g_R = 1.377 ± 0.010.     

Remanent magnetisation properties of the spin glass phase

We have made a systematic survey of the field and temperature dependence ofthe remanent magnetisation of the spin-glass system $\text{Ag}$Mn in the concentration range 1 to 24%. We parametrise this ensemble of data by the linear field dependence of the thermoremanent magnetisation (TRM), the quadratic field dependence of the isothermal remanent magnetisation (IRM), and by the saturation value of the remanent magnetisation in high field. This enables us to search for a universal behaviour of these parameters in reduced units of temperature and field. We show that at various temperatures the ensemble of reduced curves corresponding to a given concentration alloy are not identical. However, we show that this behaviour is the same at all concentrations, i.e. the field dependence of IRM and TRM depend only on T/T_g. We further show that this dependence is not affected by factors such as the time of measurement, the presence or absence of short-range order or the strength of the amisotropy energy in the system. A suitable parametrisation of this temperature dependence, which we take as exponential, allow us to compare different spin glass systems. We show that the same conclusions appear to hold in $\text{Cu}$Mn, $\text{Au}$Fe, $\text{Pt}$Mn and $\text{La}$Al₂Gd from which we obtain almost the same exponential coefficients. These facts strongly suggest that the mechanism responsible for the existence of a remanent magnetisation exclusively involves exchange interactions and is a general property of the spin-glass phase.     

Measurement of the spin-depairing interaction in Sn0.75Eu0.25Mo6S8

Mössbauer effect measurements of the ¹⁵¹ Eu resonance in the Chevrel phase superconductor Sn_0.75Eu_0.25Mo₆S₈ have been used to obtain the temperature dependence of the Eu paramagnetic relaxation rate. This consists of a temperature independent part arising from spin-spin interactions and a part linear in T due to the Korringa process. From the slope we obtain $\text{I}$ = 0.0033/Eu atom-spin, where $\text{I}$ is the exchange coupling between the rare-earth spin and the conduction electron spin, and N(E_F) is the local density of states. This value is roughly one order of magnetude lower than that measured in binary superconductors, and accounts for the very weak dependence of the transition temperature on magnetic impurity concentration.     

Spin-glass transition revisited from a partial derivative of specific heat in CuMn 0.25 at%

From general thermodynamical relations we derive the magnetic field expansion of the specific heat for the paramagnetic phase of a spin glass. Experimental results for the magnetocaloric effect of a $\text{Cu}$Mn 0.25 at% allow us to determine the successive terms of this expansion. We reach a precision of several percent for the terms which are as small as 10^-3 or 10^-4 of the total specific heat.     

Spin-glass behaviour of [La,Gd]B6 and [La,Dy]B6 alloys

Electrical resistance and absolute thermoelectric power measurements have been made in the temperature range between 2 and 30 K on a few polycrystalline specimens of [L$\text{a}$,Gd]B₆ and [L$\text{a}$,Dy]B₆ with different concentrations of rare earth ions. The resistance of these alloys varies as $\text{～ T}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ which is characteristic of spin glasses at low temperature. The thermoelectric power of all specimens but one, shows a broad positive peak in the lower part of the temperature range and becomes negative at higher temperatures, a feature that is typical of a spin glass to paramagnetic phase transition. The exceptional specimen has a large Gd concentration and its thermoelectric power remains positive to higher temperatures than would be expected for a spin glass.     

Magnetic field dependent optical dephasing in LaF3:Er3+

Optical dephasing of the 5388 Å transition between the lowest Kramers doublets of the ⁴S_{$\text{3}\text{2}$} and ⁴I_{$\text{15}\text{2}$} multiplets of Er³⁺:LaF₃ has been studied by photon echo, optical phase switching and optical free induction decay. Er³⁺?¹⁹F hyperfine interactions produce dephasing which is two orders of magnitude faster than in previously studied non-Kramers systems, but at high field changes in the spin dynamics result in microsecond dephasing. For the lower Zeeman component of ⁴S_{$\text{3}\text{2}$}, T₂ (=6μs) is independent of H₀ whereas for the upper component the dephasing is rapid and strongly field dependent. This is quantitatively accounted for by spin lattice relaxation of the upper component of ⁴S_{$\text{3}\text{2}$}. Below 20 kG concentration and temperature dependent dephasing due to electron spin diffusion is observed.     

Temperature variation of the magnetic cluster structures in an iron-nickel invar alloy

Small-angle scattering of long wavelength neutrons $\text{(λ = 6.42}\text{A}\text{?}\text{)}$ from an Fe₆₅Ni₃₅ single crystal has been measured with the applied magnetic field (6.2 kG) parallel and perpendicular to the scattering vector $\text{K}$ of the elastic scattering over the temperature range from 25 to 422°C (T_c = 227°C). The scattering cross sections due to the longitudinal spin fluctuation have been analyzed by means of Guinier's approximation $\text{(dσ/dω)}{}_0\text{exp}\text{(?κ}{}^2\text{R}{}_{\mathrm{<mtext>g</mtext>}}{}^2\text{3}\text{)}$, where the forward cross section (dσ/dω)₀ is proportional to n, which is the number of atoms in a paramagnetic cluster, and R_g is the radius of gyration of the cluster. The empirical relation between n and R_g is = 0.298 × R_g^2.34 to be compared with that calculated for a simple spherical cluster model n = 1.274 R_g³.     

