Spin Qubits Candidate in Transition-Metal-Ion doped Halide Double Perovskites

Domain: physics
Published: 2026-01-08
Editorial outcome: minor_revision

Abstract
Solid-state spin qubits offer a promising route toward scalable quantum technologies. Here we demonstrate that, despite of a nuclear-spin-rich host of halide double perovskites (HDPs), transition-metal centers (Cr3+ and Fe3+ ions) are a good candidate for spin qubits exhibiting long-lived electron spin coherence with T2 = 29.5 µs and 21.2 µs at 4 K, respectively. Notably, spin localization facilitates a well-defined electron-nuclear (e-N) spin rotation between the electron spin and the neighboring nuclear spins of 35,37Cl and 133Cs. The resulting e-N spin cluster is readily beneficial for a target nuclear-spin sensing. For the Cr3+ spin centers, the optical transitions associated with Cr3+ spin centers is spin-selective thereby paving a way for optical addressing of spins. Our findings from these spin ensemble studies establish HDPs as a new promising platform for creating solid-state spin qubits using simple and inexpensive solution-based single crystal growth methods, broadening material applications of halide perovskites.

Introduction
Solid-state spin qubits, utilizing localized defect and impurity centers in wide band-gap semiconductors, offer a promising route toward a scalable quantum network. These optically addressable, atomic-like spin centers can serve as local nodes for quantum manipulation1–6. Quantum communication is mediated by interfacing spin and photons, leveraging the selection rules of atomic-like transitions. They are highly attractive for their long spin coherence time and their compatibility with existing semiconductor technology, allowing for the integration of quantum devices with conventional electronics. The current state-of-the-art in solid-state spin qubits largely focuses on ‘defects’ systems like nitrogen-vacancy (NV) centers7–13 in diamond and divacancy centers in silicon carbide (SiC)3,14 and ‘impurity’ centers such as transition metal (TM) V4+ and Cr4+ centers in SiC15–20. These spin qubit candidates are known for their exceptionally long spin coherence times. This is partly attributed to the nature of their semiconductor hosts, which inherently possess a majority of nuclear spin-free isotopes.

While a common design principle for solid-state spin qubits suggests using nuclear-spin-free hosts to minimize electron spin decoherence due to the interaction with a nuclear spin bath, there is a rising interest in a nuclear-spin-rich host6–10,14–32. These research endeavors have initially focused on expanding the spin qubit library into systems important in optoelectronics technology, such as the recent report of defect-based solid-state spin qubits in GaN33, in transition metal dichalcogenides34, and in hexagonal boron nitride25,29,35. Furthermore, recent research has highlighted the potential of electron-nuclear (e-N) spin hybrid systems7,8,13,26–28,30,32,36 that utilize nuclear spins as quantum operating or registering nodes. This has been demonstrated using rare-earth impurity Yb centers within YVO4 26, where the tetragonal 51V acts as a spin-wave register for the Yb spin qubit.

In this context, halide perovskites are an emerging class of materials for optoelectronics and novel spintronics37–45. They are attractive due to their high performance and much low fabrication costs. The diverse chemical and structural varieties within the halide perovskite material library further allow for strategic design of their electronic properties37,38, serving various applications such as solar absorbers46, photodetectors47, X-ray detectors48, and white-lighting45. Given their potential in optoelectronics, integrating spin qubits into halide perovskite hosts could leverage existing optoelectronic and semiconductor technologies. The spin centers in HDP can be easily introduced and controlled through solution-based methods40,49. Additionally, the well-established solution-based growth methods offer flexibility in designing the spin and electronic states of the spin qubits. This is because the coordination partners and local symmetry around the spin qubits can be modified through coordination chemistry. While these techniques have been successfully implemented in optically addressable molecular spin qubits50, they are relatively less explored for solid-state spin qubits.

In this work, we report spin coherent and magneto-optical properties of prototype transition metal(TM) Cr3+ and Fe3+ spin centers (concentration < 1018 cm-3) doped in Cs2(Na,Ag)InCl6 host. We adopt the concept of using TM impurities as solid-state spin qubits, an approach that has been readily adopted and successfully demonstrated in classic host materials such as SiC15–20. These open-shell TM centers possess a “pure” spin of S ≥ 1/2 in the ground state, which allows their spin sublevel manifolds to be accessed and utilized as the quantum bit states. Furthermore, TM impurities are typically optically active (or “bright”) and exhibit sharp, atomic-like transitions. These properties are critical, as they permit the optical initialization and readout of the qubit’s spin state by leveraging spin-optical selection rules. With a typical concentration of < 1019, individual TM ions are single spin centers that are electronically and magnetically isolated due to their strong localization of electron wavefunctions and spin densities. Such isolation would in principle permit to address single spins by employing a sufficiently local probe, though significant technical challenges will arise at a high concentration of spin centers when a nano-scale probe becomes necessary.

Results
Herein, we shall show that, despite of the nuclear-spin-rich host, the studied TM spin ensemble exhibits a rather long spin coherence time T2 = 29.5 µs at 4 K (6.4 µs at 20 K). This is comparable to the other benchmark solid-state spin qubits embedded in the nuclear-spin-rich host, where creating the spin qubits requires a more complicated fabrication technique25,26. We also observe long-lived phase undulation due to strong coupling between the electron spin at the TM centers with the first and second nearest neighbor nuclear spins. We attribute this finding to a localization of TM spin wavefunction, which enables a well-defined interaction with the local nuclear spin environment that could potentially facilitate nuclear spin registration protocols. For the Cr3+ spin centers, we identify the ground and excited electronic states via magneto-optical experiments and identify their optical-transition selection rule necessary for optical addressing of the TM-spin qubit in HDPs hosts. Though limited to ensemble studies, our results shed light on a promising route towards a new library of solid-state spin qubits, thanks to the large chemical and structural diversity of halide perovskites, offering new opportunities for applications in quantum information technology potentially at a much lower cost than their alternatives.

Here we choose chromium (Cr) and iron (Fe) as TM ions in the Cs2(Na:Ag)InCl6 as our prototype spin qubits. First, unlike many halide perovskites that are prone to rapid degradation, Cs2(Na:Ag)InCl6 HDPs are wide bandgap semiconductors with exceptional stability45. Second, the Cr and Fe ions are thermodynamically stable in the 3+ charge state, substituting (InCl6)−3 by (CrCl6)−3 or (FeCl6)−3 within the cubic crystal, see Fig. 1A, B. The TM spins in this context have Oh point group symmetry with an orbitally non-degenerated A1g ground state. This configuration significantly quenches effects of the spin-orbit interaction to the first order, beneficial for maintaining a long spin-lattice relaxation time (T1) and spin coherence time (T2). Additionally, the HDP crystal has the non-magnetic B(+1) ions, Na and Ag, that work as a spacer, reducing self-aggregation of magnetic ions that are harmful for the spin qubits application. The (Na:Ag) hosts are chosen for monitoring the effect of the third nearest neighbor nuclear spins to the TM spin centers, which also provides a probe of the degree of wavefunction localization of the TM ions.

In the Oh point group symmetry, the absence of a zero-field splitting results in a single electron-paramagnetic-resonance (EPR) line observed for both Cr³⁺ (S = 3/2, g = 1.981) and Fe³⁺ (S = 5/2, g = 2.01) TM spin centers, as shown in Fig. 1C. The nuclear spin interactions are governed by the nearest-neighbor chlorine-35,37 (35,37Cl, I = 3/2) and the next-nearest-neighbor cesium-133 (¹³³Cs, I = 7/2) with six and eight lattice coordination, respectively, see Fig. 1B. The hyperfine interaction strength with these coupled nuclear spins typically falls in the range of 0.1-10 MHz. While this interaction cannot be spectrally resolved, it can significantly impact electron spin dynamics monitored in transient electron spin-echo experiments51,52.

We will now demonstrate that, despite that the Cr³⁺ and Fe³⁺ ions are embedded in a nuclear-spin-rich environment, a long T2 can be achieved thanks to a combined effect of electron spin localization and the deterministic nature of the relevant hyperfine interaction.

To measure T2, standard Hahn-echo experiments (Fig. 2A) were conducted on four representative samples: Cr and Fe ions embedded in Cs2NaInCl6 and Cs2AgInCl6 hosts, which we simply denote below as Cr[Na], Cr[Ag], Fe[Na], and Fe[Ag], respectively. All samples were powdered, and the experiments were performed using an EPR spectrometer to address ensembles of the TM spin centers. Additional details of the samples can be found in the Material and Methods section.

A representative B-field sweep echo decay of the Cr[Na] samples, showcasing the spin decoherence properties of the Cr³⁺ ions, is plotted in Fig. 2B. Two striking features are observed, namely, a long T2 and a strong undulation of electron spin-echo signals. The electron spin-echo signal exhibits a non-monotonic exponential decay with fast and slow exponential components, characterized by T2fast = 8.1 ± 0.6 µs and T2slow = 29.5 ± 1.3 µs, as fitted and shown in Fig. S1A–D. The presence of two decay components is typically observed in Hahn-echo experiments, with the fast component being associated with spin diffusion due to a possible dipolar interaction between spin centers whereas the slow component reflects the intrinsic T2 for an isolated TM center. The Hahn-echo T2 exceeding 20 µs, achieved even without implementing dynamic decoupling protocols, is comparable to that reported for spin centers in other potential candidates in solids with nuclear-spin-rich environment (see Table 1), where the spin qubit fabrication requires the more complicated fabrication techniques.

Figure 2C compares the coherent properties of Cr3+ and Fe3+, their timescale is rather similar (29.5 µs and 21.2 µs, respectively). Given that they are both orbitally non-degenerate states, we attribute the long spin coherence time to the strong wavefunction localization effects that limit the hyperfine interaction to the nuclear spins within a few nearest neighbor nuclei. This assignment is supported by a comparison of the spin coherent time of the same TM ions in two different hosts: Cs₂NaInCl₆ and Cs₂AgInCl₆ shown in the Fig. S2. By ensuring similar concentrations of the same TM ions in the two different host materials, we observe similar electron spin decoherence rates. Given that the third (3rd) nearest neighbor nuclear spins in the lattice position differ between the two hosts, Na, I = 3/2 vs Ag, I = ½ with markedly different nuclear magnetic moments, a similar coherent time implies that the dominant hyperfine interactions between the electron spin of the Cr3+ or Fe3+ ion and the surrounding nuclear spins must be limited within the second-nearest neighbor nuclei.

Upon heating up to 20 K, we obtain T2 of 6.39 ± 0.22 μs for Cr3+ and 1.97 ± 0.04 μs for Fe3+ (see Fig. 2C and Fig. S1C, D). The decoherent rate displays a constant value over the temperature range of 3-10 K, which confirm that the intrinsic spin coherence time is governed by the hyperfine interaction. Above 10-50 K the rate starts to increase exponentially. This can be modelled with a localized spin-phonon interaction53,54.

The observed strong undulation in spin echo amplitudes arises from a coherent rotation induced by the electron-nuclear (e-N) spin interaction. Here a long phase memory suggests that the phase rotation is rather homogenous, indicating that the e-N interaction is deterministic, i.e. the dominant hyperfine interaction with the surrounding nuclear spins in fixed and few lattice positions. A random placement of nuclear spins would otherwise result in a distribution of hyperfine interactions, leading to significant variations in the nuclear rotation frequency and, consequently, rapid dephasing of nuclear spin coherent rotation.

The HYSCORE experiment exploits the pulse sequences shown in Fig. 3A. The HYSCORE spectrum of Cr[Na] powder samples (Fig. 3B) yields a two-dimensional e-N coherence spectrograph obtained from the e-N spin rotation correlated between two adjacent Zeeman sublevels. Its frequency domain spectrum in Fig. 3C, therefore, exclusively correlates nuclear frequencies within the same nuclear origin, effectively resolving the complex nuclear frequency spectrum. To attribute each nuclear contribution, we simulated the HYSCORE spectrum taking into account both electron-nuclear hyperfine and nuclear spin quadrupole interactions as shown in Fig. 3D. The simulation results confirm the contribution of both 133Cs and 35,37Cl in the e-N coherence rotation in Fig. 3B, which we differentiate using different color codes - red for 133Cs and blue for 35,37Cl.

