Magnetic Field Phase Diagram Research Articles

Thermodynamic equilibrium of [formula omitted] Ising model on square lattice

We constructed a theoretical magnetic phase diagram in an external magnetic field T(P+), making it possible to determine the conditions for the existence of ferromagnets, antiferromagnets, and spin glass phases. The high-performance CUDA software package was used to the complete enumeration of all configurations of finite number spins in the ±J Ising model. We performed the rigorous numerical calculation of the partition function of N=8×8 systems of interacting spins with open boundary conditions. We used Monte Carlo methods like the Metropolis algorithm to calculate the critical temperatures for N=40×40 spins. The results of the Monte Carlo experiments are consistent with rigorous calculation data. The transition from the spin glass to the induced ferromagnetic state in an external field occurs without any critical change in the heat capacity. We used the ±J Ising model to calculate the instability line (AT—line) for the heat capacity of spin glass in the H−T diagram in an external magnetic field and the behavior of magnetic susceptibility in an external magnetic field. A rigorous calculation of the partition function allowed us to calculate all possible states and their thermodynamic probability. The calculation of the partition function meant that the model’s physics was obtained in an equilibrium state. The instability line was calculated for spin glass in the equilibrium state.

Exotic phases induced by RKKY interaction in the square lattice

We study a model of Ising spins in which direct exchange interactions compete with the Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling, which may arise effectively from itinerant electrons. We consider the model in the two-dimensional square lattice and focus on values of the RKKY coupling constant (JRKKY) and the Fermi momentum (kF) that induce strong frustration. We study the low-temperature magnetic field phase diagram using Monte Carlo simulations, considering several nearest neighbors in the RKKY interaction. Magnetic frustration yields a rich phase diagram with a variety of exotic phases. We compute the structure factors and define appropriate order parameters to describe the transitions. We also discuss the validity of the approximation made for long-range couplings and analytically demonstrate the change in the coexistence lines in the phase diagram by including up to the tenth nearest neighbors.

Skyrmion crystal formation and temperature–magnetic-field phase diagram of the frustrated triangular lattice Heisenberg magnet with easy-axis magnetic anisotropy

Skyrmion crystal formation and temperature–magnetic-field phase diagram of the frustrated triangular lattice Heisenberg magnet with easy-axis magnetic anisotropy

Observation of Magnetic Field‐Induced and Partially Switchable Electric Polarization in Spin‐Chain FePbBiO4

AbstractThe linear magnetoelectric (ME) characteristics of a quasi‐1D spin‐chain compound, FePbBiO4, are reported. Two distinct antiferromagnetic (AFM) orders occurring at ≈23 K (TN1) and 12 K (TN2) are verified using magnetization, specific heat, and conspicuous dielectric (ε′) anomalies. A striking observation is that no pyrocurrent (Ipy) is detected in the absence of magnetic field (H); however, H‐induced ferroelectric polarization (P) at TN1 and P unexpectedly partially switches or reverses below TN2 as reproduced by applying positive and negative electric fields (E). The resulting magnetic field and temperature (H‐T) phase diagram illustrates T‐dependent H‐induced spin reorientation and electric P. The interaction between T, H, spin dynamics, and lattice structures is pivotal and is qualitatively discussed and proposed as an explanation for the observed ME nature.

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.

Topological stability of spin textures in Si/Co-doped helimagnet FeGe

Element substitutions with magnetic or non-magnetic atoms are known to significantly impact the magnetic structure and related transport properties of magnets. To clarify the change of magnetic structure of B20-type magnets with element doping, we conduct real-space observations of spin textures and their temperature (T)-magnetic field (H) phase diagrams of a helimagnet FeGe with partially substituting Fe and Ge with Co and Si, respectively. The helical period (λ) changes dramatically by the element doping: λ increases by 147% to 103 nm in 30% Co-doped FeGe, whereas it decreases by around 70% to 49 nm in 30% Si-doped FeGe, compared to the λ =70 nm in FeGe. Upon applying the magnetic field normally to (001), (110), and (111) thin plates of both FeSi0.3Ge0.7 and Fe0.7Co0.3Ge, the hexagonal skyrmion crystal (SkX) state emerges. The magnetic phase diagrams observed through the real-space imaging reveal that (1) the SkX can extend to a larger T-H window by reducing the sample thickness or by cooling the sample under specific magnetic fields from temperatures above the transition temperature (TC ); (2) the stability of the SkX phase differs between Si-doped and Co-doped FeGe: the SkX phase is most unstable in the (111) FeSi0.3Ge0.7, while it remains robust in the (111) Fe0.7Co0.3Ge. These differences indicate distinct anisotropic behavior in FeGe with magnetic (Co) and non-magnetic-element (Si) dopants.

