# Publications by Junjie Liu

## Electric field control of spins in molecular magnets

Physical Review Letters American Physical Society 122 (2019) 037202

J Mrozek, J Liu, A Ardavan, WK Myers, GA Timco, B Kintzel, W Plass

Coherent control of individual molecular spins in nanodevices is a pivotal prerequisite for fulfilling the potential promised by molecular spintronics. By applying electric field pulses during time-resolved electron spin resonance measurements, we measure the sensitivity of the spin in several antiferromagnetic molecular nanomagnets to external electric fields. We find a linear electric field dependence of the spin states in Cr7Mn, an antiferromagnetic ring with a ground-state spin of S ¼ 1, and in a frustrated Cu3 triangle, both with coefficients of about 2 rad s−1=V m−1. Conversely, the antiferromagnetic ring Cr7Ni, isomorphic with Cr7Mn but with S ¼ 1=2, does not exhibit a detectable effect. We propose that the spinelectric field coupling may be used for selectively controlling individual molecules embedded in nanodevices.

## Unconventional field-induced spin gap in an S=1/2 Chiral staggered chain

Physical Review Letters American Physical Society 122 (2019) 057207-

J Liu, S Kittaka, R Johnson, T Lancaster, J Singleton, T Sakakibara, Y Kohama, J Van Tol, A Ardavan, BH Williams, SJ Blundell, ZE Manson, JL Manson, PA Goddard

We investigate the low-temperature magnetic properties of the molecule-based chiral spin chain ½CuðpymÞðH2OÞ4SiF6 · H2O (pym ¼ pyrimidine). Electron-spin resonance, magnetometry and heat capacity measurements reveal the presence of staggered g tensors, a rich low-temperature excitation spectrum, a staggered susceptibility, and a spin gap that opens on the application of a magnetic field. These phenomena are reminiscent of those previously observed in nonchiral staggered chains, which are explicable within the sine-Gordon quantum-field theory. In the present case, however, although the sineGordon model accounts well for the form of the temperature dependence of the heat capacity, the size of the gap and its measured linear field dependence do not fit with the sine-Gordon theory as it stands. We propose that the differences arise due to additional terms in the Hamiltonian resulting from the chiral structure of ½CuðpymÞðH2OÞ4SiF6 · H2O, particularly a uniform Dzyaloshinskii-Moriya coupling and a fourfold periodic staggered field.

## Molecular electronic spin qubits from a spin-frustrated trinuclear copper complex

Chemical Communications Royal Society of Chemistry 54 (2018) 12934-12937

B Kintzel, M Bohme, J Liu, J Mrozek, A Burkhardt, A Ardavan, A Buchholz, W Plass

The trinuclear copper(II) complex [Cu3(saltag)(py)6]ClO4 (H5saltag = tris(2-hydroxybenzylidene)triaminoguanidine) was synthesized and characterized by experimental as well as theoretical methods. This complex exhibits a strong antiferromagnetic coupling (J = −298 cm−1) between the copper(II) ions, mediated by the N–N diazine bridges of the tritopic ligand, leading to a spin-frustrated system. This compound shows a T2 coherence time of 340 ns in frozen pyridine solution, which extends to 591 ns by changing the solvent to pyridine-d5. Hence, the presented compound is a promising candidate as a building block for molecular spintronics.

## Implications of bond disorder in a S=1 kagome lattice

Scientific Reports Nature Publishing Group 8 (2018) 4745-

JL Manson, J Brambleby, PA Goddard, PM Spurgeon, JA Villa, J Liu, S Ghannadzadeh, F Foronda, J Singleton, T Lancaster, SJ Clark, IO Thomas, F Xiao, RC Williams, FL Pratt, SJ Blundell, CV Topping, C Baines, C Campana, B Noll

Strong hydrogen bonds such as F···H···F offer new strategies to fabricate molecular architectures exhibiting novel structures and properties. Along these lines and, to potentially realize hydrogen-bond mediated superexchange interactions in a frustrated material, we synthesized [H2F]2[Ni3F6(Fpy)12][SbF6]2 (Fpy = 3-fluoropyridine). It was found that positionally-disordered H2F+ ions link neutral NiF2(Fpy)4 moieties into a kagome lattice with perfect 3-fold rotational symmetry. Detailed magnetic investigations combined with density-functional theory (DFT) revealed weak antiferromagnetic interactions (J ~ 0.4 K) and a large positive-D of 8.3 K with ms = 0 lying below ms = ±1. The observed weak magnetic coupling is attributed to bond-disorder of the H2F+ ions which leads to disrupted Ni-F···H-F-H···F-Ni exchange pathways. Despite this result, we argue that networks such as this may be a way forward in designing tunable materials with varying degrees of frustration.

