Download Measuring Fermi Surfaces in Extreme Magnetic Fields

• Introduction and title slide….
• The presentation will go through the types of Fermi surfaces we might observe and different techniques we use to try to see them.
• When possible, throughout the presentation, I have tried to include examples of measurements that have been taken at the NHMFL. • If there is any time remaining, I also want to discuss the topic of using high pressure for measurements of Fermi surfaces as well.
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• Electron states should be a solution to Schrodinger’s equation • A real‐space description of the electron in a box in 1D can also be described in reciprocal space as having the KE shown here = (h_bar^2 k^2)/2m • This model gets us pretty far and helps in the description of heat capacity, thermal conductivity and a few other properties but it does not tell us why a material behaves like a metal.
• In a lattice with spacing “a”…electron waves will encounter Bragg reflection at the boundaries. A standing wave solution describing the electrons requires that an energy gap is opened at the zone boundaries where the energy of the electrons can be described either (b) an extended zone scheme or (c) reduced zone where the energy bands fall into the same plot with the repeated rec. lattice space.
• The Fermi level describes where the outer electrons are in the these energy bands (See the red dotted line). If you have filled energy bands then there is no way for electrons to propagate to different energy states and you have an insulator. If you have a partially filled band then you have a metal. If electrons are below the Fermi level they are trapped in their states and don’t contribute to the FS and the states above the Fermi level aren’t occupied. • Note that this only describes the electron energy in one direction (in the 2
direction of “a”) and tells us that the electrons have enough energy that the Fermi energy is in the conduction band.
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• What is a FS? The location that gives us the LT electronic properties of materials.
• More simply put, it is the energy level at which electrons are interacting in a way that we can detect with out techniques and methods here using high fields.
• We aren’t detecting electrons in lower energy orbitals near the nucleus….we are exploring electrons near the edge of an atom that interact with neighboring atoms. • These blue drawings represent some of the basic shapes that Fermi Surfaces take……the intermediate shapes are “quasi” 1D or quasi 2D…..because they aren’t 1D or 2D in their simplest form.
• Basically, the pathways for carriers through a metal…..we’ll discuss ways that we can learn more about these pathways using strong magnetic fields.
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This slide represents work done here at the lab from Luis Balicas’ group. •
Once high quality xtals have been synthesized, they can be x‐rayed.
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The xtal structure of the material and lattice parameters can be determined. What is the spacing of the atoms and simplest description of the lattice?
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With this information we can generate a first guess what the FS will look like by harnessing the power of modern computers.
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In fact, there is pre‐packaged software (WIEN 2K) that can be purchased to try to produce your own band structure and FS figures for publication. •
In this case, the FS is a complicate set of “wavy” Q1D sheets (Yellow and blue) as well as Q2D, closed (red) cylinders.
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• Back up a step and consider some simpler examples…
• The properties of metals will be described by the valence electrons. For example, the structure of Na is body‐centered cubic from Group 1 of the periodic table.
• Na has a valence electron in the 3s state which gives us the 3s conduction band for metallic Na and has this simple, nearly spherical shape.
• The Group I elements mostly have these types of surfaces since their outer electrons shells are s‐orbitals.
• Cobalt, for comparison is much more complex. It is from Group 9 in the transitions metals where the outer shells of electrons are described by more energy bands.
• In this case you end up with a number of 3D irregular shapes and pockets that make up the Fermi surfaces.
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• An example that many people have heard of……The cuprates like YBCO are two‐dimensional materials because of the stacked CuO planes. • Two isotropic dispersion relations in the x and y‐directions can give a circular orbit, as shown in the drawing (axes are k_x, k_y and E(k)).
• The carriers travel most easily in this type of circular orbit on the surface of this warped cylinder (axes are k_x, k_y and k_z).
• Similar to the more complicated element example we saw with cobalt, compounds with multiple energy bands crossing the Fermi level can create more than one orbit in a material. In the case of SrFe2P2 we see that four different somewhat cylindrical FS are predicted.
