Spin anisotropy and slow dynamics in spin glasses

We report on an extensive study of the influence of spin anisotropy on spin glass aging dynamics. New temperature cycle experiments allow us to compare quantitatively the memory effect in four Heisenberg spin glasses with various degrees of random anisotropy and one Ising spin glass. The sharpness of the memory effect appears to decrease continuously with the spin anisotropy. Besides, the spin glass coherence length is determined by magnetic field change experiments for the first time in the Ising sample. For three representative samples, from Heisenberg to Ising spin glasses, we can consistently account for both sets of experiments (temperature cycle and magnetic field change) using a single expression for the growth of the coherence length with time.     

p-Spin model in finite dimensions and its relation to structural glasses

The p-spin spin-glass model has been studied extensively at mean-field level because of the insights which it provides into the mode-coupling approach to structural glasses and the nature of the glass transition. We demonstrate explicitly that the finite-dimensional version of the three-spin model is in the same universality class as an Ising spin glass in a magnetic field. Assuming that the droplet picture of Ising spin glasses is valid we discuss how this universality may provide insights into why structural glasses are either "fragile" or "strong."     

Electricity and Magnetism,Volume 1: Third Edition,Electricity and Magnetism,Volume 2: Third Edition,by B.I. Bleaney and B. Bleaney

During the last decade the term ‘spin glass’ has become prominent in the literature on magnetism. It refers to magnetic alloys where the spins on the impurities become locked or frozen into random orientations below a characteristic temperature T ₀. In this article the properties of spin glasses are described with particular reference to the two archetypal examples AuFe and CuMn. Interest in spin glasses was mainly stimulated by some a.c. susceptibility measurements which showed sharp, cusp-like peaks, accurately defining T ₀ and suggesting that some type of phase transition was occurring. The Mossbauer effect and the anomalous Hall effect also showed clear features at T ₀ supporting this viewpoint. But measurements of the electrical resistivity and ‘specific heat’, here usually meaning the molar heat capacity, also the remanence, magnetic hysteresis and time-dependent effects observed in spin glasses were difficult to reconcile with a phase transition approach. This article discusses the results obtained from the very wide variety of experimental techniques which have been used to investigate spin glasses, and also deals with some of the important theoretical concepts which have arisen out of these studies. Then follows a short account of the many systems which have been found to exhibit spin glass behaviour and which suggest that it is a widespread magnetic state of matter. Lastly, an example is given which shows that some of the ideas of spin glasses are applicable to problems outside the sphere of magnetic alloys.     

Experimental and micromagnetic first-order reversal curves analysis in NdFeB-based bulk “exchange spring”-type permanent magnets

In this paper we present the results of applying the first-order reversal curves (FORC) diagram experimental method to the analysis of the magnetization processes of NdFeB-based permanents magnets. The FORC diagrams for this kind of exchange spring magnets show the existence of two magnetic phases—a soft magnetic phase and a hard magnetic one. Micromagnetic modeling is used for validating the hypotheses regarding the origin of the different features of the experimental FORC diagrams.     

Aging in the ferromagnetic phase of terbium

We report on aging, rejuvenation and memory effects in the ferromagnetic phase of pure terbium. We have applied an experimental method specifically for investigating slow dynamics of spin glasses, because these effects cannot be interpreted as conventional diffusion after-effects. Results show that relaxation times of the magnetic response are widely distributed, and isothermal aging shifted the distribution towards longer durations. If the sample was heated/cooled after such isothermal aging, the relaxation times shortened as if aging was starting anew; the behavior resembles that in spin glasses. Uniform magnetization experiments indicate that, unlike rejuvenation in spin glasses, ferromagnetic correlations are not returned to disorder by thermal perturbations. In contrast with memory effects in spin glasses, the effects of isothermal aging cannot be recovered once these disappear, even if the system is returned to its initial temperature. The observed results can be explained as collective pinning of the domain walls for which the potential is given by a rugged temperature-sensitive energy landscape.     

Aging, rejuvenation and memory phenomena in spin glasses

In this paper, we review several important features of the out-of-equilibrium dynamics of spin glasses. Starting with the simplest experiments, we discuss the scaling laws used to describe the isothermal aging observed in spin glasses after a quench down to the low-temperature phase. We report in particular new results on the sub-aging behaviour of spin glasses. We then discuss the rejuvenation and memory effects observed when a spin glass is submitted to temperature variations during aging, from the point of view of both energy landscape pictures and real-space pictures. We highlight the fact that both approaches point out the necessity of hierarchical processes involved in aging. Finally, we report an investigation of the effect of small temperature variations on aging in spin glass samples with various anisotropies which indicates that this hierarchy depends on the spin anisotropy.     

