## 2 Methods  
Our theoretical calculations of the equation of state and melting curve of Cr are based on density-functional theory (DFT) with the projector-augmented-wave (PAW) [15] implementation and the generalized gradient approximation (GGA) for exchange-correlation energy, in the form known as Perdew-Burke-Ernzerhof (PBE) [16]. For these calculations, Vienna Ab initio Simulation Package (VASP) [17] was used. The reason for choosing GGA instead of another implementation of DFT, namely, local density approximation (LDA), is that it has been known that LDA does not accurately describe the properties of 3d transition metals, specifically chromium, for which its predictions are in drastic disagreement with experiment [18; 19], and iron, for which it produces a wrong ground state: AF or nonmagnetic (NM) bcc [20; 21] or NM-hcp [22; 23; 24] instead of FM-bcc. LDA also fails in assessing the strength of the magnetovolume effect. On the other hand, GGA correctly predicts the structural and magnetic phase diagrams [25]. Cr was modeled using the core-valence representation [\({}^{12}\)Mg]3p\({}^{6}\)3d\({}^{5}\)4s\({}^{1}\), i.e., we assign the 12 outermost electrons to the valence. The valence electrons are represented with a plane-wave basis set with a cutoff energy of 350 eV, while the core electrons are represented by projector augmented-wave (PAW) pseudopotential (PP). The core radius (RCUT) for this PP is 2.3 a.u., or 1.22 A. Since numerical errors in the VASP calculations remain almost negligible until the nearest neighbor distance reaches 2 \(\times\) RCUT\(/(1.25\pm 0.05)\), with this PP one can study systems with densities up to \(\sim\)22.5 g/cm\({}^{3}\), at least at low \(T\). With our EOS of Cr, this corresponds to \(P\)\(\sim\)2.5 TPa. Cold (\(T=0\)) EOSs and enthalpies were calcualted using unit cells with very dense \(k\)-point meshes for high accuracy. Specifically, for bcc-Cr and hcp-Cr, \(k\)-point meshes of \(50\times 50\times 50\) and \(50\times 50\times 30\) were used. In all the non-cubic cases, we first relaxed the structure to determine its unit cell parameters at each volume. The AF bcc-Cr was studied in the framework of fully unconstrained noncollinear magnetism developed in Ref. [25]. In all the calculations including the simulations of the bcc-Cr and hcp-Cr melting curves and the inverse-Z solidification simulations discussed below, periodic boundary conditions were used. The theoretical melting curve of chromium (as the combination of those of both bcc-Cr and hcp-Cr) was calculated via ab initio quantum molecular dynamics (QMD) simulations using the Z method implemented with VASP, which is described in detail in Refs. [26; 27; 28]. We used a 432-atom (\(6\times 6\times 6\)) bcc-Cr supercell and a 392-atom (\(7\times 7\times 4\)) hcp-Cr supercell with a single \(\Gamma\)-point in each case. This was sufficient to ensure full energy convergence (to \(\stackrel{{<}}{{\sim}}\)1 meV/atom) which was checked for each simulation. We obtained a total of 12 melting points (six for bcc-Cr and six for hcp-Cr), and for each of them, 10 \(NVE\) (fixed total number of atoms \(N\), system volume \(V\), and total energy \(E\); \(V\) corresponds to one of the six densities from Table 1) runs of 10,000-20,000 time steps of 1.0 fs each. For bcc-Cr, increments of the initial \(T\) were 125 K for the 1 st, 250 K for the 2 nd, 375 K for the 3 rd and 4 th, and 500 K for the 5 th and 6 th \(T_{m}\). For hcp-Cr, those increments were also 125 K for the 1 st, 250 K for the 2 nd, 375 K for the 3 rd, 500 K for the 4 th, and 625 K for the 5 th and 6 th \(T_{m}\). The corresponding error in \(T_{m}\) is half of the increment of the initial \(T\)[28] so that it does not exceed \(\sim\)4% for each of the six bcc-Cr \(T_{m}\)s and \(\sim\)5% for each of the six hcp-Cr \(T_{m}\)s. The errors in \(P\) are negligibly small: \(\stackrel{{<}}{{\sim}}\)0.5 GPa for the first point, and 1-2 GPa for the remaining five in either case. Hence, our melting results on both bcc-Cr and hcp-Cr are very accurate.