Realizing square and diamond lattice S =1/2 Heisenberg antiferromagnet models in the α and β phases of the coordination framework, KTi(C2O4)2⋅xH2O

Provision of a PhD studentship to A.H.A. by the University of Liverpool and the Science and Technology Facilities Council (STFC) is gratefully acknowledged. The work of T.L. was funded by the University of St Andrews and China Scholarship Council (CSC) joint scholarship (201606280032). A.T. was funded by the Federal Ministry of Education and Research through the Sofja Kovalevskaya Award of Alexander von Humboldt Foundation. Work at St Andrews was supported by the Leverhulme Trust (RPG-2013-343).We report the crystal structures and magnetic properties of two pseudopolymorphs of the S=1/2 Ti3+ coordination framework, KTi(C2O4)2⋅xH2O. Single-crystal x-ray and powder neutron diffraction measurements on α−KTi(C2O4)2⋅xH2O confirm its structure in the tetragonal I4/mcm space group with a square planar arrangement of Ti3+ ions. Magnetometry and specific heat measurements reveal weak antiferromagnetic interactions, with J1≈7 K and J2/J1=0.11 indicating a slight frustration of nearest- and next-nearest-neighbor interactions. Below 1.8 K, α−KTi(C2O4)2⋅xH2O undergoes a transition to G-type antiferromagnetic order with magnetic moments aligned along the c axis of the tetragonal structure. The estimated ordered moment of Ti3+ in α−KTi(C2O4)2⋅xH2O is suppressed from its spin-only value to 0.62(3) μB, thus verifying the two-dimensional nature of the magnetic interactions within the system. β−KTi(C2O4)2⋅2H2O, on the other hand, realizes a three-dimensional diamondlike magnetic network of Ti3+ moments within a hexagonal P6222 structure. An antiferromagnetic exchange coupling of J≈54 K—an order of magnitude larger than in α−KTi(C2O4)2⋅xH2O—is extracted from magnetometry and specific heat data. β−KTi(C2O4)2⋅2H2O undergoes Néel ordering at TN=28 K, with the magnetic moments aligned within the ab plane and a slightly reduced ordered moment of 0.79 μB per Ti3+. Through density-functional theory calculations, we address the origin of the large difference in the exchange parameters between the α and β pseudopolymorphs. Given their observed magnetic behaviors, we propose α−KTi(C2O4)2⋅xH2O and β−KTi(C2O4)2⋅2H2O as close to ideal model S =1/2 Heisenberg square and diamond lattice antiferromagnets, respectively.PostprintPeer reviewe

Large easy-axis anisotropy in the one-dimensional magnet BaMo(PO4)(2)

We present an extensive experimental and theoretical study on the low-temperature magnetic properties of the monoclinic anhydrous alum compound BaMo(PO4)(2). The magnetic susceptibility reveals strong antiferromagnetic interactions theta(CW) = -167 K and long-range magnetic order at T-N = 22 K, in agreement with a recent report. Powder neutron diffraction furthermore shows that the order is collinear, with the moments near the ac plane. Neutron spectroscopy reveals a large excitation gap Delta = 15 meV in the low-temperature ordered phase, suggesting a much larger easy-axis spin anisotropy than anticipated. However, the large anisotropy justifies the relatively high ordered moment, Neel temperature, and collinear order observed experimentally and is furthermore reproduced in a first-principles calculations by using a new computational scheme. We therefore propose BaMo(PO4)(2) to host S = 1 antiferromagnetic chains with large easy-axis anisotropy, which has been theoretically predicted to realize novel excitation continua

