Magnetic Field-temperature Phase Diagram Research Articles

SrCu(OH)3Cl , an isolated equilateral triangle spin S=1/2 model system

We have investigated the magnetic ground state properties of the quantum spin trimer compound strontium hydroxy copper chloride SrCu(OH)3Cl using bulk magnetization, specific heat measurements, nuclear magnetic resonance (NMR), and electron spin resonance (ESR) spectroscopy. SrCu(OH)3Cl consists of layers with isolated Cu2+ triangles and hence provides an opportunity to understand the magnetic ground state of an isolated system of S = 1/2 arranged on an equilateral triangle. Although magnetization measurements do not exhibit a phase transition to a long-range ordered state down to T = 2 K, they reveal the characteristic behavior of isolated trimers with an exchange of J=154 K. The Curie-Weiss behavior changes around 50–80 K, as is also seen in the NMR spin-lattice relaxation rate. In zero magnetic field, our specific heat data establish a second-order phase transition to an antiferromagnetic ground state below T= 1.2 K. We have drawn a magnetic field-temperature (H−T) phase diagram based on the specific heat measurements. The ESR data show divergence of the linewidth at lower temperatures, which precedes the phase transition to an antiferromagnetic long-range ordered state with unconventional critical exponents. The temperature variation of the g-factor further confirms the antiferromagnetic phase transition and reflects the underlying magnetocrystalline anisotropy of the compound. Published by the American Physical Society 2024

SrCu(OH)3Cl , an isolated equilateral triangle spin S=1/2 model system

We have investigated the magnetic ground state properties of the quantum spin trimer compound strontium hydroxy copper chloride SrCu(OH)3Cl using bulk magnetization, specific heat measurements, nuclear magnetic resonance (NMR), and electron spin resonance (ESR) spectroscopy. SrCu(OH)3Cl consists of layers with isolated Cu2+ triangles and hence provides an opportunity to understand the magnetic ground state of an isolated system of S = 1/2 arranged on an equilateral triangle. Although magnetization measurements do not exhibit a phase transition to a long-range ordered state down to T = 2 K, they reveal the characteristic behavior of isolated trimers with an exchange of J=154 K. The Curie-Weiss behavior changes around 50–80 K, as is also seen in the NMR spin-lattice relaxation rate. In zero magnetic field, our specific heat data establish a second-order phase transition to an antiferromagnetic ground state below T= 1.2 K. We have drawn a magnetic field-temperature (H−T) phase diagram based on the specific heat measurements. The ESR data show divergence of the linewidth at lower temperatures, which precedes the phase transition to an antiferromagnetic long-range ordered state with unconventional critical exponents. The temperature variation of the g-factor further confirms the antiferromagnetic phase transition and reflects the underlying magnetocrystalline anisotropy of the compound. Published by the American Physical Society 2024

Quantum simulation of an extended Dicke model with a magnetic solid

The Dicke model describes the cooperative interaction of an ensemble of two-level atoms with a single-mode photonic field and exhibits a quantum phase transition as a function of light–matter coupling strength. Extending this model by incorporating short-range atom–atom interactions makes the problem intractable but is expected to produce new physical phenomena and phases. Here, we simulate such an extended Dicke model using a crystal of ErFeO3, where the role of atoms (photons) is played by Er3+ spins (Fe3+ magnons). Through terahertz spectroscopy and magnetocaloric effect measurements as a function of temperature and magnetic field, we demonstrated the existence of a novel atomically ordered phase in addition to the superradiant and normal phases that are expected from the standard Dicke model. Further, we elucidated the nature of the phase boundaries in the temperature–magnetic-field phase diagram, identifying both first-order and second-order phase transitions. These results lay the foundation for studying multiatomic quantum optics models using well-characterized many-body solid-state systems.

