The imperfection of strontium titanate

When you squeeze some crystals, you distort their lattice of atoms just enough to separate a pair of charged particles and that in turn gives rise to a voltage. Such materials are called piezoelectric crystals. Not all crystals are piezoelectric because the property depends on what the arrangement of atoms in the lattice is.

For example, the atoms of strontium, titanium and oxygen are arranged in a cubic structure to form strontium titanate (SrTiO3) such that each molecule displays a mirror symmetry through its centre. That is, if you placed a mirror passing through the molecule’s centre, the object plus its reflection would show the molecule as it actually is. Such molecules are said to be centrosymmetric, and centrosymmetric crystals aren’t piezoelectric.

In fact, strontium titanate isn’t ferroelectric or pyroelectric either – an external electric field can’t reverse their polarisation nor do they produce a voltage when they’re heated or cooled – for the same reason. Its crystal lattice is just too symmetrical.

The strontium titanate lattice. Oxygen atoms are red, titanium cations are blue and strontium cations are green.

However, scientists haven’t been deterred by this limitation (such as it is) because its perfect symmetry indicates that messing with the symmetry can introduce new properties in the material. There are also natural limits to the lattice itself. A cut and polished diamond looks beautiful because, at its surface, the crystal lattice ends and the air begins – arbitrarily stopping the repetitive pattern of carbon atoms.

An infinite diamond that occupies all points in the universe might look good on paper but it wouldn’t be nearly as resplendent because only the symmetry-breaking at the surface allows light to enter the crystal and bounce around. Similarly, centrosymmetric strontium titanate might be a natural wonder, so to speak, but the centrosymmetry also keeps it from being useful (despite its various unusual properties; e.g. it was the first insulator found to be a superconductor at low temperatures, in 1967).

Tausonite, a naturally occurring mineral form of strontium titanate. Credit: Materialscientist/Wikimedia Commons, CC BY-SA 3.0

So does strontium titanate exhibit pyro- or piezoelectricity on its surface? Surprisingly, while this seems like a fairly straightforward question to ask, it hasn’t been straightforward to answer.

A part of the problem is the definition of a surface. Obviously, the surface of any object refers to the object’s topmost or outermost layer. But when you’re talking about, say, a small electric current originating from the material, it’s difficult to imagine how you could check if the current originated from the bulk of the material or just the surface.

Researchers from the US, Denmark and Israel recently reported resolving this problem using concepts from thermodynamics 101. If the surface of strontium titanate is pyroelectric, the presence of electric currents should co-exist with heat. So if a bit of heat is applied and taken away, the material should begin cooling (or thermalising) and the electric currents should also dissipate. The faster the material cools, the faster the currents dissipate, and the faster the currents dissipate, the lower the depth to which the material is pyroelectric.

In effect, the researchers induced pyroelectricity and then tracked how quickly it vanished to infer how deeply inside the material it existed.

Both the bulk and the surface are composed of the same atoms, but the atomic lattice on the surface also has a bit of surface tension. Materials scientists have already calculated how deeply this tension penetrates the surface of strontium titanate, so the question was also whether the pyroelectric behaviour was contained in this region or went beyond, into the rest of the bulk.

The team sandwiched a slab of strontium titanate between two electrodes, at room temperature. At the crystal-electrode interface, which is a meeting of two surfaces, opposing charged particles on either side gather and neutralise themselves. But when an infrared laser is shined on the ensemble (as shown above), the surface of strontium titanate heats up and develops a voltage, which in turn draws the charges at its surface away from the interface. The charges in the electrode are then left without a partner so they flow through a wire connected to the other electrode and create a current.

The laser is turned off and the strontium titanate’s surface begins to cool. Its voltage drops and allows the charged particles to move away from each other, and some of them move towards the surface to once again neutralise oppositely charged particles from the other side. This process stops the current. So measuring how quickly the current drops off gives away how quickly the voltage vanishes, which gives away how much of the material’s volume developed a voltage due to the pyroelectric effect.

