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Frustrated systems with two or more competing interactions have a wide variety of phases with unconventional properties and complex symmetry. The pseudospin formalism is a powerful method to study complex magnetic systems with various degrees of freedom. Pseudospin models of anisotropic magnets are widely used to describe the properties of binary alloys, classical and quantum liquids, dilute magnets, superconductors, and many other physical systems [1]. In addition, disorder caused by introduction of impurities and defects into the system significantly affects the critical behavior and phase states of magnets [2]. This work is devoted to modelling and theoretical description of phase and critical properties of a low-dimensional site-dilute magnet with frustration caused by the competitive charge and spin orders.&lt;br/&gt;We consider the Blume-Emery-Griffiths-type spin-pseudospin model, which was initially proposed [3] to consider the competition between spin and charge orders in underdoped high-T&lt;sub&gt;c&lt;/sub&gt; cuprates like La&lt;sub&gt;2-x&lt;/sub&gt;Sr&lt;sub&gt;x&lt;/sub&gt;CuO&lt;sub&gt;4&lt;/sub&gt; in the normal state. The model considers the CuO&lt;sub&gt;2&lt;/sub&gt; planes as a system of charge triplets consisting of three many-electron mixed-valence centers [CuO&lt;sub&gt;4&lt;/sub&gt;]&lt;sup&gt;7-;6-;5-&lt;/sup&gt; (corresponding nominally to the copper ion states Cu&lt;sup&gt;1+;2+;3+&lt;/sup&gt;). Two charge states Cu&lt;sup&gt;1+;3+&lt;/sup&gt; are associated with two components of the pseudospin S=1 triplet with M&lt;sub&gt;S&lt;/sub&gt;=±1. The Cu&lt;sup&gt;2+&lt;/sup&gt; state associated with the M&lt;sub&gt;S&lt;/sub&gt;=0 component is magnetic and has a conventional spin σ=1/2. Within this pseudospin formalism, the Hamiltonian of the static spin-pseudospin model includes Ising spin exchange coupling (J), on-site (Δ) and inter-site (V) density-density correlations, which have the form of single-ion pseudospin anisotropy and Ising exchange coupling in the language of pseudospin operators. The chemical potential μ is necessary to take into account the constant charge density doped in the CuO&lt;sub&gt;2&lt;/sub&gt; plane, which gives the concentration of doped charged impurities n.&lt;br/&gt;The properties of the spin-pseudospin model in the ground state were studied with the mean-field approximation [3,4], and the temperature phase diagrams were obtained with the Bethe approximation [5]. We performed a computer simulation of a spin-pseudospin model using the classical Monte Carlo method and a modified Metropolis algorithm on a 2D square lattice with periodic boundary conditions. Phase transitions and critical properties of a dilute magnet with frustration were investigated in the framework of the theory of finite-size scaling. The system demonstrates the 2D Ising universality class as it is far from frustration, while as the system approaches the frustrated state, significant changes are observed in the critical behavior of the system: spin (charge) metastable phase states are formed, first-order phase transitions occur, and the critical exponents for second-order phase transitions depend on the parameters of the model, i.e. the critical behavior of the system becomes non-universal (for example, see Fig. 1) [6]. Also, the critical behavior becomes non-universal with an increase in the density of the doped charge n in the non-frustrated state. In addition, temperature and ground state phase diagrams were obtained, and the features of the formation of phase states with an increase in the density of doped impurities in frustration were revealed. There is a wide variety of phase states with different properties in the ground state. If the spin exchange coupling is greater than the one for pseudospin (V/J≤1), there are actually two phases in the ground state, namely the charge order (CO) and the antiferromagnetic (AFM) order, which is unstable with respect to the phase separation into charge and spin subsystems that behave like immiscible quantum liquids. Various configurations of phase separation are formed depending on the value of n, viz., a charge/AFM droplet or a charge/AFM stripe. There are 5 phases in the ground state for V/J&amp;gt;1: AFM and “ferromagnetic” orders, and three types of CO. Analysis of the system in frustration has shown that the ground state of the system turns out to be degenerate not at one specific point, but in a whole range of parameters. Under identical calculation conditions, both AFM order and CO can form with a certain probability. Charge doping in a frustrated state leads to unusual effects. When the spin exchange coupling is strong (V/J≤1), AFM order changes to CO with decreasing temperature (or vice versa, depending on the value of n), as well as reentrant order-order phase transitions [7] occur, which is shown in Fig. 2. Thus, the competition between charge and magnetic orders, leading to frustration of the system, as well as charged impurities, significantly affect the properties of a two-dimensional Ising magnet.&lt;br/&gt;This work was prepared with the financial support of Competitiveness Enhancement Program - CEP 3.1.1.1-20.

