Electric field control of interaction between magnons and quantum spin defects

Hybrid systems coupling quantum spin defects (QSD) and magnons can enable unique spintronic device functionalities and probes for magnetism. Here, we add electric field control of magnon-QSD coupling to such systems by integrating ferromagnet-ferroelectric composite multiferroic with nitrogen-vacancy (NV) center spins. Combining quantum relaxometry with ferromagnetic resonance measurements and analytical modeling, we reveal that the observed electric-field tuning is consistent with the ferroelectric polarization control of the magnon-generated fields at the NV. Exploiting this mechanism, we also propose magnon-based hybrid electric field sensors which provide the possibility of improving dc electric field sensitivity of single-spin sensors.

Figure 1

(a) Schematic illustration of the QSD-magnon hybrid system. An external voltage $V$ controls the electrical polarization of PMN-PT (as shown in schematic P-$V$ loops) resulting in lattice strain and reorientation of the magnetic anisotropy field in CoFeB (easy axis–red double arrows) from $x$ axis for $V=V_{\mathrm{off}}$ to $y$ axis for $V=V_{\mathrm{on}}$. (b) Maps of normalized $B_{\perp }(k$) as a function of $\omega -k$ for both $V_{\mathrm{off}}$ and $V_{\mathrm{on}}$. The black lines enveloping the color map are the calculated magnon dispersion lines for bulk modes $(k\parallel M)$ and surface modes $\left(k\perp M\right)$. The dashed colored lines represent the NV ESR lines ${\omega }_{\mathrm{NV}}$. (c) Change in relaxation rates of the NV ensembles enabled by electrical tuning of QSD-magnon coupling. The schematic diagram represents the pulse sequence of the measurement scheme.

Figure 2

(a), (b) Measured relaxation rate ${\mathrm{\Gamma }}_1$ as a function of external magnetic field $H_{\mathrm{ext}}$ applied parallel ($x$ axis) and orthogonal ($y$ axis) to the magnetic anisotropy field (easy axis), respectively. The dashed lines represent theoretical fits of relaxation rates ${\mathrm{\Gamma }}_1$. The inset shows the schematic variation of $H_{\mathrm{ext}}$ with respect to the easy axis and the direction of equilibrium magnetization. (c), (d) Ferromagnetic resonance (FMR) frequency $\left({\omega }_m^0\right)$ as a function of external magnetic field $H_{\mathrm{ext}}$ fitted with the Kittel formula for 20 nm CoFeB film (solid lines) for $H_{\mathrm{ext}}$ parallel ($x$ axis) and orthogonal ($y$ axis) to the anisotropy field, respectively. The dashed colored lines represent maximum spread of the NV ESR lines ${\omega }_{\mathrm{NV}}$. The color map represents the calculated values of the magnetic noise spectral density $G_m(\omega ,H_{\mathrm{ext}})$ for an effective NV height $d_{\mathrm{NV}}=77$ nm.

Figure 3

(a) FMR frequency $\left({\omega }_m^0\right)$ (black line) as a function of applied voltage extracted from the experimental results for a fixed external magnetic field $H_{\mathrm{ext}}=57$ G along the $x$ axis. The color map represents the calculated values of the magnetic noise spectral density $G_m(\omega ,V)$ for an effective NV height $d_{\mathrm{NV}}=77$ nm. The dashed colored lines represent maximum spread of the NV ESR lines ${\omega }_{\mathrm{NV}}$. The inset shows the measured magnetic anisotropy field as a function of applied voltage. We begin by polling the ferromagnet to $-200$ V and then changing the voltage in steps towards $+200$ V and back to $-200$ V. (b) Measured relaxation rates ${\mathrm{\Gamma }}_1$ as a function of applied voltage for a fixed $H_{\mathrm{ext}}=57$ G along the $x$ axis. The inset shows a schematic illustration of the magnetic anisotropy field for the two different voltages for a fixed $H_{\mathrm{ext}}$. The dashed line represents theoretical fit of relaxation rates ${\mathrm{\Gamma }}_1$

Figure 4

Estimates of magnon-sensing sensitivity, $S_m$ (blue bars), and its comparison to direct-sensing, $S_d$ (as quantified by the ratio $S_d/S_m$; black bars), for various magnetic materials (“HD” and “LD” stand for high damping and low damping, respectively. The material parameters and corresponding references are summarized in the Supplemental Material, Table I). Inset shows the proposed hybrid structure.