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Journal of the Physical Society of Japan

Antiferromagnetic Fractons in Diluted Heisenberg Systems RbMn0.4Mg0.6F3 and Rb2Mn0.598Mg0.402F4

Shinichi Itoh, Tsuneyoshi Nakayama, Mark A. Adams

Published Sep 9, 2011• 5 citations
Publisher

Abstract

The dynamical structure factors, S ( q ,ω), for antiferromagnetic fractons in diluted three-dimensional (3D) and two-dimensional (2D) Heisenberg systems, RbMn 0.4 Mg 0.6 F 3 and Rb 2 Mn 0.598 Mg 0.402 F 4 , respectively, with a magnetic concentration close to the percolation concentration, were observed through high-resolution (Δ E = 17.5 µeV) inelastic neutron scattering experiments well below T N . The exponents describing the peak intensity ( A ( q ) ∝ q - y ) and the dispersion relation ( E ( q ) ∝ q z ) were determined to be y = 2.9 ±0.1 and z = 2.5 ±0.1 for the 3D system and y = 2.9 ±0.2 and z = 1.8 ±0.2 for the 2D system, respectively. In addition, the validity of the single-length-scaling postulate (SLSP) was confirmed for S ( q ,ω) by using the above values of y and z . We experimentally demonstrated, for the first time, that the spectral dimension, \(\tilde{d}_{\text{AF}} = 1\), is universal and independent of the embedding Euclidean dimensions of the systems.

DOI
10.1143/jpsj.80.104704

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The dynamical structure factors, S ( q ,ω), for antiferromagnetic fractons in diluted three-dimensional (3D) and two-dimensional (2D) Heisenberg systems, RbMn 0.4 Mg 0.6 F 3 and Rb 2 Mn 0.598 Mg 0.402 F 4 , respectively, with a magnetic concentration close to the percolation concentration, were observed through high-resolution (Δ E = 17.5 µeV) inelastic neutron scattering experiments well below T N . The exponents describing the peak intensity ( A ( q ) ∝ q - y ) and the dispersion relation ( E ( q ) ∝ q z ) were determined to be y = 2.9 ±0.1 and z = 2.5 ±0.1 for the 3D system and y = 2.9 ±0.2 and z = 1.8 ±0.2 for the 2D system, respectively. In addition, the validity of the single-length-scaling postulate (SLSP) was confirmed for S ( q ,ω) by using the above values of y and z . We experimentally demonstrated, for the first time, that the spectral dimension, (\tilde{d}_{\text{AF}} = 1), is universal and independent of the embedding Euclidean dimensions of the systems.
We report the observations of the dynamical structure factors S(q,ω) for antifferomagnetic fractons in diluted three-dimensional (3d) and two-dimensional (2d) Heisenberg systems, RbMn0.4Mg0.6F3 and Rb2Mn0.598Mg0.402F4, with a magnetic concentration close to the percolation concentration, which were obtained by means of high-resolution (ΔE = 17.5 μeV) inelastic neutron scattering experiments. The peak intensity A(q) and the dispersion relation E(q) show the clear scaling laws following to A(q) ∝ q−y with y = 2.9 ± 0.1 and E(q) ∝ qz with z = 2.5 ± 0.1 for the 3d system, and y = 2.9 ± 0.2 and z = 1.8 ± 0.2 for the 2d system. The validity of the single-length-scaling postulate (SLSP) for S(q,ω) are demonstrated, for the first time. In addition, we show that the spectral dimension of antiferromagnetic fractons is unity independent of the embedding Euclidean dimension of the systems. These values are consistent with the theoretical predictions.
The dynamical structure factor S ( q,w ) for diluted two-dimensional Heisenberg antiferromagnet Rb 2 Mn 0.598 Mg 0.402 F 4 was investigated by means of high resolution (Δ E = 17.5μeV) inelastic neutron scattering below T N . The dynamical exponents in the peak intensity ( A ( q ) ∝ q − y ) and the dispersion relation ( E ( q ) ∝ q z ) for antiferromagnetic fractons were determined as y = 2.9±0.2 and z = 1.8±0.2, in good agreement with the numerical study. Also, the validity of the scaling based on the single-length-scaling postulate (SLSP) was confirmed.
The dynamic structure factors S ( q ,ω) of an ideal percolating network, the three-dimensional (3 d ) dilute Heisenberg antiferromagnet RbMn 0.4 Mg 0.6 F 3 , obtained from high resoluton (Δ E = 17.5 µeV) inelastic neutron scattering (INS) experiments are analyzed for the first time within the framework of the single-length-scaling postulate (SLSP). The analysis confirms the validity of the SLSP and is also used to extract the values of the key exponents governing the spin dynamics, the dynamic exponent (zAF=Df/d~AFz_{\text{AF}} = D_{\text{f}}/\tilde{d}_{\text{AF}}zAF​=Df​/d~AF​) being 2.5 ±0.1 and the spectral dimension d~AF\tilde{d}_{\text{AF}}d~AF​ for antiferromagnetic (AFM) fractons taking a value of unity.
The fracton dynamics of percolating Heisenberg antiferromagnets are studied in terms of a dynamic scaling argument and large-scale numerical analysis. It is shown that the spectral (or fracton) dimension for antiferromagnetic fractons, d~AF\tilde{d}_{\rm AF}d~AF​, is bounded by the relation d~AF≤1\tilde{d}_{\rm AF}\le 1d~AF​≤1. The densities of states (DOS) are calculated for very large percolating antiferromagnets at the critical concentration p c formed on d =2, 3, and 4 simple cubic lattices. It is concluded, from the calculated DOS's, that the spectral dimensions d~AF\tilde{d}_{\rm AF}d~AF​ are very close to unity for any Euclidean dimension d (≥2). We have also calculated the DOS for percolating antiferromagnets above p c in order to clarify the crossover behavior from extended magnons to fractons. In addition, the dynamical structure factor S ( q ,ω) is investigated both analytically and numerically. It is found, postulating a single-length scaling, that the asymptotic behaviors can be characterized by two exponents, the dynamical exponent z AF and a new exponent y . The numerical results for S ( q ,ω) support the validity of the single-length-scale postulate.