**References:**

[1] Hovhannisyan V. V. et al., Physical Review E., Vol. 96, p. 062103 (2017)&lt;br/&gt;[2] Giacomin G., Springer, Vol. 2025 (2011)&lt;br/&gt;[3] Y. D. Panov et al., J. Supercond. Novel Magn., Vol. 29, p. 1077 (2016).&lt;br/&gt;[4] Y. D. Panov et al., J. Low Temp. Phys, Vol. 187, p. 646 (2017).&lt;br/&gt;[5] Y. D. Panov et al., JMMM, Vol. 477, p. 162 (2019).&lt;br/&gt;[6] D. N. Yasinskaya et al., Acta Phys. Pol. A., Vol. 137, p. 979 (2020)&lt;br/&gt;[7] D. N. Yasinskaya, V. A. Ulitko, Y. D. Panov, Phys. Solid State, Vol. 62, p. 1713 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fc9010fa0e9f0f0bf9f53632bb55fb8e.jpg)
Dependence of critical exponents for heat capacity and susceptibility on single-ion anisotropy Δ/J for V/J=0.2, n=0. Dark gray corresponds to the universality class of the 2D Ising model, light gray corresponds to non-universal critical behavior. White color corresponds to first-order phase transitions

![](https://assets.underline.io/uploads/markdown_image/1/image/33dac2d32c21ee256bf53ecc248d2123.jpg)
Temperature phase diagram for n = 0.15, V/J=1 near the frustration. The order type changes twice when the temperature decreases, i.e. the reentrant phase transition to AFM takes place

INTERMAG 2021

 Phase States and Critical Properties of a Dilute Magnet with Frustration

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Frustrated systems with two or more competing interactions have a wide variety of phases with unconventional properties and complex symmetry. The pseudospin formalism is a powerful method to study complex magnetic systems with various degrees of freedom. Pseudospin models of anisotropic magnets are widely used to describe the properties of binary alloys, classical and quantum liquids, dilute magnets, superconductors, and many other physical systems [1]. In addition, disorder caused by introduction of impurities and defects into the system significantly affects the critical behavior and phase states of magnets [2]. This work is devoted to modelling and theoretical description of phase and critical properties of a low-dimensional site-dilute magnet with frustration caused by the competitive charge and spin orders. We consider the Blume-Emery-Griffiths-type spin-pseudospin model, which was initially proposed [3] to consider the competition between spin and charge orders in underdoped high-Tc cuprates like La2-xSrxCuO4 in the normal state. The model considers the CuO2 planes as a system of charge triplets consisting of three many-electron mixed-valence centers [CuO4]7-;6-;5- (corresponding nominally to the copper ion states Cu1+;2+;3+). Two charge states Cu1+;3+ are associated with two components of the pseudospin S=1 triplet with MS=±1. The Cu2+ state associated with the MS=0 component is magnetic and has a conventional spin σ=1/2. Within this pseudospin formalism, the Hamiltonian of the static spin-pseudospin model includes Ising spin exchange coupling (J), on-site (Δ) and inter-site (V) density-density correlations, which have the form of single-ion pseudospin anisotropy and Ising exchange coupling in the language of pseudospin operators. The chemical potential μ is necessary to take into account the constant charge density doped in the CuO2 plane, which gives the concentration of doped charged impurities n. The properties of the spin-pseudospin model in the ground state were studied with the mean-field approximation [3,4], and the temperature phase diagrams were obtained with the Bethe approximation [5]. We performed a computer simulation of a spin-pseudospin model using the classical Monte Carlo method and a modified Metropolis algorithm on a 2D square lattice with periodic boundary conditions. Phase transitions and critical properties of a dilute magnet with frustration were investigated in the framework of the theory of finite-size scaling. The system demonstrates the 2D Ising universality class as it is far from frustration, while as the system approaches the frustrated state, significant changes are observed in the critical behavior of the system: spin (charge) metastable phase states are formed, first-order phase transitions occur, and the critical exponents for second-order phase transitions depend on the parameters of the model, i.e. the critical behavior of the system becomes non-universal (for example, see Fig. 1) [6]. Also, the critical behavior becomes non-universal with an increase in the density of the doped charge n in the non-frustrated state. In addition, temperature and ground state phase diagrams were obtained, and the features of the formation of phase states with an increase in the density of doped impurities in frustration were revealed. There is a wide variety of phase states with different properties in the ground state. If the spin exchange coupling is greater than the one for pseudospin (V/J≤1), there are actually two phases in the ground state, namely the charge order (CO) and the antiferromagnetic (AFM) order, which is unstable with respect to the phase separation into charge and spin subsystems that behave like immiscible quantum liquids. Various configurations of phase separation are formed depending on the value of n, viz., a charge/AFM droplet or a charge/AFM stripe. There are 5 phases in the ground state for V/J&gt;1: AFM and “ferromagnetic” orders, and three types of CO. Analysis of the system in frustration has shown that the ground state of the system turns out to be degenerate not at one specific point, but in a whole range of parameters. Under identical calculation conditions, both AFM order and CO can form with a certain probability. Charge doping in a frustrated state leads to unusual effects. When the spin exchange coupling is strong (V/J≤1), AFM order changes to CO with decreasing temperature (or vice versa, depending on the value of n), as well as reentrant order-order phase transitions [7] occur, which is shown in Fig. 2. Thus, the competition between charge and magnetic orders, leading to frustration of the system, as well as charged impurities, significantly affect the properties of a two-dimensional Ising magnet. This work was prepared with the financial support of Competitiveness Enhancement Program - CEP 3.1.1.1-20.

