Neutron Scattering and Magnetism
Laboratory for Solid State Physics · D-PHYS

Join us

We offer exciting projects for semester and master's work in experimental solid state physics. This is real hands-on research, not an exercise: some of the projects are carried out in our laboratory on the ETH Hönggerberg campus, others involve experiments at the Paul Scherrer Institut (30 km from ETH) or at large-scale neutron scattering facilities worldwide. Quite often the data collected and interpreted by a student become part of a peer-reviewed publication from the group, and then the student is, of course, a co-author. Several of the completed projects below ended exactly that way: check the author lists.

Which projects are actually on offer in any given semester is very fluid and cannot be planned more than a few months in advance. Nor do we want to advertise our immediate plans online to our competitors. Most importantly, we always try to match the project to the background and interests of the student who will execute it. For all these reasons, if you are interested in joining us, the best thing to do is to email Prof. A. Zheludev directly and discuss the options. Just as a reference, here is an admittedly somewhat random collection of projects that were successfully carried out in our group over the years.

If you are still charting your course through the ETH physics curriculum, have a look at your path to solid state physics.

Phase diagram of a ℤ2 vortex crystal candidate

The measured magnetic phase diagram of our vortex crystal candidate material

The measured magnetic phase diagram of our candidate material in a magnetic field along the c axis, with three distinct incommensurate phases (IC1–IC3) [1].

Completed in 2026

For decades, the antiferromagnet on a triangular lattice has remained a paradigm of quantum magnetism due to the wide range of exotic phases it exhibits. Recently, theoretical work has pointed to this geometry as a platform for realizing a new, exotic quantum phase: a ℤ2 vortex crystal. This quantum phase emerges when topological defects condense into a lattice, and is yet to be experimentally observed.

We have recently synthesized a new family of triangular lattice quantum antiferromagnets. The unique combination of frustrated geometry, strong spin-orbit coupling and Kitaev interactions in these materials makes them ideal candidates for the ℤ2 vortex crystal phase. Initial work on a Ru-based member of this family has already revealed a rich phase diagram, with phases that could correspond to this ℤ2 vortex crystal. However, our efforts now turn to a different material in this family that is even more likely to exhibit this ℤ2 vortex crystal phase.

In this semester project, you will conduct state-of-the-art calorimetric and magnetic measurements on these new quantum materials. The measurements will be carried out at ultra-low temperatures (down to 50 mK) and high magnetic fields (up to 14 T). You will investigate the thermodynamic properties of the material, allowing you to map out the different quantum phases in the magnetic phase diagram of this material. This will be a pivotal step towards understanding the complex magnetic behavior of these materials. Your project is likely to contribute to a publication in a high-profile journal.

And contribute it did: the phase diagram of the Ru-based member shown above is now published [1]. Note the author list: it includes two former semester students.

An almost-Heisenberg triangular lattice antiferromagnet

Specific heat of K2Mn(SeO3)2 in magnetic fields along two crystallographic directions

Specific heat of K2Mn(SeO3)2 measured in this project. (a,b) False-color maps of C/T in magnetic fields along the two crystallographic directions chart the ordered phase; (c,d) the underlying temperature scans at sequential fields [1].

Completed in 2025

The triangular lattice antiferromagnet is the oldest paradigm of frustrated magnetism, and its S = 1/2 realizations are deep in the quantum regime. But what survives of the quantum "weirdness" when the spin is large? K2Mn(SeO3)2, the S = 5/2 sibling of our spin-supersolid cobaltate, is an almost perfect Heisenberg triangular antiferromagnet built of almost-classical spins, and thus exactly the material to ask.

In this semester project, you will map out the magnetic phase diagram of K2Mn(SeO3)2 by measuring its specific heat and magnetization at ultra-low temperatures (down to 100 mK) and in magnetic fields up to 14 T applied along different crystallographic directions. The thermodynamic survey will anchor the analysis of our neutron scattering data on this compound.

The data collected in this project became part of Ref. [1], with the semester student among the authors. The punchline of that paper: alongside conventional spin waves the material shows a broad excitation continuum, and non-linear spin wave theory reproduces both, precisely where the linear theory fails.

Braided spin-tubes in a purported kagome magnet

Exchange network and spin-tubes of Nd3BWO9 Magnetization plateaus, dilatometry and torque in Nd3BWO9

Left: the exchange network of Nd3BWO9 [3]. In the crystal planes (a) the Nd3+ ions trace a "breathing" kagome pattern, but the strongest bonds (b) run between the planes, braiding the ions into twisted triangular spin-tubes with almost-orthogonal Ising axes (c); (d) the phase diagram of the resulting spin-tube model. Right: the presaturation phases of Nd3BWO9 for fields along a: (a) magnetization plateaus at 1/4 and 1/2 of saturation; (b,c) sample dilation and magnetic torque with their field derivatives, measured in this project, pinning the same transition fields [3].

