Paramagnons and magnons: energy from heat

Take a look around, what do you see? Houses, cars, trees, people, etc. Everyone is running somewhere, everyone is in a hurry. A city resembling an anthill, especially at rush hour, is always filled with traffic. And the same picture is observed not only in the "big" world, but also at the atomic level, where innumerable particles move towards each other, collide, move away and again find a new partner for their incredibly complex and sometimes so short dance. Putting aside exaggeration and poetry, we’ll talk today about a study in which an international team of scientists from the University of North Carolina, the Oak Ridge National Laboratory, Ohio State University and the Chinese Academy of Sciences proved that paramagnons can convert temperature differences to electrical voltage. What are paramagnons, what is their unique feature, how did scientists realize their unusual “generator” and how effective is it? We learn about this from the report of the research group. Go.

Theoretical base

To begin with, we should deal with these obscure paramagnons, what they are and what they eat with. And for this you need to understand what their older brothers are - the magnons.



Magnon is a quasiparticle that corresponds to elementary excitation at the moment of spin interaction (intrinsic angular momentum of elementary particles, not related to the particle’s movement in space).



In solids with magnetic ions, thermal spin disturbances can either line up with each other (ferromagnets or antiferromagnets) or not line up (paramagnets), i.e. Ordered or not ordered.



In paramagnets, spins seem to be chaotic, unlike ferromagnets / antiferromagnets, but this is not entirely true. In fact, they form short-term, locally ordered structures of short-range interaction - paramagnons, which exist for a very, very short time (billionths of a second, or even less). In terms of propagation, the paramagnons span just a few atoms (2 to 4).



Simply put, the activity of paramagnons resembles the physical realization of the slogan “life fast, die young” (live fast, die young), from which earlier interest in them was not so great. But in the work that we are considering today, scientists have shown that even paramagnons are able to move with a temperature difference and take a couple of free electrons with them, generating thermal emf * .

Thermoelectric effect * (thermo-EMF / Seebeck effect) - the phenomenon of the appearance of an electromotive force at the ends of series-connected heterogeneous conductors, the contacts between which are at different temperatures.

This unusual phenomenon was called "paramagnon drag" (paramagnon drag), which perfectly describes the ability of paramagnons to "pull" electrons behind them.



Scientists have been able to show in practice that the paramagnon traction in manganese telluride (MnTe) extends to very high temperatures and generates thermo-emf, which is much stronger than exclusively elemental electric charges could achieve.



More precisely, scientists have found that local fluctuations of thermal magnetization in lithium-doped manganese telluride (MnTe) greatly increase its thermo-emf at temperatures up to 900 K. Below Néel temperature (T _N ~ 307 K), manganese telluride is antiferromagnetic.

Néel temperature * (Néel point, T _N ) is an analog of the Curie point, but for an antiferromagnet. When the Néel point is reached, the antiferromagnet loses its magnetic properties and turns into a paramagnet.

Magnon traction is maintained in the paramagnetic state up to> 3 x T _N due to long-lived short-term antiferromagnet-like fluctuations (paramagnons) that exist in the paramagnetic state, which was confirmed by neutron spectroscopy. In this case, the paramagnon lifetime is longer than the interaction time of the charge carrier and magnon, its spin-spin spatial correlation length is longer than the Bohr radius * and de Broglie wavelength * for free carriers.

The Bohr radius * is the radius of the orbit of the electron of the hydrogen atom closest to the nucleus in the atomic model, where the electrons move in circular orbits around the nucleus.

De Broglie wavelength * is the wavelength that determines the probability density of an object being detected at a given point in the configuration space. The de Broglie wavelength is inversely proportional to the particle momentum.

Consequently, for moving charge carriers, paramagnons look like magnons and give the thermo-EMF of paramagnon traction.



In this work, scientists used, as we already know, lithium-doped MnTe, as well as an antiferromagnetic (AFM) p-type semiconductor with an ordering temperature T _N ~ 307 K, a Curie-Weiss temperature T _C ~ −585 K and a band gap Eg ~ 1.2 eV . The hole concentration (positive charge carrier) is adjusted (2.5 × 10 ¹⁹ <n <2 × 10 ²¹ cm ⁻³ ) by changing the concentration of lithium (Li). The paramagnons were detected by neutron spectroscopy, and their lifetime (t _L = ~ 3 × 10 ^-14 s) was measured up to a temperature of 450 K.

Research results

Six polycrystalline Li _x Mn _1-x Te samples with doping levels x = 0.003, 0.01, 0.02, 0.03, 0.04, and 0.06 were prepared for analysis. The hole concentration for the samples was 5.5 × 10 ¹⁹ , 15 × 10 ¹⁹ , 29 × 10 ¹⁹ , 45 × 10 ¹⁹ , 35 × 10 ¹⁹ and 100 × 10 ¹⁹ cm ^–3, respectively.



Samples were obtained by grinding the starting elements for 8 hours in an argon-containing vessel made of stainless steel using a high-energy vibratory ball mill. After grinding, the resulting mass was hot pressed at 1173 K for 20 minutes by spark plasma sintering under an axial pressure of 40 MPa with a heating rate of 50 K / min. The obtained disk-shaped samples had a diameter of 12.7 mm, and their thickness was ~ 2 mm. Scientists have measured specific thrust and thermo-EMF on samples cut both perpendicularly and parallel to the direction of pressing. This analysis confirmed the isotropy of both sample variants (i.e., they are the same).





