Top-loading Small-sample Calorimeters for Measurements as a Function of Magnetic Field Angle

In quasi-low-dimensional systems, the existence of a particular physical state and the temperature and magnetic-field-dependence of its phase boundary often strongly depends on magnetic field orientation. To investigate magnetic field orientation dependent phase transitions in these materials, we have developed rotatable miniature and sub-miniature sample-in-vacuum calorimeters that operate in dc magnetic fields up to 18 and 45 tesla. The calorimeters cover the temperature range from below 0.1 K to above 10 K; they are able rotate a full 360 degrees relative to the applied magnetic field while remaining at base temperature. Samples are typically ontheorderof1mginmassandupto2mm2 x0.5mminvolume

Calorimetric Measurements of Magnetic-Field-Induced Inhomogeneous Superconductivity Above The Paramagnetic Limit

We report the first magnetocaloric and calorimetric observations of a magnetic-field-induced phase transition within a superconducting state to the long-sought exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state, first predicted over 50 years ago. Through the combination of bulk thermodynamic calorimetric and magnetocaloric measurements in the organic superconductor κ−(BEDT−TTF)2Cu(NCS)2 as a function of temperature, magnetic field strength, and magnetic field orientation, we establish for the first time that this field-induced first-order phase transition at the paramagnetic limit Hp is a transition to a higher-entropy superconducting phase, uniquely characteristic of the FFLO state. We also establish that this high-field superconducting state displays the bulk paramagnetic ordering of spin domains required of the FFLO state. These results rule out the alternate possibility of spin-density wave ordering in the high-field superconducting phase. The phase diagram determined from our measurements—including the observation of a phase transition into the FFLO phase at Hp—is in good agreement with recent NMR results and our own earlier tunnel-diode magnetic penetration depth experiments but is in disagreement with the only previous calorimetric report

Evolution of magnetic field induced ordering in the layered quantum Heisenberg triangular-lattice antiferromagnet Ba\u3csub\u3e3\u3c/sub\u3e CoSb\u3csub\u3e2\u3c/sub\u3e O\u3csub\u3e9\u3c/sub\u3e

Quantum fluctuations in the effective spin- 1/2 layered triangular-lattice quantum Heisenberg antiferromagnet Ba3CoSb2O9 lift the classical degeneracy of the antiferromagnetic ground state in magnetic field, producing a series of novel spin structures for magnetic fields applied within the crystallographic ab plane, including a celebrated collinear “up-up-down” spin ordering with magnetization equal to 1/3 of the saturation magnetization over an extended field range. Theoretically unresolved, however, are the effects of interlayer antiferromagnetic coupling and transverse magnetic fields on the ground states of this system. Additional magnetic field induced phase transitions are theoretically expected and in some cases have been experimentally observed, but details regarding their number, location, and physical character appear inconsistent with the predictions of existing models. Conversely, an absence of experimental measurements as a function of magnetic-field orientation has left other key predictions of these models untested. To address these issues, we have used specific heat, neutron diffraction, thermal conductivity, and magnetic torque measurements to map out the phase diagram as a function of magnetic field intensity and orientation relative to the crystallographic ab plane. For H||ab, we have discovered an additional magnetic field induced phase transition at low temperature and an unexpected tetracritical point in the high-field phase diagram, which coupled with the apparent second-order nature of the phase transitions eliminates several theoretically proposed spin structures for the high-field phases. Our calorimetric measurements as a function of magnetic field orientation are in general agreement with theory for field-orientation angles close to plane parallel (H||a) but diverge at angles near plane perpendicular; a predicted convergence of two phase boundaries at finite angle and a corresponding change in the order of the field induced phase transition are not observed experimentally. Our results emphasize the role of interlayer coupling in selecting and stabilizing field induced phases, provide guidance on the nature of the magnetic order in each phase, and reveal the need for new physics to account for the nature of magnetic ordering in this archetypal two-dimensional spin- 1/2 triangular-lattice quantum Heisenberg antiferromagnet

Evolution of Magnetic-Field-Induced Ordering in the Layered Structure Quantum Heisenberg Triangular-Lattice Antiferromagnet Ba\u3csub\u3e3\u3c/sub\u3eCoSb\u3csub\u3e2\u3c/sub\u3eO\u3csub\u3e9\u3c/sub\u3e

