Probing intrinsic magnon bandgap in a layered hybrid perovskite antiferromagnet by a superconducting resonator

Coherent interactions between different magnetic excitations can lead to formation of magnon band gaps and hybrid magnon modes, which can find their applications in magnonic devices and coherent information processing. In this work, we probe the intrinsic magnon band gap of a layered hybrid perovskite antiferromagnet by its strong coupling to a superconducting resonator. The pronounced temperature tunability of the magnon band gap location allows us to set the photon mode within the gap, leading to a reduction of effective magnon-photon coupling and eventually the disappearance of magnon-photon hybridization. When the resonator mode falls into the magnon band gap, the resonator damping rate increases due to the nonzero coupling to the detuned magnon mode. This allows for quantification of the magnon band gap using an analytical model. Our work brings new opportunities in controlling coherent information processing with quantum properties in complex magnetic materials.

Figure 1

(a) Lattice structure of layered perovskite antiferromagnet Cu-EA, with Cu filling the octahedral sites of Cl and the antiferromagnetic layers separated by the ${\mathrm{CH}}_3{\mathrm{CH}}_2{\mathrm{NH}}_3$ molecules. (b) Optical microscope image of a small Cu-EA flake mounted onto a CPW superconducting resonator. (c) Raman spectroscopy of Cu-EA showing the high-frequency octahedral modes and the low-frequency organic structure modes. (d) Broad-band ferromagnetic resonance spectra of a large Cu-EA crystal measured at 1.6 K, which is used to extract the magnon band gap $2\delta$, the interlayer exchange field $2H_E$, and magnon damping rate ${\kappa }_m$. The color bar shows the signals $\mathrm{\Delta }{S}_{21}$ after background subtraction. (e) Extracted $2H_E$ magenta and $2\delta$ as a function of $T$. (f) Mode anticrossing between magnons and photons at 5.5 K, with $H_B\perp h_{\text{rf}}^y$. The color bar shows the signals $S_{21}$ in absolute values. The red curves are the fits with $g/2\pi =45\mathrm{MHz}$. The black dashed lines denote the magnon and photon modes without interaction.

Figure 2

(a), (b) Illustration of two different in-plane field alignments and their selective mode excitations. In (a), ${\mu }_0{H}_B\perp h_{\text{rf}}^y$ and only the acoustic mode is excited. In (b), ${\mu }_0{H}_B\parallel h_{\text{rf}}^y$ and both the acoustic and optical modes are excited. (c), (d) Temperature dependence of the magnon-photon coupling evolutions from 1.5 to 6 K with two different magnetic field alignments. All the dispersion centered at the resonator photon mode (${\omega }_p/2\pi \approx 3.5$ GHz). Dashed curves are guide to eye for the acoustic mode crossing the resonator mode at ${\mu }_0{H}_a=95\mathrm{mT}$ and the optical mode crossing the resonator mode at different fields. (e)–(g) Illustration of the three regimes where the resonator mode is (e) above, (f) within, and (g) below the magnon band gap.

Figure 3

Extracted effective magnon-photon coupling $g$ as a function of $T$. The resonator mode is within the magnon band gap between 3 and 3.5 K, yielding $g=0$.

Figure 4

(a) Superconducting resonator linewidth ${\kappa }_c$ as a function of $H_B$ at $T=3.3\mathrm{K}$, where the resonator mode is inside the magnon band gap. (b) SC resonator linewidth change $\mathrm{\Delta }{\kappa }_c$ as a function of $g_{\text{eff}}^2$ for the CPW and LER resonator designs. Error bars denote the uncertainty of base resonator linewidth drift under external magnetic fields. The red line is a fit to Eq. (4), with the slope quantifying the magnon band gap $2\delta$.

Figure 5

Optical microscope images of (a) the CPW resonator and (b) the lumped-element resonator mounted with Cu-EA crystals.