Magnetic phase diagram of Cr1/3NbS2: SANS study

The magnetic structure of the Cr1/3NbS2 compound was studied with help of small-angle neutron scattering under an applied magnetic field in a wide temperature range below TN ​= ​130 К. At zero magnetic field the magnetic moments of Cr3+ ions build the helix structure with the wave vector k oriented along the c-axis of the chiral structure of P6322 space group. The detected diffraction ring is interpreted as scattering on the magnetic helices of randomly oriented crystallites within powder sample. The intensity of the diffraction peak decreases with temperature and dissolves at T ​= ​115 К. The magnetic field differently affects the crystallites with helix wave vector k along the field and those with k perpendicular to the field. The magnetic field, when applied, leads to appearance of the chiral soliton lattice in the grains with k oriented perpendicularly to the field. The period of the chiral soliton lattice increases rapidly as H approaches HC1 ​= ​0.25 ​T. The transition from chiral soliton lattice to the field-induced ferromagnet, however, is not homogeneous but is accompanied by strong ferromagnetic fluctuations in the wide field range around HC1. These fluctuations are well visible in the experiment as scattering centered at Q ​= ​0. In the grains with k parallel to the field, the chiral soliton lattice undergoes a series of transitions from helimagnet to the conical state, and then to the field-induced ferromagnet at HC2 ​= ​1.25 ​T. The period of the conical helix increases slightly (for 5%) with the field, while the transition to the field–induced ferromagnetic state is again accompanied by strong ferromagnetic fluctuations. The magnetic field–temperature phase diagrams for H perpendicular to the c-axis and for H parallel to the c-axis are plotted on the basis of the data obtained.

Widely-sweeping magnetic field–temperature phase diagrams for skyrmion-hosting centrosymmetric tetragonal magnets

We numerically investigate the stabilization mechanisms of skyrmion crystals under thermal fluctuations and external magnetic field in itinerant centrosymmetric tetragonal magnets. By adopting an efficient steepest descent method with a small computational cost, we systematically construct the magnetic field–temperature phase diagrams of the effective spin model derived from the itinerant electron model on a two-dimensional square lattice. As a result, we find that a square-type skyrmion crystal is stabilized by either or both of the high-harmonic wave–vector interaction and the biquadratic interaction under an external magnetic field. Especially, we discover that the former high-harmonic wave–vector interaction can stabilize the skyrmion crystal only at finite temperatures when its magnitude is small. In addition to the skyrmion crystal, we also find other stable multiple-Q states in the phase diagram. Lastly, we discuss the correspondence of the phase diagrams between the effective spin model and the skyrmion-hosting material GdRu2Si2. The present results suggest a variety of multiple-Q states could be driven by thermal fluctuations and external magnetic fields in centrosymmetric itinerant magnets.

Magnetic Field–Temperature Phase Diagram of CeCoSi Constructed on the Basis of Specific Heat, Magnetoresistivity, and Magnetization Measurements: Single Crystal Study

A Ce-based metallic compound CeCoSi with a tetragonal structure exhibits successive phase transitions: the one whose order parameter is unidentified at T_0 = 12 K and the antiferromagnetic one at T_N = 9.4 K. We performed specific heat, magnetoresistivity (MR), and magnetization measurements for a single crystal CeCoSi at low temperatures in magnetic fields B of up to 14 T and constructed detailed magnetic field--temperature phase diagrams for both B || [100] and [001]. The longitudinal MR measured for B || [100] shows a sign change from negative to positive across T_0 = 13 K updated in the present sample, indicating a clear change in an electronic state. In addition, the constructed magnetic phase diagrams for both the field directions have a B-induced region in each ordered state. The presence of the newly found regions would be attributed to a change in the symmetry of the order parameter or domain alignment by applying B.

Machine learning techniques to construct detailed phase diagrams for skyrmion systems

Recently, there has been an increased interest in the application of machine learning (ML) techniques to a variety of problems in condensed matter physics. In this regard, of particular significance is the characterization of simple and complex phases of matter. Here, we use a ML approach to construct the full phase diagram of a well known spin model combining ferromagnetic exchange and Dzyaloshinskii-Moriya (DM) interactions where topological phases emerge. At low temperatures, the system is tuned from a spiral phase to a skyrmion crystal by a magnetic field. However, thermal fluctuations induce two types of intermediate phases, bimerons and skyrmion gas, which are not as easily determined as spirals or skyrmion crystals. We resort to large scale Monte Carlo simulations to obtain low temperature spin configurations, and train a convolutional neural network (CNN), taking only snapshots at specific values of the DM couplings, to classify between the different phases, focusing on the intermediate and intricate topological textures. We then apply the CNN to higher temperature configurations and to other DM values, to construct a detailed magnetic field-temperature phase diagram, achieving outstanding results. We discuss the importance of including the disordered paramagnetic phases in order to get the phase boundaries, and finally, we compare our approach with other ML algorithms.

