Theory of unconventional metamagnetic electron states in orbital band systems

We extend the study of the Fermi surface instability of the Pomeranchuk type into systems with orbital band structures, which are common features in transition metal oxides. Band hybridization significantly shifts the spectral weight of the Landau interactions from the conventional $s$-wave channel to unconventional non-$s$-wave channels, which results in anisotropic (nematic) Fermi surface distortions even with ordinary interactions in solids. The Ginzburg-Landau free energy is constructed by coupling the charge-nematic, spin-nematic, and ferromagnetic order parameters together, which shows that nematic electron states can be induced by metamagnetism. The connection between this mechanism and the anisotropic metamagnetc states observed in ${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7$ at high magnetic fields is studied in a multiband Hubbard model with the hybridized quasi-one-dimensional $d_{xz}$ and $d_{yz}$ bands.

Figure 1

(a) The sketch of the magnetic part $F\left(m\right)$ in the Ginzburg-Landau free energy. The slopes of two common tangent lines mark the magnetic fields of metamagnetic transitions. (b) The dimensionless coupling function $g^{\prime }\left(m\right)$ has a peak distribution between two consecutive matamagnetic transitions.

Figure 2

(a) Dispersion of the ${\gamma }_{+}$ band for $\vec{k}=\left(k_x,0\right)$ and $\left(k_x,\pi \right)$. (b) The DOS of the ${\gamma }_{\pm }$ bands whose peaks corresponds to the van Hove singularities at $\vec{k}=\left(0,0\right),\left(0,\pi \right),\left(\pi ,0\right)$.

Figure 3

$m$ and the nematic order parameter for majority spin band $\left(n_{c\uparrow }=\left(n_c+n_{sp}\right)/2\right)$ versus the external field $h$. The topologies of the FS of the ${\gamma }_{+}$ band in each phases are sketched in the insets, where the solid and dashed lines represent the FS of the majority and the minority spin bands.