**References:**

[1] Hovhannisyan V. V. et al., Physical Review E., Vol. 96, p. 062103 (2017) [2] Giacomin G., Springer, Vol. 2025 (2011) [3] Y. D. Panov et al., J. Supercond. Novel Magn., Vol. 29, p. 1077 (2016). [4] Y. D. Panov et al., J. Low Temp. Phys, Vol. 187, p. 646 (2017). [5] Y. D. Panov et al., JMMM, Vol. 477, p. 162 (2019). [6] D. N. Yasinskaya et al., Acta Phys. Pol. A., Vol. 137, p. 979 (2020) [7] D. N. Yasinskaya, V. A. Ulitko, Y. D. Panov, Phys. Solid State, Vol. 62, p. 1713 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fc9010fa0e9f0f0bf9f53632bb55fb8e.jpg)
Dependence of critical exponents for heat capacity and susceptibility on single-ion anisotropy Δ/J for V/J=0.2, n=0. Dark gray corresponds to the universality class of the 2D Ising model, light gray corresponds to non-universal critical behavior. White color corresponds to first-order phase transitions

![](https://assets.underline.io/uploads/markdown_image/1/image/33dac2d32c21ee256bf53ecc248d2123.jpg)
Temperature phase diagram for n = 0.15, V/J=1 near the frustration. The order type changes twice when the temperature decreases, i.e. the reentrant phase transition to AFM takes place

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Two-dimensional arrays of interacting magnetic nanostructures allow the exploration of the many body physics associated with highly frustrated magnets in a convenient manner. Based on a lab-on-chip approach, artificially made structures can be viewed as experimental simulators of frustrated magnetism, complementing what can be done with chemically synthesized compounds. For example, collective magnetic phenomena such as emergent charge crystallization, magnetic moment fragmentation, and Coulomb phase physics have been recently evidenced in artificial systems. If the initial motivation was to realize an artificial ice magnet, a wide range of systems have been now investigated, including structures that have no counterparts in bulk materials. Whether they are chemically synthesized or nanofabricated, the spin dynamics of frustrated magnets generally freezes before magnetic ordering eventually sets in at very low temperature. Here, we will show how dynamical freezing can be bypassed in an artificial kagome ice to access low-energy states [1]. More specifically, we will demonstrate that the a priori dynamically inaccessible ordered ground state and fragmented spin liquid configurations can be obtained reproducibly, imaged in real space at room temperature, and studied conveniently (Figs.1 and 2). We will then identify the mechanism by which dynamical freezing occurs in the dipolar kagome ice. Besides, although artificially made structures were initially designed to address the physics of frustrated spin models, they can be used to investigate vertex models as well. Experimental strategy to fabricate artificial vertex models will be also briefly discussed [2].

**References:**

[1] V. Schanilec et al., Phys. Rev. Lett. 125, 057203 (2020). [2] Y. Perrin et al., Phys. Rev. B 99, 224434 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/06cf2e370a40d127454b84c97e8d5755.jpg)
Real space magnetic images with their associated spin-charge representations in an artificial kagome ice trapped within a fragmented spin state. Scale bar is 6 μm.

![](https://assets.underline.io/uploads/markdown_image/1/image/c53af84486a627fed47bc581cd73f8c2.jpg)
Analysis of the pairwise spin correlations.