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• A good example of a Q1D FS comes from the organic compounds built on TMTSF molecules (see left pic). • The pi‐orbitals from these molecules overlap in stacks which define the direction of highest conductivity (the a‐axis). • The anions on the system (PF6) create a buffer between the stacks. • So in the simplest truly one‐dimensional case….we would have completely flat FS sheets are shown in the top‐right.
• From this relation, the real‐space velocity stays perpendicular to the energy surface. In other words, if the sheets extend in the k_y and k_z direction that the real space velocity is in the x‐direction.
• For this material, the Fermi surfaces sheets are warped because we are not completely restricted to one‐dimension (bottom‐center figure).
• Q1D Fermi sheets allow for “nesting”, where a wavevector, Q, shows how the FS sheets mathc up across the BZ. When that happens, the behavior of a material can change completely.
• If large portions of the FS map onto each other then a change in the material (like a shift in the lattice) can easily lower the energy of a large fraction of the electrons….see the next slide.
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• There is a description of how an electron gas responds to a periodic potential called the
Lindhard response function which determines the electron density.
• The 1D case in shown here which a singularity where the wavevector between two parts
of the FS = 2k_F (left figure).
• This means that specifically in 1D systems, there an instability against a shift in the
lattice and a change in the electron density.
• The right figure provides a nice description of what is happening. At higher temperatures
we have a partially filled where the electrons move easily (a metal).
• At a transition temperature, there is an energy tradeoff:
Lattice sites (~ positive ions) shift closer together which costs energy but…
Electronic energy is lowered.
The electron density increases near the newly spaced pairs in the lattice
creating a charge density wave.
• A gap opens in the energy band at the Fermi level so the material becomes an insulator.
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• This a molecular compound based on perylene donors and is a real example of a Q1D system with a CDW transition. • The molecules are perylene (groups of carbon) and maleonitriledithiolene (mnt) w a
metal site (Au) at the cente.
• The red and blue thin bricks represent the molecules which pile on top of each other vertically (along the b‐axis) to form conducting chains.
• Carriers move easily in this direction down a temperature of ~ 12K where a gap begins to open as can be seen from the sample resistance growing as an energy gap opens at the Fermi level.
• A Peierls distortion is usually also confirmed by low temperature x‐ray data which shows the lattice shifting.
• A strong magnetic field can suppress the CDW to lower temperatures by splitting the energy bands with the Zeeman effect. The different energies of the spin up and down bands overcome the energy gap more easily.
• With an applied field of 35 T the transition temperature of the CDW can be lowered about 60%.
• This isn’t really a measurement of the FS as much as an example of how magnetic fields can be used to manipulate the carriers near the Fermi level.
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We need to explain the behavior of 2 and 3‐dimensional materials when the electrons are free to move. In the presence of a magnetic field, the momentum “p” must be replaced by “p + eA” where A is the vector potential that satisfies B = curl A.
This becomes our new Hamiltonian which includes the effect of the B field on the electrons to use on the wavefunctions to find the energy levels.
It turns out that this Hamiltonian follows the same form as the case of a harmonic oscillator and with the same energy solutions. Quantized (discrete) energy levels for the electrons which we call LANDAU LEVELS.
From the Kittel picture, the sharpness of the energy levels and Fermi level comes from low temperatures. The energy levels are spaced apart corresponding to B so as the field increases the spacing between energy levels increases too. Each time an energy level passes the Fermi energy we have a quantum oscillation.
Disorder and thermal broadening will in make the levels a little “fuzzy”.
This means we need to measure with clean samples and to take our measurements at low temperatures where the levels are well defined.
TAKE AWAY MESSAGE: • The allowed energy levels in a magnetic field are quantized! • This starts immediately even when the sample is in a small magnetic field….it is only a matter of getting clean enough data to resolve the levels.
• A good step by step derivation of the harmonic oscillator can be found in Griffiths QM book.
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• Note the figure on the lower right. When the LLs are formed they appear as tubes in 3 dimensions which are perpendicular to the applied field. The dashed line describes a spherical FS.
