Exploring the mechanisms of transverse relaxation of copper(II)-phthalocyanine spin qubits

TL;DR

The study establishes that, in CuPc molecules diluted in XPc hosts, transverse decoherence is dominated by longitudinal electron–electron dipolar interactions (via instantaneous and spectral diffusion) rather than nuclear or spin–lattice channels. By combining pulsed EPR experiments with first-principles cluster-correlation expansion simulations, the authors quantitatively separate contributions from nuclear spins, lattice interactions, and electron spins, finding negligible roles for both strongly and weakly hyperfine-coupled nuclei. The work provides a robust, transferable methodology to predict ensemble coherence times and to estimate electron spin density from $T_2$ measurements, enabling rational design of spin-density and interaction strengths for improved molecular qubits. These insights have broad relevance for molecular spintronics, quantum information processing, and hybrid quantum materials, where controlling dipolar decoherence is crucial for scalability.

Abstract

Molecular spin qubits are promising candidates for quantum technologies, but their performance is limited by decoherence arising from diverse mechanisms. The complexity of the environment makes it challenging to identify the main source of noise and target it for mitigation. Here we present a systematic experimental and theoretical framework for analyzing the mechanisms of transverse relaxation in copper(II) phthalocyanine (CuPc) diluted into diamagnetic phthalocyanine hosts. Using pulsed EPR spectroscopy together with first-principles cluster correlation expansion simulations, we quantitatively separate the contributions from hyperfine-coupled nuclear spins, spin--lattice relaxation, and electron--electron dipolar interactions. Our detailed modeling shows that both strongly and weakly coupled nuclei contribute negligibly to $T_2$, while longitudinal dipolar interactions with electronic spins, through instantaneous and spectral diffusion, constitute the main decoherence channel even at moderate spin densities. This conclusion is validated by direct comparison between simulated spin-echo dynamics and experimental data. By providing a robust modeling and experimental approach, our work identifies favorable values of the electron spin density for quantum applications, and provides a transferable methodology for predicting ensemble coherence times. These insights will guide the design and optimization of molecular spin qubits for scalable quantum devices.

Figures (4)

• Figure 1: Structural and spectral characterization of CuPc molecular systems. (a) Structure of a copper phthalocyanine (CuPc) molecule. (b) Lattice structure of $\beta$-phase CuPc:XPc crystal, where XPc denotes diamagnetic phthalocyanine (e.g., NiPc or H$_2$Pc). We indicate the distances of the Cu e- spin to the nearest intra- and inter-molecule protons, the second being the smallest. (c,d) Echo-Detected Field Sweep (EDFS) measurement results for CuPc:NiPc and CuPc:H$_2$Pc samples, respectively, taken at a fixed resonance frequency of 9.72 GHz. One of the EPR transitions ($\sim$3545 G) split by hyperfine couplings is highlighted.
• Figure 2: CuPc relaxation time characterization. (a) Normalized experimental spin-echo data for CuPc:NiPc and CuPc:H$_2$Pc at 5 K. The experimental decay times ($T_2$) are fitted to 1.0 $\mu$s and 0.3 $\mu$s for CuPc:NiPc and CuPc:H$_2$Pc, respectively. Inset of (b): simulated spin-echo decay of a single CuPc molecule (Eq. \ref{['eq:hamilton_cun']}), averaged over all molecular orientations with respect to the magnetic field (powder average). The longitudinal spin component $\langle S_z \rangle$ is significantly larger than the transverse component $\langle S_x \rangle$, indicating that only a limited fraction of the CuPc electron spin spectrum is driven into a superposition state by the microwave field. (b) Experimental inversion recovery measurements at 5 K. The experimental decay times ($T_1$) are fitted to 35 ms and 14 ms for for CuPc:NiPc = 1:140 and CuPc:H$_2$Pc = 1:45, respectively. The data are shown only for $t > 20~\mu$s, corresponding to the spin-lattice relaxation component. (c) Temperature dependent of the transverse (solid line, $1/T_2$) and longitudinal (dashed line, $1/T_1$) decay rate.
• Figure 3: Spin locking response of CuPc to quantum and classical hydrogen spin baths. (a) Spin locking (NOVEL) pulse sequence. The locking pulse acts as an effective static field along the x-axis in the rotating frame. (b--c)Spatial distribution of $^1$H nuclear spins (purple dots) surrounding the CuPc electron spin (red dot with gray spin arrow), shown for (b--d) Experimental spin locking signal and fit for CuPc:H$_2$Pc and CuPc:NiPc at varying $\Omega_x$. (e--g) Simulated spin locking signal under a quantum bath only of hydrogen spins, at the same $\Omega_x$ as in (b--d). (h-j) Signal oscillation amplitude $C_q$ and frequency $\alpha'$ (Eq. \ref{['eq:spinlockingfit']}) as a function of $\Omega_x$ for CuPc:H$_2$Pc and CuPc:NiPc extracted from fits to the experimental data (circles) and from simulations (dashed lines.) (l) Spin-locking classical decay rate $1/T_{1\rho}$ (Eq. \ref{['eq:P_classical_1']}) CuPc:H$_2$Pc and CuPc:NiPc(m) as a function of $\Omega_x$: Circles, wxperiment data; lines, Lorentzian fitting.
• Figure 4: CCE results and electron--electron spin interaction effects. The $T_2$ decay rates obtained from CCE simulations are shown as gray (CuPc:NiPc) and purple (CuPc:H$_2$Pc) curves, at varying CuPc doping percentages. The black dashed line represents the simulated total decoherence rate from electron spin bath interactions, incorporating flip-flop interactions, instantaneous diffusion, and spectral diffusion discussed in Section. \ref{['section:electron']}. Experimental data measured at doping ratios of CuPc:NiPc = 1:140 and CuPc:H$_2$Pc = 1:45 are also plotted, showing good agreement with the simulated overall electron spin bath effect.