# Field-induced Lifshitz transitions in the ferromagnetic superconductor UCoGe

*Published on 12 April 2017*

In a metal the energy levels of the electrons, which have to be all in different quantum states due to the Pauli exclusion principle, are filled up to the Fermi energy at zero temperature. The surface of constant energy in the reciprocal space separating occupied and unoccupied electronic states is called the Fermi surface. The shape of the Fermi surface is controlled by the periodicity and symmetry of the crystalline lattice and by the occupation of electronic energy bands. It is a fundamental property of each metal. Knowledge of the Fermi surface is crucial as most of the electronic and magnetic properties of a metal are determined by thermal excitations around the Fermi energy.

Usually, the Fermi surface and the electronic band structure are rather robust properties of the metallic state. They are weakly influenced by the magnetic fields available in laboratories. We do expect some changes of the Fermi surface only when the magnetic ground state is modified. In a normal metal, the Zeeman splitting induced by accessible magnetic fields (10-30meV) is weak with respect to the Fermi energy, which is usually of the order of a few electron volts. However, in some strongly correlated electron systems called “heavy fermion” very flat bands are present at the Fermi level, leading to an effective Fermi energy comparable to the accessible Zeeman splitting. These hybridized bands arise from the subtle interaction of the conduction electrons with localized f-electrons, and the resulting low energy scales make heavy fermions systems an ideal model to study electronic correlations in a metal.

Recently, in collaboration with the high magnetic field laboratory LNCMI-CNRS Grenoble, we have discovered that a magnetic field in this system not only induces a Fermi surface change, but a whole series of topological transitions of the Fermi surface. First, we have performed detailed transport measurements under magnetic field along the crystallographic direction where the magnetic moments are easily aligned, in the ferromagnetic U-based superconductor UCoGe. The Hall effect and the thermoelectric power show several distinct anomalies in the magnetic field range up to 35T (see Fig. 1a). Secondly, on these high quality single crystals, we could also detect quantum oscillations, with the resistivity and the thermoelectric power, and prove that the anomalies are indeed connected to abrupt changes of the Fermi surface topology (see Fig. 1b). Such topological transitions, often called Lifshitz transitions, are continuous quantum phase transitions at zero temperature due to the variation the band structure of a metal. They happen without spontaneous symmetry breaking, and so have no clear thermodynamic signatures. Surprisingly, we could show that in heavy fermion materials, such topological changes can be induced even in small magnetic fields.

a) Magnetic field dependence of the Hall effect (black line) measured at 0.04K and thermoelectric power at 0.45K (blue, left scale) and 0.9K (red, right scale) of UCoGe.

b) The change of the quantum oscillations frequencies proves that the anomalies in the magneto-transport are related to topological transitions of the Fermi surface.

Usually, the Fermi surface and the electronic band structure are rather robust properties of the metallic state. They are weakly influenced by the magnetic fields available in laboratories. We do expect some changes of the Fermi surface only when the magnetic ground state is modified. In a normal metal, the Zeeman splitting induced by accessible magnetic fields (10-30meV) is weak with respect to the Fermi energy, which is usually of the order of a few electron volts. However, in some strongly correlated electron systems called “heavy fermion” very flat bands are present at the Fermi level, leading to an effective Fermi energy comparable to the accessible Zeeman splitting. These hybridized bands arise from the subtle interaction of the conduction electrons with localized f-electrons, and the resulting low energy scales make heavy fermions systems an ideal model to study electronic correlations in a metal.

Recently, in collaboration with the high magnetic field laboratory LNCMI-CNRS Grenoble, we have discovered that a magnetic field in this system not only induces a Fermi surface change, but a whole series of topological transitions of the Fermi surface. First, we have performed detailed transport measurements under magnetic field along the crystallographic direction where the magnetic moments are easily aligned, in the ferromagnetic U-based superconductor UCoGe. The Hall effect and the thermoelectric power show several distinct anomalies in the magnetic field range up to 35T (see Fig. 1a). Secondly, on these high quality single crystals, we could also detect quantum oscillations, with the resistivity and the thermoelectric power, and prove that the anomalies are indeed connected to abrupt changes of the Fermi surface topology (see Fig. 1b). Such topological transitions, often called Lifshitz transitions, are continuous quantum phase transitions at zero temperature due to the variation the band structure of a metal. They happen without spontaneous symmetry breaking, and so have no clear thermodynamic signatures. Surprisingly, we could show that in heavy fermion materials, such topological changes can be induced even in small magnetic fields.

a) Magnetic field dependence of the Hall effect (black line) measured at 0.04K and thermoelectric power at 0.45K (blue, left scale) and 0.9K (red, right scale) of UCoGe.

b) The change of the quantum oscillations frequencies proves that the anomalies in the magneto-transport are related to topological transitions of the Fermi surface.