Superconductivity (SC) in so-called "unconventional superconductors" is nearly always found in the vicinity of another ordered state, such as antiferromagnetism, charge density wave (CDW), or stripe order. This suggests a fundamental connection between SC and fluctuations in some other order parameter. To better understand this connection, we used high-pressure x-ray scattering to directly study the CDW order in the layered dichalcogenide TiSe 2 , which was previously shown to exhibit SC when the CDW is suppressed by pressure [1] or intercalation of Cu atoms [2]. We succeeded in suppressing the CDW fully to zero temperature, establishing for the first time the existence of a quantum critical point (QCP) at P c = 5.1 ± 0.2 GPa, which is more than 1 GPa beyond the end of the SC region. Unexpectedly, at P = 3 GPa we observed a reentrant, weakly first order, incommensurate phase, indicating the presence of a Lifshitz tricritical point somewhere above the superconducting dome. Our study suggests that SC in TiSe 2 may not be connected to the QCP itself, but to the formation of CDW domain walls. *The term "unconventional superconductor" once referred to materials whose phenomenology does not conform to the Bardeen-Cooper-Schrieffer (BCS) paradigm for superconductivity. It is now evident that, by this definition, the vast majority of known superconductors are unconventional, notable examples being the copper-oxide, iron-arsenide, and iron-selenide high temperature superconductors, heavy Fermion materials such as CeIn 3 and CeCoIn 5 , ruthenium oxides, organic superconductors such as ϰ-(BEDT-TTF)2X, filled skutterudites, etc.Despite their diversity in structure and phenomenology, the phase diagrams of these materials all exhibit the common trait that superconductivity (SC) resides near the boundary of an ordered phase with broken translational or spin rotation symmetry. For example, SC resides near antiferromagnetism in CeIn 3 [3], near a spin density wave in iron arsenides [4], orbital order in ruthenates [5], and stripe and nematic order in the copper-oxides [6]. The pervasiveness of this "universal phase diagram" suggests that there exists a unifying framework -more general than BCS -in which superconductivity can be understood as coexisting with some ordered phase, and potentially emerging from its fluctuations.A classic example is the transition metal dichalcogenide family, MX 2 , where M=Nb, Ti, Ta, and X=Se, S, which exhibit a rich competition between superconductivity and Peierls-like charge density wave (CDW) order [7]. A recent, prominent case is 1T-TiSe 2 , which under ambient pressure exhibits CDW order below a transition temperature T CDW = 202 K [8]. This CDW phase can be suppressed either with intercalation of Cu atoms [2,9], or through the application of hydrostatic pressure [1,10], causing SC to emerge. These studies suggest that the emergence of SC coincides with a quantum critical point (QCP) at which T CDW goes to zero, suggesting that TiSe 2 exemplifies the universal phenomenon of superconductivity em...

We present temperature-dependent x-ray diffraction and temperature- and field-dependent Raman scattering studies of single-crystal Mn3O4, which reveal the magnetostructural phases that evolve in the spinels due to the interplay between strong spin-orbital coupling, geometric frustration, and applied magnetic field. We present evidence that the magnetoelastic and magnetodielectric behavior in this material is governed by magnetic-field-controlled tetragonal-to-monoclinic phase changes. Most interestingly, for an applied field transverse to the ferrimagnetic ordering direction, H parallel [110], we find evidence for a field-tuned quantum phase transition to a tetragonal spin-disordered phase, indicating that a structurally symmetric, spin frustrated phase can be recovered at T approximately 0 for intermediate transverse fields in Mn3O4.

We present temperature-, magnetic-field-, and pressure-dependent Raman scattering studies of single crystal Mn3O4, combined with temperature-and field-dependent x-ray diffraction studies, revealing the novel magnetostructural phases in Mn3O4. Our temperature-dependent studies showed that the commensurate magnetic transition at T2=33K in the binary spinel Mn3O4 is associated with a structural transition from tetragonal to orthorhombic structures. Field-dependent studies showed that the onset and nature of this structural transition can be controlled with an applied magnetic field, and revealed evidence for a field-tuned quantum phase transition to a tetragonal spin-disordered phase for H [110]. Pressure-dependent Raman measurements showed that the magnetic easy axis direction in Mn3O4 can be controlled-and the ferrimagnetic transition temperature increased-with applied pressure. Finally, combined pressure-and magnetic-field-tuned Raman measurements revealed a rich magnetostructural phase diagram-including a pressure-and fieldinduced magnetically frustrated tetragonal phase in the PH phase diagram-that can be generated in Mn3O4 with applied pressure and magnetic field.

We report temperature-dependent transport and x-ray diffraction measurements of the influence of Ti hole doping on the charge density wave (CDW) in 1T -Ta1−xTixS2. Confirming past studies, we find that even trace impurities eliminate the low-temperature commensurate (C) phase in this system. Surprisingly, the magnitude of the in-plane component of the CDW wave vector in the nearly commensurate (NC) phase does not change significantly with Ti concentration, as might be expected from a changing Fermi surface volume. Instead, the angle of the CDW in the basal plane rotates, from 11.9• at x = 0 to 16.4• at x = 0.12. Ti substitution also leads to an extended region of coexistence between incommensurate (IC) and NC phases, indicating heterogeneous nucleation near the transition. Finally, we explain a resistive anomaly originally observed by DiSalvo [F. J. DiSalvo, et al., Phys. Rev. B 12, 2220] as arising from pinning of the CDW on the crystal lattice. Our study highlights the importance of commensuration effects in the NC phase, particularly at x ∼ 0.08.

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