Dynamical freezing in an artificial kagome ice magnet

Strongly correlated materials with multiple order parameters provide unique insights into the fundamental interactions in condensed matter systems and present opportunities for innovative technological applications. A class of antiferromagnetic honeycomb lattices compounds, A4B2O9 (A = Co, Fe, Mn; B = Nb, Ta), have been explored owing to the occurrence of linear magnetoelectricity. From our investigation of magnetoelectricity on single crystalline Co4Ta2O9, we discovered strongly nonlinear and antisymmetric magnetoelectric behavior above the spin-flop transition for magnetic fields applied along two orthogonal in-plane directions. This observation suggests that two types of inequivalent Co2+ sublattices generate magnetic-field-dependent ferroelectric polarization with opposite signs. The results motivate fundamental and applied research on the intriguing magnetoelectric characteristics of these buckled-honeycomb lattice materials.

**References:**

[1] N. Lee, D. G. Oh and Y. J. Choi, Scientific Reports, vol. 10, 12362 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/14735df7b8d80e6faf7c4ad0add6d601.jpg)
Fig. 1 Temperature dependence of the anisotropic ferroelectric polarization. (a–c) T dependence of Pa obtained by integrating the pyroelectric current after poling from 100 to 2 K in at Ha, Hb*, and Hc, respectively. Pa was measured at H = 1, 3, 5, 7 and 9 T. (d–f) T dependence of Pb* measured at Ha = 9 T, Hb*, and Hc, respectively. (g–i) T dependence of Pc measured at Ha = 9 T, Hb*, and Hc, respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/1dddc0b497f4c43b1b9e466269999736.jpg)
Fig. 2 Comparison of electric and magnetic properties. (a) Hb* dependence of Pa at T = 2 K. (b) Hb* dependence of the magnetodielectric effect along the a axis, MDa (%) = {ε′(H) − ε′(0T)} / ε′(0T) × 100 , measured with AC excitation of Ea = 1 V at f = 100 kHz and T = 2 K. (c) Hb* derivative of Mb* at 2 K.

 Highly nonlinear magnetoelectric effect in buckled honeycomb antiferromagnetic Co4Ta2O9

Introduction Multiferroic materials have been attracting much attention because they have multiple ordered (ferroelastic, ferroelectric, and ferromagnetic) states. In particular, magnetic and ferroelectric material has a property that magnetization M (electric polarization P) can be controlled by electric E (magnetic H) field. Such property is called “magnetoelectric (ME) effect”. In magnetic and ferroelectric material, there is also a possibility of observing an optical response that the rate of absorption is different between the cases that light enters from one direction and the opposite direction. Such a large nonreciprocal response in the visible light region was discovered in CuB2O4 [1]. The observed nonreciprocal response in light is thought to be originated from dynamical AC ME response. The present compounds, CaBaM4O7 (M=Co, Fe), have been attracting interest for their nontrivial magnetism because of the geometrically frustrated crystal structure consisting of triangular and Kagome layers. From the viewpoints of the studies of multiferroics, we have expected that the magnetic ordering couples with the spontaneous electric polarization P due to the crystal structure with a polar point-group of mm2. Indeed, we have observed the change of Pc induced by the weak ferromagnetic ordering in CaBaCo4O7 [2]. Then the magnetic-field Hab-induced giant variation in Pc was reported and the magnetostriction mechanism was proposed to explain the observed giant ME effect [3]. Also in the case of CaBaFe4O7, the ME coefficient Hαcc defined as △Pc=HαccHc with a maximum value of 39 ps/m was reported for the measurements of Hc-induced change of Pc at 80 K below the ferrimagnetic transition temperature of 275 K [4]. In this work, we have systematically investigated nonreciprocal DC ME response, i.e., crystalline (polar) direction dependence of ME coefficients for CaBaM4O7 (M=Co, Fe) single crystals. Especially, we focused on the electric-field (Ec)-induced magnetization (Mab or Mc) in CaBaM4O7 (M=Co, Fe), which had almost not yet been performed. Results and Discussion Figure 1 shows the Schematic crystal structure of CaBaM4O7 (M = Co, Fe). The space group of CaBaCo4O7 at room temperature is orthorhombic Pbn21, which is distorted and lowered symmetry from the higher one of hexagonal P63mc. Its (magnetic) point group is (m’m2’) mm2. Those of CaBaFe4O7 are Pbn21 and mm2, which are the same as CaBaCo4O7 [2,4]. Its magnetic point group is unknown yet. Both materials have quasi-triangular lattices and quasi-Kagome ones stacked along the c-axis direction. There exists multidomain structure within the orthorhombic ab plane in spite of no such one in the c axis. A spontaneous electric polarization along the c axis (Pc) is expected from the polar point group of mm2. Figure 2(i) shows the electric field dependence of the magnetization of CaBaCo4O7 in constant magnetic fields. The magnetic field (Hab) was applied within the magnetic easy ab plane perpendicular to the c axis, and the electric field (Ec) was applied along the c axis which is the direction of spontaneous electric polarization (Pc). The configuration among the external magnetic field, electric field, and crystalline direction (spontaneous electric polarizaion) is presented in the inset of Fig. 2(ii). When the electric field is applied in the parallel direction (p) to the crystalline direction, the magnetization increases as the electric field increases. Such trends can be clearly seen as solid symbols in Fig. 2(i). Conversely, in the antiparallel (a) case, the magnetization decreases with electric field (See open symbols). Figure 2(ii) shows the magnetic field dependence of Eα32 which is a component of linear ME tensor and defined as Mab≡Eα32Ec. Depending on the configurations between the electric field and the crystal direction, Eα32 shows opposite signs. The observed crystalline-direction (polarity) dependence of change in magnetization can be regarded as a DC nonreciprocal response. As is well known for the diode, nonreciprocal response is indispensable in device applications. Therefore, we explore the novel nonreciprocal phenomena as mentioned above in the present polar magnetic compounds, CaBaM4O7 (M = Co, Fe), for the future application such as “thermal diode”.

