Supporting Information

Transcription

1 Supporting Information Cu O 3 : a new magnetically frustrated honeycomb iridate Mykola Abramchuk, Cigdem Ozsoy-Keskinbora, Jason W. Krizan, Kenneth R. Metz, David C. Bell,, and Fazel Tafti, Physics Department, Boston College, Chestnut Hill, MA 467, USA Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge MA 138, USA Chemistry Department, Boston College, Chestnut Hill, MA 467, USA Center for Nanoscale Systems, Harvard University, Cambridge MA 138, USA fazel.tafti@bc.edu Phone: (617) S1

2 Energy Dispersive X-ray Spectroscopy (EDXS) Fig. S1(a) shows the EDXS in a pressed pellet of Cu O 3. The sodium peak at 1.41 kev is absent while the copper peak at.93 kev is present. The quantitative analysis confirms the ratio Cu/ =.1(1) where the statistical error comes from repeating the measurement on several spots. Fig. S1(b) shows the EDXS in a pressed pellet that contains a mixture of Cu O 3 /Na CO 3 = 3/1. The quantitative analysis confirms the ratio Cu/Na = 3/1 as expected. Note that the total counts in Fig. S1(b) are smaller than in Fig. S1(a) but, the sodium peak is clearly observable and distinct from the copper peak. Our EDXS as well as ICP-OES confirm the absence of sodium in the structure of the material. C o u n ts (a.u.) (a ) 1 4 (b ) O / =.1 (1 ) E (k e V ) C o u n ts (a.u.) O 1 6 / = E (k e V ) Figure S1: (a) EDXS spectrum confirming the Cu/ ratio in Cu O 3. The error reported on the figure comes from statistics. The inset shows that within the resolution of our EDXS detector, the sodium peak at 1.41 kev must be distinguishable from the copper peak at.93 kev. Consistent with our ICP-OES results, sodium is absent from the structure. (b) EDXS spectrum from a pressed pellet of thoroughly ground mixture of Cu O 3 /Na CO 3 = 3/1. The inset shows that within the resolution of our EDXS detector, the sodium peak at at 1.41 kev is clearly distinguishable from the copper peak at.93 kev. The Cu/Na ratio is 3/1 as expected. S

3 Stacking Faults Fig. S presents a qualitative analysis of the asymmetric broadening in the X-ray peaks from 19 to degrees. According to ref. 17 in the main text, the asymmetric broadening can be analyzed by a sum of a Gaussian and a Cauchy function. The summation gives rise to the real part of the Voigt function and the exponent of the Gaussian term measures the percentage of the stacking faults known as the g-factor: g = /d = d d (1) where d is the interlayer spacing. Fig. S shows this fit to our x-ray data from 19 to degrees with the exponent.1 corresponding to 1% stacking faults. This value roughly correlates with the 18(9)% estimate based on the mixing of the 8f iridium site which is also due to stacking faults (Table in the article). In te n s ity (c o u n ts ) y = A e g x B + C + x A = ±. 4 6 g =.1 8 ±. 7 B = 7 8 ± 9 6 C = ± Θ (d e g re e s ) Figure S: Warren line shape is fitted to a combination of Gaussian and Cauchy distributions where the exponent of the Gaussian term provides a rough measure of stacking faults in the material. S3

4 1 4 1 (a ) 1 1 (b ) C (J / m o l K ) O 3 C (J / m o l K ) O 3 C T 3 C /T (J / m o l K ) (c ) S (J / m o l K ) (d ) Figure S3: (a) Heat capacity plotted as a function of temperature in Cu O 3 (red) from T = to 3 K. (b) Lattice contribution is approximated by a T 3 curve below 3 K. (c) C/T plotted as a function of T showing the anomaly around 5 K. (d) S plotted as a function of T showing the small entropy change due to the weak transition below 5 K confirming short-range magnetism. S4

5 Heat Capacity In the absence of a proper lattice model for Cu O 3, we used a simple T 3 model to subtract the phonon contribution to the heat capacity below 3 K. Fig. S3(a) shows C versus T in Cu O 3 from to 3 K. Fig. S3(b) shows the T 3 limiting behavior from the Debye model, extended to 3 K. The T 3 model is valid only at temperatures well below the Debye temperature. We required that the T 3 fit would meet the data at 3 K. Fig. S3(c) shows C/T = (C C lat. )/T where the anomaly at 5 K is visible. Fig. S3(d) is the result of integrating C/T to arrive at S = C/T dt. The entropy loss below 1 K is less than 5% of R ln() confirming the short-range nature of the weak magnetic order in Cu O 3. Spin-glass systems often show a broad transition in the heat capacity at about twice the spin freezing temperature. 1 This is consistent with our observation in Cu O 3. We conclude that the weak peak at.75 K in susceptibility (Fig. 6, main text) and the broad feature at 5 K in heat capacity are due to local (short-range) correlations. References (1) J. A. Mydosh, Spin Glasses: An Experimental Introduction, 1st edition. London; Washington, DC: CRC Press, S5