Spectroscopic signatures and origin of hidden order in Ba2MgReO6

Abstract

Clarifying the underlying mechanisms that govern ordering transitions in condensed matter systems is crucial for comprehending emergent properties and phenomena. While transitions are often classified as electronically driven or lattice-driven, we present a departure from this conventional picture in the case of the double perovskite Ba₂MgReO₆. Leveraging resonant and non-resonant elastic x-ray scattering techniques, we unveil the simultaneous ordering of structural distortions and charge quadrupoles at a critical temperature of T_q ~ 33 K. Using a variety of complementary first-principles-based computational techniques, we demonstrate that, while electronic interactions drive the ordering at T_q, it is ultimately the lattice distortions that dictate the specific ground state that emerges. Our findings highlight the crucial interplay between electronic and lattice degrees of freedom, providing a unified framework to understand and predict unconventional emergent phenomena in quantum materials.

Fig. 1. Lattice and electric-quadrupolar coupling and ordering.

a–c The lattice deformations (d_θ) and charge quadrupoles (q_θ) with symmetry θ = x²−y², z² and xy, respectively. The blue and orange lobes of q_θ correspond to regions with excess and reduced electronic charge, respectively. d, e Below T_q, BMRO develops a simultaneous long-range order of the local distortion $d_{\theta }^{\mathbf{k}}$ and electric quadrupoles $q_{\theta }^{\mathbf{k}}$. d The θ = x²−y² component exhibits an antiferroic order with a k = [001] propagation vector. e The θ = z² component displays ferroic, k = [000] arrangement.

Fig. 2. Direct detection of the charge quadrupolar, structural and magnetic order parameters in BMRO.

a REXS experimental setup in the $\sigma \to {\pi }^{\prime }$ scattering channel. The ψ₀ (ψ₉₀) orientation corresponds to the configuration where the crystal c axis points perpendicular (within) the vertical scattering plane. b, c Energy dependence of the Q = (5, 5, 0) Bragg reflection with the ψ₀ and ψ₉₀ crystal orientations, at various temperatures. d Azimuthal dependence of the (5, 5, 0) reflection at E_q and at 20 K demonstrates the θ = x²−y² symmetry of the antiferroic quadrupolar $q_{\theta }^{\left[001\right]}$ order. The dashed (dotted) lines depict the calculated azimuthal dependence of the quadrupoles with xy,z² (xz,yz) symmetry. e Integrated intensity of the (5, 5, 0) peak at the magnetic resonance E_m and ψ₀ azimuth indicates the onset of the antiferroic $m_{xy}^{\left[001\right]}$ order of Re magnetic dipoles below 18 K. f, g Integrated intensity of the (5, 5, 0) and (5, 3, 0) peaks measured at E_q and off-resonance, respectively, to detect the antiferroic $q_{x^2-y^2}^{\left[001\right]}$ and $d_{x^2-y^2}^{\left[001\right]}$ orders. h The (10, 0, 0) peak measured at E_q resonance which is indicative of the ferroic $q_{z^2}^{\left[000\right]}$ order. i The γ splitting of the (10,0,0) reflection to reflect the ordering of $d_{z^2}^{\left[000\right]}$. The error bars correspond to the standard deviation.

Fig. 3. Calculations of BMRO.

a The potential energy surface of a single ReO₆ octahedron in BMRO as a function of $d_{x^2-y^2}$ and $d_{z^2}$ distortions, compared to the experimental octahedral distortions (denoted with the red dots). b Total energy E_TOT versus the temperature T calculated within the mean-field approximation from the ab-initio IEI Hamiltonian (Eq. (1)). The solid and dashed curves are the total energies of the t_2g ferro-$q_{xy}^{\left[000\right]}$ and e_g antiferro-$q_{x^2-y^2}^{\left[001\right]}$ orders, respectively. Inset: the quadrupole-quadrupole block of the IEI matrix V for the nearest-neighbor xy Re–Re bond, blue (red) colors correspond to ferro (antiferro) couplings. c The electronic susceptibility χ_e over the temperature T associated with the ferro xy and antiferroic k = [001] x²−y² quadrupolar orders display Curie-Weiss behavior with a T_q ~ 50 K. On the other hand, the z² quadrupoles do not diverge at a temperature above zero and thus do not ferroically order spontaneously.