Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple-kPartial Order on the Pyrochlore Lattice

Abstract

We study the problem of partially ordered phases with periodically arranged disordered (paramagnetic) sites on the pyrochlore lattice, a network of corner-sharing tetrahedra. The periodicity of these phases is characterized by one or more wave vectors k = { 1 2 1 2 1 2 }. Starting from a general microscopic Hamiltonian including anisotropic nearest-neighbor exchange, long-range dipolar interactions and second-and third-nearest neighbor exchange, we identify using standard mean-field theory (s-MFT) an extended range of interaction parameters that support partially ordered phases. We demonstrate that thermal fluctuations ignored in s-MFT are responsible for the selection of one particular partially ordered phase, e.g. the "4-k" phase over the "1-k" phase. We suggest that the transition into the 4-k phase is continuous with its critical properties controlled by the cubic fixed point of a Ginzburg-Landau theory with a 4-component vector order-parameter. By combining an extension of the Thouless-Anderson-Palmer method originally used to study fluctuations in spin glasses with parallel-tempering Monte-Carlo simulations, we establish the phase diagram for different types of partially ordered phases. Our results elucidate the long-standing puzzle concerning the origin of the 4-k partially ordered phase observed in the Gd2Ti2O7 dipolar pyrochlore antiferromagnet below its paramagnetic phase transition temperature. Highly frustrated magnetism is one of the paradigms of modern condensed matter physics [1]. In frustrated magnets, the combination of lattice geometry and competing interactions often leads to degenerate classical states. The degeneracies are generally accidental as they are not protected by the symmetries of the spin Hamiltonian. Yet, the degenerate states may be related by transformations that form an emergent symmetry group. Near a continuous phase transition, these approximate symmetries provide "organizing principles" in determining the critical properties by distinguishing relevant perturbations from irrelevant ones. In the most interesting case, the leading degeneracy-lifting perturbations, which may be relevant or irrelevant in the renormalization group sense, are thermal or quantum fluctuations -a phenomenon called order-by-disorder (ObD) [2][3][4][5]. The competition among diverse degeneracy-lifting effects can result in a modulated long-range ordered state at nonzero wave vector k, which may or may not be commensurate with the lattice [6][7][8][9][10][11][12]. In some cases, a number of superposed symmetryrelated k modes within the first Brillouin zone form a socalled multiple-k order [6,7,13,14]. A particular interesting form of such modulated magnetism is a partially ordered state (POS) with periodically arranged "paramagnetic" sites [15][16][17][18]. These fluctuating magnetic moments decimate a fraction of the energy-costly frustrated bonds while retaining an extensive entropy, hence lowering the free energy.In this Letter, we study the convergence of the aforementioned phenomena (emergent symmet...

Order-by-disorder in theXYpyrochlore antiferromagnet

“…V, we note that the ψ 4 states are the ground states one finds for antiferromagnetic nearest-neighbor exchange with sufficiently weak nearest-neighbor pseudodipolar as well as for true 1/r 3 long-range magnetostatic dipolar interactions in the classical Heisenberg pyrochlore antiferromagnet model [25,28,29]. Interestingly, the ψ 4 states are found experimentally to be the ground state of the Gd 2 Sn 2 O 7 pyrochlore antiferromagnet [29][30][31], but not of the closely related Gd 2 Ti 2 O 7 material [32,33].…”

Long-range magnetic order in the Heisenberg pyrochlore antiferromagnets Gd2Ge2O7 and Li1, Cai2, Qi3 et al. 2016Phys. Rev. B

“…a =10.182 Å of GTO versus 10.454 Å of GSO) 7 would give rise to stronger third-neighbor exchange interactions J 31 . In a recent theoretical investigation by Javanparast et al 29 , on the other hand, thermal fluctuations are argued to be responsible for the observed partially ordered 4-k state in GTO. It should be noted that GTO is prone to structural disorders.…”

“…In addition, the partial magnetic order evidenced in GTO has attracted some recent research interest. 16,29 In order to gain more insights into these longstanding issues, we undertook in this work a detailed experimental investigation on the magnetic properties of two more gadolinium-based Heisenberg pyrochlore antiferromagnets, Gd 34 Interestingly, we found that both GGO and GPO undergo a single, strongly first-order antiferromagnetic transition with characteristic specific-heat anomaly similar to GSO, and the transition temperatures, T N = 1.4 K for GGO and T N = 1.56 K for GPO, are greatly enhanced with respect to that of GSO and GTO. In addition, the magnetic specific heat for both compounds was found to follow the T 3 -dependence as a conventional antiferromagnet with gapless spin-wave excitations, also different from that of GSO and GTO.…”

“…Since the pioneer study on GTO in this context by Raju et al, 6 the magnetic properties of these two compounds have been investigated with various experimental techniques, such as dc and ac magnetic susceptibility [6][7][8][9][10] , specific heat 6,7,11 , elastic and inelastic neutron scattering [12][13][14][15][16] , electron spin resonance [17][18][19][20] , Mössbauer 7,21 , and muon spin relaxation [22][23][24] . Besides, their interesting magnetic properties have also been the subject of several theoretical studies [25][26][27][28][29] .…”

Mott-Hubbard transition and spin-liquid state on the pyrochlore lattice

“…Also, easy axis anisotropy, long-rage dipolar interaction, etc., lead to multiple-q ordered phases 33 . It has been argued that beyond the Heisenberg limit the half-filled Hubbard model on the pyrochlore lattice can be expressed as a highly frustrated intratetrahedral spin model with weak intertetrahedral perturbations 29 .…”