Magnetic phase diagram in the three-dimensional triangular-lattice antiferromagnet Sr3CoTa2O9 with small easy-axis anisotropy

We report the results of low-temperature magnetization and specific heat measurements of ${\mathrm{Sr}}_{3}{\mathrm{CoTa}}_{2}{\mathrm{O}}_{9}$ powder, in which ${\mathrm{Co}}^{2+}$ ions with effective spin-1/2 form a uniform triangular lattice in the $ab$ plane. It was found that ${\mathrm{Sr}}_{3}{\mathrm{CoTa}}_{2}{\mathrm{O}}_{9}$ undergoes successive antiferromagnetic transitions at ${T}_{\mathrm{N}1}=0.97\phantom{\rule{4pt}{0ex}}\mathrm{K}$ and ${T}_{\mathrm{N}2}=0.79\phantom{\rule{4pt}{0ex}}\mathrm{K}$ at zero magnetic field. As the magnetic field increases, both ${T}_{\mathrm{N}1}$ and ${T}_{\mathrm{N}2}$ decrease monotonically. The obtained magnetic field vs temperature phase diagram together with a sharp magnetization anomaly at a saturation field of ${\ensuremath{\mu}}_{0}{H}_{\mathrm{s}}=2.3$ T indicates that ${\mathrm{Sr}}_{3}{\mathrm{CoTa}}_{2}{\mathrm{O}}_{9}$ is described as a spin-1/2 three-dimensional triangular-lattice antiferromagnet with a weak easy-axis anisotropy. We discuss the characteristics of the magnetic phase diagram, which approximates the phase diagram for the magnetic field perpendicular to the $c$ axis.

D0 Magnetic Skyrmions in Two‐Dimensional Lattice

AbstractMagnetic skyrmions are topologically protected chiral spin textures that hold great promise for information storage and processing. The current research efforts on magnetic skyrmions are exclusively based on d‐orbital magnetism, which restricts their existence in a narrow window of temperature‐external magnetic field (T‐B) phase diagram. Herein, employing first‐principles and Monte‐Carlo simulations, the work reports the identification of d0 magnetic skyrmions in 2D lattice of Tl2NO2. Arising from inversion asymmetry and strong spin‐orbit coupling compensated by ligand of heavy element, large Dzyaloshinskii–Moriya interaction is obtained in monolayer Tl2NO2. This, competed with p‐orbital exchange interaction, leads to the d0 skyrmion physics under external magnetic field. Importantly, different from d‐orbital topological magnetism, the d0 magnetic skyrmions can be stabilized in a wide window of T‐B phase diagram. The underlying physics is related to the small magnetic moment and delocalization character of d0 magnetism. Furthermore, the work also demonstrates that the d0 magnetic skyrmions are strongly coupled with ferroelectricity. These findings open a new direction for magnetic skyrmion research.

Field-induced spin level crossings within a quasi- XY antiferromagnetic state in Ba2FeSi2O7

We present a high-field study of the strongly anisotropic easy-plane square lattice $S=2$ quantum magnet ${\mathrm{Ba}}_{2}{\mathrm{FeSi}}_{2}{\mathrm{O}}_{7}$. This compound is a rare high-spin antiferromagnetic system with very strong easy-plane anisotropy, such that the interplay between spin level crossings and antiferromagnetic order can be studied. We observe a magnetic field-induced spin level crossing occurring within an ordered state. This spin level crossing appears to preserve the magnetic symmetry while producing a nonmonotonic dependence of the order parameter magnitude. The resulting temperature--magnetic field phase diagram exhibits two dome-shaped regions of magnetic order overlapping around 30 T. The ground state of the lower-field dome is predominantly a linear combination of $|{S}^{z}=0\ensuremath{\rangle}$ and $|{S}^{z}=1\ensuremath{\rangle}$ states, while the ground state of the higher-field dome can be approximated by a linear combination of $|{S}^{z}=1\ensuremath{\rangle}$ and $|{S}^{z}=2\ensuremath{\rangle}$ states. At 30 T, where the spin levels cross, the magnetization exhibits a slanted plateau, the magnetocaloric effect shows a broad hump, and the electric polarization shows a weak slope change. We determined the detailed magnetic phase boundaries and the spin level crossings using measurements of magnetization, electric polarization, and the magnetocaloric effect in pulsed magnetic fields to 60 T. We calculate these properties using a mean-field theory based on direct products of SU(5) coherent states and find good agreement. Finally, we measure and calculate the magnetically induced electric polarization that reflects magnetic ordering and spin level crossings. This multiferroic behavior provides another avenue for detecting phase boundaries and symmetry changes.

