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Site-Selective NMR in the Quasi-1D Conductor beta-Sr0.33V2O5

We report 51V NMR experiments in the metallic phase of the quasi-one-dimensional (1D) conductor beta-Sr0.33V2O5. The Knight shift and the quadrupole splitting of all six vanadium sites were determined as a function of the direction of magnetic field perpendicular to the conducting b-axis. Magnetic properties of the three 1D structural units are remarkably heterogeneous. In particular, the V2 ladder unit shows pronounced charge disproportionation among the two (V2a and V2b) sites. At one of these sites, the absolute value of the Knight shift and 1/(T1T) increase steeply with decreasing temperature, suggesting development of ferromagnetic correlation.


Introduction
The family of quasi-one-dimensional mixed valent vanadium oxides β-A 0.33 V 2 O 5 (A=Li, Na, Ag, Ca, Sr, and Pb) exhibit a variety of exotic phenomena such as metalinsulator transition, charge ordering, and pressure-induced superconductivity [1,2]. They provide fascinating opportunities to study mechanism for competing orders in a common monoclinic crystal structure shown in Fig. 1 [3]. There are three types of one-dimensional V-O network extending along the most conducting b-axis: a zigzag chain formed by the V1 sites, another zigzag chain formed by the V3 sites, and a two-leg ladder formed by the V2 sites. At high temperatures, the A ions are distributed randomly over two sites with 50 % occupancy in the space group C2/m. They order below a certain temperature and fully occupy a single sites in the new space group P 2 1 /a. This doubles the unit cell along the b-axis and generates two inequivalent sites for each of the three vanadium sites, which are denoted as Vna and Vnb (n=1 -3, see Fig. 1).
This ordering occurs above the room temperature (RM) in β-Sr 0.33 V 2 O 5 , which is a Pauli paramagnetic metal at RT. It undergoes a metal-insulator transition at T MIT ∼ 170 K accompanied by a simultaneous structural transition, that further triples the unit cell along the b-axis [3,4]. The magnetic susceptibility in the low T insulating phase indi-cates a singlet ground state with a spin gap. A spatial order of vanadium valence into V 4+ (3d 1 ) and V 5+ (3d 0 ) with 1:2 ratio was suggested for the low T phase from structural analysis. However, the neutron diffraction [5] and the nuclear magnetic resonance (NMR) [6] experiments ruled out such atomic localization of d electrons for β-Na 0.33 V 2 O 5 , which also shows simultaneous metal-insulator and structural transitions. In this paper we report results of 51 V-NMR experiments on a single crystal of β-Sr 0.33 V 2 O 5 and discuss charge distribution and spin dynamics in the high T metallic phase. NMR data on β-Sr 0.33 V 2 O 5 have been reported only for a powder sample so far [7].

Experiment
A single crystal of β-Sr 0.33 V 2 O 5 obtained by the Czochralski method was used in this work. It has the size 0.5×1.8×0.2 mm 3 with the largest dimension along the b-axis. The 51 V NMR spectra were obtained by summing the Fourier transform of the spin-echo signals with the frequency step of 0.3 MHz. The nuclear spin-lattice relaxation rate 1/T 1 was measured by the inversion recovery method. The magnetic field H 0 (10.509 T) was applied in the ac-plane. The direction of the field is specified by the angle (θ) measured from the a-axis.

