Chiral susceptibility in canonical spin glass and re-entrant alloys from Hall effect measurements

Abstract

The extraordinary Hall effect coefficients Rs(T ) of the canonical spin glass alloys AuF e8at% and AuM n8at% and of an archetype reentrant system AuF e18at% were measured as functions of temperature. The data show a critical cusp-like term superimposed on a smooth background for the spin glasses, and change of sign with temperature for the reentrant. The results can be interpreted consistently by invoking a chiral Hall effect contribution as proposed by Kawamura.Spin glasses have been intensively studied for more than thirty years, as paradigms for the statistical mechanics of the whole vast family of complex systems. However the origin the spin freezing in the canonical spin glasses, dilute alloys such as AuF e or CuM n where the spins are Heisenberg, has long remained an enigma. Experiments and in particular critical exponent measurements [1] have shown definitive evidence for a non-zero ordering temperature, while numerical work on Heisenberg spin glasses in dimension three indicated that there was an Edwards-Anderson type of ordering only at zero temperature [2] though recent simulations contradict this [3]. For vector spin glasses there exists a chiral order parameter in addition to the Edwards-Anderson spin parameter and there were early suggestions that chirality might play a role in vector spin glass ordering [4]. Kawamura and coworkers [5,6,7] have made concrete large scale numerical investigations of the chiral driven ordering mechanism which they postulated to explain freezing in Heisenberg spin glasses. In real samples the spin and chiral order are linked through Dzaloshinsky-Moriya (DM) random anisotropy terms which are inevitably present. Magnetic torque experiments on a range of spin glasses have shown in-field transition lines up to high applied fields [8], in excellent agreement with extensive simulations on Heisenberg systems submitted simultaneously to anisotropy and field, where both chiral and spin ordering were monitored [6,9]. The robustness of order under applied fields is a clear indication that chirality is a primary ingredient of spin glass ordering in vector systems. The torque measurements were interpreted using the chiral ordering scenario.In this context it would be of considerable interest to have a complementary direct observation of chirality in the spin glasses. Chirality is a "hidden" parameter and no technique was known with which to monitor it experimentally, until Kawamura proposed that the Hall effect should present a direct signature of the chiral susceptibility [10]. On the chiral scenario the extraordinary Hall signal (linked to the sample magnetization rather than the magnetic field) should have a critical term due to chirality. The key point is whether there is critical behaviour of the Hall coefficient R s (T ) at the glass temperature T g , and accompanying non-linear effects. R s is defined as the ratio of the Hall signal to the magnetization, once corrections have been made for the ordinary Hall term. Careful Hall experiments on spin glasses have been reported [11...

Chiral anomalous Hall effect in reentrant AuFe alloys

“…Following up [16] the present data confirm that there is a major contribution to the AHE linked to the presence of chirality which persists up to T ∼ 150K and which can be interpreted satisfactorily in terms of the chiral AB-related mechanism [11,12,13].…”

“…The difference term then appears to evolve to positive by 8%Fe as was observed at lower applied fields [16]. The change in sign in the canting term may be associated with the difference between ferromagnetic correlations among the canted spin components for the more concentrated alloys as compared to quasi-random correlations well in the spin glass region.…”

“…Hall data measured at lower fields for the region of T g in the spin glass alloys AuFe and AuMn containing 8% impurity have been analysed to provide evidence for the existence of a chiral term [16,28], and preliminary data on the re-entrant region were given. Figure 1 shows the longitudinal resistivity at zero applied field of the series of AuFe samples as functions of the temperature.…”

Monte Carlo study of the ordering of the weakly anisotropic Heisenberg spin glass in magnetic fields

“…42,43 Interestingly, very recent experiments have given support to these predictions from the chirality scenario. 44,45,46 In concluding this paper, we wish to emphasize again that, even if one sets aside the question of the detailed mechanism of the SG transition or the validity of the chirality scenario, the present numerical results have demonstrated beyond reasonable doubt that the weakly anisotropic Heisenberg SG exhibits a thermodynamic RSB transition in applied magnetic fields. In view of the fact that the property of the apparently simpler, strongly anisotropic Ising SG still remains unclear in spite of the long controversy, this finding seems surprising and somewhat ironical.…”

Relation between anomalous Hall effect and the Dzaloshisky–Moriya anisotropy in the series of alloys

“…Recently, some features [1,2] of the extraordinary Hall coefficient R s r ex =M, where r ex is the extraordinary Hall resistivity and M is the magnetization, have been reported in canonical spin glasses (SG) which are not understood by the conventional theory [3]. These results have subsequently been explained by the theories of the chirality mechanism of the Hall effect [4,5].…”