national high magnetic field laboratory
PULSED FIELD FACILITY
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strongly correlated electron systems in very high magnetic fields
Magnetic fields are powerful tools for studying the properties of correlated matter because they couple directly to the electronic charge and magnetic moments of the protons, neutrons, and electrons of which matter is made up. The properties of most materials are only weakly dependent on the strengths of the magnetic fields to which they are exposed, and for these substances, magnetic fields can be used analytically to determine fundamental properties such as their characteristic electronic energy scales and the band structures of metals and insulators, the placement of atoms in molecules, or even the internal structure and dynamics of living creatures. On the other hand, in some materials the magnetic field couples strongly and dramatically influences their properties: for example, in quantum Hall devices, magnetic materials, and superconductors. For these substances, magnetic field strength is as important a thermodynamic parameter as temperature or pressure. [“Opportunities in High Magnetic Field Science”, pub. by the U.S. National Academy of Sciences, 2005]
Thermal and lattice properties of strongly correlated electronic systems are fundamental pillars in the modern understanding of solid state physics. The specific heat, operationally defined as the amount of heat necessary to increase the temperature of a gram of a substance in one degree, is the temperature derivative of the system’s internal energy Cv = ∂U/∂T|v , which can be computed in a vast number of models providing direct comparison between numerical and laboratory data. The same is true for the coefficients of thermal expansion ∝ = (1/L)∂L/∂T, ∝v = (1/V)∂V/∂T|p although the complexity of strain tensors in real materials makes the comparison more complicated. Over the last decade a large number of highly correlated materials were studied with a combination of thermal, electric, magnetic and lattice properties probes at very low temperatures in very high magnetic fields at the NHMFL pulsed, dc and ultra low temperatures facility. An incomplete list is shown in Table I.
Table 1: An incomplete list of materials studied with a combination of thermal, magnetic, lattice, dielectric constant, electrical polarization and heat/electrical transport probes at the NHMFL.
The experimental study of quantum magnets in very large magnetic fields in the last decade, to mention one example, has been driven by measurements of specific heat, magnetocaloric effect, magnetization, magnetostriction, and dielectric constant at the NHMFL. Fig. 1 shows the temperature – magnetic field (T,H) phase diagram of a number of representative quantum magnets. All but TlCuCl3, included for comparison, were identified in the NHMFL user program. The physics that makes these systems unique is nicely represented in Fig. 2 with an animation of Goldstone modes in the XY-AFM ground state of quantum magnets, which can be approximated to a very good degree as a Bose-Einstein condensation of magnons. [Zapf, Jaime & Batista, Rev. Mod. Phys. (2012) to be published]
Figure 1: Temperature-Field phase diagram for a number of quantum magnets studied at the NHMFL.
Animation 1: Representation of the Goldstone mode in a Cu²⁺dimer system. The magnetic excitations in an ideal XY-AFM dimer system look like the gapless rotation mode displayed here. Anisotropies present in all real materials, however, corrugate the space where these excitations ‘live’, causing a collective pinning effect when they are not diluted enough.
Animation 2: Representation of the Goldstone mode in a Cu²⁺ dimer system. The magnetic excitations in an ideal XY-AFM dimer system look like the gapless rotation mode displayed here. Anisotropies present in all real materials, however, corrugate the space where these excitations ‘live’, causing a collective pinning effect when they are not diluted enough.
specific heat capacity
Dealing with short duration magnetic field pulses in calorimetry requires several considerations, regarding principally thermal equilibrium between sample and thermometry, and measurement techniques for resistive temperature sensors. Thermal equilibrium is addressed with the miniaturization of the specific heat stage. We used a Si and sapphire platforms, onto which we glue miniature amorphous-metal film heaters on Si substrates, and (typically 1x0.5x0.25) mm³ bare chip Cernox⁽ᴿ⁾and RuO thermometers. To minimize Eddy-current heating during magnetic field sweeps we mount all elements parallel to the applied magnetic field, and use fine resistive-alloy electrical wires for connections. The samples, weighting typically 0.5-2 mg depending on availability and expected contribution to the total specific heat, are polished into slabs as thin as the material would allow (typically 200-400 micrometers) with the largest surface glued to the Si platform to minimize the internal thermal time constant in the calorimeter platform, and also to minimize the sample cross section in the direction of the applied field. Extensive experience with state-of-the-art high frequency AC techniques in our lab indicates that measurement of electrical resistances between 1 Ohm and 1 kOhm are relatively easy to accomplish in a sub-millisecond timeframe, and that resistances between 1 mOhm and 10 kOhm are detectable, with anything smaller or larger requiring somewhat extraordinary measures.
Specific heat measurements in dc or flat-top pulsed magnetic fields are accomplished using techniques known as adiabatic or semi-adiabatic (often for dilution refrigeration temperatures 30mk-1K, but also useful at higher temperatures) and thermal relaxation time constant. In the first case a pulse of heat is delivered to a thermally isolated sample with a resistive heater, and the change in temperature is recorded as a function of the time. The specific heat is then computed as the heat delivered divided by the change in temperature observed in the sample Cp = Q/ΔT. This technique was used for the first ever specific heat measurements to 60T, carried out at the NHMFL (Jaime et al, Nature 405, 160 (2000)). The thermal relaxation time constant technique, used only in dc magnets, was originally developed by Sullivan & Seidel (Phys. Rev. 173, 679 (1968)) and consists in applying constant heat to the sample platform, which is thermally linked to the bath, and recording the sample temperature evolution as a function of the time. The specific heat is the computed as the (exponential) thermal relaxation time constant (τ) times the thermal conductivity of the thermal link (κ), Cp = τ.κ
An ac specific heat technique was recently developed at the NHMFL for use in pulsed magnetic fields where an alternate current of frequency causes temperature oscillations of frequency 2ω in the sample, which amplitude is inversely proportional to the sample specific heat. (Kohama et al., Rev. Sci. Instrum. 81, 104902 (2010)) This technique was successfully used to 60 T in the NHMFL long pulse magnet, as well as in a 50 T mid pulse magnet and dc superconductive/resistive magnets.