Intern
Experimental Physics III

Topological Magnetic Devices

A combination of topology and magnetism results in some interesting emergent physics. One example is the quantum anomalous Hall effect, observed in ferromagnetic topological insulators such as Cr/V-doped (Bi,Sb)2Te3 grown using molecular beam epitaxy. The main feature of the effect is quantized electrical transport in the absence of any externally applied magnetic field, which can lead to real life applications in quantum metrology. Careful analysis of the effect can also give information about the underlying electrodynamics in the system, revealing the presence of additional terms in the Maxwell’s equations. Moreover, the magnetism in Cr/V-doped (Bi,Sb)2Te3 is not yet fully understood, and is found to reveal a lot of interesting effects. Below we outline more details about various research directions.

 

Quantum metrology.

As of 2019, the base units in the new SI system are defined from fundamental constants of nature. The kilogram, which prior was defined based on a physical artifact stored in Paris, now is tied to the Planck’s constant (h). Presently the best way to experimentally determine the value of h (as well as another base SI constant e, the elementary charge) is to measure a quantized resistance (the von-Klitzing constant RK = h/e2) and quantized voltage (the Josephson constant KJ= 2e/h). A combined measurement of RK and KJ directly gives e and h. Presently RK is measured using the quantum Hall effect and the KJ using the a.c. Josephson effect. These are fundamentally incompatible with each other, as the large external magnetic fields needed to establish the quantum Hall effect make Josephson devices inoperable. The quantum anomalous Hall effect can solve this problem by providing a way to measure RK at zero external magnetic field.

So far, the resistance standard based on the quantum anomalous Hall effect at zero external magnetic field can only operate under very demanding experimental conditions: extremely low temperature (below some 0.05 K) and low electrical currents (below some 0.1 µA). Ultimately both parameters will need to be significantly improved. As a point of comparison, the QHE can work at a temperature of 4.2 K and electrical currents above 10 µA, making the effect significantly easier and cheaper to operate.

In addition to simplifying access to the constants h and e, the combined instrument (with the quantum anomalous Hall and the Josephson effects) will be a universal electrical reference. It will provide a quantum standard of voltage, resistance, and by means of Ohm’s law, current, in a compact experiment. A general desire to build simpler and more universal standards is at the forefront of modern metrology, to reach as broad industrial base as possible.

The bulk of the research in this direction has been done together with the German national metrology institute (PTB), using their expertise on precise quantum Hall measurements, allowing our resistance standard based on the V-doped (Bi,Sb)2Te3 to reach the precision and accuracy (relative to RK) at a few parts-per-billion (or 10-9) level. This research towards improving the standard is a part of the Europe-wide EURAMET metrology consortium QuAHMET (https://www.euramet.org/research-innovation/search-research-projects/details/project/quantum-anomalous-hall-effect-materials-and-devices-for-metrology).

Results on the topics related to metrology and optimizing the quantum anomalous Hall effect are published in the Refs. [1,3,5,6,12,16,18,20,21,23], and the work of the Ref. [18] resulted in a European patent filing [16].

 

Unconventional magnetism.

V(or Cr)-doped (Bi,Sb)2Te3 material turns out to be an interesting platform to study a variety of magnetic phenomena. Much of the literature calls the material a ferromagnet. There is much more than that to the story, as transport experiments show evidence for superparamagnetism, even concurrent with a perfect electronic transport quantization near zero external magnetic field.

Indeed, the electronic transport studies of lithographically patterned nanostructures reveal rich magnetic domain driven phenomenology when the device dimensions approach a characteristic magnetic domain size of some 100 nm. Individual magnetic domains can even have a ground state with magnetization pointing antiparallel relative to its neighbors, which indicates a complex competition of ferro- and antiferromagnetic domain-domain interactions. To top it all up, it has been observed that the magnetization switching dynamics from individual domains show that the switching happens via quantum tunneling. Individual magnetic domain being an ensemble of more than 10’000 magnetic atoms (each contributing a magnetic moment), not only makes it an example of macroscopic quantum tunneling of magnetization, but also makes it the largest magnetic object ever observed to show quantum tunneling.

