Precise thermal expansion and magnetostriction studies of the intermetallic compound Eu$_2$CuSi$_3$ in the temperature range between 5 and 300 K are presented. A clear sign of magnetic second order phase transition at the ferromagnetic Curie temperature $T_{\rm C}$ = 34 K indicates strong magneto-structural coupling. Uniaxial thermal expansion data show a large anisotropy between the magnetic easy $c$-axis and the hexagonal $ab$-plane, which is associated with a strongly anisotropic magnetic coupling. A spin-reorientation regime as well as a non-uniform energy scale are indicated by Grüneisen analysis of the data at low temperatures. Anomalous contributions to the thermal expansion imply ferromagnetic correlations far above in zero magnetic field. The magnetic phase diagram is constructed, showing the evolution of short- and long-range magnetic order in magnetic fields up to 15 T. The anisotropic magnetic field effect yields anomalous magnetostrictive effects up to about 200 K.
We synthesized single crystals of composition Ba$_2$CuSi$_2$O$_6$Cl$_2$ and investigated its quantum magnetic properties. The crystal structure is closely related to that of the quasi-two-dimensional (2D) dimerized magnet BaCuSi$_2$O$_6$ also known as Han purple. Ba$_2$CuSi$_2$O$_6$Cl$_2$ has a singlet ground state with an excitation gap of $Δ/k_{\rm B}\,{=}\,20.8$ K. The magnetization curves for two different field directions almost perfectly coincide when normalized by the $g$-factor except for a small jump anomaly for a magnetic field perpendicular to the $c$ axis. The magnetization curve w…
We have measured the linear thermal expansion and magnetostriction of the Ising antiferromagnet TbNi2Ge2 along its c-axis from room temperature to 2 K and in magnetic fields to 14 T. We find a magnetic phase diagram that agrees with earlier work and estimate aspects of its uniaxial pressure dependence. We also find a new high field feature near 10 T which may signal the onset of an additional field-induced phase.
Cerium diantimonide (CeSb$_2$) is one of a family of rare earth based magnetic materials that exhibit metamagnetism, enabling control of the magnetic ground state through an applied magnetic field. At low temperatures, CeSb$_2$ hosts a rich phase diagram with multiple magnetically ordered phases for many of which the order parameter is only poorly understood. In this paper, we report a study of its metamagnetic properties by Scanning Tunneling Microscopy (STM) and magnetization measurements. We use STM measurements to characterize the sample magnetostriction with sub-picometer resolution from …
Critical Berezinskii-Kosterlitz-Thouless dynamics in the archetypal two-dimensional spin system Ba$_2$CuSi$_2$O$_6$Cl$_2$
Laboratoire National des Champs Magnétiques Intenses, LNCMI-CNRS (UPR3228), EMFL, Univ. Grenoble Alpes, Univ. Toulouse, INSA-T（强磁场国家实验室）；Christ University（基督大学）；Rigetti Computing（瑞格蒂计算）；Univ. Toulouse, CNRS, Laboratoire de Physique Théorique（图卢兹大学，法国国家科学研究中心，理论物理实验室）；Univ. Lyon, ENS de Lyon, CNRS, Laboratoire de Physique（里昂大学，巴黎高等师范学院里昂分校，法国国家科学研究中心，物理实验室）；Department of Physics, Institute of Science Tokyo（东京科学大学物理系）
High-resolution thermal expansion and magnetostriction measurements were performed on single crystals of $α$-RuCl$_3$ in magnetic fields applied parallel to the Ru-Ru bonds. The length changes were measured in the direction perpendicular to the honeycomb planes. Our data show clear thermodynamic characteristics for the field-induced phase transition at the critical field $μ_0H_{c1} = 7.8(2)$ T where the antiferromagnetic zigzag order is suppressed. At higher fields, a kink in the magnetostriction coefficient signals an additional phase transition around $μ_0H_{c2} \approx 11$ T. The extracted …
The quantum magnet NiCl$_2$-4SC(NH$_2$)$_2$ is a candidate for observing Bose-Einstein Condensation of spin degrees of freedom in applied magnetic fields. An XY antiferromagnetic ordered state occurs in a dome-shaped region of the temperature-field phase diagram between H$_{c1}$ = 2.1 T and H$_{c2}$ = 12.6 T and below 1.2 K. BEC corresponds to the field-induced quantum phase transition into the ordered state. We investigate magnetostriction in single crystals of this compound at dilution refrigerator temperatures in magnetic fields up to 18 T, and as a function of magnetic field angle. We show…
