We present a brief overview on some of the most significant achievements obtained by means of NMR and muSR techniques in highly frustrated magnets. First the basic quantities measured by the two techniques will be presented and their connection to the microscopic static and dynamical spin susceptibility recalled. Then the main findings will be outlined, starting from the most simple frustrated units, the molecular nanomagnets, to artificially built frustrated systems as $^{3}$He on graphite, to magnets with a macroscopically degenerate ground-state as the ones on a pyrochlore or kagomé lattices.
PbCuTe2O6 is a rare example of a spin liquid candidate featuring a three dimensional magnetic lattice. Strong geometric frustration arises from the dominant antiferromagnetic interaction which generates a hyperkagome network of Cu2+ ions although additional interactions enhance the magnetic lattice connectivity. Through a combination of magnetization measurements and local probe investigation by NMR and muSR down to 20 mK, we provide a robust evidence for the absence of magnetic freezing in the ground state. The local spin susceptibility probed by the NMR shift hardly deviates from the macrosc…
Muon spin relaxation ($μ$SR) measurements were carried out on SrDy$_2$O$_4$, a frustrated magnet featuring short range magnetic correlations at low temperatures. Zero-field muon spin depolarization measurements demonstrate that fast magnetic fluctuations are present from $T=300$ K down to 20 mK. The coexistence of short range magnetic correlations and fluctuations at $T=20$ mK indicates that SrDy$_2$O$_4$ features a spin liquid ground state. Large longitudinal fields affect weakly the muon spin depolarization, also suggesting the presence of fast fluctuations. For a longitudinal field of $μ_0H…
We report synchrotron radiation diffraction and muon spin rotation (muSR) measurements on the frustrated pyrochlore magnet Tb2Ti2O7. The powder diffraction study of a crushed crystal fragment does not reveal any structural change down to 4 K. The muSR measurements performed at 20 mK on a mosaic of single crystals with an external magnetic field applied along a three-fold axis are consistent with published a.c. magnetic-susceptibility measurements at 16 mK. While an inflection point could be present around an internal field intensity slightly above 0.3 T, the data barely support the presence of…
We present a comprehensive review of nuclear magnetic resonance (NMR) studies performed on three nanoscale molecular magnets with different configurations of geometrically frustrated antiferromagnetic (AFM) triangles, new spin frustration systems with different novel structures: (1) the isolated single AFM triangle K$_6$[V$_{15}$As$_6$O$_{42}$(H$_2$O)]$\cdot$8H$_2$O (in short V15), (2) the spin ball [Mo$_{72}$Fe$_{30}$O$_{252}$(Mo$_2$O$_7$(H$_2$O))$_2$ (Mo$_2$O$_8$H$_2$(H$_2$O))(CH$_3$COO)$_{12}$(H$_2$O)$_{91}$]$\cdot$150H$_2$O (in short Fe30 spin ball), and (3) the twisted triangular spin tub…
Using $^{31}$P nuclear magnetic resonance (NMR) we investigate the recently discovered presaturation phase in the highly frustrated two-dimensional spin system SrZnVO(PO$_4$)$_2$ [F. Landolt et al., Phys. Rev. B 104, 224435 (2021)]. Our data provide two pieces of evidence against the presumed spin-nematic character of this phase: i) NMR spectra reveal that it hosts a dipolar spin order and ii) the 1/$T_1$ relaxation rate data recorded above the saturation field can be fitted by the sum of a single-magnon term, exponential in the gap, and a critical second-order term, exponential in the triple …
Ga NMR study of the local susceptibility in SrCr8Ga4O19: pseudogap and paramagnetic defects