## Endohedral metallofullerene as molecular high spin qubit: diverse Rabi cycles in Gd2@C79N

Journal of the American Chemical Society American Chemical Society 140 (2017) 1123-1130

Z Hu, B-W Dong, Z Liu, J-J Liu, J Su, C Yu, J Xiong, D-E Shi, Y Wang, B-W Wang, A Ardavan, Z Shi, S-D Jiang, S Gao

An anisotropic high-spin qubit with long coherence time could scale the quantum system up. It has been proposed that Grover's algorithm can be implemented in such systems. Dimetallic aza[80]fullerenes M2@C79N (M = Y or Gd) possess an unpaired electron located between two metal ions, offering an opportunity to manipulate spin(s) protected in the cage for quantum information processing. Herein, we report the crystallographic determination of Gd2@C79N for the first time. This molecular magnet with a collective high-spin ground state (S = 15/2) generated by strong magnetic coupling (JGd-Rad = 350 ± 20 cm-1) has been unambiguously validated by magnetic susceptibility experiments. Gd2@C79N has quantum coherence and diverse Rabi cycles, allowing arbitrary superposition state manipulation between each adjacent level. The phase memory time reaches 5 μs at 5 K by dynamic decoupling. This molecule fulfills the requirements of Grover's searching algorithm proposed by Leuenberger and Loss.

## Strong coupling of microwave photons to antiferromagnetic fluctuations in an organic magnet

Physical Review Letters American Physical Society 119 (2017) 147701-

M Mergenthaler, J Liu, J Le Roy, A Thompson, N Ares, S Blundell, A Ardavan, T Lancaster, L Bogani, F Luis, GAD Briggs, PJ Leek, E Laird

Coupling between a crystal of di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium (DPPH) radicals and a superconducting microwave resonator is investigated in a circuit quantum electrodynamics (cQED) architecture. The crystal exhibits paramagnetic behavior above 4 K, with antiferromagnetic correlations appearing below this temperature, and we demonstrate strong coupling at base temperature. The magnetic resonance acquires a field angle dependence as the crystal is cooled down, indicating anisotropy of the exchange interactions. These results show that multi-spin modes in organic crystals are suitable for cQED, offering a platform for their coherent manipulation. They also utilize the cQED architecture as a way to probe spin correlations at low temperature.

## Antiferromagnetism in a family of S = 1 square lattice coordination polymers NiX2(pyz)2 (X = Cl, Br, I, NCS; pyz = Pyrazine).

Inorganic Chemistry American Chemical Society 55 (2016) 3515-3529

F Foronda, TJ Woods, KE Carreiro, HE Tran, CJ Villa, JS Möller, Y Kohama, S Ghannadzadeh, J Liu, P Goddard, J Singleton, J Brambleby, PW Stephens, J Bendix, KH Stone, JL Manson, T Lancaster, F Xiao, RC Williams, FL Pratt, PJ Baker, K Wierschem, A Ardavan, SJ Blundell, SH Lapidus

The crystal structures of NiX2(pyz)2 (X = Cl (1), Br (2), I (3) and NCS (4)) were determined at 298 K by synchrotron X-ray powder diffraction. All four compounds consist of two-dimensional (2D) square arrays self-assembled from octahedral NiN4X2 units that are bridged by pyz ligands. The 2D layered motifs displayed by 1-4 are relevant to bifluoride-bridged [Ni(HF2)(pyz)2]ZF6 (Z = P, Sb) which also possess the same 2D layers. In contrast, terminal X ligands occupy axial positions in 1-4 and cause a staggering of adjacent layers. Long-range antiferromagnetic order occurs below 1.5 (Cl), 1.9 (Br and NCS) and 2.5 K (I) as determined by heat capacity and muon-spin relaxation. The single-ion anisotropy and g factor of 2, 3 and 4 are measured by electron spin resonance where no zero–field splitting was found. The magnetism of 1-4 crosses a spectrum from quasi-two-dimensional to three-dimensional antiferromagnetism. An excellent agreement was found between the pulsedfield magnetization, magnetic susceptibility and TN of 2 and 4. Magnetization curves for 2 and 4 calculated by quantum Monte Carlo simulation also show excellent agreement with the pulsed-field data. 3 is characterized as a three-dimensional antiferromagnet with the interlayer interaction (J⊥) slightly stronger than the interaction within the two-dimensional [Ni(pyz)2]2+ square planes (Jpyz).