• As the field is swept the LLs pass the FS and allowed energy states then fall to the next LL.
• Top‐left: The Bohr‐Sommerfeld quantization rule describes through QM why an electron wave packet can only travel in discrete orbits.
• We use this rule along with our definitions of the carrier momentum and eq of motion in a magnetic field (integrated wrt time) .
• Once we set up the integral we use Stokes theorem and find that both terms just give the real space area of the orbit.
• TAKE AWAY MESSAGE (LEFT SIDE): Because of this quantization rule we find the amount of flux through the orbit in quantized. • Following the right side: Using the equation of motion for the carrier, we find the relation of the real and k‐space orbit areas.
• The 2nd equation shows the k‐space orbit area. We want to determine the spacing between consecutive LLs with equal k‐space area (when they reach the FS surface).
• TAKE AWAY MESSAGE (RIGHT SIDE): This equal spacing is periodic in 1/B and we call it the frequency of the orbit. This is called Onsager’s relation.
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• A 2D example using a molecular conductor.
• The material is made of complicated molecules (DMEDT-TTF =
Dimethylethylenedithio-tetrathiafulvane) that I have drawn as these blue-colored blocks
(lower).
• The top-left shows an “end-on” view of the molecules where they make a square
network.
• The pi-orbitals from the donor molecules in the square make conducting planes where
the electrons can easily move.
• The anions act as filler between these planes and isolate them from one another.
• We assume that a material with conducting planes will have a Q2D cylindrical
FS…..This material will have similar behavior to a ruthenate, cuprate or other Q2D
structured material.
• The next slide will show what happens if we apply a magnetic field perpendicular to
these layers.
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• The initial figure shows the Landau tubes (red) when the field is applied.
• When the field is increased the Landau levels begin to pass our cylindrical FS (blue).
• The data shows a set of quantum oscillations collected up to 45T taken at a series of low temperatures (0.5 – 4.3K).
• Notice the increased spacing between the peaks as a function of field.
• When the data is plotted vs inverse field, we can see equal spacing between the peaks.
• An FFT of the data will tell the value of the frequency or you can find the frequency by determing the difference between two consecutive inverse field peaks.
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• We can rotate the sample wrt to the magnetic field.
• As shown by this yellow area, the area of the k‐space perpendicular to the applied field will increase as you move away from the initial orientation (we’ll call it theta = 0).
• The increased S_k will give a larger frequency which can be plotted vs angle.
• You can see in this figure where the FS is nearly cylindrical the frequency increased following 1/cos(theta), where the dashed line is a fit.
• In a case like this the oscillations usually cannot be resolved past ~ 50, 60 or 70 degrees.
• Angular dependence of any material will give you more information, it doesn’t have to be 2D.
• For example, in the case of BaFe2As2 the frequencies do not follow a 1/cos(theta) dependence. The blue data indicates that orbit is 3D since we can see quantum oscillations over 90 degrees.
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• 45 tesla (in the hybrid magnet) is a large continuous magnetic field but we still sometimes need more information…
• We can see two examples where there are a limited number of peaks and the FFT does not show very clear results. • As shown in the lowest panel for Luis’ work, it is hard to determine whether the weight of the multiple peaks affect each other.
• In the case of the cuprates, the critical fields can be large enough that only a few peaks are observed once the sample becomes normal again before the maximum field. • We can take a couple of approaches:
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Try to obtain cleaner results with a better S/N so QO can be resolved to lower fields (good for Luis’ case on the left).
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For Suchitra’s case we need to apply a stronger magnetic field….
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• Suchitra continued her cuprate measurements in pulsed magnetic fields up to 100T.
• With more QO, the FFT can become more clear and she observes three distinct frequencies: one very strong central peak with lower amplitude ones on the sides. • Not every measurement need to be expanded to pulsed fields. Measuring by any technique (to be discussed in a moment) can be challenging when the field is swept to the maximum in several msec.
• Although this measurement was helped with higher maximum fields, they actually used the hybrid first to explore the FS topology as we will discuss in a minute.
