Magnetic field symmetry breaking in spin glasses

Time reversible symmetry is spontaneously broken in spin glasses below their transition temperature, T_g. Under such conditions, the standard assumption about the equivalence of switching the magnetic field on or off is not justified. We show that the growth of the spin glass coherence length [ξ(t,t_w;H), where t_w is the aging time] behaves differently between the zero-field-cooled (ZFC, magnetic field turned on) and the thermoremanent magnetization (TRM, magnetic field turned off) protocols.This is shown through experiments, carried out on two CuMn single crystals, and through massive simulations on the Janus II dedicated supercomputer. In agreement with the predictions of a simple dynamical model that assumes that an ultrametric tree of states survives the switching on of a magnetic field, we conclude that (all parameters being kept equal) ξ(t.t_w;H) grows more slowly with time for a TRM protocol as compared to a ZFC protocol. This conclusion depends on the nature of the free energy barriers governing the time dependence of the protocols. If they increase linearly with diminishing overlap between the occupied states and the initial t = 0 state (increase of the Hamming distance), the two protocols yield identical time dependences for ξ(t,t_w;H). If, however, they increase faster than linearly with diminishing overlap, then ξ_ZFC(t,t_w;H) > ξ_TRM(t,t_w;H) for H > 0. This result has serious implications for the extended principle of superposition, M_ZFC(t,t_w;H) + M_TRM(t,t_w;H) = M_FC(t+t_w;H), in the presence of a finite magnetic field. Here, M_FC(t+t_w;H) is the field cooled magnetization. In particular, it holds only at

H = 0, and is violated for H > 0. In particular, for H > 0, M_ZFC(t,t_w;H) + M_TRM(t,t_w;H) > M_FC(t+t_w;H). The Janus II simulations verify this inequality. A phenomenological picture is employed that exhibits this behavior.