Completed in 2024

The rare-earth borotungstates RE3BWO9 arrived in 2020 amid great excitement: a disorder-free family of "breathing"-kagome antiferromagnets, exactly where theory told us to look for the elusive quantum spin liquid. Our thermodynamic surveys quickly showed the reality to be richer. Nd3BWO9 orders only below 0.3 K and displays several domes of magnetic order and fractional magnetization plateaus for every direction of the applied field [1]; its Pr sibling turned out to be no spin liquid at all, but a quantum paramagnet ruled by transverse-field Ising physics [2].

In this master's project, you will hunt the presaturation phases of Nd3BWO9, following its magnetization plateaus with torque magnetometry and capacitive dilatometry at temperatures below 150 mK for different orientations of the magnetic field.

The data became part of Ref. [3], with the master's student among the authors, and the punchline is a lesson in humility: neutron scattering and numerical simulations showed that the celebrated kagome planes are largely irrelevant. The strongest bonds run between the planes, braiding the spins into twisted triangular Ising tubes, and this simple one-dimensional classical model accounts for the ground state, the excitations, and every one of the plateau phases, quantitatively.

Thermodynamics of a spin supersolid

Specific heat scans of the spin supersolid K2Co(SeO3)2

Constant-field specific-heat scans of K2Co(SeO3)2 in magnetic fields along the c axis, measured in this project by the thermal-relaxation method (curves offset as indicated). (a) At the lowest temperatures, arrows mark the anomalies at the boundary of the spin-supersolid phase. (b) The same data up to 13 K: colored arrows follow the λ-anomaly at the upper boundary of the "uud" plateau phase [1].

Completed in 2023

A supersolid is a state of matter that is simultaneously "solid" and "superfluid." Proposed for helium half a century ago, it has never been convincingly observed there. Its magnetic analog, however, is very real: in the easy-axis triangular lattice antiferromagnet K2Co(SeO3)2, the spin components along the easy axis freeze into a rigid three-sublattice pattern, while the transverse components remain "superfluid."

In this semester project, you will chart the phase diagram of this remarkable material by measuring its specific heat at temperatures down to 100 mK and in magnetic fields up to 14 T. The measurements will map the dome of the supersolid phase, locate the quantum critical point at which it collapses, and follow the sharp anomaly that terminates at a critical endpoint at higher temperatures.

These scans became part of Ref. [1], with the semester student among the authors. It is a fine example of how much physics a single well-executed calorimetric survey can carry: the false-color phase-diagram map distilled from the same data set now illustrates our calorimetry page.

Magnetic phases of a frustrated zigzag-ladder antiferromagnet

Magnetostriction of Cs2CoI4 Magnetic torque of Cs2CoI4

Left: magnetostriction of Cs2CoI4 measured in this project: sample dilation and the magnetostriction coefficient in fields along the a and b axes, at temperatures from 0.2 to 4 K. Right: magnetic torque and its field derivative under the same conditions. Together, the anomalies (triangles) trace out the entire magnetic phase diagram [1].

Completed in 2023

Cs2CoI4 is the iodine sibling of Cs2CoBr4, the S = 3/2 frustrated zigzag-ladder antiferromagnet in which we observed a spectacular "Zeeman ladder" of spinon bound states. The substitution is anything but innocent: unlike any other member of the Cs2MX4 family, Cs2CoI4 first undergoes a structural phase transition, near 51 K, whose low-temperature crystal structure had never been solved, and only then orders magnetically. The reduced symmetry splits the magnetic subsystem into two inequivalent zigzag ladders. Untangling the crystallography from the magnetism is the necessary first step towards a spin Hamiltonian for this compound.

In this master's project, you will determine the magnetic structures of Cs2CoI4 by elastic neutron scattering at the Paul Scherrer Institut, and complement them with thermodynamic measurements at ultra-low temperatures: magnetostriction, dilatometry, and torque magnetometry. The combined data set will pin down the magnetic phase diagram for both in-plane field directions.

The study grew into Ref. [1], an Editor's Suggestion in Physical Review Materials, with the master's student among the authors. The story did not end there either: the same student stayed on as a Ph.D. student in the group.

Development of a low-temperature magnetic susceptibility probe

AC susceptibility of Dy2Ti2O7 at millikelvin temperatures Design and photograph of the superconducting susceptometer coil

(a) AC susceptibility demonstrates the extremely slow dynamics in the spin-ice compound Dy2Ti2O7 down to millikelvin temperatures. (b,c) The susceptometer design is based on a custom-made superconducting coil.