We theoretically study origins of the ferroelectricity in the multiferroic phases of the rare-earth (R) Mn perovskites, RMnO3, by constructing a realistic spin model including the spin-phonon coupling, which reproduces the entire experimental phase diagram in the plane of temperature and Mn-O-Mn bond angle for the first time. Surprisingly we reveal a significant contribution of the symmetric (S.S)-type magnetostriction to the ferroelectricity even in a spin-spiral-based multiferroic phase, which can be larger than the usually expected antisymmetric (SxS)-type contribution. This explains well t…
Metamagnetism in layered ruthenates has been interpreted as a novel kind of quantum critical behavior. In an external magnetic field, Ca$_{2-x}$Sr$_x$RuO$_4$ undergoes a metamagnetic transition accompanied by a pronounced magnetostriction effect. In this paper we present a mean-field study for a microscopic model that naturally reproduces the key features of this system. The phase diagram calculated is equivalent to the experimental $T$-$x$ phase diagram. The presented model also gives a good basis to discuss the critical metamagnetic behavior measured in the system.
Magnetoelectric phase diagrams of the rare-earth (R) Mn perovskites RMnO3 are theoretically studied by focusing on crucial roles of the symmetric magnetostriction or the Peierls-type spin-phonon coupling through extending our previous work [M. Mochizuki et al., Phys. Rev. Lett. 105, 037205 (2010)]. We first construct a microscopic classical Heisenberg model for RMnO3 including the frustrated spin exchanges, single-ion anisotropy, and Dzyaloshinskii-Moriya interaction. We also incorporate the lattice degree of freedom coupled to the Mn spins via the Peierls-type magnetostriction. By analyzing t…
Extensive magnetization and magnetostriction measurements were carried out on a single crystal of GdNi2B2C along the main tetragonal axes. Within the paramagnetic phase, the magnetic and strain susceptibilities revealed a weak anisotropy in the exchange couplings and two-ion tetragonal-preserving alpha-strain modes. Within the ordered phase, magnetization and magnetostriction revealed a relatively strong orthorhombic distortion mode and rich field-temperature phase diagrams. For H//(100) phase diagram, three field-induced transformations were observed, namely, at: Hd(T), related to the domain …
The (H,T)-phase diagram of the multiferroic perovskite TbMnO$_3$ was studied by high-resolution thermal expansion $α(T)$ and magnetostriction $ΔL(H)/L$ measurements. Below $T_{N}\simeq 42$ K, TbMnO$_3$ shows antiferromagnetic order, which changes at $T_{FE}\simeq 28$ K where simultaneously a spontaneous polarization $P||c$ develops. Sufficiently high magnetic fields applied along $a$ or $b$ induce a polarization flop to $P||a$. We find that all of these transitions are strongly coupled to the lattice parameters. Thus, our data allow for a precise determination of the phase boundaries and also …
The magnetic phase diagrams of RMnO3 (R = Er, Yb, Tm, Ho) are investigated up to 14 Tesla via magnetic and dielectric measurements. The stability range of the AFM order below the Neel temperature of the studied RMnO3 extends to far higher magnetic fields than previously assumed. Magnetic irreversibility indicating the presence of a spontaneous magnetic moment is found near 50 K for R=Er, Yb, and Tm. At very low temperatures and low magnetic fields the phase boundary defined by the ordering of the rare earth moments is resolved. The sizable dielectric anomalies observed along all phase boundari…
Thermal expansion, magnetostriction and magnetization measurements under magnetic field and hydrostatic pressure were performed on a $\mathrm{UAu_{2}Si_{2}}$ single crystal. They revealed a large anisotropy of magnetoelastic properties manifested by prominent length changes leading to a collapse of the unit-cell volume accompanied by breaking the fourfold symmetry (similar to that in $\mathrm{URu_{2}Si_{2}}$ in the hidden-order state) in the antiferromagnetic state as consequences of strong magnetoelastic coupling. The magnetostriction curves measured at higher temperatures confirm a bulk char…