Successive Phase Transitions and Multiferroicity in Deformed Triangular-Lattice Antiferromagnets Ca3MNb2O9 (M=Co, Ni) with Spatial Anisotropy

We constructed the magnetic field-temperature phase diagrams of new quasi-two-dimensional isosceles triangular lattice antiferromagnets (TLAF) Ca3MNb2O9 (M=Co, Ni) from dc and ac magnetic susceptibilities, specific heat, dielectric constant, and electric polarization measurements on single crystalline samples. Ca3CoNb2O9 with effective spin-1/2 Co2+ ions undergoes a two-step antiferromagnetic phase transition at T N1 = 1.3 K and T N2 = 1.5 K and enters a stripe ordered state at zero magnetic field. With increasing field, successive magnetic phase transitions, reminiscent of the up-up-down (uud) and the oblique phases, are observed. The dielectric constant of Ca3CoNb2O9 shows anomalies related to the magnetic phase transitions, but clear evidence of ferroelectricity is absent. Meanwhile, Ca3NiNb2O9 with spin-1 Ni2+ ions also shows a two-step antiferromagnetic transition at T N1 = 3.8 K and T N2 = 4.2 K at zero field. For Ca3NiNb2O9, the electric polarization in the magnetic ordered phases was clearly observed from the pyroelectric current measurements, which indicates its coexistence of magnetic ordering and ferroelectricity.

Weak ferromagnetism linked to the high-temperature spiral phase of YBaCuFeO5

The layered perovskite ${\mathrm{YBaCuFeO}}_{5}$ is a rare example of a cycloidal spiral magnet whose ordering temperature ${T}_{\text{spiral}}$ can be tuned far beyond room temperature by adjusting the degree of ${\mathrm{Cu}}^{2+}/{\mathrm{Fe}}^{3+}$ chemical disorder in the structure. This unusual property qualifies this material as one of the most promising spin-driven multiferroic candidates. However, very little is known about the response of the spiral to magnetic fields, crucial for magnetoelectric cross-control applications. Using bulk magnetization and neutron powder diffraction measurements under magnetic fields up to 9 T, we report here a temperature-magnetic field phase diagram of this material. Besides revealing a strong stability of the spiral state, our data uncover the presence of weak ferromagnetism coexisting with the spiral modulation. Since ferromagnets can be easily manipulated with magnetic fields, this observation opens new perspectives for the control of the spiral orientation, directly linked to the polarization direction, as well as for a possible future use of this material in technological applications.

Magnetic phase diagram of (Mo2/3RE1/3)2AlC, RE = Tb and Dy, studied by magnetization, specific heat, and neutron diffraction analysis

We report the results of magnetization, heat capacity, and neutron diffraction measurements on (Mo2/3RE1/3)2AlC with RE = Dy and Tb. Temperature and field-dependent magnetization as well as heat capacity were measured on a powder sample and on a single crystal allowing the construction of the magnetic field-temperature phase diagram. To study the magnetic structure of each magnetic phase, we applied neutron diffraction in a magnetic field up to 6 T. For (Mo2/3Dy1/3)2AlC in zero field, a spin density wave is stabilized at 16 K, with antiferromagnetic ordering at 13 K. Furthermore, we identify the coexistence of ferromagnetic and antiferromagnetic phases induced by magnetic fields for both RE = Tb and Dy. The origin of the field induced phases is resulting from the competing ferromagnetic and antiferromagnetic interactions.