Low-temperature and elastic properties of the 1/1 Tsai-type quasicrystal approximant GdCd6 investigated by ultrasonic measurements

Low-temperature and elastic properties of the quasicrystal approximant GdCd6 have been investigated by means of an ultrasonic measurement. Salient elastic anomalies were observed in the temperature and magnetic field dependence of the principal elastic constants, most probably being associated with the successive multiple magnetic phase transitions showing up at low temperatures. Based on the experimental data, a magnetic field vs temperature phase diagram was constructed. In a zero magnetic field, at least four phases appear to exist. However, the phase diagram both for the magnetic field applied for H// and H// is richer, and interestingly some phase boundaries correspond to the development of field-induced phases, leading to the intricate magnetic phase diagram possibly with multiple ordered phases. We discuss the elastic and electronic properties at low temperatures, and also the nature of the multiple magnetic phase transitions of GdCd6.

Topological quantum phase transition in a mixed-spin Heisenberg tetramer chain with alternating spin-1/2 and spin-5/2 dimers

We investigate magnetic quantum phases and the topological quantum phase transition between two distinct valence-bond solid (VBS) phases of a minimal interacting spin-chain model that captures a magnetic behavior of the novel low-dimensional quantum ferrimagnetic material Cu2Fe2Ge4O13. The studied mixed-spin Heisenberg tetramer chain consists of a 4-period array of spins involving two types of dimers sa−sa (sa=1/2) and Sb−Sb (Sb=5/2) under the assumption of unique intra- and inter-dimer coupling constants J1 and J2, respectively. Using the tensor-network formulation of the density-matrix renormalization group method, we have constructed the ground-state phase diagram in the parameter space magnetic field versus the interaction ratio J=J2/J1, whereby all ground states are in accordance with the Oshikawa–Yamanaka–Affleck theorem for a given period. In addition, we have implemented the recent tangential finite-size scaling method in order to characterize the critical behavior of the topological VBS transition through calculation of the critical point Jc and the critical exponent of the correlation length ν. Our results are consistent with the topological quantum phase transition from the SU(2) Wess–Zumino–Witten universality class with the critical exponent of correlation length ν=2/3 by assuming the proper logarithmic correction.

Large magnetocaloric effect in the frustrated antiferromagnet EuIr[formula omitted]P[formula omitted

We present a theoretical analysis of the magnetocaloric effect in the frustrated antiferromagnet EuIr2P2. Monte Carlo simulations indicate a large magnetic entropy change ΔSMmax∼5 J kg−1 K−1 at T=2.45 K for a moderate change in the external magnetic field ΔB=1.2 Tesla. The highest value of ΔSM seems to be associated with the presence of a multicritical point in the magnetic field versus temperature phase diagram (at Bm∼1.2 Tesla and Tm∼2.2 K) but it persists with similar large values for a broad range of temperatures T≲Tm. Single crystal EuIr2P2 magnetization vs magnetic field experiments allowed us to obtain the magnetocaloric effect for T>2 K. The results are consistent with the theoretical analysis and show a large magnetocaloric effect for T∼2.5 K. Finally, we present a phenomenological Landau functional analysis that provides a simplified description of the phase diagram and of the magnetocaloric effect. Although the magnetic frustration in this system leads to a rich phase diagram, we found no clear indication that it plays a significant role enhancing the magneticaloric effect, other than by reducing the transition temperatures and fields.

Magnetic field effects on the quantum spin liquid behaviors of NaYbS2

Spin-orbit coupling is an important ingredient to regulate the many-body physics, especially for many spin liquid candidate materials such as rare-earth magnets and Kitaev materials. The rare-earth chalcogenides (Ch = O, S, Se) is a congenital frustrating system to exhibit the intrinsic landmark of spin liquid by eliminating both the site disorders between and ions with the big ionic size difference and the Dzyaloshinskii-Moriya interaction with the perfect triangular lattice of the ions. The temperature versus magnetic-field phase diagram is established by the magnetization, specific heat, and neutron-scattering measurements. Notably, the neutron diffraction spectra and the magnetization curve might provide microscopic evidence for a series of spin configuration for in-plane fields, which include the disordered spin liquid state, 120° antiferromagnet, and one-half magnetization state. Furthermore, the ground state is suggested to be a gapless spin liquid from inelastic neutron scattering, and the magnetic field adjusts the spin orbit coupling. Therefore, the strong spin-orbit coupling in the frustrated quantum magnet substantially enriches low-energy spin physics. This rare-earth family could offer a good platform for exploring the quantum spin liquid ground state and quantum magnetic transitions.