Exploring quantum magnetism in various spin models: an experimental study

Correlated many body electron systems provide a rich source of collective quantum phenomena. These depend on the interplay of the spin and orbital degrees of freedom, the hierarchy of the interaction energy scales, alongside the host lattice geometry. This thesis presents an experimental study demonstrating the magnetic properties of various material realizations of spin models that highlight the complex magnetic behavior arising in such strongly correlated systems. In the first results chapter, a series of S = 1/2 Mo5+-based materials, AMoOP2O7, where A = Li, Na, K, and Cs, is investigated. Despite a lattice geometry that hosts pairs of Mo5+-containing chains, a combination of magnetometry, specific heat, and inelastic neutron scattering measurements reveals dominant one-dimensional interactions with no frustrating interchain couplings in A = Na, K, Cs. This conclusion is supported by the lack of long-range magnetic order in KMoOP2O7, as examined through powder neutron diffraction, and by ab-initio calculations which reveal the role of the distortions in the octahedral Mo5+ geometry in stabilizing an active magnetic orbital favoring interactions along the chain direction. Meanwhile, LiMoOP2O7 was found to adopt an alternative magnetic sublattice comprised of three-legged spin ladders containing octahedrally coordinated Mo5+ ions. Evidence for the onset of long-range magnetic order is seen across magnetic susceptibility and specific heat measurements and confirmed through a neutron powder diffraction study. Characterization using inelastic neutron scattering, combined with an ab-initio-based simulation of the experimental spectra, confirm this non-frustrated three-legged spin ladder model. However, further optimization of the model parameters remains necessary for an accurate description of the spin Hamiltonian. Next, the crystal structure and magnetic properties of a novel jeff = 1/2 Ru3+-based system, RuP3SiO11, are investigated. The trigonal R3c crystal structure of this material, which forms a honeycomb magnetic sublattice comprised of Ru3+ ions within an octahedral coordination formed by PO4 groups, is confirmed using synchrotron X-ray diffraction. Magnetometry and specific heat measurements suggest long-range magnetic order which is revealed to adopt a collinear Neel order through neutron powder diffraction. The relevance of this material to the Kitaev model is then investigated using a combination of inelastic neutron scattering measurements and ab-initio models that place RuP3SiO11 within a previously unaccessed region of the extended Kitaev phase diagram. A confirmation of the relevant exchange parameters, however, remains outstanding as a full optimization of the suggested spin model is yet to be completed. The magnetic field and temperature dependence phase diagram is also examined and suggests a critical magnetic field of Hc = 3.8 T. The last results chapter is concerned with the magnetic properties of the alpha and beta psuedo-polymorphs of the S = 1/2 T3+-based coordination framework, KTi(C2O4)2.xH2O. Using a combination of single-crystal X-ray and neutron powder diffraction studies, alpha-KTi(C2O4)2.xH2O was found to adopt a tetragonal I4/mcm space group with a crystal structure containing a square planar network of Ti3+ ions in a square antiprismatic crystal field. Analysis of magnetometry and specific heat data reveal dominant antiferromagnetic interactions along the sides of the squares and minimal frustration across the diagonal. Through a neutron powder diffraction study, a Neel ordered magnetic structure was found to describe the ordered state. These results place alpha-KTi(C2O4)2.xH2O within the unfrustrated region of the phase diagram of the S = 1/2 Heisenberg square antiferromagnet model. In contrast, beta-KTi(C2O4)2.2H2O, forms a diamond-like magnetic sublattice of Ti3+ ions within the the hexagonal P6_222 space group. Fitting the S = 1/2 Heisenberg diamond lattice antiferromagnet model to the magnetic suscpetibility and specific heat yields exchange parameters that are an order of magnitude larger than in alpha. Ab-initio calculations reveal that it is the interplay of the active magnetic orbital and the superexchange pathway that results in this discrepancy. Finally, an antiferromagnetic structure is characterized by analyzing neutron powder diffraction data. By examining these results, the alpha and beta psuedo-polymorphs are identified as material realizations of the S = 1/2 Heisenberg square and diamond lattice antiferromagnet models, respectively

Unravelling Structural Complexity within a Family of Frustrated S = ½ Kagome Antiferromagnets

Quantum spin liquids (QSLs) are exotic states of matter in which magnetic frustration and strong quantum fluctuations destroy long-range magnetic order. Here, we propose to explore the subtle structural distortions in a new family of highly frustrated quantum magnets, Cu4(OD)6FX (X = Cl, Br, I), composed of kagome networks of antiferromagnetically coupled Cu2+ ions, to understand the exchange pathways that lead to magnetic order at TN ~ 15 K. Furthermore, we have established that doping Cu4(OD)6FBr with Zn2+ forms a QSL phase, and so we wish to confirm whether highly Zn-doped analogues of ZnCu3(OD)6FX demonstrate the same series of structural distortions as their undoped counterparts, or if they maintain a higher symmetry at low temperature

Uncovering the S=1/2 Kagome Ferromagnet within a Family of Metal-Organic Frameworks

[Image: see text] Kagome networks of ferromagnetically or antiferromagnetically coupled [Image: see text] magnetic moments represent important models in the pursuit of a diverse array of novel quantum and topological states of matter. Here, we explore a family of Cu(2+)-containing metal–organic frameworks (MOFs) bearing [Image: see text] kagome layers pillared by ditopic organic linkers with the general formula Cu(3)(CO(3))(2)(x)(3)·2ClO(4) (MOF-x), where x is 1,2-bis(4-pyridyl)ethane (bpe), 1,2-bis(4-pyridyl)ethylene (bpy), or 4,4′-azopyridine (azpy). Despite more than a decade of investigation, the nature of the magnetic exchange interactions in these materials remained unclear, meaning that whether the underlying magnetic model is that of an [Image: see text] kagome ferromagnet or antiferromagnet is unknown. Using single-crystal X-ray diffraction, we have developed a chemically intuitive crystal structure for this family of materials. Then, through a combination of magnetic susceptibility, powder neutron diffraction, and muon-spin spectroscopy measurements, we show that the magnetic ground state of this family consists of [Image: see text] ferromagnetic kagome layers that are coupled antiferromagnetically via their extended organic pillaring linkers

One-dimensional quantum magnetism in the S = 1 2 Mo(V) system KMoOP 2 O 7

We present a comprehensive experimental and ab initio study of the S=1/2Mo5+ system, KMoOP2O7, and show that it realizes the S=12 Heisenberg chain antiferromagnet model. Powder neutron diffraction reveals that KMoOP2O7 forms a magnetic network comprised of pairs of Mo5+ chains within its monoclinic P21/n structure. Antiferromagnetic interactions within the Mo5+ chains are identified through magnetometry measurements and confirmed by analysis of the magnetic specific heat. The latter reveals a broad feature centered on TN=0.54 K, which we ascribe to the onset of long-range antiferromagnetic order. No magnetic Bragg scattering is observed in powder neutron-diffraction data collected at 0.05 K, however, which is consistent with a strongly suppressed ordered moment with an upper limit μord<0.15μB. The one-dimensional character of the magnetic correlations in KMoOP2O7 is verified through analysis of inelastic neutron-scattering data, resulting in a model with J2≈34 K and J1≈-2 K for the intrachain and interchain exchange interactions, respectively. The origin of these experimental findings are addressed through density-functional theory calculations