Results and Discussions
There are four V atoms for each of the six crystalographic sites in a unit cell of the metallic phase (space group P 2 1 /a). When the magnetic field is applied in the ac-plane, these four atoms become equivalent and give identical NMR spectra. Since 51 V nuclei have spin I=7/2, the electric field gradient (EFG) splits the NMR spectrum into equally spaced seven lines at the following frequencies due to first order effect of the nuclear quadrupole interaction, where γ is the nuclear gyromagnetic ratio (11.193 MHz/T), K(θ) is the Knight shift, ν Q (θ) is the quadrupole splitting, and m specifies the nuclear transitions The upper panel of Fig. 2 shows the NMR spectrum at θ = −1 • , while the lower panel displays the angle dependence of the resonance frequencies for all the lines at T =190 K. At each angle, there are several sets of equally spaced lines assigned as A -F. In many cases only a portion of the quadrupole split seven lines are clearly resolved. However, they are sufficient to determine K(θ) and ν Q (θ) from Eq. (1). In Fig. 3(a) and (b), we plot the angle dependences of K(θ) and ν Q (θ) for the A -F sites. Since K(θ) ≪ 1 and ν Q (θ) ≪ γH 0 , we need consider only the lowest order effect for the frequency shift. Then K(θ) and ν Q (θ) should obey the following angle dependences [9], These equations indeed fit the data very well as shown by the solid, dashed and dotted lines in Fig. 3(a) and (b). Thus we have completely determined K(θ) and ν(θ) for all the vanadium sites. Generally the Knight shift at transition metal sites consists of the orbital and the spin contributions, K(θ) = K orb (θ) + K spin (θ). While K spin may be either negative or positive, K orb is always positive. The fact that K(θ) is negative for the entire range of angle at all sites indicates that the dominant term is K spin , which is related to the local spin susceptibility as K spin (θ) = {A cp + A dip (θ)}χ spin . The core polarization coupling constant A cp is isotropic and negative, while the dipolar coupling constant A dip (θ) is purely anisotropic, i.e. its directional average is zero. Since χ spin is nearly isotropic except for small anisotropy of the g-value, the observed angular variation of K(θ) must be ascribed to the anisotropy of A dip (θ), which is determined by the spin density distribution of d-electrons.  In β-Sr 0.33 V 2 O 5 , each vanadium atom is surrounded by a distorted squared pyramid formed by oxygen atoms. The shortest vanadyl bonding between the vanadium and the apical oxygen lies nearly in the ac-plane for all the V sites (within 4 • ). Doublet and Lepetit investigated the local electronic structure based on the extended Hückel tightbinding calculation [8]. They proposed that the magnetic orbital accommodating the d-electrons is the d xy -orbital, where the local z-axis is parallel to the shortest V-O bonding and x and y point toward the oxygen atoms in the basal plane of the pyramid. The dipolar coupling A dip to the spin density on the d xy -orbital takes the largest negative value when the field is along the z-axis. Since A cp is negative, K(θ) is expected to be most negative when the field is along the shortest V-O bond direction.
In table 1 we compare the values of ψ K at which K(θ) becomes most negative (upper panel) with the directions of the shortest V-O bonding projected onto the ac-plane obtained from the structural data in Ref. [3] (lower part). We can immediately assign the three groups of sites (A, B), (C, D) and (E, F) to the (V1a, V1b), (V2a, V2b) and (V3a, V3b) sites, respectively. We cannot determine, however, which one in each group corresponds to "a" or "b". With this assignment the directions for the minimum of K(θ) and the shortest V-O bonding agree within ten degrees, supporting that the magnetic orbital indeed has d xy symmetry.
The data in Fig. 3(a) indicate that while K(θ) for the V3a and V3b sites are almost identical, it differs substantially between the V2a and V2b sites and between the V1a and the V1b sites. In particular, the amplitudes of the angular Table 1 The upper part lists the values of ψ K for the A to F sites. The lower part shows the directions of the shortest V-O vanadyl bonding projected onto ac plane. The angles were measured from the a-axis.
2) for the V2a and the V2b sites differ by a factor two. Since the angular variation of A dip (θ) should be similar for all the sites, the local spin susceptibility χ spin must be significantly different for the V2a and the V2b sites. Such alternation of χ spin should be ascribed to charge disproportionation. In other words, although the d-electron density is quite uniform in the V3 zigzag-chains, it alternates strongly in the V2 ladders. The strong charge disproportionation even in the metallic phase may appear surprising. However, this has been predicted by Doublet and Lepetit. They argued that ordering of Sr leads to a large difference in the energy of the d-levels, therefore, the different charge density at the V2a and the V2b sites [8].
