Paul Goddard

Abstract:

A variety of 'strange metals' exhibit resistivity that decreases linearly with temperature as the temperature decreases to zero^1-3, in contrast to conventional metals where resistivity decreases quadratically with temperature. This linear-in-temperature resistivity has been attributed to charge carriers scattering at a rate given by ħ/τ = αk_BT, where α is a constant of order unity, ħ is the Planck constant and k_B is the Boltzmann constant. This simple relationship between the scattering rate and temperature is observed across a wide variety of materials, suggesting a fundamental upper limit on scattering-the 'Planckian limit'^4,5-but little is known about the underlying origins of this limit. Here we report a measurement of the angle-dependent magnetoresistance of La_1.6-xNd_0.4Sr_xCuO₄-a hole-doped cuprate that shows linear-in-temperature resistivity down to the lowest measured temperatures⁶. The angle-dependent magnetoresistance shows a well defined Fermi surface that agrees quantitatively with angle-resolved photoemission spectroscopy measurements⁷ and reveals a linear-in-temperature scattering rate that saturates at the Planckian limit, namely α = 1.2 ± 0.4. Remarkably, we find that this Planckian scattering rate is isotropic, that is, it is independent of direction, in contrast to expectations from 'hotspot' models^8,9. Our findings suggest that linear-in-temperature resistivity in strange metals emerges from a momentum-independent inelastic scattering rate that reaches the Planckian limit.

Abstract:

The [Zn_1-xNi_x(HF₂)(pyz)₂]SbF₆ (x = 0.2; pyz = pyrazine) solid solution exhibits a zero-field splitting (D) that is 22% larger [D = 16.2(2) K (11.3(2) cm^-1)] than that observed in the x = 1 material [D = 13.3(1) K (9.2(1) cm^-1)]. The substantial change in D is accomplished by an anisotropic lattice expansion in the MN₄ (M = Zn or Ni) plane, wherein the increased concentration of isotropic Zn(II) ions induces a nonlinear variation in M-F and M-N bond lengths. In this, we exploit the relative donor atom hardness, where M-F and M-N form strong ionic and weak coordinate covalent bonds, respectively, the latter being more sensitive to substitution of Ni by the slightly larger Zn(II) ion. In this way, we are able to tune the single-ion anisotropy of a magnetic lattice site by Zn-substitution on nearby sites. This effect has possible applications in the field of single-ion magnets and the design of other molecule-based magnetic systems.

Abstract:

We present an open-source program free to download for academic use with a full user-friendly graphical interface for performing flexible and robust background subtraction and dipole fitting on magnetization data. For magnetic samples with small moment sizes or sample environments with large or asymmetric magnetic backgrounds, it can become necessary to separate background and sample contributions to each measured raw voltage measurement before fitting the dipole signal to extract magnetic moments. Originally designed for use with pressure cells on a Quantum Design MPMS3 SQUID magnetometer, SquidLab is a modular object-oriented platform implemented in Matlab with a range of importers for different widely available magnetometer systems (including MPMS, MPMS-XL, MPMS-IQuantum, MPMS3, and S700X models) and has been tested with a broad variety of background and signal types. The software allows background subtraction of baseline signals, signal preprocessing, and performing fits to dipole data using Levenberg-Marquardt non-linear least squares or a singular value decomposition linear algebra algorithm that excels at picking out noisy or weak dipole signals. A plugin system allows users to easily extend the built-in functionality with their own importers, processes, or fitting algorithms. SquidLab can be downloaded, under Academic License, from the University of Warwick depository (wrap.warwick.ac.uk/129665).

Abstract:

We examine the crystal structures and magnetic properties of several S = 1 Ni(II) coordination compounds, molecules and polymers, that include the bridging ligands HF2−, AF62− (A = Ti, Zr) and pyrazine or non-bridging ligands F−, SiF62−, glycine, H2O, 1-vinylimidazole, 4-methylpyrazole and 3-hydroxypyridine. Pseudo-octahedral NiN4F2, NiN4O2 or NiN4OF cores consist of equatorial Ni-N bonds that are equal to or slightly longer than the axial Ni-Lax bonds. By design, the zero-field splitting (D) is large in these systems and, in the presence of substantial exchange interactions (J), can be difficult to discriminate from magnetometry measurements on powder samples. Thus, we relied on pulsed-field magnetization in those cases and employed electron-spin resonance (ESR) to confirm D when J ≪ D. The anisotropy of each compound was found to be easy-plane (D > 0) and range from ≈ 8–25 K. This work reveals a linear correlation between the ratio d(Ni-Lax)/d(Ni-Neq) and D although the ligand spectrochemical properties may play an important role. We assert that this relationship allows us to predict the type of magnetocrystalline anisotropy in tailored Ni(II) quantum magnets.

Abstract:

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.