**References:**

[1] M.Saito et al., J. Phys. Soc. Jpn. 77, 013705 (2008). [2] H. Iwamoto et al., J. Phys: Conf. Ser. 400, 032031 (2012). [3] V. Caignaert et al., Phys. Rev. B 88, 174403 (2013). [4] V. Kocsis et al., Phys. Rev. B 93, 014444 (2016).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ae2bea3298433e5c1ccf14561452cfc9.jpg)
Schematic crystal structure of CaBaM4O7 (M = Co, Fe) projected onto the bc plane (a). Its quasi-triangular (b) and quasi-Kagome layers (c) are projected onto the ab plane. The rectangular boxes represent the boundaries of unit cell [2].

![](https://assets.underline.io/uploads/markdown_image/1/image/0c8e519eab7cbb2fc00b2b326156b7ec.jpg)
(i) Electric field dependence of magnetization in CaBaCo4O7. Solid symbols correspond to the parallel configuration between the electric field and the crystalline (polar) direction, and open ones to the antiparallel configuration. (ii) Magnetic field dependence of Eα32 (≡Mab/Ec) deduced from the data shown in (i). The inset is a schematic diagram of the configuration among the external magnetic/electric fields and the crystal direction.

 Polarity dependence of change in electric polarization (magnetization) induced by magnetic (electric) fields in CaBaM4O7(M=Co, Fe) single crystals

In rare-earth orthoferrites, strongly correlated order parameters have been thoroughly investigated, which aims to find multiple fuctionalities such as multiferroic or magnetoelectric properties. We have discovered highly anisotropic and nonlinear magnetodielectric effect from detailed measurements of magnetoelectric properties in single-crystalline orthoferrite, ErFeO3. Isothermal dielectric constant varies in shapes and signs depending on the relative orientations between the external electric and magnetic fields, which may be ascribed to the spin-phonon couplings. In addition, a dielectric constant with both electric and magnetic fields along the c axis exhibits two symmetric sharp anomalies, which are closely relevant to the spin-flop transition, below the ordering temperature of Er3+ spins, TEr = 3.4 K. We speculate that the magnetostriction form the exchange couplings between Er3+ and Fe3+ magnetic moments would be responsible for this relationship between electric and magnetic properties. Our results present significant characteristics of the orthoferrite compounds and offer a crucial guide for exploring suitable materials for magnetoelectric functional applications.

**References:**

[1] H. J. Shin, Y.J. Choi and N. Lee, Scientific Reports., 10:11825 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5564792e58f2025c698fb955501095ae.jpg)
Magnetodielectric effect of ErFeO3. Magnetodielectric (MD) effect defined as 
MD (%) = (ε′(H)−ε′(0T))/ε′(0T) × 100 for (a)–(c) a (MDa), (d)–(f) b (MDb), and (g)–(i) c (MDc) axes, respectively, at Ha, Hb , and Hc up to ± 9 T and T = 2 K.

![](https://assets.underline.io/uploads/markdown_image/1/image/7b3b7a8f4622c4c168fd19b029722ed0.jpg)
Temperature evolution of magnetodielectric effect along the c axis. (a)–(f) Hc dependence of MDc at T = 2, 2.5, 3, 3.5, 5 and 10 K. (g)–(l) Hc derivative of Mc and dMc/dHc measured at T = 2, 2.5, 3, 3.5, 5 and 10 K.

