Phase Transitions in Spin Glasses

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762 Nature Vol. 276 21/28 December 1978 of at least 8-10 km. Support for this scale when the magnetic field which in the time scale of the experiment. The interpretation also comes from gravity duced it is switched off. Below TF an other spins are effectively frozen in data, for to explain the steep gradient induced moment can take hours to fixed orientations and do not con in the Bouguer gravity profile near the decay away. One can immediately de tribute. For a given experimental time San Andreas fault zone it is apparently duce that some relaxation processes in scale, the further .the temperature is necessary to invoke the presence of a a spin glass take place very slowly. lowered below T F the larger the frac slab of low density ( -2.6 g em-') ex Another characteristic is ·the 'cusp' in tion of frozen spins becomes and hence tending to a depth of 8-10 km. A the magnetic susceptibility at the the smaller will be the observed sus density of 2.6 g em-• is typical of fault freezing temperature. The susceptibility ceptibility. A corollary of this hypoth gouge. as a function of temperature rises at esis is that the freezing temperature TF Wang and his coworkers go no TF to a maximum which is quite sharp, should alter with the experimental time further with their experiments; but especially when the susceptibility is scale. Lengthening the time scale they have gone far enough to show measured using small applied fields. should enable more spins to contribute that fault gouge as a possible modifier Non-analytic behaviour such as a to the susceptibility and so depress the must not be ignored when it comes to cusp usually indicates that a phase apparent freezing temperature. A considering the causes of shallow transition must be taking place. In similar effect occurs at the glass transi earthquakes. 0 1975, Edwards and Anderson (J. Phys. tion in ordinary glasses where T" falls F6, 1927; 1975) proposed a phase tran when the liquid is allowed a longer sition theory for spin glasses which time to come to equilibrium. gave a seemingly satisfactory explana A recent experiment of Murani and tion of the cusp. The order parameter Heidmann (Phys. Rev. Lett. 41, 1402; Phase transitions q of their theory is the probability that 1978) clearly indicates that lengthening any given spin is still pointing after an the time scale depresses TF. They have in spin glasses infinitely long time in the same direc carried out neutron inelastic scattering from a Correspondent tion as it was at some initial time. measurements on a Cu-8 at 'i{, Mn IF the temperature of a supercooled Above TF, q is zero, but below TF, alloy at three different energy resolu liquid is lowered sufficiently, it may which is identified as the phase tran tions. The temperature dependence of form a glass. For twenty years or more sition temperature, it is non-zero and the elastic magnetic cross section can there has been an inconclusive debate increases to unity as the temperature be extracted from the data. It is related as to whether this change is of purely approaches absolute zero. to the Edwards-Anderson order para kinetic origin, occurring when the Although we live in a three-dimen meter q on a phase transition hypoth relaxation times of the liquid become sional world, it is both interesting and esis and to the number of frozen spins longer than the patience of the experi useful to examine (theoretically! ) the on a relaxation time hypothesis. The menter, whereupon the liquid appears nature of a phase transition in worlds elastic cross section increases below a to have solid properties, or whether the of different dimensionality. There is certain temperature but the tempera change reflects an underlying phase always a 'lower critical dimension' ture at which this happens, the nominal transition. It looks as though the below which the phase transition will freezing temperature, varies with the debate on the causes of the similar not take place. Thus •the Heisenberg energy resolution employed. They phenomena found in spin glasses may type of ferromagnet does not have a argue that the time scale in their be just as lengthy and inconclusive. phase transition in two dimensions for experiment is proportional to the in A spin glass is typically a substitu its lower critical dimension is two. The verse of the energy resolution. For a tional alloy of a few percentage of a lower critical dimension for the spin time scale of w-ll s, TF is 75 K, transition metal such as iron or man glass transition is controversial, with whereas TF is about 40 K on a time ganese in a host metal such as copper arguments being advanced for two, scale of 10-2 s (this latter data is from or gold. The transition metal im three and four dimensions. Numerical separate expe1:1iments on the a.c. sus purities-the spins of the spin glass evidence derived from high-tem ceptibility). At first sight this appears can be taken as being approximately perature series expansions seems to to be strong evidence against a phase randomly distributed throughout the favour four (Reed, Phys. Lett. A68, transition (since a phase transition alloy. They interact with each other 473; 1978). If that really is the case, should take place at a unique tem through the conduction electrons of the then the phase transition theory of spin perature) and in good accord with the host metal to give a long-range coupling glass behaviour fails and an alternate explanation of spin glass behaviour in between the spins whose sign depends explanation must be sought. terms of long relaxation times and on the distance between the spins. This An explanation which ·actually pre frozen out spins. means that the interaction between dates the phase transition ·theory is that Unfortunately it is not as simple as some spins is ferromagnetic in sign spin glass behaviour is entirely a non this. A phase transition could be which favours their parallel alignment equilibrium effect resulting from the accompanied by long relaxation times while that between other pairs of spins long relaxation times which exist with which would produce an apparent is antiferromagnetic which favours in spin glasses at low rtemperatures. freezing temperature that decreased their antiparallel alignment. The net The relaxation modes probably involve with increasing experimental time effect of such a mixture of competing activation processes in which a poten scale, but which eventually saturates at interactions is to produce a ground tial barrier separating two easy orienta the true transition temperature TF for state in which the orientation of the tions of a spin has to be surmounted. a hypothetical experiment with an in spins is chaotic and which has no This will produce relaxation times finitely long time scale. There is just a resultant magnetic moment. which follow an Arrhenius law and so hint of such a possibility within their When cooled below its freezing tem rapidly increase at low temperatures. data but it is not sufficiently strong to perature TF, the properties of a spin The 'cusp' in the susceptibility is ex be compelling evidence. It is clearly glass are radically altered in much the plained on this hypothesis by observing going to be very difficult to decide same way as the properties of a super that at temperatures below TF only a from experiments of this kind whether cooled liquid are altered below the glass fraction of the total spins present will spin glass behaviour is or is not due to transition temperature Tg. Above TF contribute to the susceptibility, namely a phase transition. A new idea is an induced magnetic moment rapidly those spins or groups of spins which needed for a conclusive experimental decays away on a microscopic time can relax on a time scale shorter than test to distinguish the rival approaches.