Universal window for two-dimensional critical exponents

Ferroelasticity and Canted Antiferromagnetism in Two-Dimensional Organic-Inorganic Layered Perovskite [C6H9(CH2)2NH3]2FeCl4

Two-dimensional organic-inorganic perovskites have been attracted as candidates for multiferroic materials that exhibit two or more ferroic orders such as ferromagnetism, ferroelectricity, ferroelasticity, and ferrotoroidicity. Here, we introduce the structure, ferroelastic domains and magnetic properties of the two-dimensional organic-inorganic perovskite [C6H9(CH2)2NH3]2FeCl4 (CHEA-Fe) composed of 2-(1-cyclohexenyl)ethylammonium and FeCl4 2-. CHEA-Fe underwent two ferroelastic phase transitions from tetragonal to orthorhombic at 332 K and to monoclinic at 232 K with decreasing temperature and exhibited ferroelastic domains under polarized light as a consequence of these ferroelastic phase transitions. Magnetization measurements exhibited two magnetization jumps at the transition temperature, which agrees with ferroelastic phase transitions. Furthermore, CHEA-Fe acted as canted antiferromagnetism below T N = 85.7 K. The isothermal magnetization revealed a magnetic hysteresis when the magnetic field was applied along the stacking axis of the layers.

Observation of Three-State Nematicity and Domain Evolution in Atomically Thin Antiferromagnetic NiPS3

Nickel phosphorus trisulfide (NiPS3), a van der Waals 2D antiferromagnet, has received significant interest for its intriguing properties in recent years. However, despite its fundamental importance in the physics of low-dimensional magnetism and promising potential for technological applications, the study of magnetic domains in NiPS3 down to an atomically thin state is still lacking. Here, we report the layer-dependent magnetic characteristics and magnetic domains in NiPS3 by employing linear dichroism spectroscopy, polarized microscopy, spin-correlated photoluminescence, and Raman spectroscopy. Our results reveal the existence of the paramagnetic-to-antiferromagnetic phase transition in bulk to bilayer NiPS3 and provide evidence of the role of stronger spin fluctuations in thin NiPS3. Furthermore, our study identifies three distinct antiferromagnetic domains within atomically thin NiPS3 and captures the thermally activated domain evolution. Our findings provide crucial insights for the development of antiferromagnetic spintronics and related technologies.

Quasi-2D-Ising-type magnetic critical behavior in trigonal Cr1.27Te2

Single crystal Cr1.27Te2 samples were synthesized by using the chemical vapor transport method. Single crystal x-ray diffraction studies show a trigonal crystal structure with a P3̄m1 symmetry space group. We then systematically investigate magnetic properties and critical behaviors of single crystal Cr1.27Te2 around its paramagnetic-to-ferromagnetic phase transition. The Arrott plot indicates a second-order magnetic phase transition. We estimate critical exponents β = 0.2631 ± 0.002, γ = 1.2314 ± 0.007, and TC = 168.48 ± 0.031 K by using the Kouvel-Fisher method. We also estimate other critical exponents δ = 5.31 ± 0.004 by analyzing the critical isotherm at TC = 168.5 K. We further verify the accuracy of our estimated critical exponents by the scaling analysis. Further analysis suggests that Cr1.27Te2 can be best described as a quasi-2D Ising magnetic system.

Critical behaviors of van der Waals itinerant ferromagnet Fe3.8GaTe2

The critical behavior of the van der Waals ferromagnet Fe3.8GaTe2was systematically studied through measurements of isothermal magnetization, with the magnetic field applied along thec-axis. Fe3.8GaTe2undergoes a non-continuous paramagnetic to ferromagnetic phase transition at the Curie temperatureTc∼ 355 K. A comprehensive analysis of isotherms aroundTcutilizing the modified Arrott diagram, the Kouvel-Fisher method, the Widom scaling law, and the critical isotherm analysis yielded the critical exponent ofβ= 0.411,γ= 1.246, andδ= 3.99. These critical exponents are found to be self-consistent and align well with the scaling equation at high magnetic fields, underscoring the reliability and intrinsic nature of these parameters. However, the low-field data deviates from the scaling relation, exhibiting a vertical trend whenT Collapse

Key Words

• Fe3.8GaTe2
• critical behaviors
• critical exponent
• isothermal magnetization
• three-dimensional Heisenberg

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Affiliation(s)

Tianyang Yao School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, People's Republic of China
W L Qubie School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, People's Republic of China
Pushpendra Kumar School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
Xu Bai School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, People's Republic of China
Shixin Hu School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, People's Republic of China
Desheng Xue School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, People's Republic of China
Junli Zhang School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, People's Republic of China