Pressure as a parameter in the study of dilute magnetic alloys

A large body of data is reviewed, which illustrates how the high pressure technique can be used to gain information about the magnetic and electronic state of dilute magnetic alloys. Values for the pressure dependence of the elementary effective exchange interaction between a magnetic impurity spin and the conduction electron sea are extracted from the data and tabulated for a number of extremely dilute alloys containing both transition metal and rare earth impurities. Results of experiments on host alloy series employing ‘lattice pressure’ are compared to the present ‘external pressure’ results and critically analysed; it is shown how such a comparison can be used to give information about the extent of the electronic screening around an impurity potential. The effect of pressure on impurity-impurity interactions in spin glasses is also examined; a comparison of the pressure studies on extremely dilute alloys to those on spin glasses allows an estimate of the nature of the interaction mechanisms important in the latter case. Evidence for a pressure-induced spin glass to Kondo transition in LaCe is also presented. It is suggested that the present results fit into a larger picture that magnetism, when present, tends to be weakened when high pressure is applied.     

Spin glasses: Comments on some experimental results

Some of the experimental results on spin glasses commonly interpreted as showing a sharp magnetic phase transition are re-examined. Recent neutron scattering measurements add significantly to our understanding of the phenomena occuring in spin glasses. These results together with those on other physical properties are discussed in terms of a unified picture of freezing of spins in the binary alloys.     

Frequency dependence of the spin glass freezing temperatures in icosahedral R–Mg–Zn (R = rare earth) quasicrystals

We present ac susceptibility measurements with the frequency spanning three orders of magnitude on single grain, icosahedral R–Mg–Zn (R = rare earth) quasicrystals. The freezing temperature in Gd-based, Heisenberg spin glasses in this family increases by ～2% with a frequency increase from 10?Hz to 10?kHz, whereas the freezing temperature in the non-Heisenberg members of the family is significantly more responsive to the frequency change (by 16–22%), suggesting that an additional magnetic anisotropy distribution in the non-Heisenberg spin glasses causes changes in the low frequency magnetic dynamics.     

Concentrated spin glass state in solid solutions of antiferromagnetic garnets

Conclusion Experimental data obtained in the present work provide evidence for the fact that in magnetic dielectrics with competing exchange interactions, and in particular, in compounds with the garnet structure, various disordered phases of the spin glass type may be realized. The peculiarity of these phases lies in the fact that they occur in magnetically concentrated systems, and their nature is not related to any of the mechanism of spin glass state noted in the introduction. For this reason, physical properties of solid solutions of antiferromagnetic garnets, in which spin glass state is observed, apparently, differ from the corresponding characteristics of traditional spin glasses. In particular, our measurements have shown that the character of the maximum in dependence in MnFeG does not depend on whether the sample was cooled in a magnetic field below T_o or in the absence of the field. We were also not successful in observing any signs of relaxation behavior in MnFeG magnetization when the field was turned on and off. In CaFeCrG, there is no frequency dependence of the maximum of (T).On the other hand, the microscopic mechanism of formation of a spin glass state in the garnets studied is undoubtfully related to frustrations which occur because of the peculiar topology of exchange interactions in the garnet structure. In this sense, MnFeG, CaFeCrG, and MnFeCrG may be characterized as topological spin glasses occurring in solid solutions of those antiferromagnetic garnets which have different propagation vectors of magnetic structures.In conclusion, we note that results that we have obtained point to the existence in solid solutions of magnetic dielectrics with antiferromagnetic exchange interactions of compounds with qualitatively new, peculiar magnetic properties, and from this point of view it is of great interest to study them further.Translated from Izvestiya Vysshikh Zavedenii, Fizika, No. 10, pp. 91–104, October, 1984.     

Anomalous Hall effect as a probe of the chiral order in spin glasses

The anomalous Hall effect arising from the noncoplanar spin configuration (chirality) is discussed as a probe of the chiral order in spin glasses. It is shown that the Hall coefficient yields direct information about the linear and nonlinear chiral susceptibilities of the spin sector, which has been hard to obtain experimentally from the standard magnetic measurements. Based on the chirality scenario of spin-glass transition, predictions are given on the behavior of the Hall resistivity of canonical spin glasses.     

Measuring overlaps in mesoscopic spin glasses via conductance fluctuations

We consider the electronic transport in a mesoscopic metallic spin glass. We show that the distribution of overlaps between spin configurations can be inferred from the reduction of the conductance fluctuations by the magnetic impurities. Using this property, we propose new experimental protocols to probe spin glasses directly through their overlaps.     