 Anisotropic and nonlinear magnetodielectric effects in orthoferritre ErFeO3 single crystals

The aim of this work is to establish the influence of deviation from oxygen stoichiometry on the properties of La-Sr manganites with manganese-substituting combination of divalent and quadrivalent ions having different electron configuration: Zn2+(3d10) and Ti4+(3p6). Polycrystalline manganites of La0.7Sr0.3Mn0.9(Zn2+0.5Ti4+0.5)0.1O3+γ compositions were prepared by ceramic processing. The sintering step was performed in air at 1473 K for 10 h. Obtained samples were then divided into three groups, which were exposed to heat treatments at 1223 K for 96 h at a partial pressure of oxygen in the gas phase of PO2 = 10-1 Pa, 10-8 Pa, and 101.3 kPa. All synthesized manganites were rhombohedral. Oxygen non-stoichiometry index (γ) of the samples of above-mentioned groups was calculated from the data on unit cell volume (V) according to algorithm proposed earlier [1] with the allowance for concentrations of Mn4+ and Mn3+ ions, anion and cation vacancies. As follows from Fig.1, unit cell volume decreases as a function of γ, and specific magnetization (σ) shows a tendency to increase almost within the measurement error. Temperature dependences of dμ(T)/dT, where μ(T) is magnetic permeability as a function of temperature T, are presented on Fig.2. Curie point defined as the temperature corresponding to the maximum of │dμ(T)/dT│, is equal to 219, 226, 229 K for manganites with values of γ = -0.008, 0.000, 0.009, respectively. One can see that temperature interval of “ferromagnetic-paramagnetic” transition is sufficiently wide (from 8 to 15 K), especially in stoichiometric manganite. Broadening of the transition interval can be associated with the formation of clusters, segregations, and magnetic inhomogeneities with various magnetization and transition temperature [2]. Manganite annealed in oxygen has the narrower transition interval than those annealed in vacuum, due to vacancy mechanism of cation diffusion, which smooths out spatial variations of the composition. Scanning electron microscopy studies have revealed the existence of microinhomogeneities having various configurations, including modulated structures. Manganite annealed at PO2 = 10-8 Pa has the highest absolute value of magnetoresistance: │MR│= 60 % in the field of 9.2 kOe at 120 K. Magnetostriction constant (λ) is maximal for a sintered sample having the oxygen non-stoichiometry index of γ = 0.004. At T = 140 K, it reaches gigantic value of λ = 7×10-3 and drops to 10-4 at 293 K. Interpretation of established regularities is discussed in terms of mechanisms of charge compensation with the allowance for formation of singly charged oxygen ions [3,4], diffusion processes, electron configuration and radii of substituents, double-exchange and Coulomb interactions.

**References:**

1. D. Merkulov, A. Badelin and V. Karpasyuk, Acta Physica Polonica A, Vol. 127, p.248 (2015) 2. V. Karpasyuk, A. Badelin, and I. Derzhavin, Journal of magnetism and magnetic materials, Vol. 476, p.371 (2019) 3. J. Mizusaki, N. Mori and H. Takai, Solid State Ionics, Vol. 129, p.163 (2000) 4. V. Karpasyuk, A. Badelin and D. Merkulov, Journal of Physics: Conference Series, Vol. 1347, p.012036 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f309c2e6369525ef9191f175045927e6.jpg)
Fig.1. Dependencies of unit cell volume (1) and magnetization (2) on non-stoichiometry index

![](https://assets.underline.io/uploads/markdown_image/1/image/2031f433a7b459ba7ce2ed1f8ab2163f.jpg)
Fig.2. Temperature dependencies of dμ(T)/dT for manganites with γ = -0.008 (1); 0.000 (2); 0.009 (3)

 Structural and electromagnetic characteristics of La-Sr manganite with paired substitution of Zn and Ti for manganese depending on oxygen content

