High-Precision Measurement of the Dzyaloshinsky-Moriya Interaction between Two Rare-Earth Ions in a Solid

We report on a direct measurement of the pairwise antisymmetric exchange interaction, known as the Dzyaloshinsky-Moriya interaction (DMI), in a ${\mathrm{Nd}}^{3+}$-doped ${\mathrm{YVO}}_4$ crystal. To this end, we introduce a broadband electron spin resonance technique coupled with an optical detection scheme which selectively detects only one ${\mathrm{Nd}}^{3+}\text{−}{\mathrm{Nd}}^{3+}$ pair. Using this technique we can fully measure the spin-spin coupling tensor, allowing us to experimentally determine both the strength and direction of the DMI vector. We believe that this ability to fully determine the interaction Hamiltonian is of interest for studying the numerous magnetic phenomena where the DMI interaction is of fundamental importance, including multiferroics. We also detect a singlet-triplet transition within the pair, with a highly suppressed magnetic-field dependence, which suggests that such systems could form singlet-triplet qubits with long coherence times for quantum information applications.

Figure 1

Optical absorption spectra showing one red (I) and one blue (II) detuned satellite lines, with energy shifts of $-166$ (I) and $+48\mathrm{GHz}$ (II) with respect to the central line due to isolated ${\mathrm{Nd}}^{3+}$ ions. Note that the measured optical depth saturates for the central line. The inset shows the spectral hole burning spectra (at zero magnetic field). The hole is at zero relative frequency. The antiholes are due to distinct ground-state structures associated with each line.

Figure 2

(a) OD-ESR measurements with the field along the $c$ axis. Brighter color means a stronger OD-ESR signal (see text for details). (b) Spin resonances (blue dots) extracted from (a), and the theoretical spectrum (blue lines) calculated from the fitted spin Hamiltonian $\mathbf{H}$ (see text for details). (c) Spin resonances extracted from OD-ESR measurements with the field along the $a$ axis. The detected resonances are divided into class 1 (blue dots) and class 2 (red plus signs) according to the $g$ factor (see text for details). The corresponding theory spectra are shown as solid-blue and dashed-red lines.

Figure 3

(a) OD-ESR measurements as a function of angle to the $c$ axis, in the $a\text{−}c$ plane, for a fixed field strength of 4.3 mT. The model prediction is superimposed, with class 1 in blue and class 2 in red. (b) OD-ESR measurements with the field along the $c$ axis. The weakly field-dependent singlet-triplet transition is detected up to a field of 200 mT. The model prediction is shown as white lines.

Figure 4

Shown is a schematic of the relative positions of the interacting ${\mathrm{Nd}}^{3+}$ ions separated by 7.12 Å. The oxygen ions, offset from the line joining the ${\mathrm{Nd}}^{3+}$ ions, are likely to mediate the antisymmetric exchange interaction.