Spin-1/2 Heisenberg chains realized in π-electron systems
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Spin-state effect on the efficiency of a post-synthetic modification reaction on a spin crossover complex
The spin state of a metal center significantly influences the catalytic activity of its complex, a phenomenon so crucial that it has led to the dedicated field of spin catalysis. Here we investigate the effect of the spin state of an iron-based metal complex on the organic reactivity of its ligands. Specifically, we examined the post-synthetic modification of the spin crossover (SCO) complex [Fe(NH2trz)3](NO3)2 with p-anisaldehyde. A series of experiments were performed to study the transformation of the amino groups depending on the spin state of the metal. Owing to the wide thermal hysteresis loop of the SCO complex, both spin states were compared under identical conditions. The results revealed that the high-spin state led to the formation of 1.34 times more imine functional groups than the low-spin state, we propose that this arises from the different interactions between the solvent and the SCO at the different spin states.
Switching on and off the spin polarization of the conduction band in antiferromagnetic bilayer transistors
Antiferromagnetic conductors with suitably broken spatial symmetries host spin-polarized bands, which lead to transport phenomena commonly observed in metallic ferromagnets. In bulk materials, it is the given crystalline structure that determines whether symmetries are broken and spin-polarized bands are present. Here we show that, in the two-dimensional limit, an electric field can control the relevant symmetries. To this end, we fabricate a double-gate transistor based on bilayers of van der Waals antiferromagnetic semiconductor CrPS4 and show how a perpendicular electric displacement field can switch the spin polarization of the conduction band on and off. Because conduction band states with opposite spin polarizations are hosted in the different layers and are spatially separated, these devices also give control over the magnetization of the electrons that are accumulated electrostatically. Our experiments show that double-gated CrPS4 transistors provide a viable platform to create gate-induced conductors with near unity spin polarization at the Fermi level, as well as devices with a full electrostatic control of the total magnetization of the system.
Spin–valley protected Kramers pair in bilayer graphene
The intrinsic valley degree of freedom makes bilayer graphene (BLG) a unique platform for semiconductor qubits. The single-carrier quantum dot (QD) ground state exhibits a twofold degeneracy, where the two states that constitute a Kramers pair have opposite spin and valley quantum numbers. Because of the valley-dependent Berry curvature, an out-of-plane magnetic field breaks the time-reversal symmetry of this ground state and a qubit can be encoded in the spin–valley subspace. The Kramers states are protected against known spin- and valley-mixing mechanisms because mixing requires a simultaneous change of the two quantum numbers. Here, we fabricate a tunable QD device in Bernal BLG and measure a spin–valley relaxation time for the Kramers states of 38 s at 30 mK, which is two orders of magnitude longer than the 0.4 s measured for purely spin-blocked states. We also show that the intrinsic Kane–Mele spin–orbit splitting enables a Kramers doublet single-shot readout even at zero magnetic field with a fidelity above 99%. If these long-lived Kramers states also possess long coherence times and can be effectively manipulated, electrostatically defined QDs in BLG may serve as long-lived semiconductor qubits, extending beyond the spin qubit paradigm.
A machine-learning framework for accelerating spin-lattice relaxation simulations
Molecular and lattice vibrations are able to couple to the spin of electrons and lead to their relaxation and decoherence. Ab initio simulations have played a fundamental role in shaping our understanding of this process but further progress is hindered by their high computational cost. Here we present an accelerated computational framework based on machine-learning models for the prediction of molecular vibrations and spin-phonon coupling coefficients. We apply this method to three open-shell coordination compounds exhibiting long relaxation times and show that this approach achieves semi-to-full quantitative agreement with ab initio methods reducing the computational cost by about 80%. Moreover, we show that this framework naturally extends to molecular dynamics simulations, paving the way to the study of spin relaxation in condensed matter beyond simple equilibrium harmonic thermal baths.
Grover’s algorithm in a four-qubit silicon processor above the fault-tolerant threshold
Spin qubits in silicon are strong contenders for the realization of a practical quantum computer, having demonstrated single- and two-qubit gates with fidelities above the fault-tolerant threshold, and entanglement of three qubits. However, maintaining high-fidelity operations while increasing the qubit count remains challenging and therefore only two-qubit algorithms have been executed. Here we utilize a four-qubit silicon processor with all control fidelities above the fault-tolerant threshold and demonstrate a three-qubit Grover’s search algorithm with a ~95% probability of finding the marked state. Our processor is made of three phosphorus atoms precision-patterned into isotopically pure silicon, which localise one electron. The long coherence times of the qubits enable single-qubit fidelities above 99.9% for all qubits. Moreover, the efficient single-pulse multi-qubit operations enabled by the electron–nuclear hyperfine interaction facilitate controlled-Z gates between all pairs of nuclear spins with fidelities above 99% when using the electron as an ancilla. These control fidelities, combined with high-fidelity non-demolition readout of all nuclear spins, allow the creation of a three-qubit Greenberger–Horne–Zeilinger state with 96.2% fidelity. Looking ahead, coupling neighbouring nuclear spin registers, as the one shown here, via electron–electron exchange may enable larger, fault-tolerant quantum processors.
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