The notion of complex energy landscape underpins the intriguing dynamical behaviors in many complex systems ranging from polymers, to brain activity, to social networks and glass transitions. The spin glass state found in dilute magnetic alloys has been an exceptionally convenient laboratory frame for studying complex dynamics resulting from a hierarchical energy landscape with rugged funnels. Here, we show, by a bulk susceptibility and Monte Carlo simulation study, that densely populated frustrated magnets in a spin jam state exhibit much weaker memory effects than spin glasses, and the characteristic properties can be reproduced by a nonhierarchical landscape with a wide and nearly flat but rough bottom. Our results illustrate that the memory effects can be used to probe different slow dynamics of glassy materials, hence opening a window to explore their distinct energy landscapes. memory | energy landscape | spin jam | spin glass I f the energy landscape of a system resembles a smooth vase with a pointy bottom end, upon cooling the system goes quickly into the lowest energy state, i.e., the global ground state, that is usually associated with crystalline order. If the energy landscape is more complex with many metastable states, i.e., local minima, then cooling may lead the system into local minima resulting in a glassy order. The concept of such energy landscapes has been instrumental in explaining the glassiness that is ubiquitous in a wide range of systems, including atomic clusters (1), structural glasses (2, 3), polymers (4), brain activity (5), and social networks (6). Several different topological types of energy landscapes were proposed to characterize different glassiness and the associated slow dynamics (7,8). For instance, a rugged funnel-shaped landscape shown in Fig. 1A was proposed to understand the physics of biopolymers (9, 10) and dilute magnetic alloys called spin glass (11).Magnetic glass systems (12-16) present a unique opportunity to microscopically study the relation between the energy landscape and low temperature properties. The most studied magnetic glass state is the conventional spin glass realized in dilute magnetic alloys such as CuMn and AuFe. Here, dilute magnetic ions (Mn and Fe) in a nonmagnetic metal interact via the longrange Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction whose magnitude and sign change with distance between the randomly placed magnetic ions (11). The randomness drives the system into the spin glass state below a critical temperature, T f , that is comparable to the mean-field magnetic energy scale, i.e., the absolute value of the Curie-Weiss temperature, jΘ CW j. For instance, for Cu − 2 atomic (at.) % Mn (CuMn2% hereafter), Θ CW = −45 K and T f = 15.5 K. Another distinct glassy state called a spin jam has been recently suggested to appear in densely populated frustrated magnets (17-21). At the mean-field level, these systems are expected to remain in a classical spin liquid down to absolute zero temperature, due to macroscopic classical ground state dege...

We have performed magnetic susceptibility, heat capacity, muon spin relaxation, and neutron scattering measurements on three members of the family Ba3M Ru2O9, where M = In, Y and Lu. These systems consist of mixed-valence Ru dimers on a triangular lattice with antiferromagnetic interdimer exchange. Although previous work has argued that charge order within the dimers or intradimer double exchange plays an important role in determining the magnetic properties, our results suggest that the dimers are better described as molecular units due to significant orbital hybridization, resulting in one spin-1/2 moment distributed equally over the two Ru sites. These molecular building blocks form a frustrated, quasi-two-dimensional triangular lattice. Our zero and longitudinal field µSR results indicate that the molecular moments develop a collective, static magnetic ground state, with oscillations of the zero field muon spin polarization indicative of longrange magnetic order in the Lu sample. The static magnetism is much more disordered in the Y and In samples, but they do not appear to be conventional spin glasses.