A strong coupling between spin, orbital, charge, and lattice degrees of freedom determines the unique properties of mixed valence manganites [1]. A phase separation phenomenon plays an important role in the physics of these materials [1, 2]. However, mechanisms of spontaneous phase separation are still not fully understood that does not permit to control the process by means of the external factors such as temperature, magnetic field, and pressure. The charge ordering (CO), which is the spatial ordering of the Mn3+ and Mn4+ ions, is closely related to the phase separation and is one of the most interesting phenomena observed in the mixed valence manganites. Herewith, the CO state is observed in the different materials with the R3+1-xA2+xMnO3 general formula [3, 4]. There are studies that indicate the martensitic nature of the charge ordering state in the mixed valence manganites [5, 6]. In this work, the polycrystalline films Pr1-xSrxMnO3 with x=0.2 and 0.4 were investigated in the temperature range of 100-390 K using the electron magnetic resonance (EMR) spectroscopy in the X-band and the magnetic susceptibility measurements. The films thickness is 100-130 nm. Single-crystal zirconium oxide stabilized by yttrium (YSZ) was used as the substrate. The samples were prepared by dc magnetron sputtering with the “facing-target” scheme that allows transferring elements from a target to a substrate without changes in the composition. The magnetic susceptibility data showed that the Curie temperature (TC) of the films is 115 K for x = 0.2 and 215 K for x = 0.4. These values are significantly lower than for the single crystals of the same composition (150 K and 300 K, respectively). This situation implies the presence of the phase separation in the films and the detection of possible magnetic correlations above Tc. The presence of the Griffiths-like phase in the films above their TC was previously established using analysis of the EMR spectra [7]. This phase represents the short-range ferromagnetic correlations in the paramagnetic region. The Griffiths temperature (TG) is 145 K for x = 0.2 and 295 K for x = 0.4 and corresponds to TC of the single crystals of the same composition. New research shows the presence of the CO state in the films above their TG. Temperature dependents of the inverse magnetic susceptibility measured for the samples in the external magnetic fields of H = 0.1 - 30 kOe demonstrate a pronounced shoulder in the wide temperature range up to values above room temperature. The example is shown in the Fig. 1 for the film with x = 0.4. It is should note that the pronounced shoulder above TG was also observed on the temperature dependence of the inverse residual magnetization of the films magnetized in the field of H = 500 Oe. In the case of the film with x = 0.4, the shoulder width as well as the temperature near the charge-ordering transition (TNCO) decreases with the growth of the applied magnetic field. The TNCO dependence on the applied magnetic field was traced. Inset in the Fig. 1 shows the TNCO (H) dependence for the film with x = 0.4. In the case of the film with x = 0.2, the inverse magnetic susceptibility above TG exhibits an ambiguous behavior in the high magnetic fields. For materials in the ferromagnetic region, the resonance line expands with decreasing temperature. The resonance line broadening observed for manganites above their TC (or TG) with increasing temperature is usually explained by the presence of spin-lattice relaxation and magnetic polarons. The temperature dependence of the resonance linewidth for the film with x = 0.2 indicates the presence of the charge ordering in the range of T = 200-350 K (Inset in the Fig. 2). For the film with x = 0.4, a maximum of about 350 K is also assumed (Fig. 2). The temperature hysteresis of the inverse magnetic susceptibility of the films is observed in the weak magnetic field above their TG. The example is shown in the Fig. 1 for the film with x = 0.4. This behavior is a direct evidence of the martensitic nature of the CO state [8]. The high-temperature charge ordering (TNCO = 600 K) was previously observed in the Bi-Sr manganite with x = 0.25 [3]. This behavior was explained by the exclusive role of the 6s2 electrons of Bi3+. The role of the 6s2 electrons of Pr3+ and the effect of intrinsic strains in the samples other than strains associated with grain boundaries or substrate lattice mismatch in films are discussed.

**References:**

1. E. Dagotto, T. Hotta, A. Moreo, Phys. Rep., Vol. 344, p. 1 (2001) 2. A. Krichene, W. Boujelben, S. Mukherjee, et al., Acta Materialia, Vol. 131, p. 491 (2017) 3. J.L. Garcia-Munoz, C. Frontera, M.A.G. Aranda, et al., J. Solid State Chem., Vol. 171, p. 84 (2003) 4. D.M. Polishchuk, A.I. Tovstolytkin, E.L. Fertman, et al., J. Magn. Magn. Mat., Vol. 410, p. 109 (2016) 5. V. Podzorov, B.G. Kim, V. Kiryukhin, et al., Phys. Rev. B, Vol. 64, p. 140406 (2001) 6. S. Dhieb, A. Krichene, N. Chniba Boudjada, et al., J. Phys. Chem. C, Vol. 124, p.17762 (2020) 7. Yu.E. Samoshkina, M.V. Rautskii, E.A. Stepanova, et al., J. Exp. Theor. Phys., Vol. 125, p. 1090 (2017) 8. X. Liang, J. Bai, J. Gu, et al., J. Mater. Sci. Technol,. Vol. 44, p. 31 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e101268a634e7fa06dad7150320c4203.jpg)
Temperature dependences of the inverse magnetic susceptibility for the film with x = 0.4. The curves were measurement in two modes at H = 100 Oe: cooling (FC) and heating (FH). Inset: dependence of the temperature near the charge-ordering transition (TNCO) on the applied magnetic field. The squares are the experimental points, the line is the fit and approximation.