Mean-field description of skyrmion lattice in hexagonal frustrated antiferromagnets

Simple mean-field approach for frustrated antiferromagnets on hexagonal lattices, aimed to describe the high-temperature part of the temperature-magnetic field phase diagram, is proposed. It is shown, that an interplay between modulation vector symmetry, Zeeman energy and magneto-dipolar interaction leads to stabilization of the triple-$Q$ skyrmion lattice in a certain region of the phase diagram. Corresponding analytical expressions for phase boundaries are derived. It is argued that the developed theory can be applied for the description of the high-temperature part of the phase diagram observed experimentally for Gd$_2$PdSi$_3$ compound.

Unusual Resistive Transitions in the Nodal-Line Semimetallic Superconductor NaAlSi

NaAlSi is a quasi-two-dimensional semimetal with superconductivity below Tc = 6.8 K and a band structure characterized by nodal lines near the Fermi level and potential topological surface states. Electrical resistivity measurements on its superconducting transitions in magnetic fields were made using plate-like single crystals. In the magnetic field-temperature phase diagram, we observed a substantial reduction in resistivity in a pre-transitional zone above the bulk superconducting regime only when the magnetic fields were perpendicular to the plane, rather than parallel to it. Significant sample (thickness) dependence, reentrant behavior, and sensitivity to electrode configurations all indicate that a portion of the crystal has an upper critical field greater than the bulk superconductivity in the pre-transitional region. This fractional superconductivity may occur on the side surface of the crystal.

Determination of the tricritical point, H–T phase diagram and exchange interactions in the antiferromagnet MnTa2O6

Using the analysis of the temperature and magnetic field dependence of the magnetization (M) measured in the temperature range of 1.5 K to 400 K in magnetic fields up to 250 kOe, the magnetic field-temperature (H–T) phase diagram, tricritical point and exchange constants of the antiferromagnetic MnTa2O6 are determined in this work. X-ray diffraction/Rietveld refinement and x-ray photoelectron spectroscopy of the polycrystalline MnTa2O6 sample verified its phase purity. Temperature dependence of the magnetic susceptibility χ (=M/H) yields the Néel temperature T N = 5.97 K determined from the peak in the computed ∂(χT)/∂T vs T plot, in agreement with the T N = 6.00 K determined from the peak in the C P vs T data. The experimental data of C P vs T near T N is fitted to C P = A|T − T N|−α yielding the critical exponent α = 0.10(0.13) for T > T N (T < T N). The χ vs T data for T > 25 K fits well with the modified Curie–Weiss law: χ = χ 0 + C/(T − θ) with χ 0 = −2.12 × 10−4 emu mol−1 Oe−1 yielding θ = −24 K, and C = 4.44 emu K mol−1 Oe−1, the later giving magnetic moment μ = 5.96 μ B per Mn2+ ion. This yields the effective spin S = 5/2 and g = 2.015 for Mn2+, in agreement with g = 2.0155 measured using electron spin resonance spectroscopy. Using the magnitudes of θ and T N and molecular field theory, the antiferromagnetic exchange constants J 0/k B = −1.5 ± 0.2 K and J ⊥/k B = −0.85 ± 0.05 K for Mn2+ ions along the chain c-axis and perpendicular to the c-axis respectively are determined. The χ vs T data when compared to the prediction of a Heisenberg linear chain model provides semiquantitative agreement with the observed variation. The H–T phase diagram is mapped using the M–H isotherms and M–T data at different H yielding the tricritical point T TP (H, T) = (17.0 kOe, 5.69 K) separating the paramagnetic, antiferromagnetic, and spin-flop phases. At 1.5 K, the experimental magnitudes of the exchange field H E = 206.4 kOe and spin-flop field H SF = 23.5 kOe yield the anisotropy field H A = 1.34 kOe. These results for MnTa2O6 are compared with those reported recently in the isostructural MnNb2O6.