Completed in 2023

Magnetic susceptibility is an essential quantity to study in condensed matter systems. It provides invaluable information on the microscopic properties of materials, ranging from magnetic insulators, to spin glasses and even superconductors. Beyond static bulk properties, AC susceptibility gives also access to dynamical processes, like relaxation mechanisms [1]. As such, it is a widespread technique down to ~2 K and many commercial setups are on the market. However, state-of-the-art research in quantum magnetism demands extreme experimental conditions that are at odds with commercial solutions. Extremely versatile low-power, high-throughput devices are required to access the millikelvin regime in the presence of strong magnetic fields (> 10 T). We took up this endeavor and developed our own custom platform for AC susceptibility measurements.

In this master's project, you will develop a custom-made low-temperature susceptometer. The design will be based on a compact superconducting coil [2], specifically designed in collaboration with industry for this project. Several approaches will be taken to enhance the sensitivity of the device while keeping it low-power. In addition, you will gain insight into several areas of magnetism; various quantum materials are already available and urge for low-temperature AC susceptibility measurements. Finally, your work will contribute to establishing a cutting-edge measurement technique and will likely be part of several publications in high-impact journals.

Anomalous magnetoelastic coupling at quantum phase transitions

Sound velocity and attenuation of Cs2CoBr4 Ultrasonic phase diagram of Cs2CoBr4

Left: field dependence of the sound velocity and the acoustic attenuation of Cs2CoBr4 at temperatures between 0.1 and 1.5 K, measured in this project with the newly built pulse-echo setup (curves offset for clarity). Right: the resulting phase diagram for fields along b, a false-color map of the sound velocity with the five ordered phases labeled. Red symbols are the ultrasonic anomalies; the remaining markers are earlier specific-heat and torque data [1]. The agreement is complete.

Completed in 2022

In magnetically frustrated systems, competing interactions give rise to a host of exotic magnetic phases; the frustrated quantum antiferromagnet Cs2CoBr4, with its cascade of five distinct field-induced phases including a fractional magnetization plateau, is a case in point [1,2]. The magnetoelastic coupling, an often neglected interaction between the spin and lattice degrees of freedom, makes sound waves a probe of all of them at once: the elastic constants react to every phase transition, and can behave anomalously close to a quantum critical point.

In this master's project, you will bring a new experimental technique into the lab. You will build and commission a pulse-echo ultrasonic setup: a phase-sensitive detection scheme that measures the sound velocity and the acoustic attenuation of a small single crystal simultaneously, resolving relative velocity changes at the 10-4 level. You will then put the new instrument to work on Cs2CoBr4 at temperatures down to 0.1 K, tracking how the lattice responds at each of the field-induced transitions.

It worked beautifully: sharp anomalies appear at every one of the five transitions, in both the velocity and the attenuation, and the phase diagram measured by sound alone reproduces the one obtained by calorimetry and torque magnetometry [1]. Ultrasound has since become part of our standard toolkit (see Ultrasound among the Methods), and the master's student stayed on as a Ph.D. student in the group, going on to first-author several of our papers.

Quantum phase transitions in multiferroic spin chains

Magnetic phase diagrams of Cs2Cu2Mo3O12 Critical dielectric susceptibility of Rb2Cu2Mo3O12

Left: magnetic phase diagrams of Cs2Cu2Mo3O12 in fields along three crystal directions, measured in this project. Symbols mark transitions detected by specific heat and magnetic torque, the false-color background is the specific heat C/T, and P labels the presaturation phase [1]. Right: inverse dielectric susceptibility of Rb2Cu2Mo3O12 along the quantum critical trajectory at saturation: a power law with the exponent γ = 1.64(1), in excellent agreement with the value 3/2 expected for a three-dimensional BEC and clearly distinct from the mean-field (γ = 1) and Ising (γ = 2) alternatives [2].

Completed in 2020

The frustrated spin chains A2Cu2Mo3O12 (A = Rb or Cs) combine ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange, and the two isostructural compounds could be expected to behave identically. They do anything but. The Cs member orders antiferromagnetically near 1.8 K; the Rb member instead forms a nonmagnetic singlet ground state and orders only inside a "dome" of applied magnetic fields, in what is best described as a Bose-Einstein condensation (BEC) of magnons. Both are, on top of that, quantum multiferroics: magnetic order arrives hand in hand with an electric polarization, so a humble capacitance measurement becomes a sensitive probe of the magnetic phase transitions.

In this master's project, you will map out the magnetic phase diagrams of both compounds by calorimetry, torque magnetometry, and dielectric measurements at temperatures down to 0.1 K. The diagrams hold surprises: an entire zoo of unidentified phase pockets and, wedged just below saturation in the Cs compound, an extra presaturation phase, possibly a spin-nematic or some other multi-magnon condensate. In the Rb compound, the dielectric channel gives direct access to the critical divergence of the BEC susceptibility, a quantity normally beyond the reach of any experiment.

