The sample used was a single crystal, grown by the group of C. Geibel in Darmstadt.
For a description of the sample preparation, see e.g. [104].
CHAPTER 11. α’-NaV2O5 — A SPIN-PEIERLS COMPOUND? 95 Measurements were carried out by the torque method (section 3.2.1), using a single beam cantilever torquemeter. The magnetic field was held at a constant value, then temperature was sweeped, using a fixed sweep rate, in a4He flow cryostat.
From the resultingC(T) curves, the derivative was taken and the transition temper-ature determined as the position of the maximum (see fig. 11.3(a) for an example).
To account for temperature gradients between thermometer and sample due to the finite temperature sweep rate, measurements where done with increasing and decreasing temperature. The average of both maximum positions was then taken as the real position of the transition.
Measurements were performed for magnetic fields up to Bmax = 28 T. The de-pendence of the transition temperature on magnetic field was then extracted from the measurements (fig.11.3(b)).
11.5 Discussion
As mentioned above, one of our main original intentions was to reach the incommensurate phase in high magnetic fields.
But in fact, during our measurements (spring 1998), newest experimental results sug-gested that basic assumptions aboutα’-NaV2O5 had to be revised: By X-ray diffraction measurements [105], it turned out that instead of having a non-centrosymmetric crystal structure with two distinct V sites, leading to charge ordering (V4+/V5+) along one-dimensional chains already at room temperature,α’-NaV2O5 possesses only one type of V site and is in a mixed valence state with a formal valence of n = 4.5 above TSP. It was proposed subsequently that α’-NaV2O5 may behave as a quarter-filled spin ladder system, with spins attached to a V-O-V molecular orbital [105], or that the spins may be attached to single V ions, but with “zigzag” instead of “in-line” charge ordering [106].
By thermal expansion measurements ([104]), two distinct phase transitions were found, suggesting that the spin-singlet formation only follows a charge ordering transi-tion. NMR investigations [107] have strongly supported this point of view, qualitatively explained by a new theoretical model [108].
Our results, showing only a weak dependence of the transition temperature TSP on magnetic field, agrees well with this new point of view.
Tentatively, we tried to fit our data with the model developed by Cross [103], but as could be expected at that time, the result was a very poor fit or yielded a very unphysical value for the electron g-factor (see figure11.4).
What can we conclude?
Considering the weak field dependence, the double phase transition and the incorrect BCS value of 2∆(0)/kTSP = 6.44, one might be tempted to assume that the “real” SP transition temperature TSP,real, corresponding to the correct BCS value of3.52, is much higher (TSP,0≈60 K), but that the SP state is of course suppressed until the formation of the charge ordered state.
Our magnetic anisotropy measurements sense the magnetic phase transition con-nected with the spin singlet formation, but the primary order parameter governing the transition is the one from the charge ordering transition with its weak temperature de-pendenceTCO(B).
This leads us to the interesting speculation that the two phase transition might be decoupled at much higher fields, when TSP,real(B) ≤ TCO(B). Taking figure 11.4 as a hint, the magnetic fields needed might be of the order of B ≈80 T. However, the
rela-96 11.5. DISCUSSION
∆
Figure 11.3: (a) Example of torque measurement (data points, left axis) and its derivative (solid curve, right axis). The transition temperatureTSPwas taken as the position of the maximum of the derivative. (b) Resulting magnetic field dependence of the transition temperatureTSP
CHAPTER 11. α’-NaV2O5 — A SPIN-PEIERLS COMPOUND? 97
Figure 11.4: Tentative fit of the measured B dependence of the transition temperature TSP using the model by Cross [103], yielding an unphysical g factor, compared to predic-tion for g= 2 and the observedTSP,0 ≈33 K and the prediction using the correct BCS ratio 2∆(0)kT
SP = 3.52, yieldingTSP,0 ≈60 K.
tively small magnetic susceptibility of α’-NaV2O5 would make measurements in pulsed magnetic fields a daring undertaking.
98 11.5. DISCUSSION
Chapter 12
Conclusion
The main objective of the present work was the investigation of the vortex state in type II superconductors using the magnetostriction technique as a tool together with other, complementary methods.
In this context, the possibilities of magnetostriction as well as its limitations have been intensively studied. Its staticity and its resolution especially at high magnetic fields have proven to be indispensable in the study of the “peak effect” region and thermomagnetic history dependence effects.
An extensive survey to investigate the influence of sample geometry and suspension on results in magnetostriction yielded striking and unforeseen results. Apparently, the inhomogeneous flux, current and force density distribution inside the sample gives rise to more complex deformations than calculations assuming ideal infinite geometries would suggest. This was shown by measurement on NbTi alloy samples of different, mostly cylindrical geometries and different suspensions inside the capacitive measuring cell. A tentative qualitative explanation for some of the observed effects has been given. A geometry best suited for further investigations has been chosen based on the experience gained.
