Magnetism and local symmetry breaking in a Mott insulator with strong spin orbit interactions

Abstract

Study of the combined effects of strong electronic correlations with spin-orbit coupling (SOC) represents a central issue in quantum materials research. Predicting emergent properties represents a huge theoretical problem since the presence of SOC implies that the spin is not a good quantum number. Existing theories propose the emergence of a multitude of exotic quantum phases, distinguishable by either local point symmetry breaking or local spin expectation values, even in materials with simple cubic crystal structure such as Ba₂NaOsO₆. Experimental tests of these theories by local probes are highly sought for. Our local measurements designed to concurrently probe spin and orbital/lattice degrees of freedom of Ba₂NaOsO₆ provide such tests. Here we show that a canted ferromagnetic phase which is preceded by local point symmetry breaking is stabilized at low temperatures, as predicted by quantum theories involving multipolar spin interactions.

Figure 1. Phase diagram of Ba₂NaOsO₆ deduced from the NMR spectra.

(a) The high-temperature undistorted crystal structure of Ba₂NaOsO₆. In this case, point symmetry at the Na site is cubic leading to zero electric field gradient (EFG). Principal crystallographic axes are shown as well. (b) Sketch of the phase diagram based on our NMR measurements. Squares indicate onset temperature for the local cubic symmetry breaking, determined from our NMR data as explained in the text, in the paramagnetic (PM) phase. Circles denote T_c, transition temperature into canted ferromagnetic (cFM) phase, as deduced from the NMR data, while diamond marks T_c as determined from thermodynamic measurements in ref. . The solid line indicates phase transition into cFM state and also possible tetragonal-to-orthorhombic phase transition. The dashed line denotes cross over to the broken local point symmetry (BLPS) phase, as detected by NMR. (c) Temperature evolution of ²³Na spectra at 9 T (and at 15 T, shaded trace) magnetic field applied parallel to [001] crystalline axis. Narrow single peak spectra characterize high-temperature paramagnetic (PM) state. At intermediate temperatures, broader and more complex spectra reveal the appearance of electric field gradient (EFG) induced by breaking of local cubic symmetry. Splitting into two sets of triplet lines (labelled as I and II), reflecting the existence of two distinct magnetic sites in the lattice, is evident at lower temperatures. Zero of frequency is defined as ω₀=²³γH. PM, paramagnetic; BLPS, broken local cubic symmetry; and cFM, canted ferromagnetic. The charge density in the theoretically predicted quadrupolar phase is sketched in the inset.

Figure 2. Local cubic symmetry breaking in the ordered phase.

(a) ²³Na spectra in low temperature ordered state as a function of the angle between the applied magnetic field and [001] crystalline axis. In this case, H was rotated in the (10) plane of the crystal which contains three high symmetry directions: [001], [111] and [110]. (b) The mean peak-to-peak splitting (δ_q) between any two adjacent peaks of the triplets I and II. Error bars reflect the scattering of deduced (δ_q) values. Solid line is the fit to , where θ denotes the angle between the principal axis of the EFG (V_zz) and the applied magnetic field (H) as depicted for nuclei with spin I=3/2 and magnetic moment μ (see Supplementary Note 5). (c) Schematic of a proposed lattice distortion involving the O²⁻ ions. The distortion breaks cubic symmetry at the Na site giving rise to finite electric field gradient (EFG). Different types and colours of double arrows illustrate unequal magnitude of oxygen displacements. Displacements along different axes can comprise either from compression or elongation of the oxygen bonds (see Supplementary Note 5). Depicted distortion magnitude is not to scale with the distance between nearest neighbour Os atoms, and is amplified for clarity. (d) Schematic of the energy levels of a spin-3/2 nucleus in a finite magnetic field and in the presence of quadrupolar interaction with EFG, generated by surrounding electronic charges, and resulting NMR spectra. In the absence of quadrupolar interaction spectrum consists of a single narrow line at frequency ω and of width Δ_ω. In the presence of quadrupolar interaction, the centre transition remains at frequency ω, while the satellite transitions appear at frequencies shift by ±δ_q , proportional to the magnitude of the EFG. For small values of the EFG, satellite transition cannot be resolved and only line broadening is observed. Strictly speaking, there is also a broadening due to the distribution of magnitude of the EFG itself, but this is manifested only on the satellites and not on the central transition. In our case, this distribution can be neglected as all the lines show the same width.

Figure 3. Temperature dependence of the uniform and staggered fields.

Absolute value of the uniform internal field, H_u, (a) and the staggered internal field, H_stag, (b) as a function of reduced temperature for various . Typical error bars are on the order of a few per cent and not shown for clarity. Lines are guide to the eyes.

Figure 4. Resolution of the spin orientation in the ordered phase.

(a) The magnitude of the internal field associated with triplet I (H_I) and II (H_II) (solid symbols), and the first moment of the entire spectrum (uniform field, H_u) as a function of the angle between the applied magnetic field and [001] crystalline axis at 8 K and 15 T. Open symbols depict the angular dependence of the staggered field, H_stag. Typical error bars are on the order of a few per cent and not shown for clarity. Dotted lines are guide to the eyes. Solid lines are calculated fields from the spin model sketched in part (d), as described in the text. (b) Schematic of the net magnetization in the XY plane in the spin model, consistent with our data and proposed in ref. . Arrows of different shades depict spins from two sub-lattices, labelled as A and B. These spins of equal magnitude are canted by angle ±φ with respect to [110] direction. (c) Comparison of the angular dependence of bulk magnetization per FU (formula unit) from ref. (open symbols) and H_u determined from our NMR measurements. Lines are guide to the eyes. (d) Schematic of the spin model consistent with our data and proposed in ref. . Different shades and orientation of arrows indicate distinct ionic (spin) environments on Os site. Planes containing moments from sub-lattice A and B are shown. These equal magnitude moments in two sub-lattices are canted with respect to [110] direction.