Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Theory of Magnetoacoustic Resonance to Probe Multipole Effects Due to a Crystal Field Quartet

Mikito Koga, Masashige Matsumoto

Abstract

We present a new method of acoustically driven resonance that probes octupole degrees of freedom as well as a quadrupole usually hidden by the magnetic properties of a crystal field quartet. A characteristic of the quadrupole is reflected in the anisotropic resonance transition rate, which depends on the propagation direction of a surface acoustic wave under an external magnetic field parallel to a typical crystallographic axis. The transition rate is modulated by the anisotropic Zeeman splitting associated with octupoles. We demonstrate how to obtain information about the quartet quadrupole-strain coupling and evaluate the anisotropic octupole effect quantitatively. We also discuss the applicability of our method to identifying a quadrupole order parameter using a multipole-multipole interaction model. For large excitation energy gaps under strong magnetic fields, we propose a photon-assisted magnetoacoustic resonance formulated on the basis of the Floquet theory.

Theory of Magnetoacoustic Resonance to Probe Multipole Effects Due to a Crystal Field Quartet

Abstract

We present a new method of acoustically driven resonance that probes octupole degrees of freedom as well as a quadrupole usually hidden by the magnetic properties of a crystal field quartet. A characteristic of the quadrupole is reflected in the anisotropic resonance transition rate, which depends on the propagation direction of a surface acoustic wave under an external magnetic field parallel to a typical crystallographic axis. The transition rate is modulated by the anisotropic Zeeman splitting associated with octupoles. We demonstrate how to obtain information about the quartet quadrupole-strain coupling and evaluate the anisotropic octupole effect quantitatively. We also discuss the applicability of our method to identifying a quadrupole order parameter using a multipole-multipole interaction model. For large excitation energy gaps under strong magnetic fields, we propose a photon-assisted magnetoacoustic resonance formulated on the basis of the Floquet theory.
Paper Structure (20 sections, 97 equations, 3 figures, 1 table)

This paper contains 20 sections, 97 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Magnetic Field Effect on a Crystal Field Quartet
  3. Multipole degrees of freedom
  4. Zeeman splitting under field rotation
  5. Acoustically Driven Resonance Transition
  6. Quadrupole--strain interaction under the field rotation
  7. Single-phonon transition rate depending on propagation directions of SAW
  8. Anisotropy of Zeeman effect on quadrupole order phase
  9. Effect of a staggered moment of antiferroquadrupole order on resonance transition rate
  10. Photon-assisted single-phonon resonance transition
  11. Conclusion
  12. Multipole operators for $J = 3/2$
  13. Unitary transformation for field direction as a quantization axis
  14. Unitary transformed quadrupole operators and strain-dependent coefficients
  15. Pseudospin-1/2 representation of the $\Gamma_8$ quartet and its relation to multipole operators for $J = 3/2$
  16. ...and 5 more sections

Figures (3)

  • Figure 1: (Color online) Illustration of pseudo-quartet represented by $J = 3/2$ operator in a cubic crystalline electric field (CEF) environment, which is coupled to SAWs propagating in the $\pm x'$ directions under the static magnetic field ${\hbox{\boldmath$H$}}$. The angle $\varphi$ of the $x'$-axis is measured from the crystallographic $x$-axis.
  • Figure 2: (Color online) Polar representation of transition rate for ${\hbox{\boldmath$H$}} \parallel [110]$ with respect to the angle $\varphi$ of the SAW propagation direction in Eq. (\ref{['eqn:Wn1']}). The data plotted here are normalized by the values at $\varphi = 0$. (a) Plotting of $W_{21}^{[110]} (\varphi)$ for $g_5^2 \langle \varepsilon_{x'z}"^2 \rangle / g_3^2 \langle \varepsilon_{x'x'}^2 \rangle = 3/7$ (black), $1$ (red), and $7/3$ (blue). (b) $W_{21}^{[110]} (\varphi) + W_{21}^{[110]} (- \varphi)$ for evaluating the amplitude $C_{21}^{[110]}$ of the $\cos 4 \varphi$ term.
  • Figure 3: Analogy of photon-assisted single-phonon transition with the two-photon transition in which left-hand circularly polarized ($\sigma^-$) and linearly polarized ($\pi$) photons are absorbed between the two electronic states $| \alpha \rangle$ and $| \beta \rangle$. The transverse phonon behaves like the $\sigma^-$ photon here. The phonon (photon) absorption transition is of a nonmagnetic quadrupole (magnetic dipole) type.