BaCo$_2$V$_2$O$_8$ is a one-dimensional antiferromagnetic spin-1/2 chain system with pronounced Ising anisotropy of the magnetic exchange. Due to finite interchain interactions long-range antiferromagnetic order develops below $T_{\rm N} \simeq 5.5$ K, which is accompanied by a structural distortion in order to lift magnetic frustration effects. The corresponding temperature $vs. $ magnetic-field phase diagram is highly anisotropic with respect to the magnetic-field direction and various details are still under vivid discussion. Here, we report the influence of several substitutions on the mag…
We present high-resolution thermal expansion $α(T)$ and magnetostriction $ΔL(H)/L$ measurements of GdMnO$_3$, which develops an incommensurate antiferromagnetic order (ICAFM) below $T_{\rm N}\simeq$ 42 K and transforms into a canted A-type antiferromagnet (cAFM) below $T_{\rm c}\simeq 20 $K. In addition, a ferroelectric polarization ${\bf P}||a$ is observed below $T_{\rm FE} $ for finite magnetic fields applied along the $b$ direction. In zero magnetic field we find a strongly anisotropic thermal expansion with certain, rather broad anomalous features. In finite magnetic fields, however, very …
In antiferromagnets, the interplay of spin frustration and spin-lattice coupling has been extensively studied as the source of complex spin patterns and exotic magnetism. Here, we demonstrate that, although neglected in the past, the spin-lattice coupling is essential to ferrimagnetic spinels as well. We performed ultrahigh-field magnetization measurements up to 110 T on a Yafet-Kittel ferrimagnetic spinel, MnCr$_2$S$_4$, which was complemented by measurements of magnetostriction and sound velocities up to 60 T. Classical Monte Carlo calculations were performed to identify the complex high-fie…
Frustrated magnets with a strong spin-lattice coupling can show rich magnetic phases and the associated fascinating phenomena. A promising platform is the breathing pyrochlore magnet CuInCr$_{4}$S$_{8}$ with localized $S=3/2$ Cr$^{3+}$ ions, which is proposed to be effectively viewed as an $S=6$ Heisenberg antiferromagnet on the face-centered-cubic lattice. Here, we unveil that CuInCr$_{4}$S$_{8}$ exhibits a complex magnetic phase diagram with a small phase pocket ($A$ phase) by means of magnetization, magnetostriction, magnetocapacitance, and magnetocaloric-effect measurements in pulsed high …
The magnetoelastic coupling in multiferroic $DyMn_2O_5$ is investigated by magnetostriction measurements along the three crystallographic orientations. Strong lattice anomalies as a function of the magnetic field are detected at the low temperature magnetic and ferroelectric phase transitions. The sign and magnitude of the magnetostrictive coefficient as well as the lattice anomalies at the transitions are correlated with the Dy moment order and with the sharp changes of the dielectric constant and the ferroelectric polarization. With the magnetic field applied along the c-axis a new high-fiel…
Single crystals of Cu$_3$Bi(SeO$_3$)$_2$O$_2$Cl were investigated using high-resolution capacitance dilatometry in magnetic fields up to 15 T. Pronounced magnetoelastic coupling is found upon evolution of long-range antiferromagnetic order at T$_{\mathrm{N}} = 26.4(3)$ K. Grüneisen analysis reveals moderate effects of uniaxial pressure on T$_{\mathrm{N}}$, of $1.8(4)$ K/GPa, $-0.62(15)$ K/GPa and $0.33(10)$ K/GPa for $p \parallel a$, $b$, and $c$, respectively. Below 22 K, Grüneisen scaling fails which implies the presence of competing interactions. The structural phase transition at T$_{\math…
We report high-resolution dilatometry on high-quality single crystals of NiTiO3 grown by means of the optical floating-zone technique. The anisotropic magnetic phase diagram is constructed from thermal expansion and magnetostriction studies up to B=15T and magnetization studies in static (15T) and pulsed (60T) magnetic fields. Our data allow to quantitatively study magneto-elastic coupling and to determine uniaxial pressure dependencies. While the entropy changes are found to be of magnetic nature, Grüneisen analysis implies only one relevant energy scale in the whole low-temperature regime. T…
In the effective Ising spin-1/2 antiferromagnetic chain system BaCo$_2$V$_2$O$_8, the magnetic-field influence is highly anisotropic. For magnetic fields along the easy axis $c$, the Néel order is strongly suppressed already for low fields and an incommensurate order is entered above 4 T. We present a detailed study of the magnetic phase diagrams for different magnetic field directions, which are derived from magnetization data, high-resolution thermal expansion and magnetostriction measurements as well as from the thermal conductivity. Zero-field thermal expansion data reveal that the magneti…
