Electron spin resonance and exchange paths in the orthorhombic dimer system Sr${}_2$VO${}_4$

We report on susceptibility and electron spin resonance (ESR) measurements at X- and Q-band frequencies of Sr${}_2$VO${}_4$ with orthorhombic symmetry. In this dimer system, the ${\text{V}}^{4+}$ ions are in tetrahedral environment and are coupled by an antiferromagnetic intradimer exchange constant $J/k_B\approx$ 100 K to form a singlet ground state without any phase transitions between room temperature and 2 K. Based on an extended Hückel tight-binding analysis, we identify the strongest exchange interaction to occur between two inequivalent vanadium sites via two intermediate oxygen ions. The ESR absorption spectra can be well fitted by a single Lorentzian line and the temperature dependence of the ESR intensity, and the dc susceptibility can be modeled by using the Bleaney-Bowers approach for independent dimers. The temperature dependence of the ESR linewidth at X-band frequency can be modeled by a superposition of a linear increase with temperature with a slope $\alpha$  $=$1.35 Oe/K and a thermally activated behavior with an activation energy $\Delta /k_B$  $=$1418 K, both of which point to spin-phonon coupling as the dominant relaxation mechanism in this compound.

Figure 1

(Left) Unit cell of orthorhombic Sr${}_2$VO${}_4$ with space group $Pna{2}_1$ (see Ref. 21), showing the tetrahedral coordination of the two inequivalent vanadium sites V(1) (yellow middle-sized spheres) and V(2)(red middlesized spheres). Oxygen and strontium ions are depicted as small blue and large green spheres, respectively. (Right) Schematic of the splitting of the V${}^{4+}$ $d$ levels as described in the text.

Figure 2

Room-temperature x-ray diffraction pattern of orthorhombic Sr${}_2$VO${}_4$ (open circles) together with the result of the data refinement (black solid line). The difference between experimental and calculated intensities is shown at the bottom, the expected Bragg positions are indicated as green vertical bars.

Figure 3

Temperature dependence of the molar susceptibility for orthorhombic Sr${}_2$VO${}_4$ measured in a magnetic field of $H$  $=$1 kOe. The solid line is a fit using Eq. (1), the dashed and dash-dotted lines correspond to the Curie and dimer contribution of Eq. (1), respectively. The inset shows the corresponding energy level scheme of a spin dimer with antiferromagnetic exchange coupling $J$ as a function of the applied magnetic field.

Figure 4

(a) Projection of the orthorhombic lattice structure of ${\mathrm{Sr}}_2{\mathrm{VO}}_4$ with space group $Pna{2}_1$ on the $ac$ plane.[21] The exchange paths between neighboring V ions are denoted by the corresponding exchange constants $J_0$–$J_5$ in the sequence of increasing V$\cdots$V distance. (b)–(g) Spin dimers associated with these exchange paths. The large, middle, and small spheres show Sr, V, and O atoms, respectively. The two crystallographically inequivalent V ions are denoted as V(1) and V(2), respectively.

Figure 5

Temperature dependence of (a) the ESR intensity together with a fit using Eq. (1), (b) the effective $g$ factor, and (c) the ESR linewidth in Sr${}_2$VO${}_4$ together with a fit using Eq. (4). The insets show ESR spectra and fit curves with the derivative of a Lorentzian line shape at X-band and Q-band frequencies.