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Evidence of Temperature-Dependent Interplay between Spin and Orbital Moment in van der Waals Ferromagnet VI3

van der Waals materials provide a versatile toolbox for the emergence of new quantum phenomena and fabrication of functional heterostructures. Among them, the trihalide VI3 stands out for its unique magnetic and structural landscape. Here we investigate the spin and orbital magnetic degrees of freedom in the layered ferromagnet VI3 by means of temperature-dependent X-ray absorption spectroscopy and X-ray magnetic circular and linear dichroism. We detect localized electronic states and reduced magnetic dimensionality, due to electronic correlations. We furthermore provide experimental evidence of (a) an unquenched orbital magnetic moment (up to 0.66(7) μB/V atom) in the ferromagnetic state and (b) an instability of the orbital moment in the proximity of the spin reorientation transition. Our results support a coherent picture where electronic correlations give rise to a strong magnetic anisotropy and a large orbital moment and establish VI3 as a prime candidate for the study of orbital quantum effects.

Critical exponents of master-node network model

The dynamics of competing opinions in social network plays an important role in society, with many applications in diverse social contexts such as consensus, election, morality, and so on. Here, we study a model of interacting agents connected in networks in order to analyze their decision stochastic process. We consider a first-neighbor interaction between agents in a one-dimensional network with the shape of ring topology. Moreover, some agents are also connected to a hub, or master node, who has preferential choice or bias. Such connections are quenched. As the main results, we observed a continuous nonequilibrium phase transition to an absorbing state as a function of control parameters. By using the finite-size scaling method we analyzed the static and dynamic critical exponents to show that this model probably cannot match any universality class already known.

Continuous symmetry breaking in a two-dimensional Rydberg array

Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions1-3. The nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is illustrated by the case of discrete versus continuous symmetry breaking. Indeed, in contrast to the discrete case, the breaking of a continuous symmetry leads to the emergence of gapless Goldstone modes controlling, for instance, the thermodynamic stability of the ordered phase4,5. Here, we realize a two-dimensional dipolar XY model that shows a continuous spin-rotational symmetry using a programmable Rydberg quantum simulator. We demonstrate the adiabatic preparation of correlated low-temperature states of both the XY ferromagnet and the XY antiferromagnet. In the ferromagnetic case, we characterize the presence of a long-range XY order, a feature prohibited in the absence of long-range dipolar interaction. Our exploration of the many-body physics of XY interactions complements recent works using the Rydberg-blockade mechanism to realize Ising-type interactions showing discrete spin rotation symmetry6-9.

Field-Tunable Berezinskii-Kosterlitz-Thouless Correlations in a Heisenberg Magnet

We report the manifestation of field-induced Berezinskii-Kosterlitz-Thouless (BKT) correlations in the weakly coupled spin-1/2 Heisenberg layers of the molecular-based bulk material [Cu(pz)_{2}(2-HOpy)_{2}](PF_{6})_{2}. At zero field, a transition to long-range order occurs at 1.38 K, caused by a weak intrinsic easy-plane anisotropy and an interlayer exchange of J^{'}/k_{B}≈1  mK. Because of the moderate intralayer exchange coupling of J/k_{B}=6.8  K, the application of laboratory magnetic fields induces a substantial XY anisotropy of the spin correlations. Crucially, this provides a significant BKT regime, as the tiny interlayer exchange J^{'} only induces 3D correlations upon close approach to the BKT transition with its exponential growth in the spin-correlation length. We employ nuclear magnetic resonance measurements to probe the spin correlations that determine the critical temperatures of the BKT transition as well as that of the onset of long-range order. Further, we perform stochastic series expansion quantum Monte Carlo simulations based on the experimentally determined model parameters. Finite-size scaling of the in-plane spin stiffness yields excellent agreement of critical temperatures between theory and experiment, providing clear evidence that the nonmonotonic magnetic phase diagram of [Cu(pz)_{2}(2-HOpy)_{2}](PF_{6})_{2} is determined by the field-tuned XY anisotropy and the concomitant BKT physics.

