Fermi surface properties of the bifunctional organic metal $\kappa \text{−}{\left(\mathrm{BETS}\right)}_2\mathrm{Mn}{\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]}_3$ near the metal-insulator transition

We present detailed studies of the high-field magnetoresistance of the layered organic metal $\kappa \text{−}{\left(\mathrm{BETS}\right)}_2\mathrm{Mn}{\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]}_3$ under a pressure slightly above the insulator-metal transition. The experimental data are analyzed in terms of the Fermi surface properties and compared with the results of first-principles band structure calculations. The calculated size and shape of the in-plane Fermi surface are in very good agreement with those derived from Shubnikov-de Haas oscillations as well as the classical angle-dependent magnetoresistance oscillations. A comparison of the experimentally obtained effective cyclotron masses with the calculated band masses reveals electron correlations significantly dependent on the electron momentum. The momentum- or band-dependent mobility is also reflected in the behavior of the classical magnetoresistance anisotropy in a magnetic field parallel to layers. Other characteristics of the conducting system related to interlayer charge transfer and scattering mechanisms are discussed based on the experimental data. Besides the known high-field effects associated with the Fermi surface geometry, new pronounced features have been found in the angle-dependent magnetoresistance, which might be caused by coupling of the metallic charge transport to a magnetic instability in proximity to the metal-insulator phase boundary.

Figure 1

Calculated band structure of $\kappa \text{−}{\left(\mathrm{BETS}\right)}_2\mathrm{Mn}{\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]}_3$ based on the 15 K crystal structure [5]. The result of the full calculation is shown with solid lines, whereas the result of the calculation where the anions were replaced by a uniform background of charge is shown with dashed lines. The energy is counted from the Fermi level. $\mathrm{\Gamma }=(0,0,0),\mathrm{X}=(1/2,0,0),\mathrm{Z}=(0,0,1/2)$, and $\mathrm{M}=(1/2,0,1/2)$ in units of the monoclinic reciprocal lattice vectors.

Figure 2

2D Fermi surface of $\kappa \text{−}{\left(\mathrm{BETS}\right)}_2\mathrm{Mn}{\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]}_3$. Thin lines indicate the principal directions of the reciprocal lattice and the first Brillouin zone boundary. The arrows show the directions of the cyclotron motion on the classical (blue) and magnetic-breakdown (red) orbits in a magnetic field.

Figure 3

Calculated DOS per spin per unit cell for $\kappa \text{−}{\left(\mathrm{BETS}\right)}_2\mathrm{Mn}{\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]}_3$ at (a) $T=200\mathrm{K}$ and (b) $T=15\mathrm{K}$. The energy is counted from the Fermi level. The contribution from the lower lying band, associated with the rhombuslike Fermi pocket around point Z in Fig. 2, is shown in blue. The contribution from the higher lying band is shown in purple. The total DOS is represented by the red line.

Figure 4

Interlayer resistance of $\kappa \text{−}{\left(\mathrm{BETS}\right)}_2\mathrm{Mn}{\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]}_3$ under a pressure of 1.4 kbar, at $T=0.36\mathrm{K}$, as a function of magnetic field normal to layers.

Figure 5

Oscillatory component of the field-dependent resistance in Fig. 4 normalized to the nonoscillating background. Red lines are envelopes of the rapid $\beta$ oscillations originating from magnetic breakdown, to emphasize weak slow oscillations associated with the classical cyclotron orbit $\alpha$, see Fig. 2. Inset: the corresponding FFT spectrum.

Figure 6

Temperature dependence of the FFT amplitudes of the $\alpha$ (filled symbols) and $\beta$ (open symbols) oscillations. The lines are fits to the Lifshitz-Kosevich temperature dependence given by Eq. (2) with the normalized cyclotron mass ${\mu }_{\alpha \left(\beta \right)}=m_{c,\alpha \left(\beta \right)}/m_e$ as a fitting parameter.

Figure 7

Dingle plots for the amplitudes of the $\alpha$ oscillations (a) and the $\beta$ oscillations (b), see text. The dashed lines are fits based on Eqs.(4, 5, 6).

Figure 8

(a) Closeup of the field-dependent resistance data from Fig. 4 for fields $B<7\mathrm{T}$. The star marks the crossover between different magnetoresistance regimes, see text. (b) The nonoscillating resistance component plotted against the square root of magnetic field. Starting from $\sim 10\mathrm{T}$ the resistance acquires the $\sqrt{B}$ dependence. The dashed straight line is a guide to the eye.

Figure 9

Upper panel: Schematic of the sample orientation in a magnetic field defined by the polar angle $\theta$ and azimuthal angle $\phi$, as introduced in Sec. 2. Lower panel: Examples of the angular dependence of the resistance in a magnetic field of 28 T at different azimuthal orientations $\phi$ indicated on the right-hand side. The curves are vertically shifted for clarity. The arrows point to the positions of AMRO maxima, see text. The stars mark the $-1\mathrm{st}$ and +1st maxima corresponding to additional oscillations dominating near $\phi \simeq {90}^{\circ }$. Insets: (a) high-$\theta$ part of the $R\left(\theta \right)$ dependence at $\phi ={54}^{\circ }$ in an enlarged scale, showing high-order AMRO maxima; (b) AMRO positions plotted in the $tan\theta$ vs $N$ scale, for $\phi ={54}^{\circ }$. The positive and negative indices $N$ are shifted, respectively, to the left and to the right by $1/4$, in order to enable a common linear fit according to Eq. (7).

Figure 10

In-plane cross section of the Fermi surface determined from the AMRO data as described in the text. The red symbols are the values of $k_B^{\max }\left(\phi \right)$ in polar coordinates. Filled symbols are the data obtained directly from the $R\left(\theta \right)$ curves at the corresponding angles $\phi$; open symbols are the same data shifted by ${180}^{\circ }$. For a comparison with the theoretical predictions the Fermi surface from Fig. 2 is shown by the thick dashed line.

Figure 11

$\theta$ sweeps at $B=15$ and 28 T, at: (a) $\phi =-{36}^{\circ }$ and (b) $\phi ={93}^{\circ }$. Arrows point to the AMRO positions. Dashed vertical lines illustrate the independence of the positions of the additional, “non-AMRO” features on the field strength.

Figure 12

Angular dependence of the resistance in a field parallel to the conducting layers, at $B=15$ and 28 T. Dotted lines are guides to the eye.