Abstract
Densities of states for simple (sc) and base-centered (bcc) cubic lattices with account of nearest and next-nearest neighbour hopping integrals t and t' are investigated in detail. It is shown that at values of τ ≡ t'/t = τ*, corresponding to the change in isoenergetic surface topology, the formation of Van Hove k lines takes place. At small deviations from these special values, the weakly dispersive spectrum in the vicinity of Van Hove lines is replaced by a weak k-dependence in the vicinity of a few van Hove points which possess huge masses proportional to |τ – τ*|–1. The singular contributions to the density of states that originate from Van Hove points and lines are considered, as well as the change in the topology of isoenergetic surfaces in the k-space with the variation of τ. The closed analytical expressions for the density of states as a function of energy and τ in terms of elliptic integrals and power-law asymptotics at τ = τ* are obtained. Apart from the case of sc lattice with small τ (maximum of density of state corresponds to the energy level of X k-point), maximal value of the density of states is always achieved at energies corresponding to innerk-points of the Brillouin zone positioned in high-symmetry directions, and rather than at zone faces.
Similar content being viewed by others
REFERENCES
R. J. Jelitto, “The density of states of some simple excitations in solids,” J. Phys. Chem. Solids 30, 609–626 (1969).
R. H. Swendsen and H. Callen, “Green’s functions of the face-centered-cubic Heisenberg ferromagnet with second-neighbor interactions,” Phys. Rev. B 6, 2860–2875 (1972).
S. V. Vonsovskii, M. I. Katsnelson, and A. V. Trefilov, “Localized and itinerant behavior of electrons in metals,” Phys. Met. Metallogr. 76, 247–299 (1993).
M. I. Katsnel’son, G. V. Peschanskikh, and A. V. Trefilov, “The singularities in the density of electron states and their effect on the elasticity moduli in alkaline earth metals,” Sov. Phys. Solid State 32, 272 (1990).
V. L. Moruzzy, J. P. Janak, and A. R. Williams, Calculated Electronic Properties of Metals (Plenum, New York, 1978).
D. A. Papacostantopoulos, Handbook of Band Structure of Elemental Solids (Plenum, New York, 1986).
A. Hausoel, M. Karolak, E. Sasioglu, A. Lichtenstein, K. Held, A. Katanin, A. Toschi, and G. Sangiovanni, “Local magnetic moments in iron and nickel at ambient and Earth’s core conditions,” Nature Commun. 8, 16062 (2017).
G. Santi, S. B. Dugdale, and T. Jarlborg, “Longitudinal spin fluctuations and superconductivity in ferromagnetic ZrZn2 from ab initio calculations, Phys. Rev. Lett. 87, 247004 (2001)
A. S. Hamid, A. Uedono, Zs. Major, T. D. Haynes, J. Laverock, M. A. Alam, S. B. Dugdale, and D. Fort, “Electronic structure and Fermi surface of the weak ferromagnet Ni3Al,” Phys. Rev. B 84, 235107 (2011).
P. G. Niklowitz, F. Beckers, G. G. Lonzarich, G. Knebel, B. Salce, J. Thomasson, N. Bernhoeft, D. Braithwaite, and J. Flouquet, “Spin-fluctuation-dominated electrical transport of Ni3Al at high pressure,” Phys. Rev. B 72, 024424 (2005).
J. Inoue, Electronic structure and magnetism of Y–M (M = Mn, Fe, Co and Ni),” Physica B 149, 376 (1988);
Y. Nishihara and S. Ogawa “Itinerant electron ferromagnetism in Y2Ni7,” J. Phys. Soc. Jpn. 60, 300–303 (1991).
D. J. Singh, Electronic structure and weak itinerant magnetism in metallic Y2Ni7, Phys. Rev. B 92, 174403 (2015).
M. I. Katsnel’son and A. V. Trefilov, “Electronic phase transitions due to correlation effects,” JETP Lett. 40, 1092–1095 (1984).
M. I. Katsnelson and A. V. Trefilov, “Anomalies in properties of metals and alloys due to electron correlations,” Phys. Lett. A 109, 109–112 (1985).