In addition, this material shows some interesting anomalous Hall effect behavior at high temperatures (i. e. above 1 K or so), which indicates coexistence of more than one ferromagnetic state in the material. Systematic studies as a function of material parameters such as the doping level and layer thickness indicate that one component originates on the surface and the other in the bulk of the magnetic topological insulator layer.

Results on the topics related to magnetism in topological materials are published in the Refs. [1,2,8,9,10,14,17].

 

Axion electrodynamics.

It turns out that electrodynamics of the three-dimensional topological insulators go beyond the traditional Maxwell’s equations. Frank Wilczek proposed in 1987 that the same equations that pose a solution to the so-called “strong CP problem” in quantum chromodynamics, can describe electrodynamics in some semiconductor (later known as topological) systems, effectively enabling studying high-energy particle physics on a chip. Later, it was found that the presence of these additional (axion) terms in the Maxwell’s equations directly affects specific observable transport properties of topological systems, allowing an experimental access to these exotic properties. Indeed, one way to do it is to study the conductivity tensor elements scaling of the quantum anomalous Hall effect. A careful control of the evolution of this scaling as a function of the (V,Bi,Sb)2Te3 layer thickness shows a transition between the axionic regime for thicker layers (around 10 nm thick), and a two-dimensional regime without the axion physics (some 6 nm).

Our results on the topic of axion physics are published in the Refs. [4,7,13].

 

Superconductivity.

Stay tuned for details.

Results on the topic of interfacing superconductivity with magnetic topological materials are published in the Refs. [11,15,22].

 

 

Contact persons:

Dr. Kajetan M. Fijalkowski, email: kajetan.fijalkowski@physik.uni-wuerzburg.de

Dr. Pankaj Mandal, email: pankaj.mandal@physik.uni-wuerzburg.de

Prof. Charles Gould, email: charles.gould@physik.uni-wuerzburg.de

 

 

References:

2015:

  1. S. Grauer, S. Schreyeck, M. Winnerlein, et al., “Coincidence of superparamagnetism and perfect quantization in the quantum anomalous Hall state”, Physical Review B 92, 201304(R) (2015), DOI: 10.1103/PhysRevB.92.201304.

 

2016:

  1. T. R. F. Peixoto, H. Bentmann, P. Rüßmann, et al., “Non-local effect of impurity states on the exchange coupling mechanism in magnetic topological insulators”, Physical Review B 94, 195140 (2016), DOI: 10.1038/s41535-020-00288-0.

 

2017:

  1. M. Winnerlein, S. Schreyeck, S. Grauer, et al., ”Epitaxy and structural properties of (V,Bi,Sb)2Te3 layers exhibiting the quantum anomalous Hall effect“, Physical Review Materials 1, 011201(R) (2017), DOI: 10.1103/PhysRevMaterials.1.011201
  2. S. Grauer, K.M. Fijalkowski, S. Schreyeck et al., “Scaling of the Quantum Anomalous Hall Effect as an Indicator of Axion Electrodynamics”, Physical Review Letters 118, 246801 (2017), DOI: 10.1103/PhysRevLett.118.246801.

 

2018:

  1. M. Götz, K. M. Fijalkowski, E. Pesel, et al., “Precision measurement of the quantized anomalous Hall resistance at zero magnetic field”, Applied Physics Letters 112, 072102 (2018), DOI: 10.1063/1.5009718.
  2. M. Götz, K. M. Fijalkowski, E. Pesel, et al., “Zero-field quantized anomalous Hall resistance of (Bi,Sb)2Te3”,2018 Conference on Precision Electromagnetic Measurements (CPEM 2018) (2018), DOI: 10.1109/CPEM.2018.8501001.
  3. K. M. Fijalkowski, S. Grauer, S. Schreyeck et al., “On the Nature of the Quantum Anomalous Hall Effect”, 2018 Conference on Precision Electromagnetic Measurements (CPEM 2018) (2018), DOI: 10.1109/CPEM.2018.8500974.