The BKT transition and its dynamics in a spin fluid

We study the effect of particle mobility on phase transitions in a spin fluid in two dimensions. The presence of a phase transition of the BKT universality class is shown in an off-lattice model of particles with purely repulsive interaction employing computer simulations. A critical spin wave region 0 < T < T_BKT is found with a nonuniversal exponent η(T) that follows the shape suggested by BKT theory, including a critical value consistent with η_BKT = 1/4. One can observe a transition from power-law decay to exponential decay in the static correlation functions at the transition temperature T_BKT, which is supported by finite-size scaling analysis. A critical temperature T_BKT = 0.17(1) is suggested. Investigations into the dynamic aspects of the phase transition are carried out. The short-time behavior of the incoherent spin autocorrelation function agrees with the Nelson-Fisher prediction, whereas the long-time behavior differs from the finite-size scaling known for the static XY model. Analysis of coherent spin wave dynamics shows that the spin wave peak is a propagating mode that can be reasonably well fitted by hydrodynamic theory. The mobility of the particles strongly enhances damping of the spin waves, but the model still lies within the dynamic universality class of the standard XY model.

Z_{4}-symmetric perturbations to the XY model from functional renormalization

We employ the second order of the derivative expansion of the nonperturbative renormalization group to study cubic (Z_{4}-symmetric) perturbations to the classical XY model in dimensionality d∈[2,4]. In d=3 we provide accurate estimates of the eigenvalue y_{4} corresponding to the leading irrelevant perturbation and follow the evolution of the physical picture upon reducing spatial dimensionality from d=3 towards d=2, where we approximately recover the onset of the Kosterlitz-Thouless physics. We analyze the interplay between the leading irrelevant eigenvalues related to O(2)-symmetric and Z_{4}-symmetric perturbations and their approximate collapse for d→2. We compare and discuss different implementations of the derivative expansion in cases involving one and two invariants of the corresponding symmetry group.

Dynamic magnetic crossover at the origin of the hidden-order in van der Waals antiferromagnet CrSBr

The van-der-Waals material CrSBr stands out as a promising two-dimensional magnet. Here, we report on its detailed magnetic and structural characteristics. We evidence that it undergoes a transition to an A-type antiferromagnetic state below T_N ≈ 140 K with a pronounced two-dimensional character, preceded by ferromagnetic correlations within the monolayers. Furthermore, we unravel the low-temperature hidden-order within the long-range magnetically-ordered state. We find that it is associated to a slowing down of the magnetic fluctuations, accompanied by a continuous reorientation of the internal field. These take place upon cooling below T_s ≈ 100 K, until a spin freezing process occurs at T* ≈ 40 K. We argue this complex behavior to reflect a crossover driven by the in-plane uniaxial anisotropy, which is ultimately caused by its mixed-anion character. Our findings reinforce CrSBr as an important candidate for devices in the emergent field of two-dimensional magnetic materials.

The Magnetic Genome of Two-Dimensional van der Waals Materials

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

Magnetism and Its Structural Coupling Effects in 2D Ising Ferromagnetic Insulator VI3

van der Waals (vdW) magnets have emerged as a tunable platform for exploring a variety of layer-dependent magnetic phenomena. Here we probe the thickness-dependent magnetism of vanadium triiodide (VI₃), a material known as a layered ferromagnetic Mott insulator in its bulk form, using magnetic circular dichroism microscopy. Robust ferromagnetism is observed in all thin layers, down to the monolayer limit with large coercive fields. In contrast to known vdW magnets, the Curie temperature shows an anomalous increase as the layer number decreases, reaching a maximum of 60 K in monolayers. Second harmonic generation measurements reveal broken inversion symmetry in exfoliated flakes, down to trilayers. This observation demonstrates that the exfoliated flakes take a layer stacking arrangement that differed from the inversion-symmetric parent bulk counterpart. Our results suggest a coupling effect between magnetic and structural degrees of freedom in VI₃ and its potential for engineering layer and twist angle-dependent magnetic phenomena.

Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer

[Figure: see text].

Phase diagrams of the antiferromagnetic XY model on a triangular lattice with higher-order interactions

We study the effects of higher-order antinematic interactions on the critical behavior of the antiferromagnetic (AFM) XY model on a triangular lattice using Monte Carlo simulations. The parameter q of the generalized antinematic (ANq) interaction is found to have a pronounced effect on the phase diagram topology by inducing new quasi-long-range ordered phases due to competition with the conventional AFM interaction as well as geometrical frustration. For values of q divisible by 3, the ground-state competition between the two interactions results in a frustrated canted AFM phase appearing at low temperatures wedged between the AFM and ANq phases. For q nondivisible by 3, with the increase of q one can observe the evolution of the phase diagram topology featuring two (q=2), three (q=4,5), and four (q≥7) ordered phases. In addition to the two phases previously found for q=2, the first new phase with solely AFM ordering arises for q=4 in the limit of strong AFM coupling and higher temperatures by separating from the phase with the coexisting AFM and ANq orderings. For q=7, another phase with AFM ordering but multimodal spin distribution in each sublattice appears at intermediate temperatures. All these algebraic phases also display standard and generalized chiral long-range orderings, which decouple at higher temperatures in the regime of dominant ANq (AFM) interaction for q≥4 (q≥7) preserving only the generalized (standard) chiral ordering.