Distinguishing dxz+idyz and dx2−y2 pairing in Sr2RuO4 by high magnetic field H−T phase diagrams

Employing a realistic tight-binding model describing the Fermi surface in the normal state of $Sr_2RuO_4$ we map out magnetic field versus temperature phase diagrams for $d_{x^2-y^2} (B_{1g})$ and $d_{xz}+id_{yz} (E_g)$ pairing types. Both produce (i) a similar Knight shift suppression of $\sim\!80\%$ and (ii) a bicritical point at $T=0.88$K separating low field second order phase transitions from high field Pauli limiting first order transitions. We find, however, strikingly different phase behaviour within the high field Pauli limiting region. For $d_{x^2-y^2}$ pairing symmetry an additional lower critical line of first order transitions is found (terminating in a critical point at $T=0.09-0.22$K depending on the choice of Hubbard U parameters) while for $d_{xz}+id_{yz}$ no such additional high field phase transitions are found for any choice of Hubbard U. In conjunction with our earlier finding [{\it Physical Review B} {\bf 102} (23), 235203] for $p$-wave helical pairing of a still different high field phase structure (a lower critical field line meeting the upper critical field line exactly at the bicritical point), we suggest high field Pauli limiting phase structure as a possible route to distinguish pairing symmetries in this material.

Phase Diagram of the BCS–Hubbard Model in a Magnetic Field

We propose an extended BCS–Hubbard model and investigate its ground state phase diagram in an external magnetic field. By mapping the model onto a model of spinless fermions coupled with conserving Z 2 variables which are mimicked by pseudospins, the model is shown to be exactly solvable along the symmetric lines for an arbitrary on-site Hubbard interaction on the bipartite lattice. In the zero field limit, the ground states exhibit an antiferromagnetic order of pseudospins. In the large field limit, on the other hand, the pseudospins are fully polarized ordered. With the increase of the applied field, a first-order phase transition occurs between these kinds of phases when the on-site Coulomb interaction is less than a critical value U c. Above this critical U c, a novel intermediate phase emerges between the fully polarized and antiferromagnetic phases. The ground states in this phase are macroscopically degenerate, like in a spin ice, and the corresponding entropy scales linearly with the lattice size at zero temperature.

Linear magnetoelastic coupling and magnetic phase diagrams of the buckled-kagomé antiferromagnet [Formula: see text

Single crystals of Cu_3Bi(SeO_3)_2O_2Cl 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_{mathrm {S}} = 120.7(5) K is much more sensitive to uniaxial pressure than T_{mathrm {N}}, with strong effects of up to 27(3) K/GPa (p parallel c). Magnetostriction and magnetization measurements reveal a linear magnetoelastic coupling for Bparallel c below T_{mathrm {N}}, as well as a mixed phase behavior above the tricritical point around 0.4 T. An analysis of the critical behavior in zero-field points to three-dimensional (3D) Ising-like magnetic ordering. In addition, the magnetic phase diagrams for fields along the main crystalline axes are reported.

NdAlSi: A magnetic Weyl semimetal candidate with rich magnetic phases and atypical transport properties

Magnetic Weyl semimetals (MWSMs) have attracted significant attention due to their intriguing physical properties and potential applications in spin-electronic devices. Here we report the characterization of NdAlSi including transport, magnetization, and heat capacity on single crystals, as well as band structure calculation. It is a newly proposed MWSM candidate which breaks both time-reversal and spatial inversion symmetries. A temperature--magnetic field phase diagram is experimentally established. Remarkably, on the angular magnetoresistance, a twofold symmetric sharp peak instead of a smooth variation is observed across the phase boundary between the ferrimagnetic and antiferromagnetic phases. We argue that the tunability of both the electronic structure and magnetic properties in NdAlSi is crucial for realizing such a behavior. Our results indicate that $4f$-electron-based MWSM could provide a unique platform to explore new and intriguing quantum phenomena arising from the interaction between magnetism and electron topology.

