Surface ferro (or antiferro) magnetism in bulk antiferro (or ferro) magnets : renormalization group analysis

2014 The renormalization group techniques are applied, for the first time, to surface magnetism in bulk magnets, for all signs of surface and bulk coupling constants. The q-state Potts model is specifically focused upon, and an interesting q-evolution of the phase diagram is exhibited. In particular the Ising model (q = 2) presents a remarkable feature in the case of competing bulk-and surface interactions : surface ferro (or antiferro) magnetism can disappear while heating an antiferro (or ferro) magnet, and reappear again for higher temperatures, before the system enters in the paramagnetic phase. J. Physique 47 (1986) 1115-1118 JUILLET 1986, Classification Physics Abstracts 05.50 05.70F 64.60C 75. lOR Ordering in semi-infinite systems (such as bulk materials presenting a free surface) can in principle exhibit interesting conflicts, when the surface favours a type of ordering which competes with that favoured by the bulk. This is typically the case of surface (crystalline or amorphous) structure reconstruction. This can also be the case of magnetic systems where the surface coupling constant J$ differs in sign from the bulk coupling constant JB (see the recent review by Binder [1] and Ref. therein). This seems to be precisely the case of Cr (antiferromagnet with a Neel temperature of 312 K). Its (100) free surface has been very recently investigated [2] (using angle-resolved photoelectron spectroscopy), and it presents a ferromagnetic ordering up to 780 + 50 K. The experiment has been deviced with particular care for avoiding undesirable surface contamination effects [3]. Magnetic competition between surface and bulk has already received theoretical attention through Mean Field Techniques [4] applied to the spin 1/2 Ising model. However the problem presents a theoretical and experimental interest which deserves alternative (and more sophisticated) approaches. In the present letter we discuss theoretically the q-state Potts model (from which the Ising model is recovered for q = 2, and bond percolation for q = 1 and ferromagnetic coupling constants) in semi-infinite simple cubic lattice assuming the free surface to be a (1, 0, 0) one. The framework is a real-space renormalization group (RG) one; although such treatments are already available [5, 6] for the ferromagnetic case, this is the first time (as far as we know) they are applied allowing for all signs of Js and JB. We follow along the lines of reference [6] and use Migdal-Kadanoff like b = 3 clusters (b is the RG linear expansion factor) which have been quite satisfactory for the ferromagnetic case (Js > 0 and JB > 0). We consider the Hamiltonian where ( i, j > denotes nearest-neighbours, and Jij equals JS(JS 0) when both sites i and j belong to the free surface, and equals JB(JB > 0) otherwise. It is Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019860047070111500