Exchange-displacement waves inGdB6

Abstract

The antiferromagnetic states of GdB 6 are investigated both theoretically and experimentally. A mean-field model is introduced which predicts the coexistence of magnetic and displacement waves starting from isotropic exchange and magnetic ions in a harmonic potential. It provides a coherent interpretation of the puzzling features of GdB 6 magnetic order, in particular the first-order magnetic transition at T N and the two successive antiferromagnetic states. X-ray scattering experiments show ͗ 1 2 0 0 ͘ , ͗ 1 2 1 2 0 ͘ , and ͗ 1 4 1 4 1 2 ͘ satellites consistent with displacement waves imposed by the magnetic ͗ 1 4 1 4 1 2 ͘ structures. In the high-temperature phase, the observation of second-order displacement reflections is evidence of a multi-q, ͗ 1 2 0 0 ͘ , displacement structure: a model of magnetic structure, consistent with both the displacement pattern and the mean-field model predictions, is proposed.

Anisotropy of the Charge Transport in GdB6

“…However, the magnetic dipole ordering of Gd-Gd pairs does not correspond to the vector of magnetic structure k m obtained later from neutron studies [13,14]. Modern theory was proposed by Amara et al in [11] for AF I state of GdB 6 . They introduced a mean-field model which predicts the coexistence of magnetic and displacement waves starting from isotropic exchange.…”

“…Gadolinium hexaboride (GdB 6 ) is the S-state system (for Gd 3+ , L = 0, S = 7/2) which represents very unusual physical properties [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Similar to another rare earth (RE) hexaborides GdB 6 crystallizes in a simple bcc structure of CsCl type (s.g. P m3m−O 1 h ) and shows the flat phonon dispersion relations around 10 meV [15] corresponding to the motion of RE ions inside a rigid boron cage.…”

“…The changes between AF I and AF II phases are connected with appearance of different reflexes corresponding to the structural modulation. According to the last X-ray experiments [11,12] lattice distortions with q 1 = [1/2, 0, 0] and q 2 = [1/2, 1/2, 0] vectors were observed in AF I state whereas the same reflexes q 1 , q 2 with additional one q 3 = [1/4, 1/4, 1/2] (identical to the magnetic wave vector k m ) were detected in AF II phase below T N 2 . (The description of modulated structures in literature often contains the results of previous X-ray studies [8][9][10] with q 1 vector in AF I state and q 2 vector in AF II phase.)…”

“…(The description of modulated structures in literature often contains the results of previous X-ray studies [8][9][10] with q 1 vector in AF I state and q 2 vector in AF II phase.) * corresponding author; e-mail: anisimov.m.a@gmail.com Theoretical models presented for GdB 6 in literature [11,17] consider a coherent displacement of Gd ions inside the rigid boron cage. In particular, Kasuya [17] applied the Jahn-Teller formalism to RB 6 compounds and proposed a stable coexistence of charge dipole and magnetic dipole ordering in both AF states of GdB 6 .…”

“…(The value of T N 2 is found to be strongly sample dependent ranging in the interval T N 2 ≈ 5−10 K [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). Recent structural investigations (including X-ray [8][9][10][11][12] and neutron diffraction [13,14] experiments) have shown that commensurate magnetic structure with the wave vector k m = [1/4, 1/4, 1/2] is realized both in AF I and AF II states of GdB 6 . The changes between AF I and AF II phases are connected with appearance of different reflexes corresponding to the structural modulation.…”