Quantum fluctuations in the effective spin-1/2 layered structure triangular-lattice quantum Heisenberg antiferromagnet Ba3CoSb2O9 lift the classical degeneracy of the antiferromagnetic ground state in magnetic field, producing a series of novel spin structures for magnetic fields applied within the crystallographic ab plane, including a celebrated collinear ‘up-up-down’ spin ordering with magnetization equal to 1/3 of the saturation magnetization over an extended field range. Theoretically unresolved, however, are the effects of interlayer antferromagnetic coupling and transverse magnetic fields on the ground states of this system. Additional magnetic-field-induced phase transitions are theoretically expected and in some cases have been experimentally observed, but details regarding their number, location, and physical character appear inconsistent with the predictions of existing models. Conversely, an absence of experimental measurements as a function of magnetic-field orientation has left other key predictions of these models untested. To address these issues, we have used specific heat, neutron diffraction, thermal conductivity, and magnetic torque measurements to map out the phase diagram as a function of magnetic field intensity and orientation relative to the crystallographic ab plane. For H||ab, we have discovered an additional, previously unreported magnetic-field-induced phase transition at low temperature and an unexpected tetracritical point in the high field phase diagram, which — coupled with the apparent second-order nature of the phase transitions — eliminates several theoretically proposed spin structures for the high field phases. Our calorimetric measurements as a function of magnetic field orientation are in general agreement with theory for field-orientation angles close to plane parallel (H||a) but diverge at angles near plane perpendicular; a predicted convergence of two phase boundaries at finite angle and a corresponding change in the order of the field induced phase transition is not observed experimentally. Our results emphasize the role of interlayer coupling in selecting and stabilizing field-induced phases, provide new guidance into the nature of the magnetic order in each phase, and reveal the need for new physics to account for the nature of magnetic ordering in this archetypal 2D spin-1/2 triangular lattice quantum Heisenberg antiferromagnet

A Short Guide to Using Python For Data Analysis In Experimental Physics

Common signal processing tasks in the numerical handling of experimental data include interpolation, smoothing, and propagation of uncertainty. A comparison of experimental results to a theoretical model further requires curve fitting, the plotting of functions and data, and a determination of the goodness of fit. These tasks often typically require an interactive, exploratory approach to the data, yet for the results to be reliable, the original data needs to be freely available and resulting analysis readily reproducible. In this article, we provide examples of how to use the Numerical Python (Numpy) and Scientific Python (SciPy) packages and interactive Jupyter Notebooks to accomplish these goals for data stored in a common plain text spreadsheet format. Sample Jupyter notebooks containing the Python code used to carry out these tasks are included and can be used as templates for the analysis of new data

Why the Earth is Warming. Carbon Cycles, Bathtubs, and You!

A Sigma Xi lunchtime talk by Professor Nathanael Fortune, Department of Physics. Part of the Year on Climate Change\u27s Climate 101 series

Magnetic-field-induced 1st order transition to FFLO state at paramagnetic limit in 2D superconductors

We have recently reported the first direct calorimetric observation of a magnetic-field-induced first-order phase transition into a high-field FFLO superconducting state at the Clogston-Chandrasekar ‘Pauli’ paramagnetic limitHp in a 2D superconductor κ − (BEDT-TTF)2Cu(NCS)2. The high-field state is both higher entropy and strongly paramagnetic, as thermodynamically required for the FFLO state. Here we compare our results with theoretical predictions for the field dependence of the high-field FFLO state in the 2D limit, revealing tentative evidence for transitions between FFLO states of differing order parameter. We also present calorimetric evidence for a 1st order phase transition into the FFLO state for a second 2D organic superconductor: β − (BEDT-TTF)2SF5(CH)2(CF)2(SO)3

Calorimetric Determination of the Angular Dependent Phase Diagram of an S = 1/2 Heisenberg Triangular-lattice Antiferromagnet

An antiferromagnetic system on a 2-D triangular lattice leads to geometric topological frustration. This ideal system has been the subject of theoretical investigations. One experimental realization of this system is the compound Cs2CuCl4. Various magnetization, heat capacity, neutron scattering and NMR studies have identified several magnetic transitions when the magnetic field is applied along one of the three principal axes. The current work investigates the evolution of these phases at intermediate angles as the crystal is rotated relative to the magnetic field. These phases were investigated using a novel rotating calorimeter allowing complete coverage of the experimental parameter space. New magnetic phases only existing at intermediate angles have been found

Magnetic-field-induced Heisenberg to XY Crossover in a Quasi-2D Quantum Antiferromagnet

The magnetic-field-dependent ordering temperature of the quasi-2D quantum Heisenberg antiferromagnet (QHAF) Cu(pz)2(ClO4)2 was determined by calorimetric measurement in applied dc fields up to 33 tesla. The magnetic phase diagram shows a round maximum at 5.95 K and 17.5 T (at ≈ 1/3 of its saturation field), a 40 percent enhancement of the ordering temperature above the zero field value of 4.25 K. The enhancement and reentrance are consistent with predictions of a field-induced Heisenberg to XY crossover behavior for an ideal 2D QHAF system

Observation of Quantum Oscillations in The Low Temperature Specific Heat of SmB\u3csub\u3e6\u3c/sub\u3e

We report measurements of the low-temperature specific heat of Al-flux-grown samples of SmB6 in magnetic fields up to 32 T. Quantum oscillations periodic in \emph{1/H} are observed between 8 and 32 T at selected angles between [001] and [111]. The observed frequencies and their angular dependence are consistent with previous magnetic torque measurements of SmB6 but the effective masses inferred from Lifshitz-Kosevich theory are significantly larger and closer to those inferred from zero-field specific heat. Our results are thus consistent with a bulk density of states origin for the previously observed quantum oscillations