Novel Magnetoacoustic Resonance Technique for Exploring Hidden Quadrupoles in a Crystal Field Quartet

Abstract

Crystal field quartets with quadrupole degrees of freedom play a crucial role in hidden ordering systems, as exemplified by CeB$_6$. We present a novel magnetoacoustic resonance technique that combines acoustically induced strain fields with a linearly polarized high-frequency microwave field to probe quadrupoles inherent in the quartet hidden behind magnetic properties. This method offers the advantage of enabling quantum quadrupole resonance transitions for large excitation energy gaps within quartet sublevels under a strong magnetic field, which cannot be achieved by acoustic experiments alone. Formulating a simultaneous single-phonon-single-photon absorption transition process using Floquet theory, we demonstrate how the transition probabilities are affected by changing the propagation direction of a bulk acoustic wave. The key result is that distinct maxima in transition probabilities, attributed to specific propagation directions, indicate a characteristic of quadrupole physics and exhibit an abrupt change owing to an induced ordered moment. This photon-assisted magnetoacoustic resonance technique will promote a broader range of applications of acoustic experiments for the study of quadrupole physics.

Figures (2)

• Figure 1: (Color online) Illustration of photon-assisted magnetoacoustic resonance. Yanagisawa24 The quadrupole resonance transition between two levels of a localized electron state is achieved through the simultaneous absorption of a single phonon and a single $\pi$-photon using an acoustic wave and a linearly localized microwave. The propagation direction ($x'$-axis) of the acoustic wave is rotated in the $xy$ plane under a static magnetic field.
• Figure 2: (Color online) Transition probability $\bar{P}_{1 \rightarrow 2}^{(1,1)}$ plotted as a function of the BAW propagation direction $\varphi$ for various values of the effective induced moment $\bar{\mu}_{\rm eff}^2 = 0.0$, $0.1$, and $1.0$. At the normal phase ($\bar{\mu}_{\rm eff} = 0$), $\bar{P}_{1 \rightarrow 2}^{(1,1)}$ vanishes precisely at $\varphi / \pi = 1/4$ and $3/4$. Here, the magnetic field ${\hbox{\boldmath$H$}}$ is parallel to the [110] direction ($\varphi = \pi /4$).