Magnetism in quasi-two-dimensional tri-layer La2.1Sr1.9Mn3O10 manganite

The tri-layer La\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3-3x}$$\end{document}3-3xSr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{1+3x}$$\end{document}1+3xMn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{10}$$\end{document}10 manganites of Ruddlesden–Popper (RP) series are naturally arranged layered structure with alternate stacking of ω-MnO\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}2 (ω = 3) planes and rock-salt type block layers (La, Sr)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}2 along c-axis. The dimensionality of the RP series manganites depends on the number of perovskite layers and significantly affects the magnetic and transport properties of the system. Generally, when a ferromagnetic material undergoes a magnetic phase transition from ferromagnetic to paramagnetic state, the magnetic moment of the system becomes zero above the transition temperature (T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ _{C} $$\end{document}C). However, the tri-layer La\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2.1}$$\end{document}2.1Sr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{1.9}$$\end{document}1.9Mn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{10}$$\end{document}10 shows non-zero magnetic moment above T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ _{C} $$\end{document}C and also another transition at higher temperature T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ ^{*} \approx $$\end{document}∗≈ 263 K. The non-zero magnetization above T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ _{C} $$\end{document}C emphasizes that the phase transition in tri-layer La\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2.1}$$\end{document}2.1Sr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{1.9}$$\end{document}1.9Mn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{10}$$\end{document}10 not a ferromagnetic to paramagnetic state. We show here the non-zero magnetic moment above T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ _{C} $$\end{document}C is due to the quasi-two-dimensional nature of the tri-layer La\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2.1}$$\end{document}2.1Sr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{1.9}$$\end{document}1.9Mn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{10}$$\end{document}10 manganite. The scaling of the magnetic entropy change confirms the second-order phase transition and the critical behavior of phase transition has been studied around T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_C$$\end{document}C to understand the low dimensional magnetism in tri-layer La\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2.1}$$\end{document}2.1Sr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{1.9}$$\end{document}1.9Mn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{10}$$\end{document}10. We have obtained the critical exponents for tri-layer La\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2.1}$$\end{document}2.1Sr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{1.9}$$\end{document}1.9Mn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{10}$$\end{document}10, which belong to the short-range two-dimensional (2D)-Ising universality class. The low dimensional magnetism in tri-layer La\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2.1}$$\end{document}2.1Sr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{1.9}$$\end{document}1.9Mn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{10}$$\end{document}10 manganite is also explained with the help of renormalization group theoretical approach for short-range 2D-Ising systems. It has been shown that the layered structure of tri-layer La\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2.1}$$\end{document}2.1Sr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{1.9}$$\end{document}1.9Mn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{10}$$\end{document}10 results in three different types of interactions intra-planer (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ J_{ab} $$\end{document}Jab), intra-tri-layer (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ J_{c} $$\end{document}Jc) and inter-tri-layer (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ J' $$\end{document}J′) such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ J_{ab}> J_{c}>> J' $$\end{document}Jab>Jc>>J′ and competition among these give rise to the canted antiferromagnetic spin structure above T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ _{C} $$\end{document}C. Based on the similar magnetic interaction in bi-layer manganite, we propose that the tri-layer La\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2.1}$$\end{document}2.1Sr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{1.9}$$\end{document}1.9Mn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{10}$$\end{document}10 should be able to host the skyrmion below T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ _{C} $$\end{document}C due to its strong anisotropy and layered structure.

Controlling the anisotropy of a van der Waals antiferromagnet with light

Van der Waals magnets provide an ideal playground to explore the fundamentals of low-dimensional magnetism and open opportunities for ultrathin spin-processing devices. The Mermin-Wagner theorem dictates that as in reduced dimensions isotropic spin interactions cannot retain long-range correlations, the long-range spin order is stabilized by magnetic anisotropy. Here, using ultrashort pulses of light, we control magnetic anisotropy in the two-dimensional van der Waals antiferromagnet NiPS3 Tuning the photon energy in resonance with an orbital transition between crystal field split levels of the nickel ions, we demonstrate the selective activation of a subterahertz magnon mode with markedly two-dimensional behavior. The pump polarization control of the magnon amplitude confirms that the activation is governed by the photoinduced magnetic anisotropy axis emerging in response to photoexcitation of ground state electrons to states with a lower orbital symmetry. Our results establish pumping of orbital resonances as a promising route for manipulating magnetic order in low-dimensional (anti)ferromagnets.

