de Haas–van Alphen effect and Fermi surface properties of single-crystal CrB${}_2$

We report the angular dependence of three distinct de Haas–van Alphen (dHvA) frequencies of the torque magnetization in the itinerant antiferromagnet CrB${}_2$ at temperatures down to 0.3 K and magnetic fields up to 14 T. Comparison with the Fermi surface calculations considering an incommensurate cycloidal magnetic order suggests that two of the observed dHvA oscillations arise from electronlike Fermi surface sheets formed by bands with strong B-$p_{\text{x,y}}$ character. The third orbit could correspond to a Cr-$d$ derived Fermi surface sheet. The measured effective masses of these Fermi surface sheets display strong enhancements of a factor of about 2 over the calculated band masses which can be attributed to electron-phonon coupling and electronic correlations. Signatures of further heavy $d$-electron bands that are predicted by the calculations are not observed in the temperature and field range studied. In the view that the B-$p$ bands are at the heart of conventional high-temperature superconductivity in the isostructural MgB${}_2$, we consider possible implications of our findings for nonmagnetic CrB${}_2$ and an interplay of itinerant antiferromagnetism with superconductivity.

Figure 1

(a) The torque $\Gamma$ (black line) and the oscillatory torque ${\Gamma }_{\text{osc}}$ (light line) as a function of magnetic field $B$ for $\phi =5^{\circ }$ at $T=0.3$ K. (b) Fourier transform of ${\Gamma }_{\text{osc}}(1/B)$ revealing three distinct orbits $\alpha$, $\beta$, and $\delta$. A sketch of the experimental geometry is depicted in the inset. (c) ${\Gamma }_{\text{osc}}$ for three different angles $\psi$ at $T=0.3$ K. (d) Corresponding FFTs showing one dHvA orbit that shifts in frequency.

Figure 2

(a) Angular dependence of the dHvA frequencies for a rotation of the magnetic field in the basal plane showing three orbits $\alpha$, $\beta$ and $\delta$. (b) Expanded view of the angular dependence of $\alpha$ and $\beta$. Both orbits exhibit an apparent ${60}^{\circ }$ periodicity. Lines are guides to the eyes. (c) Rotation of the magnetic field in the $\left[001\right]$-$\left[120\right]$ plane. The middle frequency branch $\beta$ is present, whereas $\alpha$ and $\delta$ are missing. The data are fitted by a curve (solid line) expected for an ellipsoidal Fermi surface sheet (see text). The inset depicts a sketch of the experimental geometry.

Figure 3

(a) Normalized temperature-dependent FFT amplitudes $I\left(T\right)$ (symbols) and LK fit (solid line) as a function of temperature. The FFT amplitudes were obtained using a fixed-field window. In the expression for $R_{\mathrm{T}}$, the average field of this window was used. (b) Torque vs $B$ field at $T=0.3$ K (symbols) and fit (solid line) of Eq. (1) using $m^{*}=0.86m_{\text{e}}$ as determined above.

Figure 4

Calculated electronic structure of CrB${}_2$ with a cycloidal magnetic ordering wave vector $\mathbf{q}=0.3{\mathbf{q}}_{110}$ using the wien2k package. (a) Band structure of CrB${}_2$ around the Fermi level $E_{\mathrm{F}}$. In total, three bands (blue, orange, black) cross $E_{\mathrm{F}}$. (b)–(d) Fermi surface sheets of CrB${}_2$ corresponding to the three bands that cross $E_{\mathrm{F}}$ in (a). For clarity, the Fermi surface sheets corresponding to the three different bands are plotted separately. (b) The Fermi surface sheet corresponding to the blue band consists of a singly connected structure centered around the L point at the boundary of the first. Brillouin zone. It has predominantly Cr-$d$ character. (c) Fermi surface corresponding to the black band. Two ball-shaped, B-$p$ derived Fermi surface pockets are present between the A and the H points. The extremal orbit $\delta$ assigned to the experimentally observed dHvA frequency is shown in yellow. The ball shape of this pocket is quite insensitive to magnetic order (see main text). The remaining Fermi surface sheets of this band exhibit a complicated structure and are of Cr-$d$ character. Thorough analysis with SKEAF showed that none of the numerous further extremal orbits of these sheets are close to the experimental ones. (d) Two ball-shaped and two dumbbell-shaped Fermi surface pockets originate from the orange band in (a). The orbit $\beta$ is allocated to the ball-shaped pocket as indicated. This pocket is also predominantly B-$p$ like and very insensitive to the magnetic order. The dumbbell-shaped pockets have Cr-$d$ orbital character. The frequency of the $\alpha$ orbit seen in the experiment matches reasonably well to this pocket (see Table ), while the angular dependence does not. In light of the fact that the pocket is of Cr-$d$ orbital character and thus very sensitive to the exact form of the magnetic order, we refrain from a clear assignment.