Spin glass order

Spin glasses are magnetic systems in which the interactions are random and competing. The ordering in these systems poses basic conceptual problems and remains incompletely understood despite intensive study. Hyperfine interaction techniques (Mössbauer, SR, NMR, NO and PAC) have been used to obtain information on spin glasses, particularly on the relaxation at short time scales. A review of the data will be presented and a physical picture will be given of spin glass ordering in terms of the diffusion of the point presenting the system in eigenstate space.     

The temperature dependence of the magnetic susceptibility of spin glasses

The temperature dependence of the magnetic susceptibility of spin glasses is calculated exactly on the basis of a magnetic cluster model, following Néel. The susceptibility of a single cluster below its blocking temperature is taken to be negligibly small compared to its value above. A distribution of blocking temperatures may be obtained from observations on spin glasses. Conditions for the sharpness of the susceptibility peak are discussed and the low-temperature variation of the susceptibility is also obtained.     

Spin glass model based on the Onsager reaction field

Changes in the Onsager reaction field are used to account quantitatively for aging (the decrease in the magnetic susceptibility when cooling in zero field is halted below the glass temperature) and rejuvenation (the disappearance of aging phenomena on further cooling only to reappear at Tw on heating) that characterize spin glasses. These effects must be caused by interactions between the spins since, absent the interactions, the magnetic properties of N spins are just N times the magnetic property of a single spin that cannot display aging. A spin introduced at an empty site with a nonzero field becomes polarized, and the polarized spin in turn polarizes its neighbors, thereby changing the local field. This additional field is the Onsager reaction field. Ma's theory for the reaction field in spin glasses [PRB 22, 4484 (1980)10.1103/PhysRevB.22.4484] has been extended to provide a spin-glass model that can account for the experimental data.     

On the behavior of static susceptibilities in spin glasses

Linear and nonlinear susceptibilities of spin glasses in thermal equilibrium are qualitatively discussed in terms of magnetic short-range order. The apparent discrepancy between theoretical results, implying lack of Edwards-Anderson order and hence a divergence of the susceptibility at zero temperature, and experiments showing a susceptibility saturating at finite values, is considered. It is suggested that the susceptibility must indeed have a static maximum if the system exhibits a (frustrated) ferromagnetic phase with a reentrant phase boundary. At the reentrancy point, some exponents of the ferromagnet take twice their normal value, and hence a crossover near this point occurs similar to multicritical points. These observations are used to interpret a number of recent experiments, and it is shown that neither of them proves the existence of a static spin glass phase. As a quantitative example of gradual onset of order without a phase transition in three-dimensional systems, numerical results for susceptibility and specific heat of the fully frustrated Ising fcc antiferromagnet at its critical field are given.Finally the possible coexistence of spin-glass behavior and ferromagnetic long-range order in vector spin glasses with short-range interactions is discussed. Speculative arguments suggest that even for time-scales for which the spins are frozen such a coexistence should not occur, if interactions off-diagonal in the spin components (such as of dipolar origin) are included.     

Some comments on the Sherrington-Kirkpatrick model of spin glasses

In this paper the high-temperature phase of general mean-field spin glass models, including the Sherrington-Kirkpatrick (SK) model, is analyzed. The free energy in zero magnetic field is calculated explicitly for the SK model, and uniform bounds on quenched susceptibilities are established. It is also shown that, at high temperatures, mean-field spin glasses are limits of short-range spin glasses, as the range of the interactions tends to infinity.     

Majorana flipping of quarkonium spin states in transient magnetic field

We demonstrate that spin flipping transitions occur between various quarkonium spin states due to transient magnetic field produced in non central heavy ion collisions (HICs). The inhomogeneous nature of the magnetic field results in non adiabatic evolution of (spin)states of quarkonia moving inside the transient magnetic environment. Our calculations explicitly show that the consideration of azimuthal inhomogeneity gives rise to dynamical mixing between different spin states owing to Majorana spin flipping. Notably, this effect of non-adiabaticity is novel and distinct from previously predicted mixing of the singlet and one of the triplet states of quarkonia in the presence of a static and homogeneous magnetic field.     

Thermodynamic glass transition in finite dimensions

Using an effective potential method, a replica formulism is set up for describing supercooled liquids near their glass transition. The resulting potential is equivalent to that for an Ising spin glass in a magnetic field. Results taken from the droplet picture of spin glasses are then used to provide an explanation of the main features of fragile glasses.