DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 1 Pressure dependence of Curie temperature and resistivity of complex Heusler alloys Václav Drchal Institute of Physics ASCR, Praha, Czech Republic in collaboration with Shyamal Bose, Josef Kudrnovský and Ilja Turek Czech Science Foundation Project P202/09/0775
DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 2 STRUCTURE Heusler alloys (Ni x Cu 1 x ) 2 MnSn and (Ni x Pd 1 x ) 2 MnSn L2 1 structure fcc lattice A 1 = a ( 0, 1 2, ) 1 2 A 2 = a ( 1 2, 0, ) 1 2 A 3 = a ( 1 2, 1 2, 0) basis τ 1 = a(0, 0, 0)... (Cu, Ni) or (Pd,Ni) τ 2 = a ( 1 4, 1 4, 4) 1... Mn τ 3 = a ( 1 2, 1 2, 2) 1... (Cu, Ni) or (Pd,Ni) τ 4 = a ( 3 4, 3 4, 4) 3... Sn
DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 3 MOTIVATION Heusler alloys have interesting physical properties and promising technological applications magnetic shape memory magnetocaloric effects spintronics effects of high pressure: increased electron kinetic energy increased overlap of orbitals and band broadening modification of Coulomb interactions changes of Fermi surface changes of magnetic moments and exchange interactions changes of transport properties high pressure brings new information on the system new degree of freedom independent probe into physical properties serves as a test of theory
OUTLINE ELECTRONIC STRUCTURE EXCHANGE INTERACTIONS CURIE TEMPERATURES TRANSPORT PROPERTIES DISCUSSION CONLUSIONS ab initio study of Curie temperature under pressure for nonrandom Ni 2 MnSn: Sasioglu et al. Phys. Rev. B 71 214412 (2005) properties at ambient pressure: Bose et al. Phys. Rev. B 82 174402 (2010), J. Kudrnovský at DPG Dresden 2011 properties at high pressure: Bose et al. Phys. Rev. B 84 174422 (2011) and present contribution DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 4
DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 5 TB-LMTO-CPA ELECTRONIC STRUCTURE xc: Vosko-Wilk-Nusair, experimental lattice constants pressure is simulated by the reduction of lattice constant 3 % reduction corresponds approx. to 16 GPa in Ni 2 MnSn
DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 6 classical Heisenberg Hamiltonian EXCHANGE INTERACTIONS 1 H Heis = X ij J ij e i e j e i = M i M i... unit vectors exchange interactions... J ij J ij > 0 ferromagnetic coupling J ij < 0 antiferromagnetic coupling magnetic force theorem: Liechtenstein formula: Liechtenstein et al. JMMM 67 65 (1987), Turek et al. Phil. Mag. 86 1713 (2006) J ij = 1 Z 4π Im C tr L h i (z) ḡ ij (z) j(z) ḡ ji (z) i dz i (z) = P i (z) P i (z), ḡσ ij (z)... intersite block of the Green function
DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 7 EXCHANGE INTERACTIONS 2 exchange interactions between Mn atoms are calculated in the DLM state, then induced moments vanish 0.2 Ni 2 MnSn ambient (a) effects of high pressure: diminished moments increased overlaps and thus exchange interactions are stronger J Mn,Mn (D) (mry) 0.15 0.1 0.05 0-0.05-0.1 pressure (-3%) -0.15 bare interactions J bare ij = J ij /(M i M j ) H Heis = X ij J bare ij M i M j J Mn,Mn (D)/(M) 2 (mry/(µ B ) 2 ) 0.02 0.015 0.01 0.005 0-0.005-0.01 (b) ambient M(ambient)= 3.585 µ B pressure (-3%) M(pressure)= 3.343 µ B -0.015 0.5 1 1.5 2 2.5 3 Relative distance D=(d/a)
DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 8 GROUND STATE the ground state of systems with one sublattice is given by a single q-vector wave which corresponds to the maximum of the Fourier transform of exchange interactions: J(q) = X j e iq R j J 0,j DLM-Ni 2 MnSn red line: ambient pressure green line: high pressure ( 3% a) the ground state character is not changed maximum at Γ-point: ferromagnet J Mn,Mn (q) (mry) 5 4 3 2 1 0-1 -2-3 L Γ X W K Γ
DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 9 CURIE TEMPERATURE 1 k B T MFA C = 2 3 X J 0i, i 1 k B T RPA C = 3 2 1 N X q 1 J(0) J(q) 500 (Ni 1-x Pd x ) 2 MnSn U Ni = 2.0 ev 600 (Ni 1-x Cu x ) 2 MnSn U Ni = 2 ev T c (K) 450 400 350 ambient pressure 3% reduction of a T c (K) 550 500 450 400 Lattice constant reduction: 0% (ambient pressure) 0.75% 1.5% 2.25% 3% 300 350 250 0 0.2 0.4 0.6 0.8 1 Pd concentration (x) 300 0 0.2 0.4 0.6 0.8 1 Cu concentration (x) Curie temperature increases with pressure in (Ni x Pd 1 x ) 2 MnSn for all x and in (Ni x Cu 1 x ) 2 MnSn for x < 0.7 while it decreases in (Ni x Cu 1 x ) 2 MnSn for x > 0.7
DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 10 comparison with experiment: CURIE TEMPERATURE 2 data available for Ni 2 MnSn and Pd 2 MnSn shows increase of T C with pressure Austin, Mishra Phil. Mag. 15 529 (1967), Gavriliuk et al. J. Appl. Phys. 79 2609 (1999) exchange mechanisms: direct exchange: not important as d(mn-mn) > 4 Å Anderson s superexchange (AFM): becomes stronger for smaller interatomic distances, tendency to lower T C, might be important, but it does not explain behavior of Heusler alloys Stearns indirect exchange between localized and itinerant d electrons: analogy to RKKY, oscillatory (FM or AFM), necessary for explanation delicate balance of superexchange and Stearns indirect exchange: only ab initio calculations can make quantitative prediction
DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 11 TRANSPORT PROPERTIES mechanisms responsible for resistivity in magnetic metals: scattering on static atomic disorder (impurities etc.): residual resistivity ρ 0 scattering on lattice vibrations ρ vib scattering on magnetic disorder ρ mag for simplicity assume that these mechanisms are independent: ρ = ρ 0 + ρ vib + ρ mag individual contributions can be extracted from measured temperature dependence: residual resistivity ρ 0 = const. scattering on lattice vibrations ρ vib (T) T above Debye temperature (small) scattering on magnetic disorder ρ mag (T) T 2 for T < T C and ρ mag (T) const. for T > T C (large) Kubo-Greenwood: σ(e) Tr[δ(E H)Jδ(E H)J], J = i[r, H] where J is current operator and R are discrete coordinates of atomic sites Turek et al. Phys. Rev. 65 125101 (2002) spin disorder resistivity: via disordered local moment (DLM) approach
DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 12 SPIN DISORDER RESISTIVITY 1 at ambient pressure: ρ(t) = ρ 0 + ρ vib (T) + ρ mag (T) ρ vib (T) = at ρ mag (T) = 8 < : ct 2 ρ 0, a from experiment c from ab initio : T < T C ρ mag (T C ) : T > T C ρ( µω.cm) 80 60 40 20 Ni 2 MnSn (exp.) Ni 2 MnSn (theory) Pd 2 MnSn (exp.) Pd 2 MnSn (theory) c = ρ mag(t 2 C ) T 2 C 0 0 100 200 300 400 500 T (K)
DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 13 SPIN DISORDER RESISTIVITY 2 disorder at E F is weak 50 (a) Ni 2 MnSn U Ni =2.0 ev two effects of pressure: ρ( µω cm) 25 0 50 25 0 50 25 0 (b) (Ni 50,Pd 50 ) 2 MnSn (c) Pd 2 MnSn ambient pressure 3% reduction of a ambient pressure 3% reduction of a ambient pressure 3% reduction of a 0 100 200 300 400 T (K) band broadening and delocalization of states leads to a smaller ρ increase of T C causes increased ρ(t) for T C (0) < T < T C (P) mostly theoretical predictions, experiment so far missing experimental data are available only for a related compound Pd 2 MnSb: increase of resistivity above T C (Austin, Mishra 1967)
DPG Frühjahrstagung Berlin, 25. - 30. März 2012 Sektion Kondensierte Materie (SKM), 2012 p. 14 CONCLUSIONS T C in (Ni x Pd 1 x ) 2 MnSn increases with pressure there are two regimes in (Ni x Cu 1 x ) 2 MnSn: T C increases with pressure for x < 0.7 T C decreases with pressure for x > 0.7 explanation in terms of Anderson superexchange and Stearns indirect d d exchange pressure dependence of spin-disorder resistivity ρ(t) ρ(t) decreases for T < T C (0) ρ(t) increases for T > T C (0)