Our simulation analysis aligns well with the underlying physics of hyperfine interactions. For the next-nearest-neighbor 133Cs nuclear spin, there’s a weak interaction from the Fermi-contact term. The nuclear spin frequencies center around ν(¹³³Cs) ≈ 1.958 MHz and split into at least four frequencies due to the interaction between the electron spin quantum numbers (ms = ±1/2, ±3/2) and the hyperfine tensor A = (0.94, 0.94, 1.42) ± 0.3 MHz, with the principal axis along <111>, identifying that the 133Cs is indeed at the their 2nd nearest neighbor lattice site. No further splitting of nuclear frequencies is observed because 133Cs has an intrinsically weak quadrupole moment. The HYSCORE powder simulation for these given parameters is shown in red in Fig. 3D. 35,37Cl nuclear frequencies are influenced by both the hyperfine interaction with Cr³⁺ ions and the quadrupole interaction within the I = 3/2 nuclear spin. The best fit, using the spin Hamiltonian (blue color in Fig. 3D), yields A(³⁵Cl) = (0.42, 0.42, −7.12) ± 0.3 MHz, the quadrupole tensor Q(³⁵Cl) = (−2.01, −2.01, 4.02) ± 0.3 MHz, A(³⁷Cl) = (0.35, 0.35, −5.93) ± 0.3 MHz, and Q(³⁷Cl) = (−1.68, −1.57, 3.35) ± 0.3 MHz, with principal axis along <001> for both A- and Q-tensors, i.e. the octahedral lattice site of 35,37Cl. Our determined spin parameters of Cr3+ in Cs2NaInCl6 are also in line with previous reports from CW-ENDOR experiments55. The hyperfine parameters reflect the d-orbital wavefunction of the TM ions, while presence of the quadrupole coupling is expected due to the gradient of the electron wavefunction across the Cl site, given the Cr-Cl-Na imbalance in electronegativity. Our powder fitting reproduces the dominant feature, which is a crossing point around ν1=ν2=3.2 MHz, with a large spread of matching nuclear spin rotation frequencies due to the anisotropy of A and the presence of Q. We stress that the long e-N coherent rotation, as seen in the coherent ripple of HYSCORE pattern, is important in designing EPR pulsed sequence of e-N spin transfer for nuclear spin register protocol28. Such information is lacking in the previous CW-ENDOR study56, where the resonant nuclear spin transition is a semi-classic spin-flip process.

HYSCORE experiments and fitting evaluations were performed on all samples (Fig. S3A–F and Table S1). The results reveal a generally weaker hyperfine interaction between the Fe3+ electron spin and the 133Cs nuclear spin, causing all Cs-related nuclear spin frequencies to collapse to the fundamental Larmor frequency of 133Cs (1.9458 MHz). Additionally, the quadrupolar coupling of both Fe3+ and Cr3+ at the 35,37Cl sites is generally reduced in the Cs2AgInCl6 host as compared with the Cs2NaInCl6 host, as expected from a smaller electric field gradient across the Cr-Cl-Ag and Fe-Cl-Ag bonds in the former. With the given hyperfine parameters, we can evaluate the degree of electron localization using the Fermi hyperfine contact model, shown in the Supporting Information on Fig. S4. We found that the electron wavefunction is effectively diminishing below 0.02% at the 133Cs sites.

To address a target nuclear spin deterministically, we choose 133Cs instead of 35,37Cl nuclear spin, as a random presence of two different isotopes of Cl on the nearest-neighbor sites will lead to a non-deterministic variation between the TM ions. As a spin registering protocol is based on coherent rotation between e-N spin governed by a non-secular term in spin Hamiltonian. In single crystalline samples, this coherent mixing will happen only when the principal axis of electron/nuclear Zeeman terms are off the principal axis of the hyperfine and quadrupole interaction. We provide additional explanation of these in Supporting Information.

Therefore, we can minimize the spin mixing contribution of e-N spin interaction with 35,37Cl by applying magnetic field along the [001] direction in the single crystalline HDP samples, as shown in Fig. 2A, which are the principal axis of A- and Q-tensor of 35,37Cl. This way the echo-undulation by the Cl-nuclear spin is minimized, leaving the e-N spin rotation exclusive to the Cs suitable for target nuclear spin registration.

In Fig. S5A–D, we present three-pulsed stimulated echo spectra of Cr[Na] in high-quality single crystals from the one-dimension HYSCORE experiment and a nuclear frequency analysis with the external B-field aligned close to the [001], [111], and [011] crystallographic axes. The observed nuclear frequencies at each orientation are well described by the spin-Hamiltonian parameters of 133Cs and 35,37Cl obtained in the HYSCORE experiments. Notably, at B//<001>, the contribution from 35,37Cl in e-N spin mixing is suppressed as expected. Therefore, only the 133Cs nuclei become the dominant source to e-N coherent rotations.

The nuclear frequency spectra with the target 133Cs nuclear spin in the Cr[Na] sample are plotted in Fig. 4. Here we identify six dominant nuclear frequencies of 133Cs coupled with the electron spin S=3/2, namely ϑms, where ms = ±1/2, ±3/2 is the electron spin quantum number and x denote the type of electron-nuclear spin rotation, which involves: (1) I: a fundamental nuclear Larmor frequency of 133Cs (1.9458 MHz); (2) SQ: the allowed single quantum transition (Δms = ±1, ΔmI = ±1); and (3) NDQ: the forbidden nuclear double quantum transition respectively (Δms = ±1, ΔmI = ±2). We further discuss this nuclear rotation frequencies based on the energy diagram shown in Fig. S6.

Notably, each frequency further splits into four peaks, as shown in the insets. This splitting arises from the four magnetically inequivalent sites among eight 133Cs sites in the second nearest neighbor shell of the Cr3+ ion when the magnetic field (B) is slightly misaligned from the [001] direction, making them distinguishable in the frequency spectrum (see simulations in Fig. S5A–D). The ability to identify magnetically inequivalent sites of 133Cs suggests that each Cs pair can work as a distributable node of target nuclear spin registration.

The studied TM spin centers can be coherently driven in a nutation experiment, as shown in Fig. 5A, B. We plot the Rabi rotation, obtained from the powder sample Cr[Na], and Rabi oscillation frequency (ωRabi) as a function of the driving microwave frequency (ω1). We here clarify that the driving power (ω1 = 0–20 MHz) is different from the microwave resonance frequency (ωr = 9.77 GHz). The resonance frequency is the fixed energy required for a spin flip, whereas the driving power is the oscillation rate of the spin state driven by the microwave pulse. Under hard-pulse conditions ω1 > 12 MHz, we observe the expected Rabi oscillations of the TM spin qubits at ωRabi = ω1. However, as the driving frequency decreases, ωRabi exhibits a multi-peak behavior. This can be understood by considering the interplay between electron-electron self-interaction and electron-nuclear spin interactions, which introduce additional driving forces for Rabi rotations57–59. This interplay is captured by the rotating-frame spin Hamiltonian:

ℏωRabi = (g+Δg)μB S + D(S2z + 1/3(S(S+1))) + SAI + P(3I2z + I(I+1)) (1)

Here, Δg describes the inhomogeneous broadening of the TM electron spin, accounting for the fast-dephasing decay T2* and ωRabi broadening at large ω1. P is associated with Q tensor via Q = (-P/3, -P/3, 2P/3). When ω1 is comparable with the zero-field splitting D, the multi-peak ωRabi is dominated by electron-electron spin interactions. The resulting Rabi rotations are originated from S=3/259. The strength of the D tensor can be estimated from the vanishing of the multipeak and the emergence of the fundamental frequency ωRabi = ω1. This yields D ~ 12 ± 2 MHz, suggesting that the Cr³⁺ ions are slightly displaced from the ideal cubic crystallographic site. At low driving power (1.5 MHz), the e-N spin interaction also contributes to ωRabi, resulting in characteristic nuclear frequency peaks with the frequency in the range of 1-4 MHz60.

Finally, we demonstrate nuclear spin sensing experiments for the studied e-N spin clusters in the HDPs. This is achieved using standard nuclear sensing methods based on Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences61,62. Previous work has shown that the modified CPMG pulse sequences, such as Pol-CPMG28, can be used to register and read out nuclear spin states. This technique relies on the nuclear magnetic resonance (NMR) effect in CPMG dynamic decoupling28,61.

The standard CPMG experiment, with the sequence πx/2 - τ - (πy - 2τ)N - πy - τ - echo, where N is the number of πy refocusing pulse, is shown is Fig. 5C. A common misconception is that the CPMG sequence is solely a “dynamic nuclear spin decoupling protocol” that refocuses random nuclear spin baths. However, we stress that this is not the case for specific nuclear spins at fixed positions near the spin centers. In our experiment in single crystals (B//[001]), the fixed 133Cs spins on the second-nearest-neighbor sites cannot be effectively decoupled. Instead, when the inter-pulse delay, τ, matches a multiple of the inverse of the nuclear Larmor frequency

τ = n / ϑN

the refocusing pulses become ineffective. This condition, known as an NMR dip (as shown in the Fig. 5C–E), actually reinforces the electron-nuclear spin interaction rather than decoupling it. These resonance dips are the key for nuclear spin sensing experiments63.

In our CPMG results (single crystal of Cr [Na], B//[001]), we exclusively observe dips from the 133Cs nuclear spins. As shown in the Fig. 5E, we demonstrate that we can sense the 133Cs nuclear spin rotation at three of the four electron spin sublevels by performing a Fourier transformation of the CPMG coherence contrast. This is shown in the results and spin structure below. Furthermore, the long T2 time at 20 K enables CPMG nuclear spin sensing experiments at this temperature, as shown in Fig. 5D-E. This experiment thus identifies the key elements for target nuclear spin addressing within our system.

To justify that our identification of CPMG resonant dips is a beneficial first step toward target nuclear spin registers, we refer to the work of Pol-CPMG by J. E. Lang et al.11. The Pol-CPMG adjusts the πy pulses to πy + θ, one can induce polarization transfer between the electron and nuclear spin manifolds. This transfer is reflected in both the splitting and the polarization of the CPMG resonance dips, demonstrating a path toward controlled spin registers. We attempted to achieve nuclear spin registering using this polarization-transfer CPMG (Pol-CPMG) technique. However, as also noted in the Lang et al. work, this is a dynamic process that requires a large number of pulse sequence repetitions. Due to experimental limitations, our sequence was limited to N = 6, which was insufficient to demonstrate effective polarization transfer between the electron and nuclear spins. Nonetheless, our results represent a fundamental first step. By successfully demonstrating nuclear spin sensing—the ability to identify and detect specific nuclear spins—we have accomplished a necessary prerequisite for achieving nuclear spin registers.

Here we show that the studied TM spin centers can be optically accessed – a property required for a solid-state spin qubit that is also a prerequisite for potential spin-photon interface. This is achieved via the intra-d-shell optical transitions of the TM ions. We demonstrate this with the Cr3+ ions in a single crystal of Cs2NaInCl6, of which the electronic structure is depicted in 6A. Besides the S=3/2 ground state 4A1g studied in our EPR studies, the 4T2g excited state splits into four sublevels due to the spin-orbit interaction. The lowest of these excited states is the Γ7,e (ms = ±1/2) doublet. The optical transition from this lowest excited state to the ground state, i.e. Γ7,e → Γ8,g, gives rise to a sharp zero-phonon photoluminescence (PL) line at 841.4 nm at a cryogenic temperature as displayed in the right panel of Fig. 6B. The optical transitions involving higher-lying excited states are revealed in our PL excitation experiments, see the left panel of Fig. 6B.

From the predicted selection rules, see Fig. 6A, the Γ7,e → Γ8,g optical transition should be highly spin selective, providing a mean for optical access to the concerned spin states that could enable their initialization and readout. This is confirmed from our polarization-resolved magneto-optical studies of the Γ7,e (ms = ±1/2) → Γ8,g (ms = ±1/2, ±3/2) PL line, as shown in Fig. 6B. In an applied magnetic field, the 841.4 nm PL line clearly splits into several components due to the Zeeman effect. In the Faraday geometry at 2.2 K, only transitions from the lower Zeeman sublevel of the lowest excited state, Γ7,e (ms = −1/2) to the two (ms = −3/2, +1/2) of the four sublevels of the ground states Γ8,g are observed with σ+ (red) and σ− (blue) polarization, respectively. The π component associated with the Γ7,e (ms = −1/2) → Γ8,g (ms = −1/2) transition is only weekly observed between these two main peaks, which is expected in the Faraday geometry. Further experimental proof for these spin-selective transition rules from angle- and temperature-dependent magneto-PL up to B = 16 Tesla is provided in the Supporting Information in Fig. S7A–E. A detailed analysis of these magneto-optical results also yields the g-values of both ground and excited states, namely, g(Γ8,g) = 1.981 that is the same as that determined from the EPR study and g(Γ7,e) = 2.85.