Possible quantum nematic phase in a colossal magnetoresistance material

EuB6 has for a long time captured the attention of the physics community, as it shows a ferromagnetic phase transition leading to a insulator the metal transition together with colossal magnetoresistance (CMR). EuB6 has a very low carrier density, which is known to drastically change the interaction between the localized Eu moments and the conduction electrons. One of early triumphs of the quantum theory in condensed matter was the presence of Fermi surface, which is intimately linked to the symmetry of the underlying crystal lattice. This symmetry can be probed by angle resolved magnetoresistance (AMRO) measurements. Here, we present angle resolved magnetoresistance (AMRO) measurements that show a that in EuB6 this symmetry is broken, possibly indicating the presence of a quantum nematic phase. We identify the region in the temperature-magnetic field phase diagram where the magnetoresistance shows two-fold oscillations instead of the expected fourfold pattern. Quantum nematic phases are analogous to classical liquid crystals. Like liquid crystals, which break the rotational symmetry of space, their quantum analogs break the point-group symmetry of the crystal due to strong electron-electron interactions, as in quantum Hall states, Sr3Ru2O7, and high temperature superconductors. This is the same region where magnetic polarons were previously observed, suggesting that they drive the nematicity in EuB6. This is also the region of the phase diagram where EuB6 shows a colossal magnetoresistance (CMR). This novel interplay between magnetic and electronic properties could thus be harnessed for spintronic applications.

Collapse of a region of the magnetic phase diagram of elemental terbium under a strain-induced Lifshitz transition

AC susceptibility and neutron scattering measurements are used to study the magnetic field-temperature magnetic phase diagram of a Tb single crystal under uniaxial tension along its hexagonal $c$ axis. An external magnetic field is applied in the basal plane. We focus on the region in the phase diagram that corresponds to the helical antiferromagnetic phase and find that this region collapses when the uniaxial tension is increased beyond a critical value as low as 600 bar. There are strong reasons to associate this collapse with an underlying Lifshitz transition in the Fermi surface of Tb's valence electrons. We use a finite-temperature ab initio theory to analyze our measurements, obtaining a pressure-temperature magnetic phase diagram in very good agreement with experiment. Our calculations indicate that short- and long-range magnetic order has a crucial effect on the Fermi surface nesting and consequent magnetism of Tb.

Magnetoconduction in the Correlated Semiconductor FeSi in Ultrastrong Magnetic Fields up to a Semiconductor-to-Metal Transition.

Magnetoresistance of the correlated narrow-gap semiconductor FeSi was investigated by the radio frequency self-resonant spiral coil technique in magnetic fields up to 500T, which is supplied by an electromagnetic flux compression megagauss generator. Semiconductor-to-metal transition accomplishes around 270T observed as a sharp kink in the magnetoresistance, which implies the closing of the hybridization gap by the Zeeman shift of band edges. In the temperature-magnetic field phase diagram, the semiconductor-metal transition field is found to be almost independent of temperature, which is in contrast to a characteristic magnetic field associated with the hopping magnetoconduction in the in-gap localized states, exhibiting a notable temperature dependence.

Influence of microstructure on the application of Ni-Mn-In Heusler compounds for multicaloric cooling using magnetic field and uniaxial stress

Novel multicaloric cooling utilizing the giant caloric response of Ni-Mn-based metamagnetic shape-memory alloys to different external stimuli such as magnetic field, uniaxial stress and hydrostatic pressure is a promising candidate for energy-efficient and environmentally-friendly refrigeration. However, the role of microstructure when several external fields are applied simultaneously or sequentially has been scarcely discussed in literature. Here, we synthesized ternary Ni-Mn-In alloys by suction casting and arc melting and analyzed the microstructural influence on the response to magnetic fields and uniaxial stress. By combining SEM-EBSD and stress-strain data, a significant effect of texture on the stress-induced martensitic transformation is revealed. It is shown that a <001> texture can strongly reduce the critical transformation stresses. The effect of grain size on the material failure is demonstrated and its influence on the magnetic-field-induced transformation dynamics is investigated. Temperature-stress and temperature-magnetic field phase diagrams are established and single caloric performances are characterized in terms of ΔsT and ΔTad. The cyclic ΔTad values are compared to the ones achieved in the multicaloric exploiting-hysteresis cycle. It turns out that a suction-cast microstructure and the combination of both stimuli enables outstanding caloric effects in moderate external fields which can significantly exceed the single caloric performances. In particular for Ni-Mn-In, the maximum cyclic effect in magnetic fields of 1.9 T is increased by more than 200 % to -4.1 K when a moderate sequential stress of 55 MPa is applied. Our results illustrate the crucial role of microstructure for multicaloric cooling using Ni-Mn-based metamagnetic shape-memory alloys.