## Quantum interference in graphene nanoconstrictions

Nano Letters American Chemical Society 16 (2016) 4210–4216-

P Gehring, H Sadeghi, S Sangtarash, CS Lau, J Liu, A Ardavan, JH Warner, CJ Lambert, GAD Briggs, JA Mol

We report quantum interference effects in the electrical conductance of chemical vapour deposited graphene nanoconstrictions fabricated using feedback controlled electroburning. The observed multi-mode Fabry-Pérot interferences can be attributed to reflections on potential steps inside the channel. Sharp anti-resonance features with a Fano line shape are observed. Theoretical modelling reveals that these Fano resonances are due to localised states inside the constriction, which couple to the delocalised states that also give rise to the Fabry-Pérot interference patterns. This study provides new insight into the interplay between two fundamental forms of quantum interference in graphene nanoconstrictions.

## The magnetic ground state of two isostructual polymeric quantum magnets, [Cu(HF2)(pyrazine)SbF6 and [Co(HF2)(pyrazine)2]SbF6, investigated with neutron powder diffraction

Physical Review B American Physical Society 92 (2015) 134406-

P Goddard, J Brambleby, R Johnson, D Kaminski, J Liu, AJ Steele, A Ardavan, T Lancaster, P Manuel, PJ Baker, J Singleton, SG Schwalbe, PM Spurgeon, HE Tran, PK Peterson, JF Corbey, JL Manson, SJ Blundell

The magnetic ground state of two isostructural coordination polymers (i) the quasi two-dimensional S = 1/2 square-lattice antiferromagnet [Cu(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$; and (ii) a new compound [Co(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$, were examined with neutron powder diffraction measurements. We find the ordered moments of the Heisenberg S = 1/2 Cu(II) ions in [Cu(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$ are 0.6(1)$\mu_{B}$, whilst the ordered moments for the Co(II) ions in [Co(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$ are 3.02(6)$\mu_{B}$. For Cu(II), this reduced moment indicates the presence of quantum fluctuations below the ordering temperature. We show from heat capacity and electron spin resonance measurements, that due to the crystal electric field splitting of the S = 3/2 Co(II) ions in [Co(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$, this isostructual polymer also behaves as an effective spin-half magnet at low temperatures. The Co moments in [Co(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$ show strong easy-axis anisotropy, neutron diffraction data which do not support the presence of quantum fluctuations in the ground state and heat capacity data which are consistent with 2D or close to 3D spatial exchange anisotropy.

## Three-terminal graphene single-electron transistor fabricated using feedback-controlled electroburning

APPLIED PHYSICS LETTERS 107 (2015) ARTN 133105

P Puczkarski, P Gehring, CS Lau, J Liu, A Ardavan, JH Warner, GAD Briggs, JA Mol

## Quantum spin coherence in halogen-modified Cr7Ni molecular nanomagnets

PHYSICAL REVIEW B 90 (2014) ARTN 184419

D Kaminski, AL Webber, CJ Wedge, J Liu, GA Timco, IJ Vitorica-Yrezabal, EJL McInnes, REP Winpenny, A Ardavan

## Quantifying magnetic exchange in doubly-bridged Cu-X(2)-Cu (X = F, Cl, Br) chains enabled by solid state synthesis of CuF(2)(pyrazine).

Chemical communications (Cambridge, England) 49 (2013) 3558-3560

SH Lapidus, JL Manson, J Liu, MJ Smith, P Goddard, J Bendix, CV Topping, J Singleton, C Dunmars, JF Mitchell, JA Schlueter

Solid state techniques involving pressure and temperature have been used to synthesize the fluoride member of the CuX(2)(pyrazine) (X = F, Cl, Br) family of coordination polymers that cannot be crystallized by solution methods. CuF(2)(pyrazine) exhibits unique trans doubly-bridged Cu-F(2)-Cu chains that provide an opportunity to quantify magnetic superexchange in an isostructural Cu-X(2)-Cu series.