The successful determination of these optical selection rules allows us to propose a protocol for the optical initialization and readout of the Cr³⁺ spin centers, as shown in Fig. 6C, D. The high-fidelity optical initialization into the Γ8,g (ms = −3/2) state can be achieved through an optical pumping cycle shown in Fig. 6C. While the Γ8,g (ms = ±1/2) states can be directly depleted by the π-polarized resonant excitation light to the Γ7,e (ms = ±1/2) excited states, the depletion of the Γ8,g (ms = +3/2) requires a combination of the resonant π-polarized laser light associated with Γ8,g (ms = +1/2) and a resonant microwave field mw1 that links Γ8,g (ms = +3/2) with Γ8,g (ms = +1/2). The subsequent recombination processes will partially convert the spin centers originately sitting in these three states to Γ8,g (ms = −3/2) that cannot be removed by the optical pumping. Continuous optical pumping will eventually drive nearly all spin centers to the desired |−3/2〉 state, after a sufficient number of the pumping and recombination circles. We note that this optical initialization process is similar to that successfully applied to the S=3/2 spin qubits based on the negatively charged silicon vacancy in SiC64, but with an added advantage in our case where the Γ8,g (ms = +1/2) and Γ8,g (ms = −1/2) states can be separately and individually addressed as the energies of their π-polarized optical transitions are different due to the difference in the g-values between the ground and excited states, i.e. g(Γ8,g) = 1.981 vs. g(Γ7,e) = 2.85.

After initialization, spin manipulation is performed with microwave pulse trains using a combination of frequencies mw1, mw2, and mw3. This allows us to fully control the entire four-state system (ms = ±1/2, ±3/2), utilizing the high electron spin to realize a qudit, which is a multi-level quantum bit.

A key requirement for this protocol to work is that the microwave frequencies (mw1, mw2, mw3) that manipulate spin between all adjacent spin sublevels must be distinguishable. This mean that a Zero-Field Splitting (ZFS) of the S=3/2 ground state is required. We show that it’s possible to create this splitting through local-symmetry engineering. By alloying the Cs₂NaInCl₆ host with 10% Ag⁺ on the Na⁺ site, some of the Cr³⁺ centers experience a local tetragonal distortion. This distortion breaks the cubic symmetry and lifts the degeneracy of the ms = ±1/2 and ms = ±3/2 sublevels, creating the exact ZFS we need (see Fig. S8). This result highlights the chemical tunability of the double perovskite lattice, offering a powerful way to engineer the spin Hamiltonian for advanced quantum applications. The vast chemical and structural diversity of halide double perovskites make them an ideal sandbox for designing and engineering the next generation of spin qubits and qudits.

We note that, for the Fe3+ spin qubits centers, we unfortunately cannot so far observe the emission related to the Fe3+ intra-molecular transition. We attribute this to some external effect such as formation of competing non-radiative recombination channels due to the Fe incorporation into the HDP hosts, rather than a limit inherent to the Fe3+ ions. Future research efforts are required to uncover the concerned optical transition by improving material quality.

The successful identification of the optical selection rules confirms the viability of this system for the initialization and readout of spin information. While scaling to the single-spin and single-photon manipulation required for quantum communication is beyond the scope of this work, our results establish a clear pathway. Achieving this goal will necessitate further advances in materials synthesis to control the concentration and positioning of TM ions, a research direction we are actively pursuing. Nonetheless, this ensemble-level demonstration of robust spin properties and a spin-optical selection rule validates this halide double perovskite material library for quantum applications and will undoubtedly drive further research in the field.

In summary, we explore the potential of halide perovskites as a platform for solid-state spin qubits. By embedding Cr and Fe ions within the double perovskite Cs2(Na:Ag)InCl6, we have demonstrated not only a long spin coherence time despite the nuclear-spin-rich host but also the deterministic nuclear spin addressing. This is enabled by the localized nature of the electron spins and the well-defined hyperfine interactions along specific crystallographic directions. We have also shown that the spin states of the TM ions in HDPs are optically addressable for their initialization and readout. Such optical access could potentially be explored for spin-photon interfacing that is attractive for creating long-range spin qubit network and for quantum communication. These findings suggest that halide perovskites, with their chemical and structural diversity, represent a highly promising platform for developing scalable spin qubits. This, combined with superior optical properties and inexpensive material synthesis of the diverse halide perovskite family, could open up many attractive and promising opportunities of applications in optoelectronics, spintronics, spin-photonics and quantum information technology.

Methods
Sample preparation
Single crystals of Cr- and Fe-doped Cs2NaInCl6 and Cs2AgInCl6 alloys were synthesized using a hydrothermal method. The starting materials of CsCl, AgCl, NaCl, CrCl3, FeCl3, and InCl3 were dissolved in HCl using a stochastic formula ratio and then transferred to a Teflon-lined autoclave. The introduction of TM ions was done by replacing the InCl3 precursor with the small molar ratio between CrCl3 (FeCl3) : InCl3 in the range of 1−5%. A sealed autoclave was heated to 180 °C for 12 h and then cooled down to room temperature at 1 °C per hour.

The single crystals were ground to a powder form for spin-echo, Rabi rotation and HYSCORE experiments. The as-grown single crystals were used for 3P-stimulated echo, CPMG, PLE and magneto-PL experiments, where custom-made sample holders were used to align a specific crystallographic direction along the direction of an applied magnetic field.

Due to the different incorporation rates of isolated Cr³⁺ and Fe³⁺ ions into the two distinct host crystals (Cs₂NaInCl₆ and Cs₂AgInCl₆), electron paramagnetic resonance (EPR) spectroscopy was employed to monitor and precisely control their concentrations through spin-counting experiments. The Cr³⁺ concentration in the Cr[Na] and Cr[Ag] samples was found to be ~0.3-1×10²¹ cm⁻³, while the Fe³⁺ concentration in the Fe[Na] and Fe[Ag] samples was higher, at ~0.5-1×10²² cm⁻³, see Fig. S9. This observed difference is attributed to the more efficient incorporation of Fe³⁺ into the Cs₂NaInCl₆ and Cs₂AgInCl₆ host lattices.

Electron Paramagnetic Resonance Spectroscopy (EPR)
Pulsed X-band EPR measurements were performed using a Bruker ELEXSYS ESP 380 FT-EPR spectrometer equipped with a Split Ring Resonator (ER 4118X-MS5) and a closed-cycle helium gas siphon cooling (Stinger) cryostat. Large single crystals (3–12 mm lateral size) were ground into a fine powder, transferred to a 4 mm diameter quartz tube, evacuated to ~10-2 mbar, and flame-sealed. All measurements were performed at 4 K using the powdered samples unless otherwise stated in the main text.

Detailed descriptions of the pulsed EPR techniques used in this work, including Hahn-echo, HYSCORE, three-pulse stimulated echo, echo-detected electron spin nutation, and CPMG for nuclear spin sensing can be found in the Supporting Information, in Figs. S10–14.

Photoluminescence Excitation (PLE) Spectroscopy
PLE measurements were performed at 4 K using a cold-finger cryostat. A wavelength-tunable Ti:Sapphire laser served as the excitation source. The resulting fluorescence was monitored at the phonon sideband of the Cr³⁺ emission and analyzed with a spectrometer coupled to a silicon CCD array.

Magneto-Photoluminescence (Magneto-PL) Spectroscopy
Magneto-PL experiments were conducted at the High Field Magnet Laboratory (HFML) in Nijmegen, the Netherlands. Samples were placed in a cryogenic bath for measurements at 2.2 K (or at 15 K using a heater). Custom holders were used to align the crystal’s [001] and [111] axes parallel to the magnetic field. A 532-nm laser provided the excitation, and the emitted photoluminescence was analyzed by a spectrometer and a silicon CCD array. To measure the emission’s circular polarization, a quarter-wave plate (λ/4) and a linear polarizer were placed together at the entrance of the spectrometer. The detection was in a Faraday geometry.

Simulation
All the simulations were performed using the EasySpin65 toolbox developed for MATLAB, setting the spin Hamiltonian as follows:

