Ultrasensitive strain modulation of terahertz magnons at a magnetic phase transition

Abstract

Antiferromagnets typically host spin-wave (magnon) excitations in the terahertz (THz) regime, offering a promising platform for high-speed magnonic information technologies. Harnessing these excitations requires sensitive control of their spectral properties. Here we use resonant x-ray diffraction and Raman scattering to demonstrate uniaxial-strain control of the antiferromagnetic (AFM) ground state and THz magnon excitations in the layered Mott insulator Ca$_2$RuO$_4$. Although the states separated by the strain-induced phase transition differ only by the sign of the weak and partially frustrated interlayer interaction, their magnon energies differ by more than 10% (~ 0.3 THz). Our theoretical analysis explains this surprising observation by tracing the origin of both the sign reversal of the interlayer coupling and the magnon energy to the spin-orbital composition of the Ru valence electrons. The extreme strain sensitivity of the THz magnon energy near a magnetic phase transition opens up pathways towards a new generation of transition-edge magnonic devices.

Figures (5)

• Figure 1: Uniaxial strain setup, structural response and Raman spectra under compressive strain along the [1 0 0] and [1 1 0] directions. a, Schematic of the strain setup, see details in Methods and Supplementary Note 1. b, Top: schematic of strain application along the [1 0 0] direction. Lattice constants $a$ and $b$ correspond to the next-nearest Ru-Ru directions ($b > a$), with ordered pseudospins aligned along the [0 1 0] axis. Black circles represent Ru ions; black and green arrows indicate the antiparallel alignment. Bottom: lattice orthorhombicity $\frac{b-a}{b+a}$ and strain $\varepsilon$ under normalized compression $\Delta l/l$ along the [1 0 0] direction, where $\Delta l$ is the voltage-controlled piezoelectric displacement and $l$ is the sample length. Lattice orthorhombicity increases under compression along the [1 0 0] direction. c, Top: schematic of strain application along the [1 1 0] direction. Bottom: reduced orthorhombicity and corresponding strain $\varepsilon$. d, Raman spectra at 25 K under compressive strain along the [1 0 0] direction. Magnon spectra in the $B_\mathrm{1g}$ channel were acquired using cross linearly-polarized configuration for incident and scattered photons, while $A_\mathrm{g}$ phonon spectra were measured with parallel polarization geometry. Black dots mark the phonon energies. e, Raman spectra under compressive strain along the [1 1 0] direction. Additional Raman data and experimental details are provided in Supplementary Note 2 and Methods.
• Figure 2: RXD results under compressive strain along the [1 1 0] direction and the magnetic phase transition. a--b, Magnetic reflections of the A- and B-centered AFM orders measured at the Ru $L_3$ edge under varying strain at 20 K. The A-centered phase gives rise to magnetic reflections satisfying $h + l$ = odd and $k + l$ = even, while the B-centered phase corresponds to $h + l$ = even and $k + l$ = odd. Longitudinal ($\theta-2\theta$) scans were performed with synchronized sample ($\theta$) and detector (2$\theta$) motion. c, Strain dependence of the integrated intensities for the A-centered (blue) and B-centered (red) magnetic reflections. The intensities for each phase are normalized to their maximum. Error bars indicate the strain uncertainty, derived from the simultaneous measurement of lattice constants (Supplementary Note 1). Schematics of the A- and B-centered magnetic structures are shown on the sides, with arrows in two colors representing antiparallel pseudospins of Ru ions.
• Figure 3: Electronic structure of $t_\mathrm{2g}^4$ configuration and Raman results under compressive strain along the [1 0 0] direction. a, $t_\mathrm{2g}$ orbital level splitting under tetragonal $\Delta$ and orthorhombic $\Delta_\mathrm{ort}$ crystal fields. $\Delta>0$ corresponds to flattened RuO$_6$ octahedra in Ca$_2$RuO$_4$, placing the $xz/yz$ orbitals above the $xy$ orbital. $\Delta_\mathrm{ort}>0$ reflects a shorter $a$-axis relative to the $b$-axis, resulting in a higher $az$ level than $bz$. b, Energy levels of $t_\mathrm{2g}^4$ electronic configuration including the crystal field and SOC effects. The higher energy $\tilde{J}$ = 2 states are not shown. The ground state singlet and the lowest doublet $T_{x/y}$ form an effective pseudospin $S$ = 1 basis. c, Measured magnon energies (circles) and theory (line) under compressive strain along the [1 0 0] direction. Circles with different colors denote different data sets. In our theory fits, $\Delta_{\rm ort}$ increases linearly with $\varepsilon$, while $\Delta = 250$ meV remains a constant.
• Figure 4: Raman results under the compressive strain along the [1 1 0] direction. a, Measured magnon energies (blue circles: A-centered phase; red squares: B-centered phase) and theory (blue line: A-centered phase; red line: B-centered phase). Above the critical strain $\varepsilon_c \sim$ 0.15% (vertical grey line), the light blue circles and dashed line represent the residual A-centered phase. b, Strain evolution of the crystal field parameters $\Delta_{\rm ort}$ (top) and $\Delta$ (bottom) obtained from the theory fits. Colors and line styles match those in (a). In the top panel, $\Delta_{\rm ort}$ decreases linearly with strain, with a slight drop at $\varepsilon_c$. The light blue dashed line (residual A-centered phase) overlaps the red solid line (B-centered phase) for $\varepsilon > \varepsilon_c$. In the bottom panel, $\Delta$ remains constant (250 meV) before the transition. At $\varepsilon_c$, an abrupt drop of $\Delta$ to $\sim 220$ meV occurs for the B-centered phase, while $\Delta$ remains continuous for the A-centered phase. After the transition, the strain dependence of $\Delta$ is described as $\Delta = \Delta_0 [ 1+a_1 (\varepsilon-\varepsilon_c)-a_2 (\varepsilon-\varepsilon_c)^2]$, with $a_1=0.22$, $a_2=1.4$ for the B-centered phase and $a_1=0.38$, $a_2=0.7$ for the residual A-centered phase, yielding the best fit to the data.
• Figure 5: Calculated magnetic phase diagram and interlayer exchange processes.Middle: Interlayer coupling $J_c$ (in units of $t_{c}^2/U$) as a function of tetragonal crystal field $\Delta$ (solid black curve), where $J_c >$ 0 corresponds to AFM interlayer coupling. Under compressive strain along the [1 1 0] direction, $J_c$ changes sign as $\Delta$ decreases abruptly from 250 (blue circle) to 220 (red square) meV across the critical strain $\varepsilon_c$, driving the transition from A-centered to B-centered phase. At the bottom, spin-orbit wave functions for the two-hole $t_\mathrm{2g}$ configuration are visualized at different values of $\Delta$ with $2\lambda=145$ meV. Left: In the hole language where each site hosts two spins (black arrows), the schematic visualization of AFM exchange between interlayer nearest-neighbor sites $i$ and $j$ at large $\Delta$ is shown. The blue arrow indicates a spin hopping between sites, aligned antiparallel to the existing spins. Right: At small $\Delta$ with the finite $xy$ hole density, two distinct hopping processes (dashed double arrows) contribute to ferromagnetic coupling via Hund's coupling $J_\mathrm{H}$. The red arrow denotes the spin hopping parallel to the existed spins. Here, $t_{c}$ ($t_{c}^\prime$) denotes interlayer hopping between $xy$ ($az/bz$) levels. In our model, $t_{c} =2.4 t_{c}^\prime$.