On the other hand, the three groups of sites, V1, V2, and V3, show quite similar values of K 2 when averaged over the "a" and the "b" sites. Thus the d-electrons are distributed rather uniformly over the three 1D structural units. The V2a and the V2b sites exhibit also distinct Tdependence of the Knight shift. Figure 3(c) show the Tdependence of K for several sites normalized by the value at T =300 K. They were measured at "magic angles" at which ν Q (θ)=0. (No measurements were done for the B sites which do not have a magic angle in the ab-plane.) The steep increase of |K| at the D sites with decreasing temperature is in strong contrast to the nearly constant behavior at the C sites. We also note peculiar decrease of |K| with decreasing temperature at the F sites. Although the bulk susceptibility shows little T -dependence (the solid line), this must be a results of cancellation of opposite Tdependence at the D and F sites. We should mention that such strong heterogeneity within the same structural unit has not been observed in β-Na 0.33 V 2 O 5 [10] The angle dependence of ν Q (θ) shown in Fig. 3(b) also reflects the local symmetry of each V sites. There is indeed noticeable correlation between the directions of shortest V-O bonding and extrema of ν Q (θ) for many sites. However, EFG is rather difficult to analyze because of contributions not only from the on-site d-electrons but from the neighboring ions. Hence we did not attempt to make any quantitative analysis. We now discuss the spin dynamics. The nuclear relaxation rate 1/T 1 was measured also with the field along magic angles. This enabled site-selective measurements of 1/T 1 even when the line is not well isolated from others, due to strongly enhanced signal, distinct rf-pulse width for optimum excitation, and simple exponential time dependence of the nuclear magnetization recovery at magic angles. For the E and F sites, which have nearly the same magic angle, the nuclear recovery curve was fit to sum of two exponential functions. The result was checked by separate measurements on well isolated quadrupole satellite lines.
The T -dependences of 1/(T 1 T ) are shown in Fig.4. Again different sites show remarkably contrasting behavior. The V3a and V3b sites (E and F) show nearly constant behavior with the similar magnitude of 1/(T 1 T ), suggesting absence of strong spin correlations. Precisely speaking, however, the E sites show slight increase of 1/(T 1 T ) with decreasing temperature. Such increase is more clearly visible for the A sites (one of the V1 sites). The results for the V2a and V2b (C and D) sites are most anomalous. While 1/(T 1 T ) at the C sites is nearly constant, it increases strongly at the D sites with decreasing temperature. At the D sites, 1/(T 1 T ) and K 2 follow approximately the same T -dependence as indicated by nearly constant 1/(T 1 T K 2 ) shown in Fig. 4(d).
Generally for quasi 1D electron systems, spin fluctuations both at q ∼ 0 and at q ∼ 2k F contribute to 1/(T 1 T ), In the Luttinger-liquid (LL) theories, which is expected to be applicable to quasi 1D conductors, the T -dependence of each term is given as 1/(T 1 T ) q∼0 ∝ χ 2 spin , 1/(T 1 T ) q∼2kF ∝ T Kρ−1 , where K ρ =1 for non-interacting electrons but generally 0 < K ρ < 1 for repulsive interactions [11,12]. The nearly constant behavior of 1/(T 1 T K 2 ) (Fig. 4(d)) suggests that the dominant contribution to 1/(T 1 T ) at the D sites comes from q ∼ 0 spin fluctuations. Thus our results appear to support strong ferromagnetic correlation in the V2 ladder units in the high T metallic phase. Another peculiar result is the nearly constant behavior of 1/(T 1 T ) at the F sites, in spite of the substantial decrease of the Knight shift with decreasing temperature.

Conclusion
We performed site-selective 51 V NMR measurements on a single crystal of β-Sr 0.33 V 2 O 5 in the high T metallic phase. We found that the magnetic properties are remarkably heterogeneous even within the same structural unit. In particular, the V2 ladder unit shows strong charge disproportionation caused by the Sr ordering. At one of the V2 sites, the absolute value of the Knight shift and 1/(T 1 T ) increases strongly with decreasing temperature, indicating development of ferromagnetic correlation. The local spin susceptibility at one of the V3 sites decreases substantially with decreasing temperature, although 1/(T 1 T ) is nearly constant.