H = g μB B·S + gN μN B·I + S·D·S + S·A·I + I·Q·I

All the fitting parameters used in the simulation are described in the main text, and the Table S1.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this work the authors perform ESR spectroscopy on ensembles of Chromium (Cr3+) and Iron (Fe3+) ions in a nuclear spin rich perovskite (Cs2(Na:Ag)InCl6). They utilize several standard pulse sequences to characterize the coherence times of the Cr3+ and Fe3+ electron spins and various Hamiltonian parameters (such as the hyperfine tensor, A, and quadrupole tensor, Q). My three main criticisms of this work are the following:\n1. I do not believe that the platform will be viable or competitive for the applications listed by the authors.\n2. Several of the authors’ Hamiltonian characterization results were already demonstrated in a previous work [Akhmin, S. M. et al., “Ligand ENDOR of Cr3+ and Yb3+ ions in Cs2NaInCl6”, Phys.: Condens. Matter (1990)].\n3. The paper, in multiple places, greatly exaggerates the impact of the authors’ results.\nFor these reasons I cannot recommend publication of this work in Nature Communications. I provide more detail on each of these criticisms below.\nRegarding Applications of The Platform:\nThe authors claim that the applications of this platform are for “scalable quantum networks and complex quantum logic gates”. However, in my opinion neither of these are well justified:\n1. The authors haven’t demonstrated addressability of individual electron spins (i.e. qubits), only ensembles.\n2. They haven’t demonstrated (or even discussed) a coherent optical interface required for networking.\n3. The authors haven’t demonstrated the ability to initialize (or optically pump) the spins.\n4. If used exclusively as a quantum processor (i.e. no coherent optical interface) this platform would be extremely limited with only a handful of qubits, therefore it could never compete with systems such as neutral atom arrays.\nRegarding Novelty of This work:\nThere are two main results comprising this work. The first: measurement of spin echo coherence times (in the section “Electron spin echo and electron-nuclear spin entanglement”) is novel. The second: characterizing Hamiltonian parameters (in the section “Deterministic hyperfine interaction”), however, is not. Several of these parameters were already measured using similar techniques in [Akhmin, S. M. et al., “Ligand ENDOR of Cr3+ and Yb3+ ions in Cs2NaInCl6”, Phys.: Condens. Matter (1990)], which the authors do cite. One key distinction between these papers is that the present work considers multiple materials: both Cr3+ and Fe3+ in Cs2NaInCl6 and Cs2AgInCl6 were investigated. However, the coherence properties for these four material systems are extremely similar and the authors haven’t explained why different platforms should be considered or compared their advantages/disadvantages. The final two sections of the paper mostly validate the findings of the first two sections and, in my opinion, do not contribute significantly to the novelty of the work.\nRegarding Exaggerated Claims:\nThere are multiple places where the authors exaggerate the impact of their work\n• On line 137 the authors state that “This coherence time remains exceptional even when compared to various benchmark solid-state and molecular spin qubits (see Table 1).”. The observed coherence times are relatively average for solid state spins: as evidenced by the authors’ own table.\n• The claim of a “deterministic nuclear spin environment” doesn’t seem to be entirely justified given that two different Cl isotopes are present (35Cl and 37Cl with different quadrupole and hyperfine parameters). Since these isotopes both have non-negligible abundance (76% for 35Cl and 24% for 37Cl) the environment surrounding the Fe3+ and Cr3+ ions will vary.\n• On lines 166 and 167 the authors state that “This robustness against temperature fluctuations allows for high-fidelity quantum operations and the construction of robust quantum registers, mitigating operational errors.” The level of temperature fluctuation in commercial cryostats isn’t a dominant source of error in any solid-state platform. Furthermore, there are many factors that are considerably more important (e.g. initialization fidelity, pulse errors, inhomogeneity) but aren’t addressed in this manuscript.\n• On lines 169-172 the authors state that “This observation indicates that the hyperfine interaction surrounding the TM spin qubits acts favourably as a beneficial resource for manipulating electron-nuclear spin states, rather than being a major source of electron spin decoherence, as is often assumed.”. This statement is too strong, the results show that interactions with nuclear spins can be avoided to minimize decoherence, however, they don’t demonstrate coherent manipulation of electron-nuclear states as implied.\n• The title of the final section is “Coherent control and preparation of nuclear spin registration”: I assume the authors mean ‘registers’, however, they haven’t demonstrated coherent control of these registers, and they also do not demonstrate the preparation of the nuclear spins.\n• The authors claim on lines 331/332 that “Nevertheless, this CPMG nuclear register preparation indicates an efficient spin transfer between the electron and the nuclei.” I disagree with this statement, I believe that CPMG leads to a non-spin-preserving interaction with the nuclear spin bath. Furthermore, the authors haven’t demonstrated any spin transfer.\n• Also, on lines 334/335 the authors state that “They show great potential to serve as local e-N cluster nodes for complex quantum logic gates.” This is too bold of a claim: there is no experimental data or analysis regarding an electron-nuclear logic gate.\nI also have several scientific questions:\n• On line 98 the authors discuss the symmetry and energy level structure of the spins. Have any other transitions/energy levels been measured? Given the discussion of long spin-lattice relaxation times it would be good to know the energy splitting to the nearest orbital level. Also, what are the optical transition frequencies for these spins? It would be helpful to include an energy level diagram in the main text.\n• What is the predicted spin linewidth (or T2*) based on the inhomogeneity of the magnetic field generated by the nuclear spin bath?\n• Is the ratio of coherence times measured for Fe3+ and Cr3+ consistent with their g-factor ratio?\n• Could the authors provide some more detail or a reference regarding the inhomogeneous pulse excitation on line 135. I would have expected the fast timescale to be similar to T2*, however I am guessing that it is considerably slower.\n• On line 298 the authors say they can “prepare a Bell-like state”, what do the authors mean by this? Can they please provide a derivation/explanation of this in the supplementary information.\n• On line 290 the authors refer to the ‘electron-electron spin interactions’, this makes it sound like these are interactions between separate Cr3+ spins. A more appropriate term would be ‘self interaction of the electron spin’. Related to this, can the authors provide a more accurate estimate based on simulations/data rather than just ~10MHz?\n• On line 233 the authors say, “as expected for a smaller electric field gradient”, could the authors provide some more detail regarding why they expect the gradient to be smaller?\n• Please provide error bars for all fitted/extracted Hamiltonian parameters.\n• On line 199 the authors say that “there's a minor contribution from the Fermi-contact term”, please clarify what is the dominant contribution?\n• Are the hyperfine parameters extracted using HYSCORE consistent with the two-pulse echo measurements presented in Fig 2?\n• On lines 219/220, the authors state that “the quadrupole parameters agree with the gradient of the electron wave function across the Cl site”. What is the electric field gradient value and what quadrupole parameters would this correspond to? Without this, there is nothing for these experimentally determined values to agree with.\nI also have a few suggestions/comments related to the readability of the manuscript:\n• The authors need to provide a bit of important detail regarding the material, synthesis and experimental procedure in the main text (e.g. state that the samples are powdered, that ensembles of spins are addressed, and that experiments are performed in an EPR spectrometer), then reference the Methods section for full detail.\n• Subfigure 2B doesn’t provide much information/insight for the reader, all the important information is in Fig 2C, I would suggest moving 2B to the extended data.\n• On lines 53/54: there is no 131 isotope of Yb.\n• It would be helpful if the authors could plot the double-exponential fits shown in Extended Data Fig. 1 on the data in Figure 1C. This would also substantiate the claims made on lines 151/152 regarding similarity of coherence times.\n• The plots in extended data figure 4 are quite small and hard to follow. I would suggest that the authors combine all simulation results into a single predicted curve which can be compared to the data. This will considerably simplify the plot and make it easier to spot discrepancies between simulation and data.\n• It is difficult to follow the explanation of the HYSCORE measurement on lines 191-193, please provide a clearer/more detailed explanation.\n• On lines 279-281 the authors should be careful to differentiate between rabi frequencies (0-20MHz) and microwave driving frequencies (9.77GHz). The current phrasing confuses these two physical quantities.", "reviewer_2": "This manuscript explores electron-nuclear spin correlations in transition metal-doped perovskites. Single crystals of Cs₂(Na:Ag)InCl₆ were synthesized, with InCl₆ partially substituted by CrCl₃ or FeCl₃, to study the interaction between electron and nuclear spins. The T2 relaxation times in this qubit system was compared to previously reported systems. The study is well-executed, and the conclusions are supported by the measurements. The manuscript is worthy of publication; however, some revisions are necessary.\n1. The paper emphasizes that \"long-lived electron spin coherence with T2 = 29.5 microseconds is a remarkable benchmark for a spin qubit in a nuclear-spin-rich host.\" However, Table 1 includes several previous studies (at least five) that report similar or even longer T2 times, suggesting that this value is not significantly different from others in the literature. Therefore, either additional justification is needed to support this claim, or the statement should be rephrased to align more consistently with existing research.\n2. The optical properties of the perovskite material are mentioned. Is this relevant to the study? If so, please provide justification.\n3. What is the role of Indium? Would single crystals of Cs2Ag (Fe/Cr) Cl6, Cs2Na (Cr/Fe) Cl6 degrade more quickly if used instead?\n4. Figure 1A presents a schematic of the TM spin qubits embedded in spin-rich-host cubic halide double perovskites. However, the authors have not provided any supporting evidence for this for example from X-ray diffraction measurements or referenced any studies that include actual structural data for these crystals.\n5. The authors have mentioned the T2 times for Cr and Fe in [Na] host. What are the corresponding numbers for Cr and Fe in [Ag] host?\n6. Supplementary material-supplemental, note 3; CPMG nuclear spin sensing experiment: The pulse lengths are not mentioned; Figure 5, “E “ is missing.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_4": "The authors present a study of the electronic and nuclear spin coherence for transition metal centres in halide perovskite materials. The work presents coherent control of the electronic spins and claims entanglement of electron and nuclear spins. Spin coherence (T2) of 29 us at 4K is reported, and the spin coherence timescale is attributed to the localisation of electronic density on the transition metal centre. The paper presents extensive characterisation, via various EPR techniques, of the hyperfine interaction between the central electronic spin and the Cr3+ and Fe3+ nuclei.\nMy questions:\n1. The work is motivated by the search for coupled electronic-nuclear spin systems for quantum information processing technologies. The authors compare the perovskite system with other ‘disordered e-N’ systems such as defects in diamond and SiC and self-assembled quantum dots (lines 44-45). However, these systems are very different to the one presented – they are singly optically-addressable electronic spins systems. Which means they are have potential for applications that require spin-photon entanglement (ie. nodes for optical networking). It seems to me that the perovskite system is not comparable in this regard – it consists of a large ensemble of electronic and nuclear spins, and there is no mention of optical addressability. Thus, the authors should explain why it is relevant to compare to these other systems, whether it shows potential for application to similar technologies, and if not, what application they foresee for this system. The answers to this question may\n2. The authors claim to show entanglement of the electronic spin of the transition metal and the neighbouring nuclear spins. This discussion is focussed on the data shown in Fig 2(C). Here, the decoherence traces measured during the Hahn echo measurements is presented. The decoherence profiles show strong modulations due to the coupling to nuclear spins, as seen for other systems. The authors should explain why this constitutes demonstration of e-N entanglement. Entanglement should be confirmed via measurement of the density matrix of the e-N state (see Bourassa et al., Nature Materials, 2020).\n3. With regards to the T2 timescale, I agree that 29 μs is surprising for this system considering the nuclear spin composition. However, I am not sure if the factors that limit this coherence are well understood by the authors.\ni. Why does T2 show a relatively strong temperature dependence? A drop from 29 μs to 6 μs, from 4 to 20 K, is actually rather strong. I wouldn’t expect decoherence that is dominated by nuclear spins to be strongly temperature dependent.\nii. Are the modulation features in Fig. 2C consistent with a relatively weak hyperfine interaction (0.1-10 MHz)?\niii. Why are the modulations much stronger for the Cr complex than for the Fe complex?\niv. Could there be another factor that helps to decouple the electronic and nuclear spins in this system- possibly symmetry related?\n4. Related to my question above, the authors state in the text that the strong localisation of the electronic density on the transition metal is responsible for the long spin coherence timescale. This feels speculative and I don’t see any evidence for this conclusion. Can the authors support this claim with modelling?\nAdditional comments:\n1. The paper would benefit from a diagram of the electronic structure of the spin system.\n2. Line 99 should say degenerate, not degenerated."}, "author_response": "Response: We thank the reviewer for his/her careful reading of our manuscript and for providing critical feedback. These comments have been extremely helpful in improving the quality and clarity of our work. We have revised the manuscript to address each of the points raised.