M. I. Katsnelson and A. V. Trefilov, “Anomalies of electronic and lattice properties of metals and alloys, caused by screening anomalies,” Physica B 163, 182 (1990); “Anomalies caused in phonon spectra by charge density fluctuations,” JETP Lett. 42, 393–396 (1985).
V. Yu. Irkhin, M. I. Katsnelson, and A. V. Trefilov, “On the magnetic contribution to lattice properties of itinerant ferromagnets: the role of Van Hove electron spectrum singularities,” J. Magn. Mag. Mater. 117, 210–218 (1992).
T. Morita and T. Horiguchi, Calculation of the lattice Green’s function for the bcc, fcc, and rectangular lattices, J. Math. Phys. 12, 986–992 (1971).
S. Katsura and T. Horiguchi, “Lattice Green’s function for the body-centered cubic lattice,” J. Math. Phys. 12, 230–231 (1971).
Yu. A. Izyumov, “Strongly correlated electrons: the t‒J model,” Phys.–Usp. 40, 445–476 (1997).
A. Damascelli, Z. Hussain, and Z.-X. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75, 473–541 (2003).
M. A. Timirgazin, P. A. Igoshev, A. K. Arzhnikov, and V. Yu. Irkhin, “Metal–insulator transition in the Hubbard model: Correlations and spiral magnetic structures,” J. Low. Temp. Phys. 185, 651–656 (2016).
M. A. Timirgazin, P. A. Igoshev, A. K. Arzhnikov, and V. Yu. Irkhin, “Magnetic states, correlation effects and metal-insulator transition in fcc lattice,” J. Phys.: Condens. Matter 28, 505601 (2016).
P. A. Igoshev and V. Yu. Irkhin, “Metal–insulator transition in the presence of Van Hove singularities for bipartite lattices,” J. Exp. Theor. Phys. 128, 909–918 (2019).
P. E. Blochl, O. Jepsen, and O. K. Andersen, “Improved tetrahedron method for Brillouin-zone integrations,” Phys. Rev. B 49, 16223–16233 (1994).
A. A. Stepanenko, D. O. Volkova, P. A. Igoshev, and A. A. Katanin, “Kohn anomalies in momentum dependence of magnetic susceptibility of some three-dimensional systems,” J. Exp. Theor. Phys. 125, 879–889 (2017).
L. Van Hove, “The occurrence of singularities in the elastic frequency distribution of a crystal,” Phys. Rev. 89, 1189–1193 (1953).
M. Fleck, A. M. Oles, and L. Hedin, “Magnetic phases near the Van Hove singularity in s- and d-band Hubbard models,” Phys. Rev. B 56, 3159–3166 (1997).
P. A. Igoshev, E. E. Kokorina, and I. A. Nekrasov, “Investigation of the magnetocaloric effect correlated metallic systems with Van Hove singularities in the electron spectrum,” Phys. Met. and Metallogr. 118, 207–216 (2017).
T. Moriya, Spin fluctuations in itinerant electron magnetism (Springer, Berlin–Heidelberg, 1985).
P. A. Igoshev, A. V. Efremov, and A. A. Katanin, “Magnetic exchange in α-iron from ab initio calculations in the paramagnetic phase,” Phys. Rev. B 91, 195123 (2015).
M. Ulmke, “Ferromagnetism in the Hubbard model on fcc-type lattices,” Eur. Phys. J. B 1, 301–304 (1998).
ACKNOWLEDGMENTS
We are grateful to M.I. Katsnelson and A.O. Anokhin for useful discussion.
Funding
The research was carried out within the state assignment of FASO of Russia (theme Quantum no. AAAA-A18-118020190095-4) and with the support by Program 211 of the Government of the Russian Federation (Agreement 02.A03.21.0006).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Igoshev, P.A., Irkhin, V.Y. Giant Van Hove Density of States Singularities and Anomalies of Electron and Magnetic Properties in Cubic Lattices. Phys. Metals Metallogr. 120, 1282–1290 (2019). https://doi.org/10.1134/S0031918X19130088
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0031918X19130088