Interacting spin and charge density waves in kagome metal FeGe

TL;DR

This study investigates the interplay between spin density wave (SDW) and charge density wave (CDW) in the kagome metal FeGe using elastic and inelastic neutron scattering on two annealed sample sets that differ in CDW strength. It identifies two coexisting spin excitations below $T_{Canting}$: gapless incommensurate SDW at $Q=(0,0,0.5\pm\delta)$ with $\delta=0.04$, and a gapped commensurate spin waves from the A-type AFM order around $Q=(0,0,0.5)$ with $E_{gap}$ around $1.2\mathrm{meV}$. CDW status shifts $T_{Canting}$ and modulates the SDW elastic intensity, while low-energy fluctuations couple to lattice dynamics across $T_{CDW}$; Larmor diffraction reveals a tiny in-plane lattice distortion tied to SDW in the long-range CDW sample but not in the no-CDW sample, evidencing spin–lattice coupling that differs from Cr. The results challenge the double-cone AFM picture, showing FeGe hosts closely coupled energy scales among CDW, SDW, and orbital degrees, making it a unique platform for tunable spin-charge-lattice phenomena in kagome systems.

Abstract

Unveiling the interplay between spin density wave (SDW) and charge density wave (CDW) orders in correlated electron materials is important to obtain a comprehensive understanding of their electronic, structural, and magnetic properties. Kagome lattice materials are interesting because their flat electronic bands, Dirac points, and van Hove singularities can enable a variety of exotic electronic and magnetic phenomena. The kagome metal FeGe, which exhibits a CDW order deep within an A-type antiferromagnetic (AFM) phase, was found to respond dramatically to post-growth annealing - with the ability to tune the CDW repeatedly from long-range order to no (or extremely weak) order. Additionally, neutron scattering studies suggest that incommensurate magnetic peaks that onsets at $T_{Canting}$ = $T_{SDW} \approx$ 60 K in the system arise from a SDW order instead of the AFM double cone structure. Here we use inelastic neutron scattering to show two distinct spin excitations exist below $T_{Canting}$ corresponding to two coexisting magnetic orders in the system in both sets of annealed samples with and without CDW. While CDW order or no order can dramatically affect the onset temperature of $T_{Canting}$ and elastic incommensurate magnetic scattering, its impact on low-energy spin fluctuations is more limited. In both samples, a pair of gapless incommensurate spin excitations arising from the SDW order wavevector coexist with gapped commensurate spin waves from the A-type AFM order across $T_{Canting}$. Low-energy spin excitations for both samples couple dynamically to the lattice through enhanced magnetic scattering intensity on cooling below $T_{CDW}$, regardless the status of the static long-range CDW order. The incommensurate SDW order in the long-range CDW ordered sample also induces a tiny in-plane lattice distortion of the kagome lattice that is absent in the no CDW ordered sample.

Figures (4)

• Figure 1: a. A-type antiferromagnetic order on the FeGe kagome lattice. Two Ge positions are identified as Ge1 and Ge2. b. Schematic of reciprocal space showing the locations of various CDW, nuclear, commensurate and incommensurate magnetic Bragg peaks at base temperature in long-range CDW ordered samples. c. Order parameter scan of the CDW Bragg peak $\textbf{Q} = (0,0,0.5)$ for samples with no CDW order and long-range CDW order. d. Order parameter scan of the incommensurate magnetic Bragg peaks $\textbf{Q} = (0,0,0.5\pm \delta)$ for both sample types. e-f. Reciprocal space map in log scale of sample with no CDW and long-range CDW order respectively at 5 K. Peaks not located at integer or half-integer in e are a result of a second grain within the single crystal and can be ingored, as these peaks randomly coincide with the $[H,0,L]$ plane of the primary aligned crystal grain. g-h.Q-cuts of the incommensurate magnetic Bragg peaks around $\textbf{Q}=(0,0,0.5)$ and $(2,0,0.5)$ respectively comparing long-range CDW samples (blue) and no CDW samples (red). Reciprocal space map intensities, and by consequence Q-cuts, of both annealed samples are normalized to the $\textbf{Q} = (0,0,1)$ nuclear Bragg peak. Error bars correspond to one standard deviation.
• Figure 2: a. Low energy excitation spectra of the long-range CDW ordered sample at 90 K. b. Constant energy cuts along $\textbf{Q} = [0,0,L]$ using the integrated intensity range depicted by rectangles in a. c-d. Same as a-b but for samples with no CDW order. e. Commensurate excitation intensity as a function of temperature extracted from the three-gaussian fits to the Q-cuts at 1.2 meV in b,d for samples with and without long-range CDW order. f. Incommensurate excitation intensity as a function of temperature extracted from the three-gaussian fits to the Q-cuts at 0.6 meV in b,d. The dashed line in e-f is the Bose population factor. Error bars correspond to one standard deviation.
• Figure 3: a-d. Low energy excitation spectra along $\textbf{Q}=[0,0,L]$ for long-range CDW ordered samples at 30, 70, 90, and 120 K respectively. e-h. Same as a-d, but for samples with no CDW order. i-l. Difference of e-h and a-d respectively. The excitation spectra of no CDW samples and long-range CDW ordered samples are normalized to the nuclear Bragg peak $\textbf{Q}=(1,0,0)$ and background subtracted to appropriately take the difference in i-l.
• Figure 4: a. Sample fitting of the commensurate energy gap using Eq. 2 and integration range $\textbf{Q}=(0,0,0.5\pm 0.01)$. b. Commensurate energy gap size extracted from fits described in a as a function of temperature for no CDW samples (red) and long-range CDW samples (blue). c-d. Isothermal magnetic susceptibility heat map demonstrating the evolution of the spin flop transition in no CDW and long-range CDW samples respectively. e. Lattice spacing evolution of $\textbf{Q}=(0,2,0),\ (2,0,0),\ \text{and}\ (2,-2,0)$ nuclear Bragg pea ks as a function of temperature using neutron Larmor diffraction in a long-range CDW sample. f. A zoomed in view of e showing spontaneous lattice expansion at $T_{SDW}$ and $T_{CDW}$, plus Larmor diffraction across $T_{SDW}$ in the sample with no CDW. Error bars represent one standard deviation.