\nConcerning the competitiveness of our proposed spin centers in nuclear-spin-rich halide double perovskites for spintronics applications, we understand that, in terms of spin coherence properties, they cannot compete with color centers in few-nuclear-spin or isotope-purified nuclear-spin-free diamond and SiC, nor is it meant to be. The competitive edge of spin centers in halide double perovskites rather center at their low-cost material synthesis as compared with the vastly more costly diamond and SiC, the availability of a large library of monovalent and trivalent cations (spin centers) without introducing excess charge noise, relative ease in incorporating spin centers in crystals without involving damaging processes with high-energy particles required to generate vacancies in diamond and SiC, superior and widely tunable optical properties covering a wide spectral range from UV to infrared, etc. Therefore, any potential spin components utilizing halide double perovskites are not meant for the highest performance but they could rather find application areas where cost concern becomes paramount such as mass-production dispersible consumer electronics. At this early stage of spintronic research on this newly emerging materials system, the aim of our present work is to assess (1) whether the essential properties of spin centers in halide double perovskites are still within the acceptable range for quantum applications; (2) whether the nuclear-spin rich environment can be controlled and even harnessed for further applications. Indeed, we find in our study that spin coherence of the studied spin centers is reasonably long and robust despite of abundant surrounding nuclear spins. We demonstrate that the electron wavefunction is strongly localized to within the first two nearest neighbors such that the detrimental effect of a randomly fluctuating nuclear spin bath, commonly known as a major source of spin decoherence and spin relaxation, can be largely minimized. We further show that under optimal experimental configurations the influence of the nearest-neighbor Cl nuclear spins can be suppressed, whereas the next-nearest neighbor Cs nuclear spins can be selectively controlled for potential electron-nuclear spin transfer. We also provide experimental evidence for the optical signature of the spin centers and spin-dependent selection rules in their optical transitions, paving the way for optical initialization and readout in a similar fashion as the well-known color centers in diamond and SiC. Our study sheds light on design rules to identify promising candidates of spin centers and their perovskite host crystals, which could potentially provide a viable and competitive platform for low-cost quantum spintronics.\nWe thank the reviewer for pointing out the earlier work by Akhmin et al. (1990). We want to clarify that our work, while it does report some spin-Hamiltonian parameters, has a different primary purpose. Our main goal is to identify the specific nuclear spin species that are crucial for coherent electron-nuclear spin rotation. This analysis provides an essential foundation for future applications that rely on the transfer of spin information between electron and nuclear spins. We stress that our results are novel and could not have been obtained from the previous report. The Akhmin et al. paper focuses on cw ligand ENDOR to study the local environment of the ions, whereas our time-resolved EPR study provides detailed dynamic information on the coherent interactions between the electron spin and specific nuclear spins, which is a fundamentally different and new contribution.\nWe thank the reviewer for cautioning us on the claims made in the initial manuscript. We have carefully revised the manuscript to ensure our conclusions are well-justified and to avoid any overstatement of our results.\nWe have adopted a new title ‘Spin Qubits Candidate using Transition-Metal Centers in Halide Double Perovskites’ to better reflect the main scope of our revised manuscript. Please also find our point-by-point response to the reviewer’s comments below.\nRegarding Applications of The Platform:\nThe authors claim that the applications of this platform are for “scalable quantum networks and complex quantum logic gates”. However, in my opinion neither of these are well justified:\n1. The authors haven’t demonstrated addressability of individual electron spins (i.e. qubits), only ensembles.\nOur response: We appreciate the reviewer's point regarding the necessity of demonstrating individual spin addressability for scalable spin qubit applications. We agree that this is a critical requirement for a fully realized quantum processor. As mentioned above, at this early stage of spintronic research on this newly emerging class of halide double perovskites, the primary goal of our current work is to perform some groundwork to assess the feasibility of transition-metal ions as potential spin qubits in halide perovskites by evaluating key physical properties such as the factors controlling spin coherence time. It is far too early to speculate any specific applications. We apologize for having overstated in the original manuscript, which has been removed in our revised manuscript.\nThough limited to ensembles, we believe that the general knowledge of the spin physics gained in our study should still be valid for single centers. For example, the spin coherence time measured from the ensembles sets the low bound for a single center. Such knowledge will be highly valuable for future studies of a corresponding single-center system once it has been identified to be a promising system from ensemble studies and once it becomes available.\nWe also believe that scaling down to a single spin system is feasible with our material, given recent advancements in fabrication technology for halide double perovskites.\n2. They haven’t demonstrated (or even discussed) a coherent optical interface required for networking.\nResponse: A coherent optical interface required for networking is beyond the scope of the present work. Our work is meant to present the first fundamental study of spin dynamics that may have implications for possible future applications as spin qubits. We are now able to demonstrate the optical addressability of the studied spin centers through our new photoluminescence (PL), PL excitation and magneto-optical investigations, which could potentially provide a mean for spin-photon interface. These new results are described in the new section of “Optical addressability of the TM spins in HDPs” in the revised manuscript. We apologize for the overstatement in the original manuscript. We have now removed all overstatements from the manuscript.\n3. The authors haven’t demonstrated the ability to initialize (or optically pump) the spins.\nResponse: We agree that the optical spin pumping is a critical component for an optically-addressable spin qubit. We have now added a new section ‘Optical addressability of the TM spins in HDPs’ in the revised manuscript, where we present our new experimental magneto-optical results that have firmly identified the optical transition between the ground and excited states of the Cr3+ spin center and their spin selection rules. Based on these findings we have proposed a possible protocol for optical initialization and readout. Unfortunately, its direct experimental demonstration is currently not possible in our laboratory because resonant optical pumping of the Cr³⁺ centers require an excitation bandwidth (i.e. laser spectral linewidth) in the few gigahertz range that we do not have access to at present. The large inhomogeneous broadening of the PL linewidth of the spin ensembles also poses additional difficulty for performing resonant excitation (which shall be mitigated by a single spin study). Based on the electronic structure of the Cr³⁺ spin center, however, there is no fundamental limit to the proposed protocol and it is entirely feasible.\n4. If used exclusively as a quantum processor (i.e. no coherent optical interface) this platform would be extremely limited with only a handful of qubits, therefore it could never compete with systems such as neutral atom arrays.\nResponse: The solubility of TM ions in halide double perovskites is very high, typically up to 0.1-1:1 ratio with respect to the concentration of the TM precursor used in the solution process crystal growth. Therefore, the TM spin centers have much higher concentrations than that of the best-known color centers in diamond and SiC (such as NV center in diamond and silicon vacancy in SiC).\nRegarding Novelty of This work:\nThere are two main results comprising this work. The first: measurement of spin echo coherence times (in the section “Electron spin echo and electron-nuclear spin entanglement”) is novel. The second: characterizing Hamiltonian parameters (in the section “Deterministic hyperfine interaction”), however, is not. Several of these parameters were already measured using similar techniques in [Akhmin, S. M. et al., “Ligand ENDOR of Cr3+ and Yb3+ ions in Cs NaInCl ”, Phys.: Condens. Matter (1990)], which the authors do cite. One key distinction between these papers is that the present work considers multiple materials: both Cr3+ and Fe3+ in Cs NaInCl and Cs AgInCl were investigated. However, the coherence properties for these four material systems are extremely similar and the authors haven’t explained why different platforms should be considered or compared their advantages/disadvantages. The final two sections of the paper mostly validate the findings of the first two sections and, in my opinion, do not contribute significantly to the novelty of the work.\nResponse: We appreciate the reviewer's concerns regarding the novelty of the reported spin-Hamiltonian parameters. We respectfully disagree with the reviewer on this point. While our analysis does yield these parameters; we wish to emphasize that the core contribution of our work lies in the dynamic coherent information that cannot be obtained through continuous-wave techniques like ligand ENDOR (as the reviewer mentions in the comment). Our study provides crucial insights into the electron-nuclear spin coherence, which could have significant implications for quantum applications.\nWe apology for not being clear in each subsection in the hyperfine interaction study, which may misguide the purpose for each specific subsections towards the determination of spin parameters only. The purpose of each section is as follows.\n1. In the section on \"Electron spin-echo and electron-nuclear spin entanglement, in the original manuscript\" we demonstrate a long-lived coherence modulation profile arising from the non-secular term of the hyperfine interaction. While analyzing this profile provides the spin-Hamiltonian parameters, the primary significance of this observation is the demonstration of coherent information transfer between the electron and nuclear spins. The long-lived nature of this undulation indicates that it originates from a well-defined, rather than a random nuclear spin environment. This is a critical distinction, as a random distribution of nuclear spin frequencies would lead to rapid dephasing and the loss of this modulation pattern. This finding establishes the feasibility of using our spin center for nuclear spin registration. The standard protocol for nuclear spin registration relies on pulsed ESR techniques that enable coherent electron-nuclear spin rotation. Our results show that our spin centers are capable of coherently interacting with both the nearest-neighbor (35,37Cl) and the next-nearest-neighbor (133Cs) nuclear spins, making them suitable for this application.\n2. In the section on \"Deterministic hyperfine interaction (renamed to ‘target coupling of electron-nuclear spins’ in the revised manuscript for a better clarity) \", we further elaborate on the strategy for addressing specific nuclear spins at different lattice sites. In this section, the 3P-stimulated echo experiment has been performed on single-crystal samples, with the aim to suppress the contribution of the nearest-neighbor 35,37Cl nuclear spins, and target addressing 133Cs at the second nearest neighbor sites. This approach is based on controlling the degree of electron-nuclear spin mixing, which causes the undulation of the pulsed-EPR signals. The degree of this mixing is highly dependent on the orientation of the external magnetic field (B) relative to the principal axes of the hyperfine tensor. The modulation depth of the electron spin coherence, which is a measure of the degree of nuclear spin mixing, can be estimated using the following formula:\n𝐴2\n𝑛𝑜𝑛𝑠𝑒𝑐𝑢𝑙𝑎𝑟\n𝑘 = \n𝜔2 +𝐴2\n𝐼 𝑠𝑒𝑐𝑢𝑙𝑎𝑟\nWhere, 𝜔 is the nuclear spin frequency. The secular and nonsecular terms of the\n𝐼\nhyperfine tensor (in the LAB frame) are extracted from the hyperfine tensor in principal axis form 𝑨 = (𝐴 ,𝐴 ,𝐴 ). In our case, let the external field point to the z-\n𝒑𝒓𝒊𝒏𝒄𝒊𝒑𝒂𝒍 𝑥 𝑦 𝑧\naxis, so that 𝐴 = 𝐴 = 𝐴 and 𝐴 = 𝐴 .\n𝑥 𝑦 ⊥ 𝑧 ∥\nBy rotating the 𝑨 to the LAB frame using the Euler angle rotation matrix, we\n𝒑𝒓𝒊𝒏𝒄𝒊𝒑𝒂𝒍\nwill get\n𝐴 = 𝐴 sin2𝜃 +𝐴 cos2𝜃\n𝑠𝑒𝑐𝑢𝑙𝑎𝑟 ⊥ ∥\n𝐴 = (𝐴 −𝐴 )𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃\n𝑛𝑜𝑛𝑠𝑒𝑐𝑢𝑙𝑎𝑟 ∥ ⊥\nwhere θ is the angle between the external magnetic field vector and the principal z-axis of the hyperfine tensor. When the magnetic field is aligned along the principal axis (e.g., the <001> direction), the non-secular term approaches zero, effectively \"turning off\" the spin mixing for that specific nuclear species.\nWe leverage this effect to demonstrate targeted nuclear spin addressing. For example, by aligning the magnetic field along the <001> direction, the 35,37Cl nuclear spins' contribution to spin mixing is suppressed (𝐴 = 0), allowing the 133Cs spins to\n𝑛𝑜𝑛𝑠𝑒𝑐𝑢𝑙𝑎𝑟\nbe addressed as the sole target of nuclear spin registration, as the principle axis of the hyperfine tensor of 133Cs is along [111] direction. This interaction is deterministic because the number of available sites is reduced to the four magnetically equivalent sites of the eight Cs atoms. Furthermore, slightly rotating the magnetic field off the <001> direction allows us to distinguish between these four different magnetically equivalent Cs sites (Cs1, Cs2, Cs3, Cs4, as shown in the inset of Figure 4), which is the key for addressing individual nuclear spins (or a pair of nuclear spin in our case).\n3. In the CPMG section, we show that our electron-nuclear spin studies have identified a critical condition for achieving a strong interaction via pulsed ESR. This is crucial for applications like spin sensing and nuclear spin registers.\nA common misconception is that the CPMG sequence is solely a \"dynamic nuclear spin decoupling protocol\" that refocuses random nuclear spin baths. However, we stress that this is not the case for specific, fixed nuclear spins. In our system, the fixed 133Cs spins at the second-nearest-neighbor sites cannot be effectively decoupled. Instead, when the inter-pulse delay, τ, matches a multiple of the inverse of the nuclear Larmor frequency\n𝝉 = 𝒏/𝝑\n𝑵\nthe refocusing pulses become ineffective. This condition, known as an NMR dip (as shown in the figure below), actually reinforces the electron-nuclear spin interaction rather than decoupling it.\nThese resonance dips are the key for nuclear spin sensing experiments. This principle was used in the work of T. Staudacher et al. (Science 339,561-563(2013)), using a derivative of the CPMG sequence (XY8).\nIn our CPMG results (single crystal, B//<001>), we exclusively observe dips from the 133Cs nuclear spins. The hyperfine spin mixing from the 35Cl and 37Cl nuclear spins is effectively suppressed when the magnetic field is aligned with the <001> direction, which is the principal axis of the chlorine hyperfine tensor. For the Cr3+ centers, the system is described by the interaction between the electron spin S = 3/2 and the 133Cs nuclear spin I = 7/2.