| Quantum materials,which have abundant emergent physical phenomena,have attracted much attention in recent years.The mechanism research and multi-field control of novel quantum states in quantum materials have become one of the most crucial frontiers in condensed matter physics.Quantum materials include those whose electronic states at the orbital,charge,and spin degrees of freedom levels are best described as having a nontrivial quantum-mechanical origin and cannot be described in terms of semiclassical particles.Among them,strongly correlated electronic systems such as high-temperature superconductors and topological quantum materials are two typical quantum materials.They both have broad prospects in the application and important value in basic research,which may promote the establishment of new paradigms in condensed matter physics.In these two types of materials,magnetic interaction is an important source for forming various exotic quantum states,such as unconventional superconductivity,charge/spin density wave,electronic nematic fluctuations,and anomalous Hall effect.The basic premise for understanding these quantum phenomena is to fully understand the characteristics of magnetic interactions,including their basic composition,energy scale,and dynamical behavior.Thanks to the charge neutrality and the magnetic moment of neutrons,elastic and inelastic neutron scattering experiments can accurately provide critical information such as magnetic structure,magnetic phase transition,magnetic excitation and magnetic exchange coupling energy in quantum materials.Polarized neutron scattering can further analyze magnetic anisotropy which provides the essential characteristics of spin-orbit coupling.Therefore,neutron scattering has always been a vital probe for studying quantum materials.This thesis focuses on the neutron scattering studies on the neutron spin resonance in 1144-type iron-based superconductor CaK(Fe1-xNix)4As4 and the spin excitations and magnetoelastic response in magnetic Weyl semimetal Co3Sn2S2,to understand the role of magnetic interactions in unconventional superconductivity and magnetic topological states.The main contents contain five parts as follows:1.Preferred spin excitations in iron-based superconductor CaK(Fe1-xNix)4As4 with spin-vortex crystal(SVC)order.Iron-based superconductors are typical multiband unconventional superconductors.All five 3d Fe orbitals may participate in superconducting electron pairing near Fermi energy,which leads to the complexity of the superconducting gap and brings many difficulties for the study of superconducting mechanism.Although many theories suggest that spin fluctuations are essential for unconventional superconducting pairing,and the critical evidence is the neutron spin resonance mode formed in the superconducting state,it is worth exploring whether there are some common mechanisms for spin fluctuations to participate in superconducting pairing in multi-band and multi-orbital situations.In iron-pnictide superconductors,due to different spin-orbit coupling effects,there are three different magnetic patterns listed below:the stripe spin-density wave(SSDW)with collinear stripe-type order with in-plane moments,the charge-spin-density wave(CSDW)with collinear axial order with c-axis polarized moments,and the spin-vortex crystal(SVC)phase with the noncollinear,coplanar order with in-plane moments.The previous polarized neutron scattering results show that the spin fluctuations in SSDW and CSDW states exhibit preferentially polarized along c-axis.Even if the spin fluctuations in the normal state prefer to stay in ab-plane,the c-axis polarized fluctuations will dominate in the superconducting state.To explore the spin anisotropy in the unexplored magnetic order SVC phase,we have successfully grown sizeable single crystals of CaK(Fe0.96Ni0.04)4As4 by self-flux method,whose superconductivity(Tc=20 K)coexists with SVC magnetic order(TN=48 K).We studied its spin resonance using unpolarized neutron scattering.The results show that two spin resonance modes with odd and even L modulation similar to the undoped compound CaKFe4As4(Tc=35 K)exist at 7 and 15 meV,respectively.Furthermore,we used polarized neutron scattering to compare the spin anisotropy in the undoped sample without magnetic order and the Ni-doped sample with SVC order.The polarization analysis reveals that there is significant spin anisotropy at low energy,and the spin anisotropy persists up to the paramagnetic phase.Especially the odd mode in superconducting state is highly c-axis polarized.Therefore,we have established a common picture of c-axis preferred spin excitations.No matter the orientation of the moments in the magnetic order state,the spin fluctuations below the superconducting transition temperature Tc are c-axis preferred.The universality of the c-axis preferred spin resonance supports the orbital-selective pairing in iron-pnictide superconductors.2.In-plane dispersions of neutron spin resonance in 1144-type iron-based superconductors CaK(Fe1-xNix)4As4.Two spin resonance modes with odd and even L modulations