Image No. 1



Figure 1A shows the temperature dependence of thermo-EMF for all six samples. All the curves on the graph have a common feature - after the peak of phonon traction in the region of 30 K, the thermo-EMF slowly increases at T <150 K, then there is a sharp jump at 150 K <T ≤ T _N , and then a gradual increase at 150 K <T <750 K.



Graphs 1B and 1C show specific thrust and thermal conductivity data that are used to calculate the quality factor (Z _{T T} ) shown in Figure 1D . The value of Z _{T T} = 1 is achieved at a doping level of x = 0.03 and a temperature of T = 850 K.



Neutron scattering measurements were also carried out to study the magnetic structure of the sample with x = 0.03 in the paramagnetic mode. This study plays an important role, since a high figure of merit is achieved precisely in the paramagnetic mode.



In the AFM phase at 250 K, scattering of magnons is observed, emanating from the magnetic Bragg peaks * at 0.92 and 1.95 Å ⁻¹ . The magnon regions expand to a maximum energy of ~ 30 meV.

The Bragg curve * is a graph of the dependence of the particle energy loss on the penetration depth into the substance.

Image No. 2



When the temperature reaches an index above ~ 350 K, there is a clear scattering of paramagnons at 0.92 Å ⁻¹ , and the magnon region disappears at 30 meV. Thus, we can say that paramagnon scattering correlates with temperature in intensity and energy distribution up to 450 K ( 2B - 2D ). In addition, paramagnon scattering does not depend on the Li concentration in the studied range from 0.3 to 5 at.% ( 2F and 2G ).



Scientists note another curious fact: data changed over a period of 1 minute ( 2B ) show the same features as data measured over a period of 1 hour ( 2C and 2D ).





Image No. 3



The concentration of charge carriers ( n ) was also measured from measurements of the Hall effect in the AFM (antiferromagnetic) mode ( 3A ). The Hall coefficient shows the anomaly at T _N (Néel temperature), and also in different samples it can show values ​​in the PM (paramagnetic) mode that are different from the values ​​in the AFM mode. Since the carrier concentration is determined by the doping level of Li, which is temperature independent, the concentration itself is also temperature independent for n> 6 x 10 ¹⁹ cm ⁻³ .



Regarding the specific heat capacity of magnon (C _m ), it was determined experimentally from measurements of the total specific heat capacity. The specific heat capacity ( C ) of all six samples has the same temperature dependence curve and does not show a field dependence up to 7 T. Figure 3B shows the specific heat capacity of a sample doped with 6% Li, which consists of the Debye temperature * , the electronic contribution at T <6 K and magnetic contribution.

Debye temperature * is the temperature at which all vibration modes in a solid are excited.

The electron part at low temperature follows diffusion thermo-EMF, the phonon part follows the Debye function, and the magnetic part follows magnon traction. At low temperatures, the specific heat of both phonons and magnons is proportional to magnon traction, and the specific heat of electrons is proportional to temperature.



Graph 3C shows the Hall charge mobility, which was used to calculate the electron scattering time ( 3D ).



In AFM mode, the total thermo-EMF ( a ) is defined as the sum of the magnon traction ( a _md ) and diffusion thermo-EMF ( a _d ).





Image No. 4



In the PM mode, the data show that the total thermo-EMF also has two components: diffusion thermo-EMF and additional thermo-EMF, independent of temperature up to 800 K.



In the graphs above, the diffusion thermo-EMF is represented by a dashed line at T> T _N. Here you can see confirmation that thermo-EMF increases with temperature in the PM mode. In this case, the experimental value of thermo-EMF is very different from the calculated value. This difference is an indicator of thermo-EMF magnon traction at T _N. This area of ​​the difference on the graph, attributed to magnon traction, in the PM mode expands, from which it can now be reliably attributed to paramagnon traction. Observations show that this phenomenon remains independent of temperatures up to 800 K, but continues to exist up to 900 K.



For a more detailed acquaintance with the nuances of the study, I recommend that you look into the report of scientists and additional materials to it.

Epilogue

A study of the thermoelectric properties of lithium-doped MnTe showed that the calculated (theoretical) magnon thermo-EMF in a magnetically ordered state agrees well with what has been obtained in practice. Scientists also confirmed the existence of paramagnons in the PM MnTe mode and their significant contribution to the formation of thermo-EMF.



A Q factor of 1 was also obtained at 900 K in a sample doped with 3% Li. This shows that paramagnons can be a new round in the study of high-performance thermoelectric materials.



Such studies can play an important role in improving the technology of collecting thermal energy, which can be realized in the form of converting automobile exhaust gases into electricity and even for wearable electronics powered by the heat of the human body.



Now there is a tendency to seek energy wherever it can be. Again, this is quite explainable by the situation in which mankind is now in the aspect of limited resources and growing demand for energy-efficient technologies. It is impossible to say that this is bad, but many with open skepticism relate to such initiatives, claiming that it is either ineffective or too late. However, as the old saying goes, late is better than never.



Thank you for your attention, remain curious and have a good working week, guys! :)



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