The project grew into two publications [1,2], with the master's student among the authors of both. The dielectric story of these chains did not end there either: it is now one of our running research themes (see Quantum multiferroics).

A presaturation state in a triangular lattice system

Magnetic phase diagrams of Cs2CoBr4

Magnetic phase diagrams of Cs2CoBr4, measured in this project: false-color maps of Cp/T for (a) transverse and (b) longitudinal magnetic fields. Circles and squares mark the anomalies in calorimetric temperature and field scans, crosses those in low-temperature magnetometry. In the longitudinal geometry, a cascade of five ordered phases (A–E) unfolds below 1 K [1].

Completed in 2020

In Cs2CoBr4, two frustration mechanisms compete head-on. The Co2+ ions form a distorted triangular lattice, and their single-ion easy planes alternate in orientation from site to site, leaving only one direction common to all of them: an emergent Ising axis that no individual ion asked for. What happens when a magnetic field is applied along that axis was, at the outset, anyone's guess.

In this semester project, you will find out, by mapping the magnetic phase diagram of this material with calorimetric, magnetometric, and torque measurements at temperatures down to 0.1 K. The answer is spectacular: a cascade of five ordered phases, among them two distinct magnetization plateaux, a collinear one stabilized by the anisotropy and an "up-up-down" one that is the hallmark of triangular-lattice physics [1].

The study became Ref. [1], with the semester student among the authors. The cascade has kept the group busy ever since: neutron scattering identified a rare spin-density-wave phase competing with the plateau [2], while the presaturation states just below saturation remain not fully understood, a mystery that later student projects, including the ultrasound study described above, keep chipping away at.

Magnetometry at ultra-low temperatures

Miniature Faraday force magnetometer Magnetization of a spin ladder measured with the Faraday magnetometer

Left: the miniature Faraday force magnetometer, small enough to fit almost any cryostat: the sample sits on a flexible cantilever that forms a force-sensing capacitor between a pair of gradient coils; below, the capacitance response to the alternating gradient current [1]. Right: the proof: magnetization of the spin ladder (C5H12N)2CuBr4 measured with the device at 100 mK reproduces the published NMR data point by point, and the full temperature evolution up to 8 K follows [1].

Completed in 2020

Measuring the uniform magnetization is one of the first steps in any experimental study of a magnetic material, and down to about 2 K it is routine. Below that, the commercial techniques run out, precisely where quantum magnetism gets interesting: the field-induced quantum phase transitions we care about live at millikelvin temperatures and in high magnetic fields.

In this master's project, you will develop, test, and commission a home-built Faraday force magnetometer. The principle is disarmingly simple: the sample sits on a flexible cantilever, a small superimposed field gradient converts its magnetic moment into a force, and the cantilever's deflection is read out as a capacitance. Making this work reliably at 100 mK, in fields up to 14 T, and with a moment resolution better than 10-7 A m2 is the hard part. You will then put the instrument to use on magnetization scaling near a field-induced quantum critical point.

The device became Ref. [1], with the master's student among the authors, and a workhorse of the lab ever since: several of the magnetization curves shown elsewhere on this page were measured with it or its descendants. The student, meanwhile, stayed on as a Ph.D. student in the group.

Exact scaling at a magnetic quantum critical point

Enlarged view: Specific heat scaling from BPCB paper

(a) Magnetic specific heat of the spin ladder (C5H12N)2CuBr4 near the field-induced quantum critical point. (b) Below 0.5 K, the same data collapse, in scaled variables, onto the exact free-fermion scaling function, drawn with no adjustable parameters [1].

Completed in 2016

Quantum critical points occur at zero temperature, where a ground state changes abruptly as some non-thermal parameter is tuned. At first glance this sounds like an abstraction of no experimental consequence. In truth, criticality controls a wide swath of the phase diagram at finite temperatures: thermodynamic quantities are predicted to obey universal scaling laws, with all microscopic detail reduced to a couple of exponents and a universal scaling function. Clean experimental tests are rare, though; one needs a real material whose critical point sits at an accessible magnetic field, and measurements at very low temperatures.

In this master's project, you will study the spin ladder (C5H12N)2CuBr4 near the field-induced transition at which the spin gap closes, a condensation of magnons with the dynamical exponent z = 2. You will measure the magnetic specific heat down to below 0.2 K across the transition, and test the predicted scaling. The prediction here is special: in one dimension the condensing bosons behave as free fermions, and the scaling function is known exactly.

The scaling held, with no adjustable parameters, and inelastic neutron scattering later extended the test to the finite-temperature dynamics, in spectacular quantitative agreement with the theory. The study grew into Ref. [1], with the former master's student as its first author: he had stayed on as a Ph.D. student in the group, and this work became a centerpiece of his doctorate.