In the geometrically frustrated materials with the low-dimensional and small spin moment, the quantum fluctuation could interfere with the complicated interplay of the spin, electron, lattice and orbital interactions, and host exotic ground states such as nematic spin-state and chiral liquid phase. While the quantum phases of the one-dimensional chain and S -½ twodimensional triangular-lattice antiferromagnet (TLAF) had been more thoroughly investigated by both theorists and experimentalists, the work on S = 1 TLAF has been limited. We induced the lattice distortion into the TLAFs, A3NiNb2O9 (A = Ba, Sr, and Ca) with S (Ni 2+ ) = 1, and applied the thermodynamic, magnetic and neutron scattering measurements. Although A3NiNb2O9 kept the non-collinear 120° antiferromagnetic phase as the ground state, the Ni 2+ -lattice changed from the equilateral triangle (A = Ba) into isosceles triangle (A = Sr and Ca). The inelastic neutron scattering data were simulated by the linear spin-wave theory, and the competition between the single-ion anisotropy and the exchange anisotropy from the distorted lattice was discussed. I. INTRODUCTIONIn the geometrically frustrated system, the complicated interaction(s) between electron, phonon, spin and orbital could lead to degenerate ground states, which introduce exotic properties and attracted a lot attention over the past decades [1][2][3]. Meanwhile, those degenerate states would easily be held by the symmetrical inconsistency and be destroyed by significant quantum fluctuations, not only induced by the complicated interactions among low dimensionality, geometrical frustration, small spin and the applied magnetic field, but also modified the classical Heisenberg model [4][5]. The triangular-lattice antiferromagnet (TLAF), one of the simplest frustrated two-dimensional (2D) material, had been suggested to be strongly influenced by the strong quantum spin fluctuations with small effective spin (S = 1/2 or 1) and exhibited a rich variety of interesting physics [6][7][8].A striking example of these quantum phenomena is the transition from a non-collinear 120° spin configuration at 0 T into fractional-magnet lattice under a finite range of applied magnetic field, such as a collinear up-up-down (uud) phase corresponding to a magnetization plateau with one-third of its saturation value [9][10][11][12][13].Recently, the theoretical research indicated the uud state as a commensurate analogue of the incommensurate spin-density-wave which was predicted and observed for frustrated one-dimensional spin-1 chains and S = ½ TLAF [14, 15], and suggested the possibility for exotic magnetic excitations. While there was an enormous theoretical activity in the domain, a full consensus on the origin of the uud state, (even the ground magnetic state, non-collinear 120 o at zero field) was limited. This is true as well for the state-of-the art experimental investigation of its spin excitations due to the lack of a triangular-lattice materials. Although the lattice distortion has been believed to influence t...

We present measurements on a series of materials, Li_{2}In_{1-x}Sc_{x}Mo_{3}O_{8}, that can be described as a 1/6th-filled breathing kagome lattice. Substituting Sc for In generates chemical pressure which alters the breathing parameter nonmonotonically. Muon spin rotation experiments show that this chemical pressure tunes the system from antiferromagnetic long range order to a quantum spin liquid phase. A strong correlation with the breathing parameter implies that it is the dominant parameter controlling the level of magnetic frustration, with increased kagome symmetry generating the quantum spin liquid phase. Magnetic susceptibility measurements suggest that this is related to distinct types of charge order induced by changes in lattice symmetry, in line with the theory of Chen et al. [Phys. Rev. B 93, 245134 (2016)PRBMDO2469-995010.1103/PhysRevB.93.245134]. The specific heat for samples at intermediate Sc concentration, which have the minimum breathing parameter, show consistency with the predicted U(1) quantum spin liquid.

Magnetoelectrics offer tantalizing opportunities for devices coupling ferroelectricity and magnetism but remain difficult to realize. Breakthrough strategies could circumvent the mutually exclusive origins of magnetism and ferroelectricity by exploiting the interaction of multiple phonon modes in geometric improper and hybrid improper ferroelectrics. Yet, the proposed instability of a zone-boundary phonon mode, driving the emergence of ferroelectricity via coupling to a polar mode, remains to be directly observed. Here, we provide previously missing evidence for this scenario in the archetypal improper ferroelectric, yttrium manganite, through comprehensive scattering measurements of the atomic structure and phonons, supported with first-principles simulations. Our experiments and theoretical modeling resolve the origin of the unusual temperature dependence of the polarization and rule out a reported double-step ferroelectric transition. These results emphasize the critical role of phonon anharmonicity in rationalizing lattice instabilities in improper ferroelectrics and show that including these effects in simulations could facilitate the design of magnetoelectrics.