Competing antiferromagnetic-ferromagnetic states in a d7 Kitaev honeycomb magnet

The Kitaev model is a rare example of an analytically solvable and physically instantiable Hamiltonian yielding a topological quantum spin liquid ground state. Here we report signatures of Kitaev spin liquid physics in the honeycomb magnet Li3Co2SbO6, built of high-spin d 7 (Co2+) ions, in contrast to the more typical low-spin d 5 electron configurations in the presence of large spin-orbit coupling. Neutron powder diffraction measurements, heat capacity, and magnetization studies support the development of a long-range antiferromagnetic order space group of C C 2/ m , below T N   =   11 K at μ 0 H   =   0 T . The magnetic entropy recovered between T   =   2 and 50 K is estimated to be 0.6 R ln2 , in good agreement with the value expected for systems close to a Kitaev quantum spin liquid state. The temperature-dependent magnetic order parameter demonstrates a β value of 0.19(3), consistent with XY anisotropy and in-plane ordering, with Ising-like interactions between layers. Further, we observe a spin-flop-driven crossover to ferromagnetic order with space group of C 2/ m under an applied magnetic field of μ 0 H   ≈   0.7 T at T   =   2   K . Magnetic structure analysis demonstrates these magnetic states are competing at finite applied magnetic fields even below the spin-flop transition. Both the d 7 compass model, a quantitative comparison of the specific heat of Li3Co2SbO6, and related honeycomb cobaltates to the anisotropic Kitaev model further support proximity to a Kitaev spin liquid state. This material demonstrates the rich playground of high-spin d 7 systems for spin liquid candidates and complements known d 5 Ir- and Ru-based materials.

Magnetic critical behavior of the van der Waals Fe5GeTe2 crystal with near room temperature ferromagnetism

The van der Waals ferromagnet Fe₅GeTe₂ has a Curie temperature T_C of about 270 K, which is tunable through controlling the Fe deficiency content and can even reach above room temperature. To achieve insights into its ferromagnetic exchange that gives the high T_C, the critical behavior has been investigated by measuring the magnetization in Fe₅GeTe₂ crystal around the ferromagnetic ordering temperature. The analysis of the measured magnetization by using various techniques harmonically reached to a set of reliable critical exponents with T_C = 273.7 K, β = 0.3457 ± 0.001, γ = 1.40617 ± 0.003, and δ = 5.021 ± 0.001. By comparing these critical exponents with those predicted by various models, it seems that the magnetic properties of Fe₅GeTe₂ could be interpreted by a three-dimensional magnetic exchange with the exchange distance decaying as J(r) ≈ r^−4.916, close to that of a three-dimensional Heisenberg model with long-range magnetic coupling.

Investigation of thermal behavior of mixed-valent iron borates vonsenite and hulsite containing [OM4]n+ and [OM5]n+ oxocentred polyhedra by in situ high-temperature Mössbauer spectroscopy, X-ray diffraction and thermal analysis

The investigation of elemental composition, crystal structure and thermal behavior of vonsenite and hulsite from the Titovskoe boron deposit in Russia is reported. The structures of the borates are described in terms of cation-centered and oxocentred polyhedra. There are different sequences of double chains and layers consisting of oxocentred [OM₄]ⁿ⁺ tetrahedra and [OM₅]ⁿ⁺ tetragonal pyramids forming a framework. Elemental composition was determined by energy-dispersive X-ray spectroscopy (EDX). Oxidation states and coordination sites of iron and tin in the oxoborates are determined using Mössbauer spectroscopy and compared with EDX and X-ray diffraction data (XRD). According to results obtained from high-temperature Mössbauer spectroscopy, the Fe²⁺ to Fe³⁺ oxidation in vonsenite and hulsite occurs at approximately 500 and 600 K, respectively. According to the high-temperature XRD data, this process is accompanied by an assumed deformation of crystal structures and subsequent solid-phase decomposition to hematite and warwickite. It is seen as a monotonic decrease of volume thermal expansion coefficients with an increase in temperature. A partial magnetic ordering in hulsite is observed for the first time with T_c ≃ 383 K. Near this temperature, an unusual change of thermal expansion coefficients is revealed. Vonsenite starts to melt at 1571 K and hulsite melts at 1504 K. Eigenvalues of thermal expansion tensor are calculated for the oxoborates as well as anisotropy of the expansion is described in comparison with their crystal structures.

