A spin glass perspective on ferroic glasses
Article first published online: 11 MAR 2014
© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
physica status solidi (b)
Special Issue: Ferroic Glasses: Magnetic, Polar and Strain Glass
Volume 251, Issue 10, pages 1967–1981, October 2014
How to Cite
Sherrington, D. (2014), A spin glass perspective on ferroic glasses. Phys. Status Solidi B, 251: 1967–1981. doi: 10.1002/pssb.201350391
- Issue published online: 7 OCT 2014
- Article first published online: 11 MAR 2014
- Manuscript Accepted: 24 JAN 2014
- Manuscript Received: 11 DEC 2013
- 445–62., in: Spin Glasses, edited by and (Springer, Heidelberg, 2006), pp.
- 11164–235., , and (eds.), Stealing the Gold (Oxford University Press, Oxford, 2005), pp.
- 13Theory of Neural Information Processing Systems (Oxford University Press, Oxford, 2005)., , and ,
- 18In fact, frustration can arise with purely anti-ferromagnetic interactions, for example via different neighbours, and even nearest-neighbour ferromagnetism can be frustrated if there are other constraints, such as the ‘spin ice rule’.
- 19The reader is referred to the literature, such as cited above (e.g. ()), for further details of the theory of SK-type spin glasses. We do, however, note again that its solution has exposed many new concepts which have had significant consequences in several branches of the science of complex systems (e.g. ) and in mathematics (e.g. ()).
- 23177–199., in: Disorder and Strain Induced Complexity in Functional Materials, edited by T. Kakeshita, T. Fukuda, A. Saxena, and A. Planes (Springer, Berlin, 2012), pp.
- 25For the thermoremanent magnetization (TRM) the system is cooled in the field. For the isothermal remanent magnetization (IRM), the field is applied only after cooling.
- 26J. Phys. Colloq. 35, C4-229 (1974).and ,
- 32J. Phys. Colloq. 35, C4-199 (1974).and ,
- 33Usp. Mat. Nauk 11, 77 (1956); J. Math. Phys. 1, 48 (1960).and ,
- 34Dokl. Akad. Nauk SSSR 115, 1097 (1957); Sov. Phys. Dokl. 2, 416 (1958).,
- 37165, 372 (1938)., Proc. R. Soc. A
- 3841 (1961)., Phys. Rev. 124,
- 392, 414 (1972)., , and H. C. Jamieson, Proc. 13th Int. Conf. Magn.
- 4010, 3149 (1977).and , J. Phys. C
- 4112, L929 (1979)., J. Phys. C
- 4297, 653 (1954).and , Dokl. Akad. Nauk SSSR
- 432, 2906 (1960) [Sov. Phys. Solid State 2, 2584 (1961)]., , , and , Fiz. Tverd. Tela
- 4494, 147602 (2005)., T. W. Darling, J. , Th. Proffen, , J. S. Park, , , and T. Egami, Phys. Rev. Lett.
- 4568, 847 (1992)., , and , Phys. Rev. Lett.
- 46W. Kleemann and 199, 1 (1997)., Ferroelectrics
- 4757, 11204 (1998)., , C. Filipič, and , Phys. Rev. B
- 4876, 241 (1987)., Ferroelectrics
- 4915, R367 (2003), J. Phys.: Condens. Matter
- 5060, 229 (2011)., , , , and , Adv. Phys.
- 51A. Simon, J. Ravez, and M. Maglione, J. Phys.: Condens. Matter 16, 963 (2004)
- 522008)., , and , J. Am. Ceram. Soc. 91, 1769 (
- 53379, 77 (2009)., , and , Ferroelectrics
- 54102, 232907 (2013)., , , and , Appl. Phys. Lett.
- 552012)., , E. J. Walter, A. Al-Barakaty, and , Phys. Rev. Lett. 108, 257601 (
- 56111, 227601 (2013)., Phys. Rev. Lett.
- 57Note that strain coupling is required to get the tetragonal crystal structure distortion of the ferromagnetic phase at larger x. However, the present interest is in the relaxor phase which has neither overall polarization nor change in average crystal structure.
- 5852, 6301 (1995)., , and , Phys. Rev. B
- 6081, 064408 (2010).and , Phys. Rev. B
- 61As noted earlier, the discussion above has excluded the strain coupling and absorbed the Ba and O ion effects into an effective B– B interaction. To deal with the ferroelectric phase more completely these need to be included.
- 62192–210., in: Stealing the Gold, edited by P. M. Goldbart, N. Goldenfeld, and D. Sherrington (Oxford University Press, Oxford, 2005), pp.
- 64The so-called Burns temperature presumably corresponds to the onset of nanodomains, given by when the density of states of the Anderson-like equation cross zero, while the onset of non-ergodicity and the relaxor transition occurs when the lower Anderson mobility edge crosses zero.
- 65J. Phys. Soc. Jpn. 28, 26 (1970).,
- 67The ionic radii of Pb++ and Ba++ are, respectively, 133 and 149 pm. That of O −−is 126 pm.
- 70J. Phys.: Condens. Matter 20, 304213 (2008).,
- 73Note that even pure TiNi is often referred to as an alloy, as in ‘shape-memory alloy’, but in fact it is a compound. When the expression ‘alloy’ is used in this paper it refers to systems that deviate in a random fashion from a periodic structure.
- 77Note, however, that actually the V of Eq. (19) (and its extension to higher dimension) decays with an inverse power law just beyond the realm of applicability of the proof of (), together with an extra angular factor. Hence boundary effects are more important in this pure case. But the main interest here is in the disordered alloy extension.
- 78Note that for the twinned phase will have defects.
- 79The SK model, exact for infinite-ranged interactions, has a ‘mixed’ phase for an x-region above , but such a phase in short-ranged spin glasses is contentious. In the martensitic alloys the interactions are power-law, which may suffice.
- 8190, 141 (2010)., , , , , , , , , , and , Philos. Mag.
- 84Note that the phase lines in the strain glass predictions shown in the figures are schematic. In particular, the sign of the slope between the martensitic phase and the mixed phase in the figure for a continuous is not calculated and hence its prediction is currently uncertain.
- 85125–136., in: Heidelberg Colloquium on Spin Glasses, edited by I. Morgenstern and L. van Hemmen (Springer, Berlin, Heidelberg, 1983), pp.
- 86J. Phys. Soc. Jpn. Suppl. 52, 229 (1983).,
- 91J. Phys. A 11, 083 (1978.and ,
- 95For low fields the GT shift goes as and the AT crossover as , where H is the applied field.
- 98This paper does not, however, cite these predictions.
- 101By ‘non-trivial’ we refer to a situation where the random fields are essential for the phase transition. Thus, the (soluble) infinite-ranged ferromagnet with random fields is ‘trivial’ in that the only phases are paramagnet and ferromagnet.
- 103Note, however, that the spin glass phase is not induced by the random fields, so this system is still ‘trivial’ in the sense of footnontrivial although the solution of this model requires subtle mathematics.
- 104When Ti are displaced in relaxor BZT they do provide extra quasi-random fields but these are secondary to the interaction-driven terms discussed above.