\nAs shown in the figure below, we demonstrate that we can sense the 133Cs nuclear spin rotation at three of the four electron spin sublevels by performing a Fourier transformation of the CPMG coherent contrast. This is shown in the results and spin structure below. This experiment thus identifies the key elements for target nuclear spin addressing within our system.\nTo justify that our identification of the CPMG resonant dips is a beneficial first step toward target nuclear spin registers, we refer the reviewer to the work of J.E. Lang et al., \"Quantum Bath Control with Nuclear Spin State Selectivity via Pulse-Adjusted Dynamical Decoupling\" (Phys. Rev. Lett. 123, 210401, 2019).\nTheir study showed that by deliberately adjusting the π pulses to π +θ, one can induce\nY Y\npolarization transfer between the electron and nuclear spin manifolds. This transfer is reflected in both the splitting and the polarization of the CPMG resonance dips, demonstrating a path toward controlled spin registers.\nWe have now stated in the revised manuscript that we attempted to achieve nuclear spin registering using this polarization-transfer CPMG (Pol-CPMG) technique. However, as also noted in the Lang et al. work, this is a dynamic process that requires a large number of pulse sequence repetitions. Due to experimental limitations, our sequence was limited to N=6, which was insufficient to demonstrate effective polarization transfer between the electron and nuclear spins.\nAll the above discussion has been now added throughout the revised manuscript and in the revised Supporting Information. We apologize to the reviewer again for not being clear on these points in the original manuscript.\nBefore our study, there is no report on spin coherence of TM ions in halide double perovskites. That is why we have investigated both Cr3+ and Fe3+ in Cs NaInCl and Cs AgInCl with the\n2 6 2 6\nhope that any difference or indifference between them will shed light on the physics underpinning spin interactions and spin dynamics, which will provide a guideline for identifying the most promising spin centers and their hosts for future applications. Only through such a comparative study have we reached the conclusion that the electron spin density of the studied TM ions is highly localized within the next-nearest shell, which is important to predict the relative contribution from nearby nuclear spins in spin coherence as well as effects of defect or impurity residing in different sublattices.\nRegarding Exaggerated Claims:\nThere are multiple places where the authors exaggerate the impact of their work\n• On line 137 the authors state that “This coherence time remains exceptional even when compared to various benchmark solid-state and molecular spin qubits (see Table 1).”. The observed coherence times are relatively average for solid state spins: as evidenced by the authors’ own table.\nResponse: We agree with the reviewer that our 𝑇 time is comparable to other spin qubit\n2\ncandidates embedded in nuclear-spin-rich hosts. We have revised the manuscript to present a more balanced discussion, avoiding claims of \"remarkable properties\" and instead focusing on the inherent value of our platform.\n• The claim of a “deterministic nuclear spin environment” doesn’t seem to be entirely justified given that two different Cl isotopes are present (35Cl and 37Cl with different quadrupole and hyperfine parameters). Since these isotopes both have non-negligible abundance (76% for 35Cl and 24% for 37Cl) the environment surrounding the Fe3+ and Cr3+ ions will vary.\nResponse: It’s true that in terms of Cl the nuclear spin environment is random. However, its influence in electron-nuclear spin mixing can effectively be turned off by aligning the magnetic field along the <001> directions as discussed above when we can target addressing 133Cs nuclear spins that doesn’t have other natural abundance isotopes. We have now modified the related statements to accurately reflect this.\n• On lines 166 and 167 the authors state that “This robustness against temperature fluctuations allows for high-fidelity quantum operations and the construction of robust quantum registers, mitigating operational errors.” The level of temperature fluctuation in commercial cryostats isn’t a dominant source of error in any solid-state platform. Furthermore, there are many factors that are considerably more important (e.g. initialization fidelity, pulse errors, inhomogeneity) but aren’t addressed in this manuscript.\nResponse: We thank the reviewer for pointing out this and we have now revised this section of the manuscript accordingly.\n• On lines 169-172 the authors state that “This observation indicates that the hyperfine interaction surrounding the TM spin qubits acts favourably as a beneficial resource for manipulating electron-nuclear spin states, rather than being a major source of electron spin decoherence, as is often assumed.”. This statement is too strong, the results show that interactions with nuclear spins can be avoided to minimize decoherence, however, they don’t demonstrate coherent manipulation of electron-nuclear states as implied.\nResponse: The presence of strong CPMG dips in our results already demonstrates that we can effectively reinforce the electron-nuclear spin interaction. This ability is a crucial resource for both sensing and manipulating nuclear spins.\n• The title of the final section is “Coherent control and preparation of nuclear spin registration”: I assume the authors mean ‘registers’, however, they haven’t demonstrated coherent control of these registers, and they also do not demonstrate the preparation of the nuclear spins.\nResponse: We agree that the title of our final section, \"Coherent control and preparation of nuclear spin registration,\" is an overstatement of the work presented. The reviewer is correct that we do not directly demonstrate the coherent control of nuclear spin registers or the explicit preparation of the nuclear spins. Our intent was to describe the foundational work that prepares the system for these future steps.\nWe have revised the title of this section to be more accurate and reflective of our actual findings. The new title is \" Coherent control and addressing nuclear spin through electron-nuclear spin phase rotation\". This revised title more accurately describes our work, which focuses on characterizing the coherent properties of the electron-nuclear spin system and establishing the necessary conditions for future nuclear spin registration. We have also edited the text within this section to ensure the language is consistent with the new title and to avoid claims beyond the scope of our experimental results.\n• The authors claim on lines 331/332 that “Nevertheless, this CPMG nuclear register preparation indicates an efficient spin transfer between the electron and the nuclei.” I disagree with this statement, I believe that CPMG leads to a non-spin-preserving interaction with the nuclear spin bath. Furthermore, the authors haven’t demonstrated any spin transfer.\nResponse: We agree that our original statement was imprecise, as the CPMG sequence itself does not demonstrate direct spin transfer between the electron and nuclear spins. We have revised the manuscript to remove this inaccurate statement.\nThe significance of the CPMG sequence in our work is its role as a critical first step toward nuclear spin registration. While it does not perform spin transfer, it is a fundamental tool used to probe the coherent interaction between the electron spin and its surrounding nuclear spins. The long-lived oscillations observed in the CPMG decay provide concrete evidence that a specific subset of nuclear spins is coherently coupled to the electron spin, a prerequisite for subsequent quantum operations.\nThis approach is foundational to demonstrated nuclear spin sensing experiments and serves as the basis for derivative pulse sequences like polarization-controlled CPMG (pol-CPMG), which can be used for nuclear spin registration. Although instrumental limitations currently prevent us from performing a pol-CPMG experiment, our use of the standard CPMG sequence lays the essential groundwork for future experiments that will demonstrate deterministic spin transfer and the preparation of a nuclear register.\n• Also, on lines 334/335 the authors state that “They show great potential to serve as local e-N cluster nodes for complex quantum logic gates.” This is too bold of a claim: there is no experimental data or analysis regarding an electron-nuclear logic gate.\nResponse: We agree with the reviewer and have removed this statement from the revised manuscript.\nI also have several scientific questions:\n• On line 98 the authors discuss the symmetry and energy level structure of the spins. Have any other transitions/energy levels been measured? Given the discussion of long spin-lattice relaxation times it would be good to know the energy splitting to the nearest orbital level. Also, what are the optical transition frequencies for these spins? It would be helpful to include an energy level diagram in the main text.\nResponse: We thank the reviewer for this excellent suggestion. We have now performed photoluminescence (PL), PL excitation and magneto-optical experiments to determine both the optical transition frequencies and the spin-selective optical selection rules, which can pave the way for optical access of the concerned spin states. The corresponding results are summarized in the section “Optical addressability of the TM spins in HDPs” whereas the selection rules of the optical transitions and the transition/energy levels diagram are now plotted in Figure 6A of the revised manuscript.\n• What is the predicted spin linewidth (or T *) based on the inhomogeneity of the magnetic field generated by the nuclear spin bath?\n2\nabove 120 ns. It is worth noting that the decay in Rabi oscillations can also be attributed to spin inhomogeneity due to the dispersion of Rabi frequencies associated with inhomogeneities in the applied microwave field across the sample. This leads to a randomization of the Rabi oscillation phase. As such, the 𝑇 * alone unfortunately cannot be used to exclusively describe\n2\nthe effect of inhomogeneous broadening of the nuclear spin bath.\n• Is the ratio of coherence times measured for Fe3+ and Cr3+ consistent with their g-factor ratio?\nResponse: Yes, it is consistent. A stronger deviation of g-value for Fe3+ (Δ𝑔 = +0.095) compared with that for Cr3+ (Δ𝑔 = -0.005) indicates a stronger contribution of the orbital degree of freedom in Fe3+, which leads to the worse coherent properties found for Fe3+.\n• Could the authors provide some more detail or a reference regarding the inhomogeneous pulse excitation on line 135. I would have expected the fast timescale to be similar to T *, however\nResponse: We thank the reviewer for bringing attention to the physical interpretation of the fast decay timescale. As mentioned above, our 𝑇 * is in the range of 120 ns, which is much\n2\nfaster than the timescale of the fast components.\nThe multi-decay components can be attributed to the inhomogeneous distribution of TM ions. We suggest that the fast component originates from the area where the TM ions are close together where the effect of dipole interaction between TM ions causes the spin decoherence. In this sense, the long component reflects ‘isolated’ TM ion and serves as the intrinsic 𝑇\n2\nrelaxation time. Our suggestion is based on supplemental measurements performed on the samples with varying concentrations of TM ions, where the increased TM incorporation led to the fast 𝑇 . Close to single exponential decay was observed at high TM concentration. We have\n2\nadded this discussion on page 6, in the revised manuscript, in red.\n’\nFigure R1: the T of the Cr[Na] samples with increasing Cr concentration by increased percentage of CrCl molar\n2 3\nratio.\n• On line 298 the authors say they can “prepare a Bell-like state”, what do the authors mean by this? Can they please provide a derivation/explanation of this in the supplementary information.\nResponse: We thank the reviewer for this insightful comment. We agree that our statement on line 298, claiming the ability to \"prepare a Bell-like state,\" was inaccurate and misleading. True Bell state preparation requires precise phase manipulation of the spin states, which is not demonstrated in our current work. The statement has been removed from the revised manuscript.\nThe origin of this imprecise claim was our observation that by tuning the driving frequency, we can manipulate the electron spin state (S=3/2) to behave like an effective S=1/2 system or create a superposition of m = ±1/2, ±3/2 states. However, as the reviewer correctly points out, true Bell state preparation requires precise phase manipulation of the spin states, which is not demonstrated in our current work.\n• On line 290 the authors refer to the ‘electron-electron spin interactions’, this makes it sound like these are interactions between separate Cr3+ spins. A more appropriate term would be ‘self interaction of the electron spin’. Related to this, can the authors provide a more accurate estimate based on simulations/data rather than just ~10MHz?\nResponse: We have rephase electron-electron spin interactions to self-interaction.\nThe estimated self-interaction parameter of ~10MHz was deduced based on the Rabi frequency experimental results of Figure 5A. This was deduced when the Rotation becomes a spin ½-like, serving a condition 𝜔 = 𝐷, where 𝜔 is the driving frequency (proportional to a microwave\n𝐷 𝐷\npower with a driving oscillation amplitude 𝐵 ). However, our microwave attenuators limit the\n1\nnumber of data points around the transition of ½-like Rabi oscillation. At best, we can provide the estimated error, which is about ± 2MHz.\nWe have now revised the manuscript with the self-interaction parameter of ~12± 2 MHz.\n• On line 233 the authors say, “as expected for a smaller electric field gradient”, could the authors provide some more detail regarding why they expect the gradient to be smaller?\nResponse: This sentence compares the atomic value of electron negativity of the atoms in the vicinity of Cl, as listed in the table below (in Pauling scale).\nElements Cr Fe Cl Na Ag\nElectronegativity 1.66 1.83 3.16 0.93 1.93\nWe used this table as a guideline to compare the electric field gradient across a linear chain of Cr-Cl-Na, Cr-Cl-Ag, Fe-Cl-Na and Fe-Cl-Ag. The general trend is that the Na-containing chains will experience a stronger gradient due to the larger differences of electronegativity along the linear chain.\n• Please provide error bars for all fitted/extracted Hamiltonian parameters.\nResponse: we have provided the estimated error bars in the reported spin-Hamiltonian parameters in Extended Table 1 of the revised manuscript.\n• On line 199 the authors say that “there's a minor contribution from the Fermi-contact term”, please clarify what is the dominant contribution?\nResponse: We thank the reviewer for the question. We now understand that our phrasing in the sentence led to a misconception. The dominant contribution is from the Fermi-contact term, but this is weak due to the electron wave function localisation at the transition metal centres. We have rephased line 199 as ‘a weak hyperfine interaction that is dominated by the Fermi contact’. We also added the following discussion in the supporting information, to clarify the role of Fermi contact and to estimate a degree of wave function localisation of electron spin:\nThe Fermi contact interaction is a part of hyperfine interaction of electrons in approximately spherical-like orbital and surrounded nuclear environment. It can be expressed by:\n2\n𝐴 = 𝜇 𝑔 𝛽 𝑔 𝛽 |Ψ|2\n𝑖𝑠𝑜 3 0 𝑒 𝑒 𝑁 𝑁\nThis can also demonstrate the electron spin localization, where the percentage of electron density, |Ψ|2, distributing at the neighbor atoms is estimated by calculating the ratio between the electron density distribution caused by hyperfine interaction and free electron localized at each nuclear site:\n2\n|Ψ | |𝐴 |\nℎ𝑦𝑝𝑒𝑟𝑓𝑖𝑛𝑒 𝑖𝑠𝑜,𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡\n=\n2 |𝐴 |\n|Ψ | 𝑖𝑠𝑜,𝑓𝑟𝑒𝑒\n𝑓𝑟𝑒𝑒\nIn our case, we consider 3 nuclear sites representing the nearest neighbors (35Cl and 37Cl) and the next-nearest neighbors (133Cs) of the incorporated transition metal. By inserting the hyperfine coupling strength, we can obtain the percentage of electron localization at each nuclear site (See Figure R2 and Table R1).