本文首次用Ga（4 f）NMR研究了Kagome基阻挫反铁磁体原型SrCr $_{8}$ Ga $_{4}$ O $_{19}$中Cr的磁化率.我们的主要发现是受抑晶格的磁化率在50 K附近经历一个最大值。我们的数据也支持存在顺磁性自旋“团簇”，这是在低温下宏观磁化率中观察到的居里行为的原因。这些结果为几何阻挫磁体的物理学争论不休提供了新的特征。
We report magnetization, heat capacity, 7Li - nuclear magnetic resonance (NMR), and muSR (muon spin roration) measurements on the honeycomb 4d5 spin liquid candidate Li2RhO3. The magnetization in small magnetic fields provides evidence of the partial spin-freezing of a small fraction of Rh4+ -moments at 6 K, whereas the Curie-Weiss behavior above 100 K suggests a pseudo-spin-1/2 paramagnet with a moment of about 2.2 muB. The magnetic specific heat (Cm) exhibits no field dependence and demonstrates the absence of long range magnetic order down to 0.35 K. Cm/T passes through a broad maximum at a…
We report on a detailed neutron diffraction and $^1$H-NMR study on the frustrated spin-1/2 chain material linarite, PbCuSO$_4$(OH)$_2$, where competing ferromagnetic nearest neighbor and antiferromagnetic next-nearest neighbor interactions lead to frustration. From the magnetic Bragg peak intensity studied down to 60 mK, the magnetic moment per Cu atom is obtained within the whole magnetic phase diagram for $H \parallel b$ axis. Further, we establish the detailed configurations of the shift of the SDW propagation vector in phase V with field and temperature. Finally, combining our neutron diff…
The spin-nematic phase is an intriguing state of matter that lacks usual long-range dipolar order, yet it exhibits higher multipolar order. This makes its detection extremely difficult and controversial. Recently, nuclear magnetic resonance (NMR) has been proposed as one of the most suitable techniques to confirm its existence. We report a $^{17}$O NMR observation of the reduction of the local magnetization in the polarized state of the frustrated spin-1/2 chain $β$-TeVO$_4$, which was previously proposed to be a fingerprint of the spin-nematic behavior. However, our detailed study shows that …
The cubic double perovskite Ba$_2$YIrO$_6$ has been investigated by the local probe techniques nuclear magnetic resonance ($^{89}$Y NMR) and muon spin rotation (muSR). Both methods confirm the absence of magnetic long-range order in this compound but find evidence for diluted localized paramagnetic moments. NMR spin-lattice relaxation rate 1/T1 measurements suggest a slowing down of localized spin moments at low temperatures. An increase of the muSR spin-lattice relaxation rate lambda confirms the presence of weak magnetism in Ba$_2$YIrO$_6$ . However, these findings cannot be explained by the…
The frustrated one-dimensional (1D) quantum magnet LiCuSbO$_4$ is one rare realization of the $J_1-J_2$ spin chain model with an easily accessible saturation field, formerly estimated to 12~T. Exotic multipolar nematic phases were theoretically predicted in such compounds just below the saturation field, but without unambiguous experimental observation so far. In this paper we present extensive experimental research of the compound in the wide temperature (30mK$-$300K) and field (0$-$13.3T) range by muon spin rotation ($μ$SR), $^7$Li nuclear magnetic resonance (NMR) and magnetic susceptibility…
We report muSR experiments on Mg{x}Cu{4-x}(OH)6Cl2 with x \sim 1, a new material isostructural to Herbertsmithite exhibiting regular kagome planes of spin 1/2 (Cu^{2+}), and therefore a candidate for a spin liquid ground state. We evidence the absence of any magnetic ordering down to 20 mK (\sim J/10^4). We investigate in detail the spin dynamics on well characterized samples in zero and applied longitudinal fields and propose a low T defect based interpretation to explain the unconventional dynamics observed in the quantum spin liquid phase.
