Kimberly A. Modic

UTe ₂ exhibits the remarkable phenomenon of re-entrant superconductivity, whereby the zero-resistance state reappears above 40 tesla after being suppressed with a field of around 10 tesla. One potential pairing mechanism, invoked in the related re-entrant superconductors UCoGe and URhGe, involves transverse fluctuations of a ferromagnetic order parameter. However, the requisite ferromagnetic order—present in both UCoGe and URhGe—is absent in UTe ₂ , and neutron scattering shows instead that the magnetic susceptibility is peaked at an antiferromagnetic wavevector. Here, we measure the magnetotropic susceptibility of UTe ₂ across two field-angle planes. This quantity is sensitive to the magnetic susceptibility in a direction transverse to the applied magnetic field—a quantity that is not accessed in conventional magnetization measurements. We observe a very large decrease in the magnetotropic susceptibility over a broad range of field orientations, indicating a large increase in the transverse magnetic susceptibility. Because our technique probes the magnetic susceptibility in the long wavelength ( q = 0) limit, this suggests that the strong transverse susceptibility arises from ferromagnetic spin fluctuations. These ferromagnetic fluctuations are likely important for understanding the pairing mechanism in UTe ₂ , as all three superconducting phases of UTe ₂ surround this region of enhanced susceptibility in the field-angle phase diagram.

The magnetotropic susceptibility is the thermodynamic coefficient associated with the rotational anisotropy of the free energy in an external magnetic field and is closely related to the magnetic susceptibility. It emerges naturally in frequency-shift measurements of oscillating mechanical cantilevers, which are becoming an increasingly important tool in the quantitative study of the thermodynamics of modern condensed-matter systems. Here we discuss the basic properties of the magnetotropic susceptibility as they relate to the experimental aspects of frequency-shift measurements, as well as to the interpretation of those experiments in terms of the intrinsic properties of the system under study.

Resonant ultrasound spectroscopy and machine learning are used to rule out many theories of hidden order in URu ₂ Si ₂ .

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

We present a high magnetic field study of NbP—a member of the monopnictide Weyl semimetal (WSM) family. While the monoarsenides (NbAs and TaAs) have topologically distinct left and right-handed Weyl fermi surfaces, NbP is argued to be “topologically trivial” due to the fact that all pairs of Weyl nodes are encompassed by a single Fermi surface. We use torque magnetometry to measure the magnetic response of NbP up to 60 tesla and uncover a Berry paramagnetic response, characteristic of the topological Weyl nodes, across the entire field range. At the quantum limit B^* (≈32 T), τ/B experiences a change in slope when the chemical potential enters the last Landau level. Our calculations confirm that this magnetic response arises from band topology of the Weyl pocket, even though the Fermi surface encompasses both Weyl nodes at zero magnetic field. We also find that the magnetic field pulls the chemical potential to the chiral n = 0 Landau level in the quantum limit, providing a disorder-free way of accessing chiral Weyl fermions in systems that are “not quite” WSMs in zero magnetic field.

Unusual behavior in quantum materials commonly arises from their effective low-dimensional physics, reflecting the underlying anisotropy in the spin and charge degrees of freedom. Here we introduce the magnetotropic coefficient k = ∂²F/∂θ², the second derivative of the free energy F with respect to the magnetic field orientation θ in the crystal. We show that the magnetotropic coefficient can be quantitatively determined from a shift in the resonant frequency of a commercially available atomic force microscopy cantilever under magnetic field. This detection method enables part per 100 million sensitivity and the ability to measure magnetic anisotropy in nanogram-scale samples, as demonstrated on the Weyl semimetal NbP. Measurement of the magnetotropic coefficient in the spin-liquid candidate RuCl₃ highlights its sensitivity to anisotropic phase transitions and allows a quantitative comparison to other thermodynamic coefficients via the Ehrenfest relations.

Cranking up the field: Cuprate superconductors have many unusual properties even in the “normal” (nonsuperconducting) regions of their phase diagram. In the so-called “strange metal” phase, these materials have resistivity that scales linearly with temperature, in contrast to the usual quadratic dependence of ordinary metals. Giraldo-Gallo et al. now find that at very high magnetic fields—up to 80 tesla—the resistivity of the thin films of a lanthanum-based cuprate scales linearly with magnetic field as well, again in contrast to the expected quadratic law. This dual linear dependence presents a challenge for theories of the normal state of the cuprates. Science , this issue p. 479