Criticality of the O(2) model with cubic anisotropies from nonperturbative renormalization

We study the O(2) model with Z_{4}-symmetric perturbations within the framework of the nonperturbative renormalization group (RG) for spatial dimensionality d=2 and 3. In a unified framework we resolve the relatively complex crossover behavior emergent due to the presence of multiple RG fixed points. In d=3 the system is controlled by the XY, Ising, and low-T fixed points in the presence of a dangerously irrelevant anisotropy coupling λ. In d=2 the anisotropy coupling is marginal and the physical picture is governed by the interplay between two distinct lines of RG fixed points, giving rise to nonuniversal critical behavior, and an isolated Ising fixed point. In addition to inducing crossover behavior in universal properties, the presence of the Ising fixed point yields a generic, abrupt change of critical temperature at a specific value of the anisotropy field.

Thickness-dependent magnetic order in CrI3 single crystals

Two-dimensional (2D) materials with intrinsic ferromagnetism provide unique opportunity to engineer new functionalities in nano-spintronics. One such material is CrI₃, showing long-range magnetic order in monolayer with the Curie temperature (T_c) of 45 K. Here we study detailed evolution of magnetic transition and magnetic critical properties in response to systematic reduction in crystal thickness down to 50 nm. Bulk T_c of 61 K is gradually suppressed to 57 K, however, the satellite transition at T ^* = 45 K is observed layer-independent at fixed magnetic field of 1 kOe. The origin of T ^* is proposed to be a crossover from pinning to depinning of magnetic domain walls. The reduction of thickness facilitates a field-driven metamagnetic transition around 20 kOe with out-of-plane field, in contrast to the continuous changes with in-plane field. The critical analysis around T_c elucidates the mean-field type interactions in microscale-thick CrI₃.

Suppression of magnetic ordering in XXZ-type antiferromagnetic monolayer NiPS3

How a certain ground state of complex physical systems emerges, especially in two-dimensional materials, is a fundamental question in condensed-matter physics. A particularly interesting case is systems belonging to the class of XY Hamiltonian where the magnetic order parameter of conventional nature is unstable in two-dimensional materials leading to a Berezinskii-Kosterlitz-Thouless transition. Here, we report how the XXZ-type antiferromagnetic order of a magnetic van der Waals material, NiPS3, behaves upon reducing the thickness and ultimately becomes unstable in the monolayer limit. Our experimental data are consistent with the findings based on renormalization-group theory that at low temperatures a two-dimensional XXZ system behaves like a two-dimensional XY one, which cannot have a long-range order at finite temperatures. This work provides the experimental examination of the XY magnetism in the atomically thin limit and opens opportunities of exploiting these fundamental theorems of magnetism using magnetic van der Waals materials.

Collective magnetism in an artificial 2D XY spin system

Two-dimensional magnetic systems with continuous spin degrees of freedom exhibit a rich spectrum of thermal behaviour due to the strong competition between fluctuations and correlations. When such systems incorporate coupling via the anisotropic dipolar interaction, a discrete symmetry emerges, which can be spontaneously broken leading to a low-temperature ordered phase. However, the experimental realisation of such two-dimensional spin systems in crystalline materials is difficult since the dipolar coupling is usually much weaker than the exchange interaction. Here we realise two-dimensional magnetostatically coupled XY spin systems with nanoscale thermally active magnetic discs placed on square lattices. Using low-energy muon-spin relaxation and soft X-ray scattering, we observe correlated dynamics at the critical temperature and the emergence of static long-range order at low temperatures, which is compatible with theoretical predictions for dipolar-coupled XY spin systems. Furthermore, by modifying the sample design, we demonstrate the possibility to tune the collective magnetic behaviour in thermally active artificial spin systems with continuous degrees of freedom.