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What techniques can we actually use to measure the Fermi surface?
One way is by measuring using AC susceptibility. This is usually done by making a set of coils that detect the sample that are wound in opposing directions (shown here in white) with an excitation coil around them. With no sample in place and with the excitation coil producing a strong AC signal, the detection coils should be well‐balanced and not give a response. When a sample is placed in one of the detection coils the sample magnetization can be detected.
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Another technique is dilatometry. Although this drawing looks complex it is actually a very simple concept. There is a parallel plate capaciator where the gap between the plates (red arrow). The lower plate is held by a spring and rests on top of a sample and when the length of the sample changes during quantum oscillations, a change in capacitance is seen. These length changes can be at the nm or even Angstrom size. The RSI by G. S. has all of the details of the apparatus.
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In the lower left there is a drawing of a capacitance cantilever for torque magnetometry. The black sample is sitting on top of a piece of metal foil where a small piece is held down by these screws. The base of the platform also has metal foil but these two pieces are separated by an insulating material at the base of the cantilever arm. When the magnetization changes a torque is produced which makes the upper foil move up and down and changes the cap signal.
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There is a second torque magnetoemeter technique is used in a similar way using a piezo‐resistive cantilever. A sample is attached to a cantilever where the base of the cantilever has a piezo‐resistive part, which changes resistance value when the cantilever is flexed. The is a matching reference piezo‐resistance value without a sample attached (both resistive parts enclosed in green). These resistances are used in a Wheatstone bridge configuration with two external resistors to balance the bridge. The whole circuit is very sensitive to torque through the very small changes in resistance as the sample cantilever moves up and down.
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A torque is only created for an anisotropic Fermi surface. For a 2D FS (a cylinder) the change in frequency at theta = 0 is zero so nearly 2D sample must be tilted away from this orientation to observe any torque signal. AC susceptibility and dilatometry could be used for any FS.
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• A discussion about the construction of a set of AC susceptibility coils:
• A cartoon of the coils is shown here with the detection pair of coils in blue and the excitation coil in orange (the sample is black).
• Details regarding the detection coils are listed. • The drive (excitation) coil should be carefully made to fit carefully on the outside of the detection coils.
• AC coil sets are often made to be used in pressure cells where the detection coils are about 3mm in diameter.
• This data collected for elemental Cr was taken from a set of coils with about 4500 total turns for the detection coil and ~ 500 turns for the excitation coil. • The overall signal collected is shown on the left axis.
• A polynomial background was subtracted for the data shown on the right axis. • Less than 1% of the overall signal contributes to QO which are observed at the uV level (a pretty small signal). • The FFT confirmed that we see several distinct orbits.
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• Transport is a great way of to measure the Fermi surface of materials if they have sufficient resistance that it is appropriate. • Depending on the size, shape and electrical anisotropy of the sample you might choose a few different contact configurations.
• A plate‐like sample morphology might indicate 2D characteristics (anisotropy) including having a lower resistance along the plate. • Measuring higher resistance is easier so we might measure through the thickness of the sample, if possible to perform an “inter‐plane” measurement.
• Items to keep in mind for transport measurements: 1) large RRR 2) 4 terminal measurements and 3) careful selection of sample currents. • Two simple formulas to remember:
• Ohm’s law when considering how much current you will need to resolve a reasonable signal. If the voltage will be too small you always amplify it.
• Power is the current squared times the resistance. A low resistance sample with one high resistance contact can create a source of self‐heating by using a high current. • Philip’s data: One way to make life easier is to increase the resistance of your sample. • In recent years, Philip Moll has been using a FIB (
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• For samples where making contacts can be difficult, measurements can be made with contacts all.
• The sample is placed at the center of a wire coil (photo‐left) that is part of a resonant circuit as shown (top‐right). The dashed line indicates the part of the circuit that is at lower temperatures at the end of a probe.
• As long as the tunnel diode is biased into a negative conductance region of the tunnel diode IV curve (center figure), you should see a resonant frequency from the circuit.
