- Sr3Ru2O7 and the phase diagram
- thermodynamic probes
- qu. critical entropy pileup
- a novel phase with nematic transport properties
- broader perspectives: relevance to surface spectroscopy, electronic nematics, heavy fermions...
Take H=8 T. Find \rho~T^2 to the left and right of this critical point, but directly above it, one finds \rho linear in T, indicating appearance of a new phase (to be discussed in what follows).
S. Grigera, Science ...
Low temperature magnetization of Sr-237. Experimentally - use Faraday force magnetometer with customized design. Picks up a mix of torque and magnetization signals, which one can separate from each other by doing a clever subtraction of two signals.
J. Mercure et al: PRL 09, PRB '10
dHvA osicallations are seen below and above the metamagnetic transition, with similar frequencies, i.e. the carrier density does not change much through these transitions.
Magnetocaloric effect and specific heat:
A.W. Rost, Science 325, 1360 (2009). Plot of Cv/T coefficient and entropy dS/T both show divergence as Bc=8T is approached from above and below. However right around 8T, dS/T shows a wiggle. This would indicate a diverging mass of the Fermi liquid, however no direct observation of strongly B-dependent mass in dHvA. A puzzle!
Remark: the fact that C~\gamma T in the FL would mean that also entropy S~\gamma T. And indeed, on approach to Bc, both entropy and specific heat are on top of each other. Conclusion - Sr327 is a solid Fermi liquid away from Bc=8T.
Specific heat: C/T ~ log(T/T0) below T~10K - a work by S. Nakatsuji and Y. Maeno.
- Sr-214 shows a classic FL behaviour with C/T = \gamma + b*T^2.
- Sr-327 at B=7.9T (at Bc): Above 15K, Sr-327 looks like a FL with gamma = 75 mJ/(K^2.mol). However at low-T it shows log-divergence.
The speaker shows on the board his interpretation of the data:
Assume that DOS has a narrow peak at E=Ep just below the Fermi level. In finite temperature so that Ep < T < E_Fermi, this would explain the excess entropy is dS =0.1Rln2 (as measured between the B=0 specific heat data and the Fermi liquid fit C/T = gamma + bT^2). However to explain how this excess entropy is seen at low temperature, the logical assumption is that this narrow peak in the DOS must become narrower and narrower as temperature goes to zero, so that Ep < T is always satisfied. This is obviously a phenomenological observation, and we don't know how to justify it microscopically. [Note: it is pointed out from the audience, that Rln2 is the spin entropy (for S=1/2). Generally, there are also electron charge degrees of freedom, so that total entropy would be Rln4. Unless of course one has strong enough Hubbard U that would suppress charge fluctuations.]
Whatever that feature is in the DOS, it is NOT just a rigid band feature through which one simply Zeeman shifts. See Iwaya, PRL 2007; J. Farrel, PRB .
* The novel nematic phase
Observed in a narrow region of fields around the Bc=7.9T below T~1K (showing a curved "roof" feature).
Tentatively explained by a weak Pomeranchuk distortion in the d-symmetry (l=2) channel. See theory by Ho and Schofield who analysed the region of stability of such a Pomeranchuk (nematic) phase.
At Bc, C/T keeps rising as T->0. However away from Bc, C/T saturates to a Fermi liquid value.
Use the experimental reconstruction of S(T) to try to delineate which theory is right!
E.g. (C/T)exp ~ [H-Hc]^{-1}
whereas Hertz-Millis prediction would be [H-Hc]^{-1/3}.
Something else we might be missing? S. Hartnoll, PRB 76, 144502 (2007).
CONCLUSIONS:
Questions:
Q. Could you comment on spin anisotropy? What is the dependence on the field direction?
A. Everything shown was for field along c-axis. We are able, in principle, to measure the angle-dependent specific heat, but so far not possible due to design of the experimental setup.
Q. A. Chubukov: Belitz and Kirkpatrick claim that C ~ T^3 log T in their theory. Do you see any deviation from C~T^3 at higher temperatures?
A: You can indeed see C/T deviating from T^2, but the details are unclear. Postpone till private discussion.
Q. S.-W. Cheong.
1) Are all 3 transitions true phase transitions or crossovers.
2) you may have a phase coexistence?
A: 2) Indeed, coexistence, with domains may be possible.
1) only one is a true transition, the other two are crossovers.
Q. R. Fernandez: Can you see nematic phase by measuring anisotropy in resistivity?
A. It's more complicated, since the domains, if they exist, would change their orientation as the field is rotated.
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