We report the thermodynamic properties studied by thermal expansion, magnetostriction, magnetisation, and specific heat measurements as well as the low-energy magnetic excitations of \mto\ and investigate how magneto-elastic coupling and magnetic anisotropy affect the evolution of long-range order and the magnetic phase diagram. Specifically, we utilise high-resolution capacitance dilatometry and antiferromagnetic resonance (AFMR) studies by means of high-frequency electron spin resonance (HF-ESR) spectroscopy. The role of anisotropy is reflected by spin-reorientation at $B_{\rm{SF}}$~$\simeq …
The phase diagram of the quasi two-dimensional antiferromagnet BaNi$_{2}$V$_{2}$O$_{8}$ is studied by specific heat, thermal expansion, magnetostriction, and magnetization for magnetic fields applied perpendicular to $\mathbf{c}$. At $μ_0H^{*}\simeq1.5$ T, a crossover to a high-field state, where $T_N(H)$ increases linearly, arises from a competition of intrinsic and field-induced in-plane anisotropies. The pressure dependences of $T_N$ and $H^{*}$ are interpreted using the picture of a pressure-induced in-plane anisotropy. Even at zero field and ambient pressure, in-plane anisotropy cannot be…
In this work, we investigate the evolution and settling of magnon condensation in the spin-1/2 dimer system Sr$_{3}$Cr$_{2}$O$_{8}$ using a combination of magnetostriction in pulsed fields and inelastic neutron scattering in a continuous magnetic field. The magnetic structure in the Bose-Einstein condensation (BEC) phase was probed by neutron diffraction in pulsed magnetic fields up to 39~T. The magnetic structure in this phase was confirmed to be an XY-antiferromagnetic structure validated by irreducible representational analysis. The magnetic phase diagram as a function of an applied magneti…
Through powder x-ray diffraction we have investigated the structural behavior of SmVO3, in which orbital and magnetic degrees of freedom are believed to be closely coupled to the crystal lattice. We have found, contrary to previous reports, that SmVO3 exists in a single, monoclinic, phase below 200 K. The associated crystallographic distortion is then stabilized through the magnetostriction that occurs below 134 K. The crystal structure has been refined using synchrotron x-ray powder diffraction data measured throughout the structural phase diagram, showing a substantial Jahn-Teller distortion…
We present a study of the anisotropy of the dielectric, magnetic and magnetoelastic properties of the multiferroic clinopyroxene NaFeGe$_2$O$_6$. Pyroelectric currents, dielectric constants and magnetic susceptibilities as well as the thermal expansion and the magnetostriction were examined on large synthetic single crystals of NaFeGe$_2$O$_6$. The spontaneous electric polarization detected below $T_{\rm C}\simeq 11.6$ K in an antiferromagnetically ordered state ($T_{\rm N}\simeq 13$ K) is mainly lying within the $ac$ plane with a small component along $b$, indicating a triclinic symmetry of t…
Combined experimental and modeling studies of the magnetocaloric effect, ultrasound, and magnetostriction were performed on single-crystal samples of the spin-dimer system Sr$_3$Cr$_2$O$_8$ in large magnetic fields, to probe the spin-correlated regime in the proximity of the field-induced XY-type antiferromagnetic order also referred to as a Bose-Einstein condensate of magnons. The magnetocaloric effect, measured under adiabatic conditions, reveals details of the field-temperature ($H,T$) phase diagram, a dome characterized by critical magnetic fields $H_{c1}$ = 30.4 T, $H_{c2}$ = 62 T, and a …
We discuss the implications that new magnetocaloric, thermal expansion and magnetostriction data in $α$-RuCl$_{3}$ single crystals have on its temperature-field phase diagram and uncover the magnetic-field dependence of an apparent energy gap structure $Δ(H)$ that evolves when the low temperature antiferromagnetic order is suppressed. We show that, depending on how the thermal expansion data is modeled, $Δ(H)$ can show a cubic field dependence and remain finite at zero field, consistent with the pure Kitaev model hosting itinerant Majorana fermions and localized $\mathbb{Z}_{2}$ fluxes. Our ma…