\nFigure R2: The example illustration of electron density localization at each nuclear site (35,37Cl, 133Cs) around the incorporated Cr3+.\nTable R1:\n𝐴\n𝑖𝑠𝑜,𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡\n𝐴 +𝐴 +𝐴 𝐴 % electron\nNuclear site = 𝑥 𝑦 𝑧 𝑖𝑠𝑜,𝑓𝑟𝑒𝑒\n3 (MHz) localization\n(MHz)\nCr[Na]\n133Cs 1.1 9.2x103 0.012%\n35Cl -2.1 80 2.6%\n37Cl -1.6 66 2.5%\nNa - - -\nCr[Ag]\n133Cs 1.5 9.2x103 0.017%\n35Cl -2.3 80 2.9%\n37Cl -1.8 66 2.7%\nAg - - -\nFe[Na]\n133Cs 0.1 9.2x103 0.001%\n35Cl -2.2 80 2.8%\n37Cl -1.7 66 2.6%\nNa - - -\nFe[Ag]\n133Cs 0.1 9.2x103 0.001%\n35Cl -2.4 80 3.0%\n37Cl -1.8 66 2.8%\nAg - - -\nWe have added this discussion in the revised Supporting information.\n• Are the hyperfine parameters extracted using HYSCORE consistent with the two-pulse echo measurements presented in Fig 2?\nResponse: Precisely simulating the nuclear spin frequencies from spin echo is notoriously difficult. That's because interactions with multiple nuclei in the crystal lattice create complex combination frequencies—sums and differences of the fundamental nuclear frequencies. Accurately simulating these would require an impractically large basis set.\n• On lines 219/220, the authors state that “the quadrupole parameters agree with the gradient of the electron wave function across the Cl site”. What is the electric field gradient value and what quadrupole parameters would this correspond to? Without this, there is nothing for these experimentally determined values to agree with.\nResponse: We agree that this sentence is merely speculative and have removed it from the discussion.\nI also have a few suggestions/comments related to the readability of the manuscript:\n• The authors need to provide a bit of important detail regarding the material, synthesis and experimental procedure in the main text (e.g. state that the samples are powdered, that ensembles of spins are addressed, and that experiments are performed in an EPR spectrometer), then reference the Methods section for full detail.\nResponse: We have revised the manuscript according to the reviewer’s suggestion. The form of samples for each specific type of experiment has been clearly stated throughout the revised manuscript. In the Method Section we also stated: ‘The single crystals were ground to a powder form for spin-echo, Rabi rotation and HYSCORE experiments. The as-grown single crystals were used for 3P-stimulated echo, CPMG, PLE and magneto-PL experiments, where the custom-made sample holders were used to align the direction of magnetic field along the specific crystallographic direction.’\n• Subfigure 2B doesn’t provide much information/insight for the reader, all the important information is in Fig 2C, I would suggest moving 2B to the extended data.\nResponse: We appreciate the reviewer’s suggestion. However, we would like to keep Figure 2B as it contains the information that only one spin species can be detected. In this sense, there are no other harmful defect centers being introduced by our growth methods, and therefore, the solution growth of HDP can serve as controlled growth of spin centers.\n• On lines 53/54: there is no 131 isotope of Yb.\nResponse: We have corrected this accordingly\n• It would be helpful if the authors could plot the double-exponential fits shown in Extended Data Fig. 1 on the data in Figure 1C. This would also substantiate the claims made on lines 151/152 regarding similarity of coherence times.\nResponse: We have provided the double-exponential plot is Figure 2C\n• The plots in extended data figure 4 are quite small and hard to follow. I would suggest that the authors combine all simulation results into a single predicted curve which can be compared to the data. This will considerably simplify the plot and make it easier to spot discrepancies between simulation and data.\nResponse: We have provided the new plots following the reviewer’s suggestion.\n• It is difficult to follow the explanation of the HYSCORE measurement on lines 191-193, please provide a clearer/more detailed explanation.\nResponse: We have now added a more detailed explanation of the HYSCORE experiment in the main text on page 9 (marked in red color).\n• On lines 279-281 the authors should be careful to differentiate between rabi frequencies (0-20MHz) and microwave driving frequencies (9.77GHz). The current phrasing confuses these two physical quantities.\nResponse: We have mentioned the difference between the microwave resonant frequency 𝜔\n𝑅\n= 9.77GHz and the Rabi driving frequency 𝜔 = 0-20MHz, by rephasing to a driving power.\n𝑅𝑎𝑏𝑖\nPlease see in the main text which is marked in red color (page 14).\nReviewer #2 (Remarks to the Author):\nThis manuscript explores electron-nuclear spin correlations in transition metal-doped perovskites. Single crystals of Cs₂(Na:Ag)InCl₆ were synthesized, with InCl₆ partially substituted by CrCl₃ or FeCl₃, to study the interaction between electron and nuclear spins. The T relaxation times in this qubit system was compared to previously reported systems. The\n2\nstudy is well-executed, and the conclusions are supported by the measurements. The\nmanuscript is worthy of publication; however, some revisions are necessary.\nResponse: We thank the reviewer for recognizing the importance of our electron-nuclear spin correlation studies of the transition-metal spin centers in halide double perovskites. We have addressed the reviewer’s suggestion and have revised our manuscript according. Please find our detailed response below.\n1. The paper emphasizes that \"long-lived electron spin coherence with T = 29.5 microseconds\n2\nis a remarkable benchmark for a spin qubit in a nuclear-spin-rich host.\" However, Table 1 includes several previous studies (at least five) that report similar or even longer T times,\n2\nsuggesting that this value is not significantly different from others in the literature. Therefore, either additional justification is needed to support this claim, or the statement should be rephrased to align more consistently with existing research.\nResponse 1: We agree that our T time is comparable with the other spin-qubit candidates\n2\nembedded in a nuclear-spin-rich host. We have toned down the discussion over the manuscript, without claiming the remarkable properties. We now more focus on searching for spin qubits in a material system of HDPs that are low cost, with the added benefits in the flexibility to control the spin and electronic properties of the spin centers, given a large structural and chemical library of the halide perovskites in general. We added this discussion on page 3-4 of the main text (marked in red).\n2. The optical properties of the perovskite material are mentioned. Is this relevant to the study? If so, please provide justification.\nResponse 2: Optical properties associated with the atomic-like transitions of transition-metal (TM) ions are crucial for e.g. optical initialization and optical readout of spin qubits, as commonly employed in well-known solid-state spin qubits such as NV center in diamond and silicon vacancy in SiC. Therefore, we have now included a new section dedicated to the optical properties of Cr3+ photoluminescence in Cs NaInCl . Within this section, titled 'Optical\n2 6\nAddressability of the Transition-metal Spin Qubits', we report new results identifying an atomic-like, spin-selective luminescence transition directly linked to our spin center. Based on them, a possible protocol is suggested for optical initialization and readout of the Cr3+ spin qubit.\n3. What is the role of Indium? Would single crystals of Cs Ag (Fe/Cr) Cl , Cs Na (Cr/Fe)Cl\n2 6 2 6\ndegrade more quickly if used instead?\nResponse 3: The In3+ ions, being diamagnetic (having no free electrons), serve as non-magnetic spacers for the transition-metal ions. This arrangement effectively reduces detrimental spin-spin interactions between TM ions, which are known to harm spin coherence properties.\nIndeed, increasing the concentration of Fe or Cr (e.g., by moving towards Cs Ag(Fe/Cr)Cl or\n2 6\nCs Na(Cr/Fe)Cl alloys) significantly shortens the T coherence time. This effect is\n2 6 2\ndemonstrated in Figure R2.\n’\nFigure R2: the T of the Cr[Na] samples with increasing Cr concentration by increased percentage of CrCl molar\n2 3\nratio.\n4. Figure 1A presents a schematic of the TM spin qubits embedded in spin-rich-host cubic halide double perovskites. However, the authors have not provided any supporting evidence for this for example from X-ray diffraction measurements or referenced any studies that include actual structural data for these crystals.\nResponse 4: We have now provided an appropriate citation to a previous X-ray diffraction study of the host Cs NaInCl and Cs AgInCl , that confirms the cubic crystal structure\n2 6 2 6\n(https://www.nature.com/articles/s41586-018-0691-0). The crystal structure file can be found\nat:\nhttps://next-gen.materialsproject.org/materials/mp-989571 (Cs NaInCl )\n2 6\nhttps://next-gen.materialsproject.org/materials/mp-1096926 (Cs AgInCl )\n2 6\n5. The authors have mentioned the T times for Cr and Fe in [Na] host. What are the\n2\ncorresponding numbers for Cr and Fe in [Ag] host?\nResponse 6: The 𝑇 for Cr[Ag] and Fe[Ag] is 5 and 4 𝜇𝑠, which is the same as compared with\n2\nsimilar order of magnitude shown in Extended figure 2 in the main manuscript. We also update the figure and provide the fitting in the new version of Extended figure 2B.\n6. Supplementary material-supplemental, note 3; CPMG nuclear spin sensing experiment: The pulse lengths are not mentioned; Figure 5, “E “ is missing.\nResponse 6: We have corrected these issues in the revised paper.\nReviewer #3 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This\nis part of the Nature Communications initiative to facilitate training in peer review and to\nprovide appropriate recognition for Early Career Researchers who co-review manuscripts.\nWe thank Reviewer 3 for the valuable comments.\nReviewer #4 (Remarks to the Author):\nThe authors present a study of the electronic and nuclear spin coherence for transition metal\ncentres in halide perovskite materials. The work presents coherent control of the electronic\nspins and claims entanglement of electron and nuclear spins. Spin coherence (T2) of 29 us at\n4K is reported, and the spin coherence timescale is attributed to the localisation of electronic\ndensity on the transition metal centre. The paper presents extensive characterisation, via\nvarious EPR techniques, of the hyperfine interaction between the central electronic spin and\nthe Cr3+ and Fe3+ nuclei.\nResponse: We thank the reviewer for recognizing our extensive effort in coherence studies of electron nuclear spin system in halide double perovskites. Please find our detailed response to the reviewer’s comments below.\nMy questions:\n1. The work is motivated by the search for coupled electronic-nuclear spin systems for quantum\ninformation processing technologies. The authors compare the perovskite system with other\n‘disordered e-N’ systems such as defects in diamond and SiC and self-assembled quantum dots\n(lines 44-45). However, these systems are very different to the one presented – they are singly\noptically-addressable electronic spins systems. Which means they are have potential for\napplications that require spin-photon entanglement (ie. nodes for optical networking). It seems\nto me that the perovskite system is not comparable in this regard – it consists of a large\nensemble of electronic and nuclear spins, and there is no mention of optical addressability. Thus, the authors should explain why it is relevant to compare to these other systems, whether\nit shows potential for application to similar technologies, and if not, what application they\nforesee for this system. The answers to this question may\nResponse: We apologize for not having clearly described earlier the transition-metal (TM) spin\ncenters in halide double perovskites studied in our present work. These centers are in fact just\nlike the defects in diamond and SiC. They are atomic impurity ions with well-defined intra-d-\nshell optical transitions, which are governed by spin-dependent selection rules such that they\ncan be individually addressed. Such optical access provides the means for optical initialization\nand readout as well as the potential for spin-photon interfacing, similar to the defects in\ndiamond and SiC. The main difference between the TM center in halide double perovskites\nand the defects in diamond and SiC is a stronger electron-nuclear spin interaction in the former\nwith a nuclear-spin-rich host lattice, due to a stronger electron localization. This means a\nstronger perturbation of the electron spin by the nuclear spin environment, leading to spin\ndecoherence. On the other hand, a stronger electron localization limits the number and\nrandomness of nuclear spins (only within the nearest-neighbor 35,37Cl and the next-nearest\nneighbor 133Cs) that the electron spin can interact, making the corresponding electron-nuclear\nspin interactions well-defined and site-specific. This allows us either to avoid the non-\ndeterministic dephasing from different isotopes like 35Cl and 37Cl, or to selectively control spin\ncoherence using the non-dephasing 133Cs nuclei. The latter can further drive electron-nuclear\nspin transfer, just like that demonstrated for the NV center in diamond between the electron\nspin and a nearby 13C nuclear spin.\nThe experimental evidence for the optical addressability of the studied Cr³⁺ spin center in\nCs₂NaInCl₆ can be found in the new section of \" Optical addressability of the TM spins in\nHDPs\" on page 16.\nWe understand that, in terms of spin coherence properties, the TM center in halide double\nperovskites cannot compete with color centers in few-nuclear-spin or isotope-purified nuclear-\nspin-free diamond and SiC, nor is it meant to be. The competitive edge of spin centers in halide double perovskites rather center at their low-cost material synthesis as compared with the vastly more costly diamond and SiC, the availability of a large library of monovalent and trivalent\ncations (spin centers) without introducing excess charge noise, relative ease in incorporating\nspin centers in crystals without involving damaging processes with high-energy particles\nrequired to generate vacancies in diamond and SiC, superior and widely tunable optical\nproperties covering a wide spectral range from UV to infrared, etc. Therefore, any potential\nspin components utilizing halide double perovskites are not meant for the highest performance,\nbut they could rather find application areas where cost concern becomes paramount such as\nmass-production dispersible consumer electronics. At this early stage of spintronic research on\nthis newly emerging materials system, the aim of our present work is to assess (1) whether the\nessential properties of spin centers in halide double perovskites are still within the acceptable\nrange for quantum applications; (2) whether the nuclear-spin rich environment can be\ncontrolled and even harnessed for further applications. We hope that our study sheds light on\ndesign rules to identify promising candidates of spin centers and their perovskite host crystals, which could potentially provide a viable and competitive platform for low-cost quantum\nspintronics.