• When the sample in the coil changes resistance (or magnetization) there is a shift in the circuit frequency.
• The data shown is from BaFe2As2: • The circuit frequency of about 50 MHz is mixed and filtered to make the signal cleaner and to avoid noise from other RF signal. • The lower red line shows an overall change of about 2 MHz in our circuit frequency as we sweep the field to 35 T. • The black line shows a derivative of the results where quantum oscillations are pretty clear. • The upper panel of the figure shows that we can resolve the oscillation all the way down to about 3.5 T where the amplitude is about 50 Hz.
• This shows that you can resolve a signal of about 1 part per million using this technique.
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• Lifshitz and Kosevich came up with a description for the oscillation amplitude. • The magnetization or normalized conductivity is periodic in inverse field and also contains a number of damping terms which decrease the size of the oscillations.
• R_T: Quantum oscillations will get smaller as a function of increasing temperature. This can be seen directly by looking at oscillation amplitudes after subtracting the background or from looking at the changing amplitude of the peaks in the FFT. • R_D: The Dingle factor looks at the amplitude of the QO as a function of field. With the effective mass already known from the temperature fitting, the Dingle temperature can be found.
• The Dingle temperature can then be used to estimate the scattering rate in the material.
• R_S: The spin factor takes into account spin up and down electrons will have slightly different energies. The mass of a material also shifts as a function of angle so there are angles when this term will give zero amplitude for the oscillations (when p*g*mu = odd integer). • If the mass is well known then you can extract the Lande g‐factor which is usually about 2 for free electrons. 21
‐ Phase diagram (right): Squares (B//a) and circles (B//c) for ambient pressure.
‐ The Neel field (AFM suppressed) was determined through heat capacity in a PPMS and pulsed fields and dHvA oscillations.
‐ Hall effect transport does not show QO in this case but does show some abrupt changes that allow us to help define our phase boundary.
‐ Specifically the higher field “kink” at LT tells us that something is happening to the carriers in the material.
‐ The Fourier spectra show an evolution of higher frequency (i.e. larger k‐
space size) orbits with higher fields.
‐ This tells us that Ce‐4f electrons are moving from localized to itinerant.
‐ This is supported by the fact that an analogous compound, LaRhIn5 does not show the emergence of these large orbits.
‐ This story might become even more compelling by using high pressure. This would shift around the phase boundaries and we could see how quickly these new orbits emerge if you squeeze the lattice a little bit.
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• Angular dependent measurements of layered systems:
• If you have a material with a warped or “corrugated” Q2D Fermi surface (example: top‐
right) you can learn a lot through angular dependence.
• See the side view of a warped 2D FS….the warping is dependent on the stacking distance between the layers (pi/c).
• When the field is aligned vertically there will be smaller necks and wider bellies.
• As you rotate this warped type of FS there will be points when all of the orbits have the same area.
• These are called angular dependent MR oscillations or AMRO.
• As the sample is rotated the conventional QO (SdH) will still be observed. • But at some angles you will also see a peak in the angular dependence data.
• These peak angles can be plotted following Yamaji’s formula and the Fermi wavevector
can be found.
• If you then decide to rotate the sample in the plane (in phi) you can repeat the measurement. In this way the entire Fermi surface can be mapped out for warped 2D FS.
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• Suchitra Sebastian worked with a team to complete a tour‐de‐force set of AMRO measurements on cuprates.
• They used an RF technique like the one we discussed to observe resistance changes in the sample without actually attaching wires.
• The proposed FS contains cylinders in two locations: The gamma orbit is a Q2D warped
cylinder and the alpha cylinder which is not corrugated. The beta orbit is not easily observed.
• They completed a large set of AMRO measurements to map out the FS of the gamma FS by using the fact it is warped. • The resulting Fermi wavevector was then included in a model with information for the alpha orbit which fits well to the actual data.
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What type of apparatus can be used to actually pull off this measurement?
‐ We have a small piezo‐rotation platform that rotates in phi (green arrow) but sending voltage pulses to piezo actuators in the base.