Theoretical and experimental work have not provided a consistent picture of the phase diagram of the nearly ideal Ising ferromagnet LiHoF4 in a transverse magnetic field. Using a newly fabricated capacitive dilatometer, we have investigated the thermal expansion and magnetostriction of LiHoF4 in magnetic fields applied perpendicular to the Ising direction. Critical points for the ferromagnetic phase transition have been determined from both methods in the classical paramagnetic to ferromagnetic regime. Excellent agreement has been found with existing experimental data suggesting that, in this …
(NH$_4$)$_2$[FeCl$_5$(H$_2$O)], a member of the family of antiferromagnetic $A_2$[Fe$X_5$(H$_2$O)] compounds ($X$ = halide ion, $A$ = alkali metal or ammonium ion) is classified as a new multiferroic material. We report the onset of ferroelectricity below ~6.9 K within an antiferromagnetically ordered state ($T_N \sim 7.25 K$). The corresponding electric polarization can drastically be influenced by applying magnetic fields. Based on measurements of pyroelectric currents, dielectric constants and magnetization we characterize the magnetoelectric, dielectric and magnetic properties of (NH$_4$)$…
We present a comprehensive macroscopic thermodynamic study of the quasi-one-dimensional (1D) $s = \tfrac{1}{2}$ frustrated spin-chain system linarite. Susceptibility, magnetization, specific heat, magnetocaloric effect, magnetostriction, and thermal-expansion measurements were performed to characterize the magnetic phase diagram. In particular, for magnetic fields along the b axis five different magnetic regions have been detected, some of them exhibiting short-range-order effects. The experimental magnetic entropy and magnetization are compared to a theoretical modelling of these quantities u…
We report a comprehensive experimental investigation of the magnetic structure of the cycloidal phase in Ca$_3$Ru$_2$O$_7$, which mediates the spin reorientation transition, and establishes its magnetic phase diagram. In zero applied field, single-crystal neutron diffraction data confirms the scenario deduced from an earlier resonant x-ray scattering study: between $46.7$~K $< T < 49.0$~K the magnetic moments form a cycloid in the $a-b$ plane with a propagation wavevector of $(δ,0,1)$ with $δ\simeq 0.025$ and an ordered moment of about 1 $μ_{\rm{B}}$, with the eccentricity of the cycloid evolv…
A study of the antiferromagnet CeRh$_2$Si$_2$ by torque, magnetostriction, and transport in pulsed magnetic fields up to 50 Tesla and by thermal expansion in static fields up to 13 Tesla is presented. The magnetic field-temperature phase diagram of CeRh$_2$Si$_2$, where the magnetic field is applied along the easy axis $\mathbf{c}$, is deduced from these measurements. The second-order phase transition temperature $T_{N}$ and the first-order phase transition temperature $T_{1,2}$ (=~36 K and 26 K at zero-field, respectively) decrease with increasing field. The field-induced antiferromagnetic-to…
The itinerant quasi-ferromagnetic metal MnSi has been studied by detailed thermal expansion measurements under pressures and magnetic fields. A sudden decrease of the volume at the critical pressure Pc ~1.6 GPa has been observed and is in good agreement with the pressure variation of the volume fraction of the spiral magnetic ordering. This confirms that the magnetic order disappears by a first order phase transition. The energy change estimated by the volume discontinuity on crossing Pc is of similar order as the Zeeman energy of the transition from the spiral ground state to a polarized para…
The phase diagram of the filled skutterudite CeOs$_4$Sb$_{12}$ has been mapped in fields $H$ of up to 60 T and temperatures $T$ down to 0.5 K using resistivity, magnetostriction, and MHz conductivity. The valence transition separating the semimetallic, low-$H$, low-$T$, $\cal{L}$ phase from the metallic high-$H$, high-$T$ $\cal{H}$ phase exhibits a very unusual, wedge-shaped phase boundary, with a non-monotonic gradient alternating between positive and negative. This is quite different from the text-book "elliptical" phase boundary usually followed by valence transitions. Analysis of Shubnikov…