Quasi-2D Heisenberg Antiferromagnets [CuX(pyz)2](BF4) with X = Cl and Br

Two Cu²⁺ coordination polymers [CuCl(pyz)₂](BF₄) 1 and [CuBr(pyz)₂](BF₄) 2 (pyz = pyrazine) were synthesized in the family of quasi two-dimensional (2D) [Cu(pyz)₂]²⁺ magnetic networks. The layer connectivity by monatomic halide ligands results in significantly shorter interlayer distances. Structures were determined by single-crystal X-ray diffraction. Temperature-dependent X-ray diffraction of 1 revealed rigid [Cu(pyz)₂]²⁺ layers that do not expand between 5 K and room temperature, whereas the expansion along the c-axis amounts to 2%. The magnetic susceptibility of 1 and 2 shows a broad maximum at ∼8 K, indicating antiferromagnetic interactions within the [Cu(pyz)₂]²⁺ layers. 2D Heisenberg model fits result in J_∥ = 9.4(1) K for 1 and 8.9(1) K for 2. The interlayer coupling is much weaker with | J_⊥| = 0.31(6) K for 1 and 0.52(9) K for 2. The electron density, experimentally determined and calculated by density functional theory, confirms the location of the singly occupied orbital (the magnetic orbital) in the tetragonal plane. The analysis of the spin density reveals a mainly σ-type exchange through pyrazine. Kinks in the magnetic susceptibility indicate the onset of long-range three-dimensional magnetic order below 4 K. The magnetic structures were determined by neutron diffraction. Magnetic Bragg peaks occur below T_N = 3.9(1) K for 1 and 3.8(1) K for 2. The magnetic unit cell is doubled along the c-axis ( k = 0, 0, 0.5). The ordered magnetic moments are located in the tetragonal plane and amount to 0.76(8) μ_B/Cu²⁺ for 1 and 0.6(1) μ_B/Cu²⁺ for 2 at 1.5 K. The moments are coupled antiferromagnetically both in the ab plane and along the c-axis. The Cu²⁺ g-tensor was determined from electron spin resonance spectra as g _x = 2.060(1), g _z = 2.275(1) for 1 and g _x = 2.057(1), g _z = 2.272(1) for 2 at room temperature.

Critical behavior of the van der Waals bonded high T C ferromagnet Fe3GeTe2

Fe₃GeTe₂ is a promising candidate for van der Waals bonded ferromagnet because of its high Curie temperature and the prediction that its ferromagnetism can maintain upon exfoliating down to single layer. Here, we have reported the critical behavior to understand its ferromagnetic exchange. Based on various techniques including modified Arrott plot, Kouvel-Fisher plot, and critical isotherm analysis, a set of reliable critical exponents (β = 0.327 ± 0.003, γ = 1.079 ± 0.005, and δ = 4.261 ± 0.009) has been obtained. The critical behavior suggests a three-dimensional long-range magnetic coupling with the exchange distance decaying as J(r) ≈ r^−4.6 in Fe₃GeTe₂. The possible origin of three-dimensional magnetic characteristics in van der Waals bonded magnets is discussed.

An electric-field representation of the harmonic XY model

The two-dimensional harmonic XY (HXY) model is a spin model in which the classical spins interact via a piecewise parabolic potential. We argue that the HXY model should be regarded as the canonical classical lattice spin model of phase fluctuations in two-dimensional condensates, as it is the simplest model that guarantees the modular symmetry of the experimental systems. Here we formulate a lattice electric-field representation of the HXY model and contrast this with an analogous representation of the Villain model and the two-dimensional Coulomb gas with a purely rotational auxiliary field. We find that the HXY model is a spin-model analogue of a lattice electric-field model of the Coulomb gas with an auxiliary field, but with a temperature-dependent vacuum (electric) permittivity that encodes the coupling of the spin vortices to their background spin-wave medium. The spin vortices map to the Coulomb charges, while the spin-wave fluctuations correspond to auxiliary-field fluctuations. The coupling explains the striking differences in the high-temperature asymptotes of the specific heats of the HXY model and the Coulomb gas with an auxiliary field. Our results elucidate the propagation of effective long-range interactions throughout the HXY model (whose interactions are purely local) by the lattice electric fields. They also imply that global spin-twist excitations (topological-sector fluctuations) generated by local spin dynamics are ergodically excluded in the low-temperature phase. We discuss the relevance of these results to condensate physics.

Collinear antiferromagnetism in trigonal SrMn2As2 revealed by single-crystal neutron diffraction

Iron pnictides and related materials have been a topic of intense research for understanding the complex interplay between magnetism and superconductivity. Here we report on the magnetic structure of SrMn₂As₂ that crystallizes in a trigonal structure ([Formula: see text]) and undergoes an antiferromagnetic (AFM) transition at [Formula: see text] K. The magnetic susceptibility remains nearly constant at temperatures [Formula: see text] with [Formula: see text] whereas it decreases significantly with [Formula: see text]. This shows that the ordered Mn moments lie in the [Formula: see text] plane instead of aligning along the [Formula: see text]-axis as in tetragonal BaMn₂As₂. Single-crystal neutron diffraction measurements on SrMn₂As₂ demonstrate that the Mn moments are ordered in a collinear Néel AFM phase with [Formula: see text] AFM alignment between a moment and all nearest neighbor moments in the basal plane and also perpendicular to it. Moreover, quasi-two-dimensional AFM order is manifested in SrMn₂As₂ as evident from the temperature dependence of the order parameter.