‐ A brass platform was made to attach sample wires to the top. The blue is stycast epoxy where we have glued down some wire pads and there is very thin wire running through the center hole of the rotator.
‐ Next, we can see a larger version of this platform that is mounted in a brass assembly. This assembly fits into our SCM2 rotation probe (you will see this during your measurements with Ju‐Hyun Park and Hong Woo Baek). ‐ The red, dashed line indicates theta rotation for everything together.
‐ Some clever person could make a really nice Labview program to do all of the work automatically and we hope to have that in the future.
‐ (Pop‐up) Here we have taken a sample of PdCoO2 from Naoki Kikugawa and connected it to the platform.
‐ We see a peak each time that the field is aligned with the layers so if there is a small amount of backlash in the probe, then we can adjust for that.
‐ After we rotate in theta ~ 140o then we rotate  about 20o and then rotate in theta again.
‐ By changing phi discretely and then continuously through theta we obtain a set of data which looks like this.
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‐ THEN…we can use the spacing of the Yamaji oscillations to determine the Fermi wavevector for this specific value of phi.
‐ In this case, we can see the 60 degree symmetry of the FS, similar to the actual morphology of the crystal.
‐ As a high field user there are considerations to think about:
‐ Each angle sweep can take time….how much resolution do you need in your measurement?
‐ If you try this measurement in a resistive magnet, how much power are you willing to use? Usually this measurement is conducted at one, constant field. If you did only this measurement for one 10 hour magnet shift in a resistive magnet at max field, you would probably consume close to your weekly power budget.
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• There are additional reasons to see quantum oscillation‐like features in data.
• In the top‐right is a pair of Q1D warped Fermi surfaces. At the points C and E the FS are closer together.
• When both sheets are together on one side of the Brilluoun zone the carriers are moving in the same direction as shown by the red arrows.
• There is gap in energy between these surfaces but after the MB field the carriers can interfere with each other when they pass these closer nodes. • Oscillations will appear which correspond to the k‐space area shown in green.
• This same sort of phenomenon is observed with a Q1D and Q2D surface together (see lower‐left FS network). • With a strong enough field, carriers overcome the energy between surfaces and combinations of frequencies will be observed (see lower‐right FFT). 26
• Recently, a number of users at the lab have brought devices like the one shown here graphene on a boron nitride substrate. • The position of the Fermi level can be adjusted in the linear dispersion of graphene.
• The inset to the lower figure shows that conventional QO can be observed when the sample is gated.
• Now, typically many users use the magnets to sit at a maximum field and sweep the gate of the device to observe phenomenon like the fractional quantum Hall effect.
‐ Next slide begins a discussion of high pressure.
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• The cartoon states what we do with high pressure measurements. • Stan Tozer’s high pressure research advice is shown to the left.
• How is measuring materials under pressure useful? • Look at this project that Scott Hannahs worked on long ago….the back panel of the figure shows the temp‐field phase diagram for this organic material.
• Using pressure gives a 3rd axis of information to like about a material as you manipulate the molecular or atomic spacing.
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• Pressure work can be difficult…..
• This slide offers a rough outline for the pressure portion of the presentation.
• First, pressure is simply force divided by area it is applied.
• The units we often switch between for scientific measurements are GPa and kbar where 1 GPa = 10 kbar = 10,000 x atmospheric pressure.
• For a feel for the scale of these units, the really deep part of a swimming pool is only ~ 30% above atmospheric pressure
• Deep in the Marianas Trench (near Guam) the pressure is ~ 1000 atm.
• Using the feeling of water on you to describe pressure is accurate since it completely surrounds you as opposed to just a simple force (i.e. like gravity if you are falling).
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• There are a number of questions to consider before beginning pressure measurements.
• First, which device to you want to use based on the pressure that you need? What is the sample size that can be used?
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• There are a number of pressure cells available for magnet users in Tallahassee.
• Let’s look at the details of the HPI.
• Note the penny for scale to the pressure cell.
• The HPI is unique because the pressure can be changed while the same is in place in a magnet or dewar.