We propose a new form of the frustrated Heisenberg antiferromagnetic Hamiltonian with spatially anisotropic exchange parameters Jc, Ja, and Jac extended along the c, a, and a +/- c lattice directions and apply it to describe fascinating physics of copper carbodiimide CuNCN in the assumption of resonating valence bond (RVB) type of its phases. These are invoked to explain the intriguing absence of magnetic order in CuNCN down to 4 K. We show that the quasiparticle spectrum of the RVB model of the proposed Hamiltonian has three principal regimes: (i) one with two pairs of lines of nodes, (ii) on…
(Pu) has an unusually rich phase diagram that includes seven distinct solid state phases and an unusually large 25% collapse in volume from its delta phase to its low temperature alpha phase via a series of structural transitions. Despite considerable advances in our understanding of strong electronic correlations within various structural phases of Pu and other actinides, the thermodynamic mechanism responsible for driving the volume collapse has continued to remain a mystery. Here we utilize the unique sensitivity of magnetostriction measurements to unstable f electron shells to uncover the …
Time reversal symmetry and magnetoelastic correlations are probed by means of high-resolution volume dilatometry in URu2Si2 at cryogenic temperatures and magnetic fields more than enough to suppress the hidden order state at H_HO(T = 0.66 K) approximately 35 T. We report a significant crystal lattice volume expansion at and above H_HO(T), and even above T_HO, possibly a consequence of field-induced f-electron localization, and hysteresis at some high field phase boundaries that confirm volume involvement. We investigate in detail the magnetostriction and magnetization as the temperature is red…
The centrosymmetric tetragonal itinerant magnet EuAl$_{4}$ exhibits an intricate magnetic phase diagram including rhombic and square skyrmion-lattice (SkL) phases in the external magnetic field. Here, we report a multi-axis dilatometric investigation of EuAl$_{4}$ by means of a newly designed fiber-Bragg-grating technique complemented by a resonant x-ray scattering experiment, revealing anisotropic magnetostriction and magnetovolume effect associated with successive phase transitions. The rhombic and square SkL phases are found to possess $\sim$0.10% and $\sim$0.03% orthorhombic structural dis…
Temperature-pressure phase diagram of the Kitaev hyperhoneycomb iridate $β$-Li$_2$IrO$_3$ is explored using magnetization, thermal expansion, magnetostriction, and muon spin rotation ($μ$SR) measurements, as well as single-crystal x-ray diffraction under pressure and ab initio calculations. The Neel temperature of $β$-Li$_2$IrO$_3$ increases with the slope of 0.9 K/GPa upon initial compression, but the reduction in the polarization field $H_c$ reflects a growing instability of the incommensurate order. At 1.4 GPa, the ordered state breaks down upon a first-order transition giving way to a new …
Competing Interactions and the Effects of Uniaxial Out-of-plane Perturbations in the Honeycomb Antiferromagnet Na$_2$Co$_2$TeO$_6$
Kirchhoff Institute for Physics, Heidelberg University（海德堡大学基尔霍夫物理研究所）；Institute of Physics, Academia Sinica（中央研究院物理学研究所）；Department of Physics, Sungkyunkwan University（成均馆大学物理系）
The effect of Pd doping on the superconducting phase diagram of the unconventional superconductor UPt3 has been measured by (magneto)resistance, specific heat, thermal expansion and magnetostriction. Experiments on single- and polycrystalline U(Pt1-xPdx)3 for x<= 0.006 show that the superconducting transition temperatures of the A phase, Tc+, and of the B phase, Tc-, both decrease, while the splitting DTc increases at a rate of 0.30(2)K/at.%Pd. We find that DTc(x) correlates with an increase of the weak magnetic moment m(x) upon Pd doping. This provides further evidence for Ginzburg-Landau sce…
Isotropic and anisotropic magnetic behavior of the frustrated spin chain compound $β$-TeVO$_4$ is reported. Three magnetic transitions observed in zero magnetic field are tracked in fields applied along different crystallographic directions using magnetization, heat capacity, and magnetostriction measurements. Qualitatively different temperature-field diagrams are obtained below 10 T for the field applied along $a$ or $b$ and along $c$, respectively. In contrast, a nearly isotropic high-field phase emerges above 18 T and persists up to the saturation that occurs around 22.5 T. Upon cooling in …