Magnetic field-temperature phase diagram, exchange constants and specific heat exponents of the antiferromagnet MnNb2O6

This work presents the magnetic field-temperature (H–T) phase diagram, exchange constants, specific heat (C P) exponents and magnetic ground state of the antiferromagnetic MnNb2O6 polycrystals. Temperature dependence of the magnetic susceptibility χ (=M/H) yields the Néel temperature T N = 4.33 K determined from the peak in the computed ∂(χT)/∂T vs T plot in agreement with the transition in the C P vs T data at T N = 4.36 K. The experimental data of C P vs T near T N is fitted to C P = A|T − T N|−α yielding the critical exponent α = 0.12 (0.15) for T > T N (T < T N). The best fit of χ vs T data for T > 50 K to χ = χ 0 + C/(T − θ) with χ 0 = −1.85 × 10−4 emu mol−1 Oe−1 yields θ = −17 K, and C = 4.385 emu K mol−1 Oe−1, the latter giving magnetic moment μ = 5.920μ B per Mn2+ ion. This confirms the effective spin S = 5/2 and g = 2.001 for Mn2+ and the dominant exchange interaction being antiferromagnetic in nature. Using the magnitudes of θ and T N and molecular field theory (MFT), the exchange constants J 0/k B = −1.08 K for Mn2+ ions along the chain c-axis and J ⊥/k B = −0.61 K as the interchain coupling perpendicular to c-axis are determined. These exchange constants are consistent with the expected χ vs T variation for the Heisenberg linear chain. The H–T phase diagram, mapped using the M–H isotherms and M–T data at different H combined with the reported data of Nielsen et al, yields a triple-point T TP (H, T) = (18 kOe, 4.06 K). The spin–flopped state above T TP and the forced ferromagnetism for H > 192 kOe are used to estimate the anisotropy energy H A ≈ 0.8 kOe.

Electric Quadrupolar Contributions in the Magnetic Phases of UNi_{4}B.

We present acoustic signatures of the electric quadrupolar degrees of freedom in the honeycomb-layer compound UNi_{4}B. The transverse ultrasonic mode C_{66} shows softening below 30K both in the paramagnetic phase and antiferromagnetic phases down to ∼0.33 K. Furthermore, we traced magnetic field-temperature phase diagrams up to 30T and observed a highly anisotropic elastic response within the honeycomb layer. These observations strongly suggest that Γ_{6}(E_{2g}) electric quadrupolar degrees of freedom in localized 5f^{2} (J=4) states are playing an important role in the magnetic toroidal dipole order and magnetic-field-induced phases of UNi_{4}B, and evidence some of the U ions remain in the paramagnetic state even if the system undergoes magnetic toroidal ordering.

Periodic Anderson model for magnetism and superconductivity in UTe2

We provide and analyze a periodic Anderson model for studying magnetism and superconductivity in UTe$_2$, a recently-discovered candidate for a topological spin-triplet superconductor. The 24-band tight-binding model reproduces the band structure obtained from a DFT$+U$ calculation consistent with an angle-resolved photoemission spectroscopy. The Coulomb interaction of $f$-electrons enhances Ising ferromagnetic fluctuation along the $a$-axis and stabilizes spin-triplet superconductivity of either $B_{3u}$ or $A_{u}$ symmetry. When effects of pressure are taken into account in hopping integrals, the magnetic fluctuation changes to antiferromagnetic one, and accordingly spin-singlet superconductivity of $A_{g}$ symmetry is stabilized. Based on the results, we propose pressure-temperature and magnetic field-temperature phase diagrams revealing multiple superconducting phases as well as an antiferromagnetic phase. In particular, a mixed-parity superconducting state with spontaneous inversion symmetry breaking is predicted.