due to the bilayer coupling are found.For further understanding the physical characteristics of resonant modes,we carried out inelastic neutron scattering experiments with a 4D energy-momentum manifold on single crystals of CaKFe4As4(Tc=35 K)and CaK(Fe0.96Ni0.04)4As4(Tc=20 K)using the time-of-flight spectrometer by rotating the sample,to obtain the spin excitations spectra in the 3D momentum space below and above Tc.While no dispersion along L in both odd mode and even mode is observed,in-plane dispersions along both H and K of the odd modes are found both in two samples and the dispersion along K is sharper than H.The center energy of the odd mode is far away from the total superconducting gaps of the hole and electron pocketsΔtot,and the energies where resonances disappear are below the sums of superconducting gaps on the hole and electron pockets.Due to the long-range magnetic order,the in-plane dispersions in the Ni-doped sample are both sharper than those in the undoped sample.These results of the odd mode are basically consistent with the spin-exciton scenario with s±-wave pairing.In addition,the energy of the even mode in CaKFe4As4(≈18 meV)and the estimated threshold of resonance ωc≈20.6 meV are both lower than Δtot.The energy of the even mode in CaK(Fe0.96Ni0.04)4 As4 is still relatively high(13～19 meV).As considering its Tc is significantly lower,its Δtot should be lower than 14 meV.It means that the even mode may exceed Δtot.The specific analysis is related to the data processing methods of the time-of-flight spectrometer,and precise measurements and comparison of superconducting energy gaps are required for the final precise conclusions.3.Low-energy spin excitations and spin wave gap in the magnetic Weyl semimetal Co3Sn2S2.Co3Sn2S2 is the first magnetic Weyl semimetal confirmed by experiments.To explore the connection between magnetic interactions and topological electronic states,we first measured the low-energy spin waves of Co3Sn2S2 using the thermal neutron triple-axis spectrometer.Both in-plane and out-of-plane dispersions of the spin waves are observed in the ferromagnetic state,indicating that the spin excitations are revealed with 3D characteristics in contrast to its quasi-2D lattice structure.Dispersive and damped spin excitations are found in the paramagnetic state,suggesting that Co3Sn2S2 has a moderate correlation.The effective exchange interactions are estimated using a semi-classical Heisenberg model to consistently reproduce the experimental Curie temperature TC and spin stiffness.The out-plane interactions are about one third of the in-plane interactions.Then we measured the temperature dependence of spin wave gap at the cold neutron triple-axis spectrometer with high resolution.A full spin wave gap below 2.3 meV is observed at 4 K,considerably larger than the estimated magnetic anisotropy energy～0.6 meV.Furthermore,the temperature dependence does not fully follow the behavior of ferromagnetic order parameters,and the contribution from anomalous Hall conductance cannot be ignored,which suggests that the low-energy spin dynamics can interact with the Weyl nodes in the magnetic Weyl semimetals.4.Spin excitations and phonon excitations spectra in magnetic Weyl semimetal Co3Sn2S2.We measured a series of spin excitations and phonon excitations spectra of a big piece of high-quality single crystal at several temperatures at time-of-flight spectrometer,to find the relationship between topological electron states/quasiparticles and magnons or phonons.At low temperature,the dispersions of spin waves in ab-plane are isotropic,and still basically follow the relationship E=Eg+Dq2 up to 60 meV.The spin excitations at higher energies become rapidly damped and may have entered the Stoner continuum excitations.The linear spin wave theory is used to fit the dispersion below 60 meV to determine the possible magnitude of magnetic exchange interaction.The dispersion and intensity change slightly below TC,but become diffuse and weak above TC.Meanwhile,we have obtained comprehensive phonon excitations spectra,which can be simulated well by numerical calculation,but found no clear evidence of the interactions between the phonons and magnons in Co3Sn2S2.5.Anisotropic magnetoelastic response in magnetic Weyl semimetal Co3Sn2S2.We carried out an elastic neutron scattering experiment on Co3Sn2S2 single crystal under the magnetic field up to 10 T using the triple-axis spectrometer.A strongly anisotropic magnetoelastic response is found.The in-plane magnetic field dramatically suppresses the Bragg peak intensity,probably by tilting the moments and lattice,while only a weak enhancement of the Bragg peaks is observed under the out-of-plane magnetic field.The magnetoelastic response starts from TC and strengthens below TA.It is nonmonotonic against the field between TA and TC due to the competition from another in-plane magnetic order.These results imply that a magnetic field can be used to tune the Co3Sn2S2 lattice and related topological states by the magnetoelastic effect. |
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