Blogged by Piers Coleman
Colin gives the overview. He says that they've discovered a mesoscopic spin resonance and they'd love feedback on this new result about to appear in PRL. He begins with a review o V2O3. Its one of the classic examples of a Mott system. There is a doping tuned transition from a spin density wave (SDW) into an antiferromagnetic (AF) Mott insulator (AFI). In this system, one can understand the helical spin density wave using RPA, which has a susceptibility that peaks at the observed Q vector.
Colin reviews neutron scattering and the RPA description chi(q) = (chi0^-1(q)-J(q))^-1. In V2O3, they have not yet been able to use pressure to drive the Tc of V2O3 to zero. Another approach is to use a heavy fermion system, governed by much lower energy scales. He shows the tetragonal structure, and the afm phase below 70mK that is suppressed by a field. The standard understanding of this system, is as a result of the interplay of RKKY interactions with the Kondo ineteraction. Increasing J causes the magnetism to melt, into a heavy fermi liquid. Shows the figure from Schroeder et al (2003). Is the transition an SDW, or do we go from a local moment AFM into a state where the 4f electron is delocalized. This would involve a metal insulator transition at the magnetic transition. This is in contrast to V2O3, where an SDW separates the AFI from the metal.
Colin reviews the hall jump at the QCP measured by Friedemann, Paschen et al (PNAS, 2010). He shows that with Iridium/Co doping, one can split the localizing transition from the magnetic transition. This type of treatment does not explain why the localization and magnetization transition coincide without doping.
Q: How are the lines measured?
A: Not my data, but there are various thermodynamic anomalies that are followed to map out the phase diagram.
YRS is a problem for neutrons. Rh absorbs neutrons. Crystals are small. So combine 200 5x5 mm^2 crystals. Absorption of neutrons causes heating, which limits physics at the moment to T>0.1K.
Trying hard to go down to lower T, but not there yet - so the quantum critical region has not yet been accessed.
There are 4 crystal field doublets measured by neutrons. The lowest excitation is at 80mK, so the ground-state doublet is pretty well isolated. The GS doublet is a mix of 3/2 and -5/2. The system is quite anisotropic, and has most of its Curie response in the easy plane. (20 x smaller in c-axis).
Now neutrons see an incommensurate feature around (002), with some incommensuration in the HH2 direction, at H~ +- 0.14 reciprocal lattice units (rlu). The incommensurate feature survives down to 0.1K, with a correlation length of about 3.6 (a+b). With a energy of about 0.1 meV. The band structure would give 0.7,0.7,0 - not quite the right wavevector, but he speculates that there might be an indication of the origin of the incommesurate wave vector.
Q: would this have the 80mV crystal field split off
Mike Norman - even the dft differs. One needs a renormalized band structure calculation.
Silke Paschen - this may have been done by Gertrude Zwicknagl.
So - since one can't look at low enough temperatures, try applying a field to see the effect. On heating, the detailed incommensurate structure merges into a ferromagnetic peak. Now one can follow this as a function of field. This reminds one of MnSi (manganese silicide, which has similar behavior. ) The spectrum broadens with temperature. The width of the spectrum broadens with temperature. Quite unusual says Colin. (Blogger, but seen in CeCu6-xAu_x).
Gamma = C T
Leads to omega/T scaling, he says. And indeed it is! Get a scaling exponent of alpha = 1.
chi'' (E,T) = 1/T^alpha f(E/T)
This is not deep into the qcp regime, but certainly consistent with the linear resistivity regime and specific heat.
Q: From the blogger - does this exponent also appear in the uniform susceptibilty, a la Schroeder et al?
A: It must do - if it fails, there would be something inconsistent with our experiment! But we should check it.
He shows how the intensity scales, as expected with M^2. Now back down in temperature, what is the effect of field? The signal shifts to finite energy - about 0.35 meV. By applying a field, the excitation is still there. This he says, would tend to favor an SDW picture. (blogger - but E/T scaling?)
The neutron scattering is able to see the ESR mode - one extracts the same g factor of 3.86 (neutron)
vs gperp = 3.56 in ESR. This is one of the first time that an ESR resonance has been seen in neutron scattering - it has been moved by field up into the regime where it can be seen by neutrons.
He points out that a similar FM spin resonance is seen in MnSi, but what is distinct in this case, the excitation has a dispersive form. Is a similar propagating mode seen here.
NO! There isn't! Its a "spot" in energy momentum space, out at 1meV, with a width of 0.04 in qspace and 0.05meV in energy. How should we interpret this localized excitation? It should be regarded as a completely collective precession of all of the f-electron spins. A spatially extended spin density - a "mesoscopic spin resonance" . The size that we can extract from the peak is associated with the resonance -
Makes the analogy with the spins that develop as an edge state in Haldane spin chains. In that case, there is an extended spin=1/2 excitation. Here, the correlation length is about
xi ~ 6(2) Angstroms
This is similar to a Kondo length scale
xi ~ v_F/TK ~ 15A.
Using the gamma in a field to get vF.
Q: in the spin chain example - does it exist for only one frequency?
A: change field, the resonance moves along.
Many conclusions (below).
- Main result - FM scritical regime for T> 1K.
- Lower Incommensurate critical flus at Q= (q,q,0) q=0.14
- SDW instability may arise from nesting of hole fermi surfaces
- B suppresses SDW favoiring FM polarized metal
- Mesoscopic spin precession indicates Kondo screened 4f spin degree of freedom
- SDW correlations persist at lower energies in magnetized Kondo lattice state.
Q: from Andrey C. Do you still see E/T scaling at lower temperatures? Can you still do it below 1K?
A: can't answer this yet - I feel we need to go to lower T. Our resolution is such that to answer this, with our resolution, will require the next generation of experiments.
Q: from Mike Norman. If you look at the AC susceptibility in LiHoFl - it also shows lifting up - one has large ferromagnetic clusters. I think you have to use a similar idea here.
A: Blogger missed it - seemed to agree.
Q: fluctuating moment - how big is it?
A: 4 mu_B^2 - really large. Now the size of the ordered moment - can't say yet. 0.01 would be very small - has to be a way of accounting for why its so small, yet with such a large fluctuating moment.
Q: is there a change in the width of the esr type line with field?
A: no.
Q: There seems to be a double peak at o.1meV in your data 15K?
A: doesn't look healthy to me. When we went to higher fields - moved to higher energy - see commensurate peak at the esr energy and incomensurate peak sustained at lower energies (0.5meV).
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