Collinear order in the spin- 52 triangular-lattice antiferromagnet Na3Fe(PO4)2

We set forth the structural and magnetic properties of the frustrated spin-$5/2$ triangle lattice antiferromagnet ${\mathrm{Na}}_{3}\mathrm{Fe}{({\mathrm{PO}}_{4})}_{2}$ examined via x-ray diffraction, magnetization, heat capacity, and neutron diffraction measurements on the polycrystalline sample. No structural distortion was detected from the temperature-dependent x-ray diffraction down to 12.5 K, except a systematic lattice contraction. The magnetic susceptibility at high temperatures agrees well with the high-temperature series expansion for a spin-$5/2$ isotropic triangular lattice antiferromagnet with an average exchange coupling of $J/{k}_{\mathrm{B}}\ensuremath{\simeq}1.8$ K rather than a one-dimensional spin-$5/2$ chain model. This value of the exchange coupling is consistently reproduced by the saturation field of the pulse field magnetization data. It undergoes a magnetic long-range order at ${T}_{\mathrm{N}}\ensuremath{\simeq}10.4$ K. Neutron diffraction experiments elucidate a collinear antiferromagnetic ordering below ${T}_{\mathrm{N}}$ with the propagation vector $k=(1,0,0)$. An intermediate value of frustration ratio ($f\ensuremath{\simeq}3.6$) reflects moderate frustration in the compound which is corroborated by a reduced ordered magnetic moment of $\ensuremath{\sim}1.52{\ensuremath{\mu}}_{\mathrm{B}}$ at 1.6 K, compared to its classical value ($5{\ensuremath{\mu}}_{\mathrm{B}}$). Magnetic isotherms exhibit a change of slope envisaging a field induced spin-flop transition at ${H}_{\mathrm{SF}}\ensuremath{\simeq}3.2$ T. The magnetic field vs temperature phase diagram clearly unfold three distinct phase regimes, reminiscent of a frustrated magnet with in-plane ($XY$-type) anisotropy.

Angular-field magnetic phase diagram of b-plane at 4 K of YAlGe-type TbAlGe with zigzag-chain

Orthorhombic YAlGe-type TbAlGe is expected to have an interesting magnetic anisotropy due to zigzag chains of the Tb ions. We have grown the single crystal for the first time and measured the AC magnetic susceptibility and specific heat from 1.3 K to 60 K, and the vector magnetization for the b-plane up to 7 T at 4 K. The specific heat and AC magnetic susceptibility indicate that there are two antiferromagnetic transitions at T N1 = 38 K and TN2 = 7.6 K, where the transition at T N2 is first-order like. The magnetization curve at 4 K for the a-axis shows a large hysteresis, and metamagnetic transition appears at H 1 = 1.6 T in the field increasing process, and another metamagnetic transition at H2 = 3.5 T in addition to H 1 in the decreasing field process. The magnetization curves of the b- and c-axis are linear up to 7 T. The measurement of vector magnetization at 4 K reflects the hysteresis of the magnetization curve, and there is a large hysteresis. From this vector magnetization measurement, we have made the angular magnetic field phase diagram at 4 K for the b-plane. In this phase diagram, there are phase lines that cannot be obtained by ordinary magnetization measurement.

Nature of field-induced antiferromagnetic order in Zn-doped CeCoIn5 and its connection to quantum criticality in the pure compound

Quantum criticality plays an important role in the unconventional nature of superconductivity in strongly correlated electron systems. However, the intrinsic antiferromagnetic (AFM) order parameter responsible for quantum criticality has been unidentified in the prototypical unconventional superconductor ${\mathrm{CeCoIn}}_{5}$. In this work, magnetization and specific-heat measurements for $\mathrm{CeCo}{({\mathrm{In}}_{1\ensuremath{-}x}{\mathrm{Zn}}_{x})}_{5}$ with $x\ensuremath{\le}0.07$ demonstrate that the field-induced AFM order develops with Zn doping, along with a continuous increase in its critical field up to 10 T at $x=0.07$. The weak signals associated with the AFM phase transition strongly suggest spatially inhomogeneous evolution of the AFM phase, whose feature becomes pronounced with decreasing the Zn concentration. The temperature, magnetic field, and Zn concentration phase diagram is constructed from those experimental results. It is found that, in this diagram, extrapolating the $x$ dependence of the AFM critical field yields the value of $\ensuremath{\approx}5\phantom{\rule{4pt}{0ex}}\mathrm{T}$ for $x\ensuremath{\rightarrow}0$, which coincides with the location of the quantum critical point in ${\mathrm{CeCoIn}}_{5}$. The specific heat shows $\ensuremath{-}lnT$ diverging behavior characteristic of the non-Fermi-liquid state at the AFM critical fields for all of the $x$ range. The scaling analysis for the specific-heat data above critical fields leads to continuous variations of the scaling parameters as a function of $x$. These findings provide strong evidence that the quantum critical fluctuations in ${\mathrm{CeCoIn}}_{5}$ originate from the order parameter corresponding to the field-induced AFM state observed in Zn-doped systems.