Random-Field Effects in Two- and Three-Dimensional Ising Antiferromagnets

Abstract

Neutron scattering experiments have been performed in the diluted antiferromagnets Rb 2 Co 0#7 Mg 0>3 F 4 and Co 0#3 Zn 0e7 F 2 in a uniform magnetic field. These systems are isomorphous to, respectively, two-and three-dimensional Ising ferromagnets in a site-random magnetic field. It is shown that small random magnetic fields destroy the long-range order at all temperatures, consistent with three as the lower marginal dimensionality; the structure factor in the disordered state is predominantly a squared Lorentzian.

Understanding complex magnetic order in disordered cobalt hydroxides through analysis of the local structure

“…3,4,19 In those random dilute systems, the formation of magnetic microdomains and the disruption of magnetic long-range order is driven by local random-field energy. 19 While a different experiment here, the magnetic reflections from neutron diffraction have significantly increased Lorenztian widths and low diffracted intensities, which also indicate disrupted long-range order of the magnetic structure.…”

“…2 Upon zero-field cooling, neutron diffraction reveals a Néel state; however, the random fields decrease the diffracted peak intensity from disrupted long-range order (LRO) and field cooling completely destroys the LRO. 3,4 Because these systems show no preference for chemical or short-range order within a disordered nuclear unit-cell, 4 it is difficult to structurally distinguish the role of the impurities in establishing the random fields and microdomains.…”

Lower-critical spin-glass dimension from 23 sequenced hierarchical models

“…For example, the lower-critical threshold for ferromagnetic ordering in magnetic systems is d L = 1 for one-component (Ising) spins and d L = 2 for spins with more than one component. Similarly, the lower-critical dimensions for ferromagnetic ordering under quenched random fields [1][2][3][4][5][6][7] are respectively d L = 2 and d L = 4 for one-component spins and for spins with more than one component. The method that we use in this study gives correctly the lower-critical dimensions of the Ising and q-state Potts models (d L = 1), of the (n > 1)-component vector spin models (d L = 2), of the Ising model with quenched random fields (d L = 2), as well as the algebraic order of the XY model at its lower-critical dimension d L = 2 [7][8][9][10][11][12][13].…”

Barkhausen noise in the random field Ising magnetNd2Fe14B

“…The original experimental studies of the RFIM followed a proposal by Imry and Ma, 12 in which a site-diluted Ising antiferromagnet in a large static magnetic field forms a realization of the RFIM Hamiltonian. While this approach proved fruitful for studying quantities such as the thermodynamic critical exponents 13,14 and correlation lengths, 15 the lack of a net long wavelength moment in antiferromagnets limits the potential probes and hence the set of physical questions that can be addressed. Uniaxial relaxor ferroelectrics were subsequently shown to be realizations of the RFIM 16,17 and similarly have provided insights into the critical and scaling behavior.…”