Measurements of magnetization on several NbTi samples have been performed for comparison and as a complement to magnetostriction results. It was shown that mea-surements of torque, though presenting the advantage of a static measurement just like the magnetostriction technique, suffer from complications due to torque contributions probably arising from the inhomogeneous distribution of magnetization inside the sam-ple. This effect gets especially important inside the peak effect region. Magnetization measurements using an extraction setup, on the other hand, expose the sample to an oscillating magnetic field contribution due to unavoidable magnetic field gradients, re-sulting in a strong distortion of the flux distribution inside the sample, again particularly at high magnetic fields.
Resistivity measurements were performed simultaneously with magnetostriction in-vestigations in order to compare the irreversibility fieldBirrto the upper critical fieldBc2. A narrow, almost temperature independent reversible region was found just belowBc2, in contradiction with existing calculations and earlier investigations on the irreversibility line.
As a second system in addition to polycrystalline isotropic NbTi, single crystalline, highly anisotropic 2H-NbSe2 was chosen. In measurements of both magnetostriction and magnetization, three different contributions could be disentangled. From the compari-son of de Haas-van Alphen oscillations in magnetostriction and magnetization, a huge value for the pressure dependence of the Fermi surface’s extremal cross section was
ex-99
100
tracted. A monotonic logarithmic contribution was shown to be related to a kink in thermal expansion measurements and therefore to the thermodynamic superconducting magnetostriction. From the irreversible part of the measurements, pinning induced mag-netostriction could be deduced.
For both NbTi and 2H-NbSe2, parameters of the peak effect region have been deter-mined and their temperature dependence studied. Evidence of a disappearence of the peak at a temperature lower than the critical temperature was found. A scaling analysis was performed for both systems in both the low field and the peak region. For the latter, no compliance to scaling rules was observed in either sample. This supports the view that the concept of scaling is not applicable to the peak region. In particular it puts into perspective statements that the non-applicability of scaling rules separates certain classes of pure, weak pinning compounds from “conventional” superconductors. For low fields, scaling was remarkably well observed in NbTi and satisfying in NbSe2. A comparison of the peak’s onset and offset field for several samples yielded scaling of the difference between both fields by the linear dimension of the sample perpendicular to the magnetic field. This supports the hypothesis that this difference is only due to the flux gradient inside the sample and is not to be interpreted as evidence of a first order transition in vortex matter from an ordered to a disorderd state.
Finally, the topic of thermomagnetic history dependence in magnetostriction was studied on NbTi samples. Two types of memory effects were found in the peak effect region and at lower magnetic fields. These have been interpreted in terms of two different types of disorder in vortex matter: intrinsic disorder generated at elevated fields, marked by the peak effect, and an extrinsic type of disorder generated by flux movement through imperfect surfaces, observed in a wide field range. Strong similarities in the behaviour of both strong pinning polycrystalline NbTi and different high quality single crystals seem to indicate a high degree of universality in the properties of vortex matter.
In collaboration with the Max-Planck Institute for the Chemical Physics of Solids in Dresden, two subjects off the main topic have been studied:
Resistivity measurements under hydrostatic pressure on YbCo2Ge2 have been per-formed in the framework of an investigation of the compound’s low temperature prop-erties. It appears that the sample belongs to a class of intermediate valence compounds with a characteristic temperatureT0 ≈90 K, which tends to increase at high pressure.
Even though the compound has a high magnetic susceptibility and anisotropy, no trace of metamagnetism was found forB≤28 T.
Concerningα’-NaV2O5, it is expected that this system will continue to attract consid-erable attention in the future. Even though it has become clear during recent years that one of the key expectations from the first measurements — to find a simple, prototypical, inorganic spin-Peierls compound — was not met,α’-NaV2O5 offers a rich playground for a gain in the knowledge concerning low-dimensional magnetic systems. Our measure-ments give a hint to the possible benefits of performing very high field measuremeasure-ments, which might prove a decoupling of the charge ordering and the spin-Peierls transition in this compound.
Chapter 13
Zusammenfassung
Kurzabriß
Die vorliegende Arbeit widmet sich im wesentlichen der Untersuchung des gemischten Zustandes in Typ-II-Supraleitern durch Messung der Magnetostriktion. Diese Deforma-tion im Magnetfeld entsteht durch die Wechselwirkung von Flußschläuchen (Vortizes) mit Strömen im Probeninnern, welche aus einer inhomogenen Verteilung des magnetischen Flusses, bedingt durch Pinning (Anhaften von Vortizes an Verunreinigungen) resultieren.
Im Brennpunkt der Untersuchungen stehen dabei neben Auswirkungen der Probenge-ometrie vor allem Gedächtniseffekte, d.h. Abhängigkeiten magnetischer Eigenschaften von der thermischen und magnetischen Vorgeschichte. Zusätzlich zu bekannten Effek-ten dieser Art im Magnetfeldintervall des Peak-Effektes nahe dem oberen kritischen Feld Hc2wurden dabei neuartige Gedächtniseffekte bei niedrigeren Feldern nachgewiesen. Ein erster Erklärungsansatz führt als Ursache hierfür die Propagation metastabiler ungeord-neter Vortex-Strukturen durch die Oberfläche und innerhalb der Probe an.