The penetration depth the group measured was in line with the calculations based on surface tension: about 1.2 nm. To be sure the effect didn’t involve the bulk, the researchers repeated the experiment with a thin layer of silica (the major component of sand) on top of the strontium titanate surface, and there was no electric current when the laser was on or off.

In fact, according to a report in Nature, the team also took various precautions to ensure any electric effects originated only from the surface, and due to effects intrinsic to the material itself.

… they checked that the direction of the heat-induced current does not depend on the orientation of the crystal, ruling out a bulk effect; and that the local heating produced by the laser is very small…, which means that the strain gradients induced by thermal expansion are insignificant. Other experiments and data analysis were carried out to exclude the possibility that the induced current is due to molecules … adsorbed to the surface, charges trapped by lattice defects, excitation of free electrons induced by light, or the thermoelectric Seebeck effect (which generates currents in semiconductors that contain temperature gradients).

Now we know strontium titanate is pyroelectric, and piezoelectric, on its surface at room temperature – but this is not all we know. During their experiments (with different samples of the crystal), the researchers spotted something odd:

The pyroelectric coefficient – a measure of the strength of the material’s pyroelectricity – was constant between 193 K and 225 K (–80.15º C to –48.15º C) but dropped sharply above 225 K and vanished above 380 K. The researchers note in their paper, published on September 18, that others have previously reported that the strontium titanate lattice near the surface changes from a cubic to a tetragonal structure at around 150 K, and that a similar transformation could be happening at 225 K.

In other words, the surface pyroelectric effect wasn’t just producing a voltage but could in fact be altering the relative arrangement of atoms itself. What the precise mechanism of action could be we don’t know – nor any other features that might arise in the material as a result. The researchers hope future studies can resolve these questions.

The magnetic sky

On May 6, the team behind the now-inoperative Planck space telescope released a map of the magnetic field pervading the Milky Way galaxy.


Titled ‘Milky Way’s Magnetic Fingerprint’, the map incorporates two textures to visualize the magnetic field’s dual qualities: striations for direction and shading for intensity.

Planck was able to measure the polarization by studying light. Light is a wave (apart from being a particle, too). As a wave, it is composed of electric and magnetic fields vibrating perpendicular to each other. Overall, however, the two fields could vibrate in any direction. So when they choose to vibrate in a particular direction, the light is said to be polarized.

Such light is emitted by dust grains strewn in the space between Milky Way’s stars. As Dr. Chris Tibbs, an astrophysicist from Caltech, told me over Twitter, “Dust grains absorb light from stars, which heats up the grains, and [they] then radiate away this heat producing the emission.”

The grains are oriented along the Milky Way’s magnetic field, so the light they emit is polarized along the magnetic field. Because the grains are so small, the light they emit is of very low intensity (i.e. very long wavelength), so it takes a powerful telescope like Planck, perched on its orbit around the Sun, to study it.

It used a technique that’s the opposite of polarized sunglasses, which use filters to eliminate polarized light and reduce glare. The telescope, on the other hand, used filters to eliminate all but the polarized light, and then studied it to construct the map shown above.

As the astrophysicist Katie Mack pointed out on her Facebook page, the Planck team that released this image has carefully left out showing the magnetic fields in the region of the sky studied by the BICEP2 telescope at the South Pole which, on March 17, announced the discovery of evidence pointing to cosmic inflation. According to Katie,

The amount of polarized dust emission in the region where BICEP2 made its observation is unknown, but if it turns out to be a lot, it could mean that the signal BICEP2 saw was not entirely primordial.

This means we’ve to wait until the end of the year to know if the BICEP2 announcements were all they were made out to be.

The Big Bang did bang

The Hindu
March 19, 2014

On March 17, the most important day for cosmology in over a decade, the Harvard-Smithsonian Centre for Astrophysics made an announcement that swept even physicists off their feet. Scientists published the first pieces of evidence that a popular but untested theory called cosmic inflation is right. This has significant implications for the field of cosmology.

The results also highlight a deep connection between the force of gravitation and quantum mechanics. This has been the subject of one of the most enduring quests in physics.

