Strong Coupling of Microwave Photons to Antiferromagnetic Fluctuations in an Organic Magnet

Coupling between a crystal of di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium radicals and a superconducting microwave resonator is investigated in a circuit quantum electrodynamics (circuit QED) architecture. The crystal exhibits paramagnetic behavior above 4 K, with antiferromagnetic correlations appearing below this temperature, and we demonstrate strong coupling at base temperature. The magnetic resonance acquires a field angle dependence as the crystal is cooled down, indicating anisotropy of the exchange interactions. These results show that multispin modes in organic crystals are suitable for circuit QED, offering a platform for their coherent manipulation. They also utilize the circuit QED architecture as a way to probe spin correlations at low temperature.

Figure 1

Experimental schematic. The coplanar resonator (inset photograph) is mounted in a dilution refrigerator and measured via two-port microwave transmission. A DPPH crystal (purple in schematic, black in photograph) is attached with vacuum grease near the magnetic field antinode of the resonator’s fundamental mode. Axes of the in-plane static magnetic field are indicated.

Figure 2

Transmission as a function of external magnetic field $B_{x,y}$ and resonator probe frequency $f$, measured at two different temperatures. Transmission maxima occur at resonance frequencies of the combined system, with anticrossings indicating hybridization between crystal magnetic resonances and the cavity modes. Superimposed on each panel are fits to the resonance frequencies (dashed lines) using Eq. (1).

Figure 3

(a) Resonance magnetic field as a function of field angle $\theta$. Measuring at $T=15\mathrm{mK}$, the resonance field varies sinusoidally with $\theta$, with amplitude $\mathrm{\Delta }{B}_0=10.6\mathrm{mT}$ for the fundamental mode ($f_0=5.92\mathrm{GHz}$, circles) and $\mathrm{\Delta }{B}_1=12.3\mathrm{mT}$ for the first harmonic mode ($f_1=11.64\mathrm{GHz}$, squares). At high temperature, the fundamental mode shows nearly isotropic resonance (triangles). (b) Plot of the MR frequency as a function of resonance magnetic field. Data points are the resonance magnetic fields along $x$ (circles) and along $y$ (diamonds), taken from the maximum and minimum data points of (a) for data at the fundamental or first harmonic mode. The black dotted line is the PM dispersion relation with Landé factor $g=2.0037$. The dashed orange and dot-dashed cyan lines are fits using a PM dispersion relation, with separate $g$ factors along the two axes taken as fit parameters. From the insets it is apparent that these fits do not describe the data well. Red and blue solid curves are a fit to the AFM dispersion relation in Eq. (3), which agrees well with the data.

Figure 4

(a) Temperature evolution of $g_{\mathrm{eff}}$ for $\mathbf{B}$ applied along $x$ and $y$. Above $T\sim 500\mathrm{mK}$, the data agree with a PM model [dashed lines, fit to Eq. (4) over the shaded temperature range]. Inset right: similar data and fits at the resonator’s first harmonic. Inset left: effective spin-temperature calculated with Eq. (4) (points). (b) Filled symbols: resonance magnetic field along $x$ and $y$ as a function of temperature. As temperature decreases, the resonance magnetic field moves away from its paramagnetic value (assuming $g=2.0037$). At intermediate temperatures, both branches are fit by a spin chain model (solid curves; see text). Unfilled symbols: $B_{\mathrm{MR}}$ along $x$ and $y$ as a function of effective temperature according to Eq. (4). The data for $T\le 3\mathrm{K}$ is fit by a spin chain model (dashed curve; see text). Inset: similar data at the first harmonic mode.