• The compressor unit takes the He gas pressure in a cylinder of He gas (~ 200 bar) and compresses it with a series of pistons.
• The compressed gas around the sample being measured eventually freezes to He ice at low temperatures as shown in the phase diagram for Helium.
• There is not really a liquid phase for Helium above 25 bar because then it sublimates between gas and solid.
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• An example of data collected with the HPI….note that the resistance shown in on a log scale.
• This material at ambient pressure is a CDW insulator at low temperature.
• With pressure added the energy gap is closed and oscillations begin to emerge from quantum intereference between the Q1D FS sheets.
• Oscillations observed from QI show the same angular dependence as if they were from closed circular orbits (with data collected in a different cell capable of rotation).
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• A large volume PCC is the pressure cell that almost everyone tries first.
• It is reasonably simple to mount your sample on top of the platform, place a teflon cup filled with fluid over it and assemble the cell.
• Once the cell is assembled we use external thds (not shown) to hang the PCC from a load stand before using a press to push on the ram.
• The ram pushes down on the piston and the top clamp is used to lock in the pressure.
• The cells can usually reach ~ 2.5 GPa and are made from non‐magnetic materials for our high field research.
• They can be used in the DR and there are many types in case you need to rotate you sample.
• There is an article by Walker in RSI where he goes into the details about working with PCCs.
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• This is an example of data collected using a PCC. We measured this pnictide material using a TDO coil inside the cell.
• The left panel shows the FSs that are predicted from calculations. The wider orbit labelled “3” is shown here and we found how the orbit area is modified with pressure….as the P in increased the diameter gets larger.
• For the cigar‐shaped orbit shown with “2” the frequency increased much more rapidly and a small orbit unexpected orbit is observed above 0.9 GPa.
• This gives an idea of how we can observe pressure modifying a Fermi surface….as example which shows off a more recent topic is shown with the next slide….
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• This set of measurements also really shows off what simply squeezing a sample can do….
• Left side: Dispersion relation in the x and y directions….note the large outer FS and very small inner FS
• Center: Now we look at the FS…the z‐axis is now reciprocal lattice space rather than energy.
• Right side: We can see how these results evolve with pressure…the outer FS (larger) becomes a little easier to observe but the frequency decreases slightly
• This means the orbit with the yellow arrows is getting smaller
• The inner FS (smaller) is growing slowly…..the ratio of these orbits, even under ~ 20,000x atm pressure is really about 100:1.
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• Consider your materials when designing your cell. Think about the environment of safety (first!) and the dimensions within your cryostat.
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• NHMFL has a few different sizes of small volume PCCs.
• With enough time, AC coils (as shown) can be made for the large or small volume PCCs.
• The smaller cell can rotate even in the hybrid magnet and was recently used for studies using the long‐pulse magnet in LANL.
• Typically metal pressure cells will generate too much heat from eddy currents as the magnet is pulsed but it was shown that heat doesn’t reach the sample until the pulse is finished.
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• DACs are challenging to use for high pressure research but offer a higher limit.
• The diamond can be used on a sample directly or will a gasket in place to allow for a more hydrostatic measurement.
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• Gasket materials—Stan has tried elephant tusk, warthog tusk, oyster shells, lobster shells, metals, plastics, ceramics, wood and many types of coatings
• Preindenting & relocation
• Insulation—alumina, diamond powder, c‐BN plus epoxy
• Drilling or EDMing the hole—rule of thumb culet:Øhole:height::3:1:0.1
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• There can be a lot of stored energy in a pressure cell. This estimate shows that ½ x (compressibility) x (volume of the liquid) x (pressure^2).
• With a typical piston cylinder cell at ~ 2.0 GPa, this approaches almost 100 J of energy.
• This is more than half of the energy from a small caliber handgun so safety is a big concern. 42
• Note to safe pressure users: I have had visitors come to Tallahassee with pressure cells in the past 2 years that have no idea what the cell is made from our the safe limit to apply a load.
• Know your material limits and stay safe!
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