Research at the Laboratory of Crystallography

Charge density waves in Er₅Ir₄Si₁₀ and related compounds

The rare earth metal (R) transition metal silicides R₅Ir₄Si₁₀ have complicated phase diagrams. They exhibit Charge-density wave (CDW) transitions at temperatures TCDW in the range 80 K < T_CDW < 210 K, depending on the rare earth element R. At much lower temperatures phase transitions from paramagnetic to antiferromagnetic states have been found in the compounds with localized magnetic moments due to the f electrons on the R atoms, while non-magnetic compounds, e.g. with R = Lu, become superconducting.

Fig. 1:  All compounds R₅Ir₄Si₁₀ crystallize in the Sc₅Co₄Si₁₀ structure type with the tetragonal space group P4/mbm and with lattice parameters of approximately a = 12.5 and c = 4.2 A at room temperature. View of the basic structure approximately along the tetragonal c-axis. Large circles represent R atoms, intermediate circles are Ir, and small circles denote Si.

Temperature dependent x-ray diffraction was measured on single crystals of the compounds R₅Ir₄Si₁₀ with R = Ho, Er, Tm, Lu, (Lu_0.36Er_0.64) and (Lu_0.16Er_0.84). Weak satellite reflections could be found due to the use of synchrotron radiation. The results show a remarkable variation of superstructures that allow the rationalization of the qualitatively different temperature dependencies of the physical properties in these compounds. In compounds with R = Ho, Er, Tm and (Lu_0.16Er_0.84) a commensurate CDW (q₁ = 0.5 c*) and an incommensurate CDW (q₂ = ±0.25 ±d  c* with d = 0.03) simultaneously develop at T_CDW, while commensurate CDWs (q = n/7 c*) develop in compounds with R = Lu and (Lu_0.34Er_0.66).

Fig. 2:   q-scans of the positions of the satellite reflections of Ho₅Ir₄Si₁₀ between (4, 8, -3.9) and (4, 8, -3.1). One scan in the incommensurate phase (T = 100 K) and one scan below the lock-in transition (T = 90 K) are shown.

A model was proposed that explains the simultaneous occurrence of commensurate and incommensurate modulations at T_CDW [1]. In this model a structural phase transition towards a doubled unit cell is supposed to take place at T_CDW. The modified electronic band-structure of this superstructure then provides the proper nesting conditions for the incommensurate CDW [1]. This model was supported by the observation of diffuse scattering above T_CDW for the commensurate satellites only [2], and by the anomalous increase of the electrical resistivity below T_CDW.

Fig. 3:   Temperature dependence of the positions of the satellite reflections in the x-ray diffraction of Ho₅Ir₄Si₁₀ on the line (4, 8, l) (left), and of Tm₅Ir₄Si₁₀ on the line (5, -12, l) (right).

The compounds with an incommensurate CDW exhibit a second transition at T_lock-in < T_CDW. In Ho₅Ir₄Si₁₀ and Er₅Ir₄Si₁₀ this is a pure lock-in transition at which d  becomes zero. In Tm₅Ir₄Si₁₀ and (Lu_0.16Er_0.84)₅Ir₄Si₁₀ d also becomes zero, but additional satellite reflections appear. They are found at commensurate positions n/8 c* in Tm₅Ir₄Si₁₀, and at incommensurate positions (n/8 ±0.01) c* in (Lu_0.16Er_0.84)₅Ir₄Si₁₀. The development of this second CDW can be understood by a two-step mechanism similar to the mechanism for the development of the primary CDW [3]. At T_lock-in the primary CDW becomes commensurate, leading to a partly restoration of the Fermi surface, as evidenced by an anomalous decrease of the electrical resistivity for T below T_lock-in in Ho₅Ir₄Si₁₀ and Er₅Ir₄Si₁₀. The modified Fermi surface then provides the favorable nesting conditions for the development of a second CDW in Tm₅Ir₄Si₁₀ and (Lu_0.16Er_0.84)₅Ir₄Si₁₀. The electronic character of this transition is suggested by the anomalous increase of the resistivity for T belowt T_lock-in.

Fig. 4:   Temperature dependence of the electrical resistance of Tm₅Ir₄Si₁₀ along the c-axis (circles) and along the a-axis (squares). The normalized resistance (R(T)/R(T=300K)) is given for cooling (open symbols) and heating (filled symbols). The transition temperatures as obtained by x-ray diffraction are marked by arrows.

Fig. 5:   Temperature dependence of the electrical resistance of polycrystalline bars of Ho₅Ir₄Si₁₀ (circles) and (Lu_0.12Er_0.88)₅Ir₄Si₁₀ (squares). The normalized resistance (R(T)/R(T=300K)) is given for cooling (open symbols) and heating (filled symbols).

Table 1:   Phase diagrams of the compounds R₅Ir₄Si₁₀ with R = Ho, Er, Tm, Lu, (Lu_0.36Er_0.64) and (Lu_0.16Er_0.84). All compounds are tetragonal P4/mbm at room temperature. n denotes an integer; d are numbers in the range of 0.01 to 0.04. Standard deviations are given in parentheses. An accuracy of ±t indicates that incommensurate satellites were observed at T_lock-in+t, and that commensurate satellites were observed at T_lock-in-t.

 
More experimental results and a more extensive discussion, including a tentative (x,T) phase diagram for (Lu1-xEr_x)₅Ir₄Si₁₀, can be found in the publications given below.

Publications:

[1] F. Galli, S. Ramakrishnan, T. Taniguchi, G.J. Nieuwenhuys, J.A. Mydosh, S. Geupel, J. Lüdecke and S. van Smaalen, Phys. Rev. Lett. 85 158-161 (2000). Charge-Density-Wave transitions in the local-moment magnet Er₅Ir₄Si₁₀.
[2] F. Galli, R. Feyerherm, R.W.A. Hendrikx, E. Dudzik, G.J. Nieuwenhuys, S. Ramakrishnan, S. Brown, S. van Smaalen and J.A. Mydosh, J. Phys.: Condens. Matter 14, 5067-5075 (2002). Coexistence of Charge density wave and antiferromagnetism in Er₅Ir₄Si₁₀.
[3] S. van Smaalen, M. Shaz, L. Palatinus, P. Daniels, F. Galli, G. J. Nieuwenhuys and J.A. Mydosh, Phys. Rev. B 69, 014103 (2004) (11 pages). Multiple charge-density waves in R₅Ir₄Si₁₀ (R = Ho, Er, Tm and Lu).