ESR aspects of the Mn2+−Cu2+ coupled pair

Recent ESR experimental data on Mn²⁺?Cu²⁺ pairs, obtained by doping with manganese the dimeric Cu (pyridine N-oxide) Cl₂·.H₂O complex, are interpreted by means of a strong isotropic exchange model. Theg values of the pair and the hyperfine constants at the manganese and copper nuclei, for the observed effective spin S = 2, are given by the relations

$\text{g =}\text{7}\text{6}\text{g}{}_{\mathrm{Mn}}\text{?}\text{1}\text{6}\text{g}{}_{\mathrm{Cu}}$

,

$\text{A}\text{?}{}_{\mathrm{Mn}}\text{=}\text{7}\text{6}\text{A}{}_{\mathrm{Mn}}\text{,}\text{A}\text{?}{}_{\mathrm{Cu}}\text{= ?}\text{1}\text{6}\text{A}{}_{\mathrm{Cu}}$

, where g_Mn, g_Cu,A_Mn and A_Cu are the characteristic single-ion values for the quoted constants. The antiferromagnetic coupling between the Mn²⁺ spin $\text{(}\text{5}\text{2}\text{)}$ and the Cu²⁺ spin $\text{(}\text{1}\text{2}\text{)}$ is responsible for the observed g values, all measurably lower than the free electron value. Also to be noted are the enhancement of the hyperfine constant at the manganese nucleus, and the curious change of sign for that at the copper nucleus.     

A phenomenological investigation of ππ → KK partial-wave amplitudes from hyperbolic dispersion relations

We calculate the $\text{ππ →}\text{K}\text{K}$ partial-wave amplitude g_J^(+-), J = 0, 1, 2, 3, in the unphysical region below the $\text{K}\text{K}$ threshold using partial-wave relations derived from hyperbolic dispersion relations. For g₁^(?) the results are in agreement with earlier calculations and we confirm the current low-energy predictions. For g_o⁽⁺⁾ we favour a down-type solution with a large positive $\text{K}\text{K}\text{→}\text{K}\text{K}$ s-wave scattering length.     

Analysis of the two-state model and its application for amorphous iron alloys

The magnetic phase diagram for the two-state Weiss model is calculated in the mean field approximation (MFA) for low spin S₀ = $\text{1}\text{2}$ and high spin S₁ = $\text{3}\text{2}$. We show that the two-state model together with the assumption of the strong shor t range order (SRO) can account for the observed Curie temperature data in amorphous Fe_1-xA_x (A = B, Hf, Ti, Zr) alloys.     

Free energies of the spherical model of a spin glass

Free energies g(m, m_s) and f(m, q) of the spherical spin glass (SG) model due to Kosterlitz et al. are calculated explicitly as functions of the uniform magnetization m, and SG order parameter m_s and the Edwards-Anderson order parameter q. It is shown that g(0, m_s) and f(0, q) below the transition temperature T_g are constant in the ranges 0 ≦ m_s ≦ m_s⁰ and 0 ≦ q ≦ q₀ respectively, where $\text{q}{}_0\text{= (1 -?}\text{T}\text{T}{}_{\mathrm{g}}\text{) = m}{}^2{}_{\mathrm{s}}{}^0$. The proper equilibrium values of m_s( = m_s⁰) and q( d=q₀) are then fixed from the inspection of their behaviors under infinitesimal uniform field proproportional to N^-a($\text{a ≧ 0}$).     

Solving φ1,24 field theory with Monte Carlo

We study lattice g₀φ⁴ field theory for all g₀ and fixed renormalized mass M in one and two dimensions using Monte Carlo techniques. We calculate the dimensionless renormalized coupling constant $\text{g}{}_{\mathrm{<mtext>R</mtext>}}\text{=}\text{g}{}_{\mathrm{<mtext>R</mtext>}}\text{M}{}^{\mathrm{4?d}}\text{,}\text{where}\text{d}$ is the dimension of space—time, at fixed small values of the lattice spacing a for various g₀ and lattice sizes. Our results are in quantitative agreement with the analyses of high temperature and strong coupling series which rely on extrapolation from large to small lattice spacing.     

The average structure of 5.10-Dihydro-5.10-Diethylphenazinium-Iodide (E2P·I1.6): A new linear chain Polyiodide compound

Upon oxidation of 5.10-dihydro-5.10-diethylphenazine (E₂P) with iodine golden-green lustrous crystals of a compound with stoichiometry E₂P.I_1.6 were isolated. The compound crystallizes in the tetragonal space group D₄² with $\text{a = 12.321(2)}\text{A}\text{?}$ and $\text{c = 5.330(2)}\text{A}\text{?}$. The E₂P and I form interpenetrating incommensurate sublattices along c, with an iodine repeat distance of 9.7 Å. Static susceptibility measurements at room temperature give χ_g = + 0.994 × 10^?6g^?1 × cm³. This corresponds to one unpaired electron spin per two formular units. Single-crystal EPR indicates that the paramagnetism is associated with weakly interacting E₂P⁺ cation radicals. The 300K-d.c. conductivity of 3×10^?2Ω^?1cm^?1 and activation energy of 0.17±0.02eV for single crystals is consequently associated with the polyiodide chains, and not with the E₂P⁺ cation radicals.     

Exactly solvable model of a spin glass

Sherrington and Kirkpatrick presented a solvable model of a spin glass. In the solution, they used a mathematically unwarranted procedure. In the present article, we show that the problem is exactly solved by starting with the virial expansion formula, and confirm the results of Sherrington and Kirkpatrick. The solution is obtained for the random Ising magnet in which the external field of each site and the exchange integral between each pair of sites are random variables. We obtain the exact thermodynamic properties for this system in the limit of n_w→∞, assuming that the exchange integrals of a spin with O(n_w) neighbours are $\text{O(n}{}_{\mathrm{w}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{)}$ and the average value of each is O(n_w^?1). The system is found to show the spin-glass state as well as the paramagnetic and the ferromagnetic state.