Direct evidence for a dynamical ground state in the highly frustrated Tb$_2$Sn$_2$O$_7$ pyrochlore
对“有序自旋冰”Tb $_2$ Sn $_2$ O $_7$烧绿石化合物的粉末样品进行了MuSR实验。在基温（T=35mK），μ子弛豫具有动力学性质，表明在铁磁相变（T_C=0.87K）以下仍存在强涨落。长程序的暗示表现为μ子极化在外场作用下的振荡和T_C以下的滞后行为。我们提出了一个动态的和强相关的情况下，动力学的结果从大自旋团簇的波动与“有序自旋冰”的结构。
In frustrated spin-1/2 chains the competition between the nearest- and next-nearest-neighbor exchange interactions leads to a rich phase diagram that becomes even richer in the presence of perturbations in their material realizations. These effects are still largely unexplored, so that new insight into static and dynamic magnetism, in particular by sensitive local probes, is highly desired. Here we present a comprehensive $^{17}$O nuclear magnetic resonance study of $β$-TeVO$_4$, where the anisotropy of the main exchange interactions and additional weak interchain exchange interactions complem…
7Li NMR spectra were measured in a magnetic field up to 17 T at temperatures 5-30 K on single crystalline LiCu2O2. Earlier reported anomalies on magnetization curves correspond to magnetic field values where we observe changes of the NMR spectral shape. For the interpretation of the field and temperature evolutions of our NMR spectra, the magnetic structures were analyzed in the frame of the phenomenological theoretical approach of the Dzyaloshinskii-Landau theory. A set of possible planar and collinear structures was obtained. Most of these structures have an unusual configuration; they are c…
There is now strong theoretical evidence that a wide range of frustrated magnets should support quantum spin-nematic order in applied magnetic field. Nonetheless, the fact that spin-nematic order does not break time-reversal symmetry makes it very difficult to detect in experiment. In this article, we continue the theme begun in [Phys. Rev. B 88, 184430 (2013)], of exploring how spin-nematic order reveals itself in the spectrum of spin excitations. Building on an earlier analysis of inelastic neutron scattering [Phys. Rev. B 91, 174402 (2015)], we show how the NMR 1/T_1 relaxation rate could b…
Magnetization, magnetic torque, neutron diffraction and NMR experiments are used to map out the $H$$-$$T$ phase diagram of the prototypical quasi-two-dimensional ferro-antiferromagnet Pb$_2$VO(PO$_4$)$_2$ in magnetic fields up to 27 T. When the field is applied perpendicular to the axis of magnetic anisotropy, a new magnetic state emerges through a discontinuous transition and persists in a narrow field range just below saturation. The measured NMR spectra suggest a complex and possibly incommensurate magnetic order in that regime.
In this paper, we study the spin excitation properties of the frustrated triangular-lattice antiferromagnet Yb(BaBO$_3$)$_3$ with nuclear magnetic resonance. From the spectral analysis, neither magnetic ordering nor spin freezing is observed with temperature down to $T=0.26$ K, far below its Curie-Weiss temperature $|θ_w|\sim2.3$ K. From the nuclear relaxation measurement, precise temperature-independent spin-lattice relaxation rates are observed at low temperatures under a weak magnetic field, indicating the gapless spin excitations. Further increasing the field intensity, we observe a spin e…
Disorder-driven coexistence of distinct dynamical states in frustrated Sr$_3$CuNb$_2$O$_9$: a microscopic $μ$SR and $^{93}$Nb NMR study
Shiv Nadar Institution of Eminence（希夫纳达尔卓越机构）；Leibniz Institute for Solid State and Materials Research Dresden（德累斯顿莱布尼茨固体与材料研究所）；Technische Universität Dresden（德累斯顿工业大学）；Paul Scherrer Institut（保罗谢尔研究所）
We report a $^7$Li nuclear magnetic resonance (NMR) study of a frustrated three-dimensional \mbox{spin-$\frac12$} antiferromagnet Li$_{2}$CuW$_{2}$O$_{8}$ and also explore the effect of non-magnetic dilution. The magnetic long-range ordering in the parent compound at $T_{\rm N}\simeq$ 3.9~K was detected from the drastic line broadening and a peak in the spin-lattice relaxation rate ($1/T_1$). The NMR spectrum above $T_{\rm N}$ broadens systematically, and its full width at half maximum (FWHM) tracks the static spin susceptibility. From the analysis of FWHM vs. static susceptibility, the coupli…
The phase diagram of the quasi-one-dimensional magnet NaCuMoO$_4$(OH) is established through single-crystal NMR and heat-capacity measurements. The $^{23}$Na and $^1$H NMR experiments indicate a spiral and a collinear spin-density-wave (SDW) order below and above $B_c$ = 1.5-1.8 T, respectively. Moreover, in the paramagnetic state above the SDW transition temperature, the nuclear spin-lattice relaxation rate $1/T_1$ indicates anisotropic spin fluctuations that have gapped excitations in the transverse spectrum but gapless ones in the longitudinal spectrum. These static and dynamic properties a…
We performed nuclear magnetic resonance (NMR) and muon spin relaxation (μSR) experiments to identify the magnetic ground state of the frustrated quantum A-site spinel, CuAl2O4. Our results verify that the ground state does not exhibit a long-range magnetic ordering, but a glass-like transition manifests at T*=2.3 K. However, the Gaussian shape and the weak longitudinal field dependence of μSR spectra below T* show that the ground state has dynamic spin fluctuations, distinct from those of conventional spin-glasses.