Critical exponents and scaling invariance in the absence of a critical point

The paramagnetic-to-ferromagnetic phase transition is classified as a critical phenomenon due to the power-law behaviour shown by thermodynamic observables when the Curie point is approached. Here we report the observation of such a behaviour over extraordinarily many decades of suitable scaling variables in ultrathin Fe films, for certain ranges of temperature T and applied field B. This despite the fact that the underlying critical point is practically unreachable because protected by a phase with a modulated domain structure, induced by the dipole–dipole interaction. The modulated structure has a well-defined spatial period and is realized in a portion of the (T, B) plane that extends above the putative critical temperature, where thermodynamic quantities do not display any singularity. Our results imply that scaling behaviour of macroscopic observables is compatible with an avoided critical point.

Thermodynamic observables develop power laws and singularities when approaching the Curie point of a ferromagnetic phase transition. Here, Saratz et al. demonstrate that topological excitations (that is, magnetic domains in Fe/Cu(100) films that even persist above the Curie point) remove those singularities compatibly with an avoided critical point.

Dimensional Reduction in Quantum Dipolar Antiferromagnets

We report ac susceptibility, specific heat, and neutron scattering measurements on a dipolar-coupled antiferromagnet LiYbF_{4}. For the thermal transition, the order-parameter critical exponent is found to be 0.20(1) and the specific-heat critical exponent -0.25(1). The exponents agree with the 2D XY/h_{4} universality class despite the lack of apparent two-dimensionality in the structure. The order-parameter exponent for the quantum phase transitions is found to be 0.35(1) corresponding to (2+1)D. These results are in line with those found for LiErF_{4} which has the same crystal structure, but largely different T_{N}, crystal field environment and hyperfine interactions. Our results therefore experimentally establish that the dimensional reduction is universal to quantum dipolar antiferromagnets on a distorted diamond lattice.

Magnetic critical properties and basal-plane anisotropy of Sr₂IrO₄

The anisotropic magnetic properties of Sr2IrO4 are investigated, using longitudinal and torque magnetometry. The critical scaling across T(c) of the longitudinal magnetization is that expected for the 2D XY universality class. Modeling the torque for a magnetic field in the basal plane, and taking into account all in-plane and out-of-plane magnetic couplings, we derive the effective fourfold anisotropy K4 ≈ 1 × 10(5) erg mol(-1). Although larger than for the cuprates, it is found to be too small to account for a significant departure from the isotropic 2D XY model. The in-plane torque also allows us to set an upper bound for the anisotropy of a field-induced shift of the antiferromagnetic ordering temperature.

Columnar order and Ashkin-Teller criticality in mixtures of hard squares and dimers

We show that critical exponents of the transition to columnar order in a mixture of 2×1 dimers and 2×2 hard squares on the square lattice depends on the composition of the mixture in exactly the manner predicted by the theory of Ashkin-Teller criticality, including in the hard-square limit. This result settles the question regarding the nature of the transition in the hard-square lattice gas. It also provides the first example of a polydisperse system whose critical properties depend on composition. Our ideas also lead to some interesting predictions for a class of frustrated quantum magnets that exhibit columnar ordering of the bond energies at low temperature.

Two-dimensional ferromagnetism of a 3He film: influence of weak frustration

(3)He films adsorbed on the atomically flat surface of graphite provide a model system for the study of two-dimensional magnetism on a triangular lattice. We have made a study of the regime in which the T=0 ground state of the second (3)He layer is a fully polarized ferromagnet. NMR, using broadband SQUID detection, at a range of low fields above the spin-flop transition, and over a wide temperature range 0.3-200 mK, has enabled us to disentangle the influence of sample finite size effects and magnetic field on the spin-wave spectrum. We demonstrate that the spin-wave spectrum is governed by a different effective exchange constant than that determining the high temperature magnetism. This is understood in terms of frustrated atomic ring exchange.

Dimensionality and confinement effects in δ-doped Pd(Fe) layers

We address the dimensionality aspects of the magnetic ordering in δ-doped Pd(Fe) structures. The key property we investigate, via magneto-optic Kerr measurements, is the magnetization induced by iron in palladium, over a wide temperature range 5 K < T < 300 K. The dimensional crossover we observe cannot be rationalized on the basis of structural considerations alone, since we find the dimensionality of the low temperature and of the critical region can differ. We discuss the crossover in terms of the temperature dependence of the magnon modes, giving rise to lower dimensionality at low temperatures.