Marc Kamionkowski, professor of physics and astronomy at Johns Hopkins University, said the results were a “smoking gun for inflation,” at a news conference. Avi Loeb, a theoretical physicist from Harvard University, added that “the results also tell us when inflation took place and how powerful the process was.” Neither was involved in the project.

Rapid expansion

Cosmic inflation was first hypothesized by American physicist Alan Guth. He was trying to answer the question why distant parts of the universe were similar even though they couldn’t have shared a common history. In 1980, he proposed a radical solution. He theorized that 10-36 seconds after the Big Bang happened, all matter and radiation was uniformly packed into a volume the size of a proton.

In the next few instants, its volume increased by 1078 times – a period called the inflationary epoch. After this event, the universe was almost as big as a grapefruit, expanding to this day but at a slower pace. While this theory was poised to resolve many cosmological issues, it was difficult to prove. To get this far, scientists from the Centre used the BICEP2 telescope stationed at the South Pole.

BICEP (Background Imaging of Cosmic Extragalactic Polarization) 2 studies some residual energy of the Big Bang called the cosmic microwave background (CMB). This is a field of microwave radiation that permeates the universe. Its temperature is about 3 Kelvin. The CMB consists of electric (E) and magnetic (B) fields, called modes.

Polarized radiation

Before proceeding further, consider this analogy. When sunlight strikes a smooth, non-metallic surface, like a lake, the particles of light start vibrating parallel to the lake’s surface, becoming polarized. This is what we see as glare. Similarly, the E-mode and B-mode of the CMB are also polarized in certain ways.

The E-mode is polarized because of interactions with scattered photons and electrons in the universe. It is the easier to detect than the B-mode, and was studied in great detail until 2012 by the Planck space telescope. The B-mode, on the other hand, can be polarized only under the effect of gravitational waves. These are waves of purely gravitational energy capable of stretching or squeezing the space-time continuum.

The inflationary epoch is thought to have set off gravitational waves rippling through the continuum, in the process polarizing the B-mode.

To find this, a team of scientists led by John Kovac from Harvard University used the BICEP2 telescope from 2010 to 2012. It was equipped with a lens of aperture 26 cm, and devices called bolometers to detect the power of the CMB section being studied.

The telescope’s camera is actually a jumble of electronics. “The circuit board included an antenna to focus and filter polarized light, a micro-machined detector that turns the radiation into heat, and a superconducting thermometer to measure this heat,” explained Jamie Bock, a physics professor at the California Institute of Technology and project co-leader.

It scanned an effective area of two to 10 times the width of the Moon. The signal denoting effects of gravitational waves on the B-mode was confirmed with a statistical significance of over 5σ, sufficient to claim evidence.

Prof. Kovac said in a statement, “Detecting this signal is one of the most important goals in cosmology today.”

Unified theory

Despite many physicists calling the BICEP2 results as the first direct evidence of gravitational waves, theoretical physicist Carlo Rovelli advised caution. “The first direct detection is not here yet,” he tweeted, alluding to the scientists only having found the waves’ signatures.

Scientists are also looking for the value of a parameter called r, which describes the level of impact that gravitational waves could have had on galaxy formation. That value has been found to be particularly high: 0.20 (+0.07 –0.05). This helps explain why galaxies formed so rapidly, how powerful inflation was and why the universe is so large.

Now, astrophysicists from other observatories around the world will try to replicate BICEP2’s results. Also, data from the Planck telescope on the B-mode is due in 2015.

It is notable that gravitational waves are a feature of theories of gravitation, and cosmic inflation is a feature of quantum mechanics. Thus, the BICEP2 results show that the two previously exclusive theories can be combined at a fundamental level. This throws open the door for theoretical physicists and string theorists to explore a unified theory of nature in new light.

Liam McAllister, a physicist from Cornell University, proclaimed, “In terms of impact on fundamental physics, particularly as a tool for testing ideas about quantum gravity, the detection of primordial gravitational waves is completely unprecedented.”