Magnetic properties of the geometrically frustrated S=1/2 antiferromagnets, La2LiMoO6 and Ba2YMoO6, with the B-site ordered double perovskite structure: Evidence for a Collective Spin Singlet Ground State
We present results of $^{23}$Na and $^{19}$F nuclear magnetic resonance (NMR) measurements on NaCaCo$_2$F$_7$, a frustrated pyrochlore magnet with a Curie-Weiss temperature, $T_{cw}$ ~-140 K, and intrinsic bond disorder. Below 3.6 K both the $^{23}$Na and $^{19}$F spectra broaden substantially in comparison to higher temperatures accompanied by a considerable reduction (80 \%) of the NMR signal intensity: This proves a broad quasi-static field distribution. The $^{19}$F spin-lattice relaxation rate $^{19}(1/T_1$) exhibits a peak at 2.9 K already starting to develop below 10 K. We attribute the…
Spin liquid state in a three-dimensional pyrochlore-like frustrated magnet
Indian Institute of Technology Madras（马德拉斯理工学院）；Institute for Basic Science（基础科学研究院）；CEA（法国原子能和替代能源委员会）；CNRS（法国国家科学研究中心）；Université Paris-Saclay（巴黎萨克雷大学）；Institut Laue-Langevin（朗之万研究所）；STFC Rutherford Appleton Laboratory（STFC卢瑟福阿普尔顿实验室）；Sungkyunkwan University（成均馆大学）；Quantum Centre of Excellence for Diamond and Emergent Materials, Indian Institute of Technology Madras（马德拉斯理工学院钻石与新兴材料量子卓越中心）
Local magnetism and spin correlations in the geometrically frustrated cluster magnet LiZn$_2$Mo$_3$O$_8$
LiZn $_2$ Mo $_3$ O $_8$已被提出包含$S~=~1/2$ Mo $_3$ O $_{13}$磁性团簇，其排列在具有反铁磁最近邻相互作用的三角晶格上。在这里，微波和太赫兹电子自旋共振（ESR）、$^7$ Li核磁共振（NMR）和μ子自旋旋转（$μ\textrm{SR}$）光谱被用于表征LiZn $_2$ Mo $_3$ O $_8$的局部磁性。这些结果表明，在LiZn $_2$ Mo $_3$ O $_8$中的磁性来自于每个团簇的单个各向同性$S~=~1/2$电子，并且没有静态长程磁有序到$T~=~0.07\,\textrm{K}$。此外，有证据表明，随着温度的降低，自旋波动会减缓的无隙自旋激发。这些数据表明，强的自旋相关性，与以前的数据一起，提出了低温共振价键态的LiZn $_2$ Mo $_3$ O $_8$。
We have performed NMR experiments on the quasi one-dimensional frustrated spin-1/2 system LiCuVO$_4$ in magnetic fields $H$ applied along the c-axis up to field values near the saturation field $H_{\rm sat}$. For the field range $H_{\rm c2}<H<H_{\rm c3}$ ($μ_0H_{\rm c2}\approx 7.5$T and $μ_0H_{\rm c3} = [40.5 \pm 0.2]$T) the $^{51}$V NMR spectra at $T$ = 380mK exhibit a characteristic double-horn pattern, as expected for a spin-modulated phase in which the magnetic moments of Cu$^{2+}$ ions are aligned parallel to the applied field $H$ and their magnitudes change sinusoidally along the magneti…
Fractional spin textures in the frustrated magnet SrCr$_{9p}$Ga$_{12-9p}$O$_{19}$
我们认为原型阻挫反铁磁体SrCr $_{9p}$ Ga $_{12-9p}$ O $_{19}$在其众所周知的自旋液体状态，并证明了一个Cr $^{3+}$自旋$S=3/2$离子在直接接近一对空位（在无序$p<1$样品）是由一个空间扩展的自旋纹理，编码的母自旋液体的相关性掩盖。在这种自旋液体状态下，组合的物体具有与长度为$S/2 = 3/4$的经典自旋相同的磁响应，其在纯系统的小的固有磁化率上占主导地位。这种分数自旋纹理留下一个明确无误的印记上测得的$^{71}$ Ga核磁共振（NMR）的线形，我们使用蒙特卡罗模拟计算和实验数据进行比较。