 

2020:

  1. K. M. Fijalkowski, M. Hartl , M. Winnerlein, et al., “Coexistence of Surface and Bulk Ferromagnetism Mimics Skyrmion Hall Effect in a Topological Insulator”, Physical Review X 10, 011012 (2020), DOI: 10.1103/PhysRevX.10.011012.
  2. A. Tcakaev, V. B. Zabolotnyy, R. J. Green, et al., “Comparing magnetic ground-state properties of the V- and Cr-doped topological insulator (Bi,Sb)2Te3”, Physical Review B 101, 045127 (2020), DOI: 10.1103/PhysRevB.101.045127.
  3. T. R. F. Peixoto, H. Bentmann, P. Rüßmann, et al., “Non-local effect of impurity states on the exchange coupling mechanism in magnetic topological insulators”, npj Quantum Materials 5, 87 (2020), DOI: 10.1038/s41535-020-00288-0.
  4. M. Kayyalha, D. Xiao, R. Zhang et al., “Absence of evidence for chiral Majorana modes in quantum anomalous Hall-superconductor devices”, Science 367, 6473, 64-67 (2020), DOI: 10.1126/science.aax6361.

 

2021:

  1. K. M. Fijalkowski, N. Liu, P. Mandal, et al., “Quantum anomalous Hall edge channels survive up to the Curie temperature”, Nature Communications 12, 5599 (2021), DOI: 10.1038/s41467-021-25912-w.
  2. K. M. Fijalkowski, N. Liu, M. Hartl et al., “Any axion insulator must be a bulk three-dimensional topological insulator”, Physical Review B 103, 235111 (2021), DOI: 10.1103/PhysRevB.103.235111.

 

2022:

  1. N. Liu, S. Schreyeck, K. M. Fijalkowski, et al., “Antiferromagnetic order in MnBi2Te4 films grown on Si(111) by molecular beam epitaxy”, Journal of Crystal Growth 591, 126677 (2022), DOI: 10.1016/j.jcrysgro.2022.126677.
  2. P. Mandal, N. Taufertshöfer, L. Lunczer et al., “Finite Field Transport Response of a Dilute Magnetic Topological Insulator-Based Josephson Junction”, Nano Letters 22, 3557-3561 (2022), DOI: 10.1021/acs.nanolett.1c04903.

 

2023:

  1. K. M. Fijalkowski, C. Gould, “Quantization breakdown protection for semiconductors and in particular topological insulators”, European patent filing EP23162996.5 (2023).
  2. K. M. Fijalkowski, N. Liu, P. Mandal, et al., “Macroscopic Quantum Tunneling of a Topological Ferromagnet”, Advanced Science 10, 2303165 (2023), DOI: 10.1002/advs.202303165.

 

2024:

  1. K. M. Fijalkowski, N. Liu, M. Klement, et al., “A balanced quantum Hall resistor”, Nature Electronics 7, 438-443 (2024), DOI: 10.1038/s41928-024-01156-6.
  2. K. M. Fijalkowski, C. Gould, “A voltage-balanced device for quantum resistance metrology”, Nature Electronics7, 436-437 (2024), DOI: 10.1038/s41928-024-01168-2.
  3. D. K. Patel, K. M. Fijalkowski, M. Kruskopf, et al., “A zero external magnetic field quantum standard of resistance at the 10-9 level”, Nature Electronics 7, 1111-1116 (2024), DOI: 10.1038/s41928-024-01295-w.
  4. D. K. Patel, M. Kruskopf, K. M. Fijalkowski, et al., “High-accuracy measurements of the quantum anomalous Hall effect for resistance metrology”, 2024 Conference on Precision Electromagnetic Measurements (CPEM 2024) (2024), DOI: 10.1109/CPEM61406.2024.10646071
  5. P. Mandal, S. Mondal, M. P. Stehno et al., “Magnetically tunable supercurrent in dilute magnetic topological insulator-based Josephson junctions”, Nature Physics 20, 984-990 (2024), DOI: 10.1038/s41567-024-02477-1.

 

2025:

  1. N. J. Huáng, J. L. Boland, K. M. Fijalkowski, et al., “Quantum anomalous Hall effect for metrology”, Applied Physics Letters 126, … (2025), to be published.