Date Published: March 02, 2018
Publisher: John Wiley and Sons Inc.
Author(s): Jagath Gunasekera, Ashutosh Dahal, Yiyao Chen, Jose A. Rodriguez‐Rivera, Leland W. Harriger, Stefan Thomas, Thomas W. Heitmann, Vitalii Dugaev, Arthur Ernst, Deepak K. Singh.
Quantum magnetic properties in a geometrically frustrated lattice of spin‐1/2 magnet, such as quantum spin liquid or solid and the associated spin fractionalization, are considered key in developing a new phase of matter. The feasibility of observing the quantum magnetic properties, usually found in geometrically frustrated lattice of spin‐1/2 magnet, in a perovskite material with controlled disorder is demonstrated. It is found that the controlled chemical disorder, due to the chemical substitution of Ru ions by Co‐ions, in a simple perovskite CaRuO3 creates a random prototype configuration of artificial spin‐1/2 that forms dimer pairs between the nearest and further away ions. The localization of the Co impurity in the Ru matrix is analyzed using the Anderson localization formulation. The dimers of artificial spin‐1/2, due to the localization of Co impurities, exhibit singlet‐to‐triplet excitation at low temperature without any ordered spin correlation. The localized gapped excitation evolves into a gapless quasi‐continuum as dimer pairs break and create freely fluctuating fractionalized spins at high temperature. Together, these properties hint at a new quantum magnetic state with strong resemblance to the resonance valence bond system.
The quantum spin fluctuation is key to the understanding of the microscopic mechanism behind the novel quantum critical phenomenon or the quantum spin liquid state.1, 2, 3 The quantum spin liquid state arises from the phase coherent quantum fluctuation of entangled spin‐1/2 with net spin of 0 and 1 μB.4 Depending on the nature of the entanglement, whether it is an ordered partitioning of nearest neighbor spins or the superposition of an infinite partitioning of nearest as well as further away spins that are simultaneously pointing along different directions, the collective ensemble of dimers can be characterized as the valence bond solid (VBS) or the valence bond liquid (VBL), respectively.5, 6, 7 Since the moment is in continuous quantum fluctuation mode, the singlet state is either excited to the triplet state or the valence bond breaks and a continuum excitation due to the fluctuation of individual spin yields a liquid‐like gapless state.5, 8 An inherent frustration in the disorder free triangular lattice plays an important role in the realization of these novel effects. However, creating a disorder free magnetic lattice is a difficult task to achieve.9, 10
Detailed inelastic neutron scattering (INS) measurements were performed at cold spectrometers MACS and SPINS, using final neutron energies of Ef = 5 meV and 5 meV at which the spectrometers resolution were ≃ 0.32 and 0.28 meV, respectively. In Figure6a–f, we plot the background corrected and thermally balanced Q–E spectra at few characteristic temperatures in zero magnetic field (also see Figure S5, Supporting Information). Two types of trends are immediately observed in the Q‐E maps: first, at low temperature of T = 80 mK, a well‐defined gapped excitation at E = 5.9 meV develops at Q = 1 Å−1. The dynamic structure factor is much broader than the instrument resolution in both momentum and energy space (Figure 6a–c). Also observable is a much weaker excitation at Q = 2 Å−1 at the same energy, which follows Co form factor. Given the fact that no magnetic order was detected in any of these materials, the observation of localized excitation is completely surprising. The excitation is non‐dispersive in nature. No such localized excitation was observed in CaRuO3 or Ca(CoxRu1−x)O3 with low substitution coefficient (see Figure S7, Supplementary Materials).11 It further suggests that the gapped excitation arises due to the Co4 +‐Co4 + interaction. As temperature increases, the excitation gradually weakens before becoming indistinguishable from the remnant background.
Our experimental results provide new perspective to the study of quantum magnetism in spin‐1/2 system for three reasons: first, the absence of any type of magnetic order rules out the ordered dimer arrangement of artificial spin‐1/2, ultimately responsible for the VBS state. Similarly, the disorder in the lattice would prohibit coherent spin fluctuation, hence, the VBL state. However, the dimer formation in the insulating composition of Ca(CoxRu1−x)O3 involves simultaneous superposition of nearest neighbor and further separated artificial spin‐1/2, pointing in random directions, by virtue of disorder. The dimer–dimer interaction exhibits gapped singlet‐to‐triplet transition. Second, the break away spins of dimer pairs at high temperature create freely fluctuating fractionalized spins that occupy large cross section of the energy‐momentum space. We also note that the fluctuation spectrum persists to much lower energy, as found in the ac susceptibility measurements where the dynamic susceptibility exhibits stronger frequency‐dependence at higher temperature. Thus, the localized gapped excitation evolves into a gapless quasi‐continuum spectrum as a function of temperature.30, 31, 32 These two phenomena combined with the absence of magnetic order in Ca(CoxRu1−x)O3, where 0.15 < x < 0.2, qualify to be a new quantum magnetic state, which depicts remarkable similarity to the resonant valence bond state. Additionally, this quasi‐continuum spectrum persists to very high temperature, T ≃ 250 K. The persistence of quasi‐continuum to such an unusually high temperature extends the investigation to the semi‐classical regime, which is a new frontier in the study of the quantum‐mechanical properties in magnetic systems. Third and most important, we successfully demonstrate that a combination of disorder and the non‐frustrated lattice can provide a new platform for future researches on quantum magnetism via the creation of local artificial spin‐1/2. First‐principles calculations of electronic and magnetic properties of Ca(CoxRu1−x)O3 were performed using a self‐consistent Green function method within the density functional theory. The high purity polycrystalline samples of Ca(CoxRu1−x)O3 were synthesized by conventional solid state reaction method using ultrapure ingredients of CoO, RuO2, and CaCO3. Starting materials were mixed in stoichiometric composition, pelletized, and sintered at 950° for 3 d in oxygen‐rich environment. The furnace‐cooled samples were grinded, pelletized, and sintered at 1000° for another 3 d. Samples were intentionally synthesized at slightly lower temperature and for longer duration to preserve the oxygen stoichiometry. Resulting samples were characterized using Siemens D500 powder X‐ray diffractometer (XRD), confirming the single phase of material, see Figure S1 in the Supporting Information. The X‐ray diffraction data were analyzed using the FullProf suite for the Reitveld refinement, confirming the high quality single phase of materials (see Figure S1, Supporting Information). As shown in Figure S1 (Supporting Information), every single peak of the XRD pattern is identified with the orthorhombic structure of Ca(CoxRu1−x)O3. Four‐probe technique was employed to measure electrical properties of Ca(CoxRu1−x)O3 using a closed‐cycle refrigerator cooled 9 T magnet with measurement temperature range of 1.5–300 K. Detailed ac susceptibility measurements were performed using a Quantum Design Physical Properties Measurement System with a temperature range of 2–300 K.33 Elastic neutron scattering measurements were performed on the pristine powder samples of Ca(CoxRu1−x)O3 at the thermal triple‐axis spectrometer TRIAX at MURR and cold triple‐axis spectrometer SPINS at the NIST Center for Neutron Research with fixed final energies of 14.7 and 5 meV, respectively. Inelastic measurements were performed on cold spectrometers MACS and SPINS with fixed final neutron energies of 5 and 5 meV at which the spectrometers' energy resolutions were determined to be ≃ 0.32 and 0.28 meV, respectively. The authors declare no conflict of interest. Source: http://doi.org/10.1002/advs.201700978