\nWe have now included the above discussion in the revised Introduction section of the revised\nmanuscript.\n2. The authors claim to show entanglement of the electronic spin of the transition metal and the\nneighbouring nuclear spins. This discussion is focussed on the data shown in Fig 2(C). Here,\nthe decoherence traces measured during the Hahn echo measurements is presented. The\ndecoherence profiles show strong modulations due to the coupling to nuclear spins, as seen for\nother systems. The authors should explain why this constitutes demonstration of e-N\nentanglement. Entanglement should be confirmed via measurement of the density matrix of the\ne-N state (see Bourassa et al., Nature Materials, 2020).\nResponse We agree that our statement was inaccurate and that the observed modulations in the\nHahn echo decay do not, in themselves, constitute a demonstration of entanglement. The\nreviewer is correct that such a claim requires more advanced measurements, such as quantum\nstate tomography to reconstruct the density matrix. Unfortunately, our instrument limits such\ndemonstration as we do not have a capability to perform electron-nuclear spin double\nresonance.\nWe have revised the manuscript to remove the claim of \"entanglement\". The purpose of our\ndiscussion on these decoherence traces is to highlight the presence of a strong, coherent\ncoupling between the electron and nuclear spins. The long-lived modulation profiles in the\nHahn echo decay provide concrete evidence that the electron spin is coherently coupled to a\nwell-defined nuclear spin environment at the lattice sites. This coherent interface is a\nprerequisite for creating and manipulating entangled states.\n3. With regards to the T timescale, I agree that 29 μs is surprising for this system considering\n2\nthe nuclear spin composition. However, I am not sure if the factors that limit this coherence are\nwell understood by the authors.\ni. Why does T show a relatively strong temperature dependence? A drop from 29 μs to 6 μs,\n2\nfrom 4 to 20 K, is actually rather strong. I wouldn’t expect decoherence that is dominated by\nnuclear spins to be strongly temperature dependent.\nResponse: We thank the reviewer for the valuable suggestion of the temperature dependence\nof 𝑇 . We have now performed a detailed temperature dependent study of 𝑇 and our findings\n2 2\nindicate that the 𝑇 remains at a constant value below 10 K as expected from the hyperfine\n2\ninteraction that are temperature independent. The sharp rising of the decoherent rates above 10\nK are dominated by the spin-phonon interaction, where the localized phonon frequency of\nabout 50-70 cm-1 is associated with the activation of lower-lying phonon modes associated with\nCs and Cl atomic motions.\nFigure R3: Comparison between the temperature dependence of spin decoherence and spin relaxation rates in\nall four samples. Above 10 K the spin relaxation rate rapidly accelerated, dominating over the spin decoherence\nat T > 20K.\nFigure R4: Temperature dependence and model fitting of spin relaxation rate based on localized spin phonon\ninteraction.\nii. Are the modulation features in Fig. 2C consistent with a relatively weak hyperfine\ninteraction (0.1-10 MHz)?\nResponse: Yes, this is consistent.\nThe modulation depth in an electron spin echo experiment is a direct result of electron-nuclear\n(e-N) spin mixing. This mixing allows normally forbidden EPR transitions—those where both\nthe electron and a nuclear spin flip simultaneously—to become weakly allowed. The efficiency\nof this process determines how strongly the echo signal is modulated.\nAnalytically, the modulation depth, k, can be estimated by:\n𝐴2\n𝑘 = 𝑛𝑜𝑛𝑠𝑒𝑐𝑢𝑙𝑎𝑟…(1)\n𝜔2+𝐴2\n𝐼 𝑠𝑒𝑐𝑢𝑙𝑎𝑟\nHere, ω is the nuclear Larmor frequency, and the secular (A ) and non-secular (A )\nI secular nonsecular\nterms are the orientation-dependent components of the hyperfine tensor in the lab frame.\nThe observed weak modulation, especially in the data from the powder sample shown in Figure\n2C, can be attributed to two main factors.\nFirst, the system is intrinsically far from the ideal conditions for strong modulation. The depth\nis maximized when the cancellation condition, 2ω≈∣A ∣, is met. For our system's nuclei, the\nI iso\nvalues are not close:\n ¹³³Cs: 2ω I =3.9 MHz, while ∣A iso ∣, = 1.1 MHz. \n ³⁵,³⁷Cl: 2ω I ≈ 6.4 MHz, ∣A iso ∣ ≈ 1.6−2.1 MHz. Since this condition isn't met, deep\nmodulation isn't expected even in a single crystal.\nSecond, the use of a powder sample further weakens the observed modulation due to orientation\naveraging. In a powder, all possible orientations of the crystallites relative to the external\nmagnetic field exist simultaneously. The modulation depth k is highly dependent on this\norientation angle, θ. For an axial hyperfine tensor, the components in Equation (1) vary with\norientation as:\n𝐴 = 𝐴 sin2𝜃 +𝐴 cos2𝜃\n𝑠𝑒𝑐𝑢𝑙𝑎𝑟 ⊥ ∥\n𝐴 = (𝐴 −𝐴 )𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃\n𝑛𝑜𝑛𝑠𝑒𝑐𝑢𝑙𝑎𝑟 ∥ ⊥\nWhile some specific orientations might produce deep modulation, the total measured signal is\nan average over all angles. This averaging process washes out the sharp features, resulting in\nthe weak, broad undulation seen in the final spin echo signal.\niii. Why are the modulations much stronger for the Cr complex than for the Fe complex?\nResponse: The hyperfine interaction involving the Cs atom is much greater for Cr3+ as\ncompared with Fe3+, which causes a stronger modulation.\niv. Could there be another factor that helps to decouple the electronic and nuclear spins in this system- possibly symmetry related?\nResponse: That's an excellent point. Yes, we agree with the reviewer that symmetry is indeed\nan important factor in both coupling and decoupling of electronic and nuclear spins in our\nsystem.\nThis high degree of symmetry is precisely what enables our experimental control over spin\nmixing in the single-crystal sample. By changing the orientation of the external magnetic field\nrelative to the crystal axes, we can precisely tune the strength of the electron-nuclear coupling.\nThis orientational control allows us to selectively turn the interaction with specific nuclear\nspecies \"on\" or \"off.\"\nThis technique is the essential key to our method. It allows us to directly address and\nmanipulate the ¹³³Cs nuclear spins while simultaneously decoupling the electron spin from the\n³⁵,³⁷Cl nuclear spins.\nWe have now included a discussion of this point in the sections on single-crystal CPMG and\n3-pulse stimulated echo experiments in the revised manuscript.\n4. Related to my question above, the authors state in the text that the strong localisation of the\nelectronic density on the transition metal is responsible for the long spin coherence timescale.\nThis feels speculative and I don’t see any evidence for this conclusion. Can the authors\nsupport this claim with modelling?\nResponse: We are grateful to the reviewer for this suggestion. Indeed, we can provide both\nexperimental evidence and the modelling supporting our claim.\nFirst, by experimentally comparing the electron spin decoherence between Na and Ag hosts,\nwe show that the change in the third nearest neighbour (Na/Ag) does not affect the spin\ncoherence time. This implies that the localisation of the electron wavefunction would be within\nthe second-nearest neighbour nuclear spins. We have highlighted this discussion in the main\ntext (in red) on page 7.\nSecond, we can estimate the degree of localization based on the Fermi hyperfine contact model,\nwhich shows that the electron wavefunction is indeed localized within the core of spin centres,\neffectively diminishing below 0.02 % at the 133Cs sites.\nWe have included the corresponding discussion in the main text, page 12 and also in a separate\nsection of ‘Supporting Information.’ The section reads as follows:\nThe Fermi contact interaction is a part of the hyperfine interaction of electrons in approximately\nspherical-like orbital and surrounding nuclear environment. It can be expressed by:\n2\n𝐴 = 𝜇 𝑔 𝛽 𝑔 𝛽 |Ψ|2\n𝑖𝑠𝑜 3 0 𝑒 𝑒 𝑁 𝑁\nThis can also demonstrate the electron spin localization, where the percentage of electron\ndensity, |Ψ|2, distributing at the neighbor atoms is estimated by calculating the ratio between\nelectron density distribution caused by the hyperfine interaction and free electron localized at\neach nuclear site:\n2\n|Ψ | |𝐴 |\nℎ𝑦𝑝𝑒𝑟𝑓𝑖𝑛𝑒 𝑖𝑠𝑜,𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡\n=\n2 |𝐴 |\n|Ψ | 𝑖𝑠𝑜,𝑓𝑟𝑒𝑒\n𝑓𝑟𝑒𝑒\nIn our case, we consider 3 nuclear sites representing the nearest neighbours (35Cl and 37Cl) and\nthe next-nearest neighbours (133Cs) of the incorporated transition metal. By inserting the\nhyperfine coupling strength, we can obtain the percentage of electron localization at each\nnuclear site (See Figure S1 and Table S1).\nFigure S1: The example illustration of electron density localization at each nuclear site (35,37Cl, 133Cs) around\nthe incorporated Cr3+.\nTable S1:\n𝐴\n𝑖𝑠𝑜,𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡\n𝐴 +𝐴 +𝐴 𝐴 % electron\nNuclear site = 𝑥 𝑦 𝑧 𝑖𝑠𝑜,𝑓𝑟𝑒𝑒\n3 (MHz) localization\n(MHz)\nCr[Na]\n133Cs 1.1 9.2x103 0.012%\n35Cl -2.1 80 2.6%\n37Cl -1.6 66 2.5%\nNa - - -\nCr[Ag]\n133Cs 1.5 9.2x103 0.017%\n35Cl -2.3 80 2.9%\n37Cl -1.8 66 2.7%\nAg - - -\nFe[Na]\n133Cs 0.1 9.2x103 0.001%\n35Cl -2.2 80 2.8%\n37Cl -1.7 66 2.6%\nNa - - -\nFe[Ag]\n133Cs 0.1 9.2x103 0.001%\n35Cl -2.4 80 3.0%\n37Cl -1.8 66 2.8%\nAg - - -\nAdditional comments:\n1. The paper would benefit from a diagram of the electronic structure of the spin system.\nResponse We have added this in Figure 6A.\n2. Line 99 should say degenerate, not degenerated.\nResponse We have corrected this accordingly."}, {"round": 2, "reviewer_comments": {"reviewer_2": "The authors have addressed all the points raised in our previous review. The manuscript has been substantially improved, with the claims now appropriately moderated. New data and discussion on optical properties included with clarifications on structural and compositional properties. The presentation is clear and all our concerns have been satisfied. I am happy with the revision and recommend acceptance of the manuscript in its current form.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_4": "One of my main concerns about the manuscript in the first round was that it was comparing the perovskite system to single optically addressable spins in diamond, and other single spin-photon interface platforms. I stated that these are very different systems, because the fomer offer single qubits, whereas the perovskite system is an ensemble (of which there are many). I don't believe the authors understood or answered this question adequately. I can see reviewer 1 had the same concern. This means the motivation of the paper- and impact- is questionable. Despite the authors having retracted much of the language from the first round, I still feel the title, abstract and first paragraph of the introduction are misleading, and potentially confusing for people getting into the field.\nFor this reason, I can not support publication in Nature Communications in the current form."}, "author_response": "Our response:\nWe thank the reviewer for his/her concern on comparing the perovskite system to single optically addressable spins in diamond and other single spin-photon interface platforms. We apologize for not having clarified this issue adequately in our previous revision.\nA physical system of solid-state spin qubits is a solid material that contains an ensemble of isolated localized single spins where each spin can be individually addressed and entangled with another qubit, either another stationary spin qubit or a flying photon qubit through electrical or optical means. With a typical concentration of < 1019, spin centers based on deep-level vacancy defects and TM impurities in diamond, SiC and perovskites remain electronically and magnetically isolated due to their strong localization of electron wavefunctions and spin densities. Therefore, as a physical system, the spin-qubit system based on isolated TM ions in perovskites studied in our work is conceptually similar to the well-known color-center spin qubits in diamond and SiC whether they are vacancy defects or TM ions. Here, the notion of a single spin or an ensemble of spins does not refer to a fundamental limit in material classes but is merely a matter of how many spins are probed that is determined by the size of an experimental probe. With a large probe size a large volume of a sample containing an ensemble of localized spins are detected, whereas a sufficiently small probe can focus down to a single localized spin even on the same sample. How small the experimental probe is required depends on the distance between adjacent spin centers and therefore its concentration. For example, with a confocal optical probe with a typical detection volume of 0.1-1 m3, single-spin detection will require a concentration of the localized spin centers to be lower than 1012 cm-3. Ideally, a higher concentration of spin centers is generally preferred in actual device applications that demand miniaturization and reduced material footprint. Here, on-chip integration with nanophotonic components for nanoscale light generation, transmission and detection need to be developed that is currently unavailable even for the technologically far-more advanced SiC.\nWe should also note that the incorporation of the TM ions in the perovskites remains within the doping range (< 1019) in our study, far from the regime of alloying where TM ions can interact with each other. Therefore, these TM ions are predominantly isolated. For single-spin detection by a standard confocal optical microscopy, however, a lower doping concentration than that in the studied samples is required. Intense research efforts are under way to overcome technical challenges to significantly decrease doping concentration and to reduce the experimental probe size or/and sample volume (e.g. nanocrystals). We believe that single-spin detection is feasible in the near future, given recent advancements in fabrication technology for halide double perovskites.\nThe impact and motivation of our paper are to introduce this new class of chemically versatile and low-cost TM-doped HDP platform for spin qubits and to provide the first demonstrations that it possesses the essential quantum properties (long 𝑇 , deterministic nuclear coupling , and\n2\nspin-selective optical transitions) required to be a viable candidate for a solid-state spin qubit system. Though limited to ensemble studies, we believe that the general knowledge of the spin physics gained in our study should be valid for single spin centers. For example, the spin coherence time measured from the ensembles sets the low bound for a single center. These ensemble-level demonstrations represent a necessary and critical first step to validate the platform before any future work to scale it down to the single-spin level is to be undertaken.\nWe should point out that the foundation of the currently highly successful single-spin studies in diamond and SiC is indeed based on earlier ensemble studies [e.g., Foehl, Buckley, Heremans, Calusine and Awschalom, Nature 479, 84 (2011)] that demonstrated the potential of these solid-state spin qubit systems and stimulated the intense follow-up research leading to many breakthroughs.\nWe have now modified the title, abstract and introduction of our manuscript to clarify these aspects. We hope that the reviewer will now find our response and the revision satisfactory."}]

Decision letter