![](https://assets.underline.io/uploads/markdown_image/1/image/01cf1051a8b0d0dd510c299280e7246d.jpg)
Temperature dependence of the inverse magnetic susceptibility at H = 3 kOe and the resonance linewidth in the X-band for the film with x = 0.4. Inset: temperature dependence of the inverse magnetic susceptibility at H = 3 kOe and the resonance linewidth for the film with x = 0.2.

 High-Temperature Martensitic Transformation in Pr-Sr Manganites

5d metals are used in electronic architectures because of their high spin-orbit coupling (SOC) leading to efficient spin ↔ electric conversion and strong magnetic interactions. When C60 is grown on a metal, the electronic structure is altered due to hybridisation and charge transfer. Previously, it has been shown that this can lead to the emergence of spin ordering [1]. This interfacial effect is also critical in spin filtering and spin transport effects [2]. We have studied the spin Hall magnetoresistance (SHMR) for YIG/Pt/C60 and YIG/Ta/C60. [3]. The SHMR at room temperature are up to a factor 6 higher than for the pristine metals, with the spin Hall angle increased by 20-60%. Here we studied YIG/PtMn with without C60. PtMn is an antiferromagnet that has been shown to have a strong spin Hall effect [4]. This will allow us to determine if the molecular orientation can play a role in the enhanced SOC observed in Pt. We aim to: investigate the mechanisms that generate spin orbit scattering at the hybrid conducting interface and maximise the effect. By fitting the SHMR data, we can extract the spin Hall angle which is significantly higher with the molecular overlayer. The SHMR saturates once the applied field saturates the magnetisation out-of-plane, at 0.1-0.15 T for a YIG film, and no higher than 0.5 T for any measured condition. However, above this field range, other contributions such as Koehler MR, localisation and the Hanle effect can result in significant linear contributions to the MR that would artificially enhance the SHMR ratio and spin hall angle [Fig1]. Thus, the spin Hall angle ΘSH is bigger for PtMn/C60 than PtMn, which we attribute to an enhancement of the spin orbit coupling (SOC) by the C60. Figure 2 shows the maximum SHMR measured as a function of the PtMn thickness for both pure metal and PtMn covered on molecules. Also, the PtMn/C60 SHMR value is increased after annealing the sample at 200 C.

**References:**

References: 1. F. Al ma’mari, et al., Nature. 524, 69—73 (2015) 2. M. Cinchetti, et al., Nature materials. 16, 507 (2017) 3. S. Alotibi, et al., arXiv preprint: 1912. 02712, 2020. 4. Y. Ou, Phys. Rev. B 93, 220405(R) (2016).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/081f905ccccdb5556742fbf743fdc34e.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/5ec866da85e77a56bbedc861a638dbe0.jpg)

 Effects of a Molecular C60 Interfaces on the Spin Hall Magnetoresistance of YIG/PtMn

Topological chiral semi-metal CoSi exhibit unusual quasi-particles excitations near the band crossing point, which have spin-1 and charge-2 chiral charge [1]. Like Dirac and Weyl semimetals, these semimetals also show some unusual electrical transport behavior, such as large magneto-resistance, mobility, and anomalous Hall effects. Therefore, we have performed temperature and magnetic field dependent electrical transport measurements on the topological chiral semimetal CoSi poly-crystals. We observed that while χ versus T indicates the paramagnetic nature of poly-crystals (inset of image1), 1/χ versus T behavior indicates that there is the presence of some weak antiferromagnetic exchange interaction at low temperature [2]. These poly-crystals show anomalous behavior in resistivity versus temperature measurements in the vicinity of such magnetic exchange interaction. The temperature and angle-dependent magneto-resistance (MR) measurements show negative behavior at low temperature, which is in contrast to the single crystal counterpart of CoSi, probably due to the presence of weak exchange interaction [3,4].

**References:**

 1. D. Takane, and T. Sato, Phys. Rev. Lett. 122, 076402, (2019). 2. Banik, S. et al. Phys. Rev. B 77, 224417 (2008). 3. X. Xu and S. Jia, Phys. Rev. B 100, 045104 (2019). 4. S.S Samatham, D Venkateshwarlu, and V Ganesan, Mater. Res. Express 1 026503, (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b58415af3c3b708d66c150d5bdbaeaab.jpg)
Temperature dependence of 1/χ showing the presence of exchange interaction at low temperature. Inset shows the temperature dependence of χ

![](https://assets.underline.io/uploads/markdown_image/1/image/18e6611ba53e53bfc851fc126014ccff.jpg)
Temperature-dependent magnetoresistance(MR) showing a change in MR from negative to positive as the temperature is increased

 Magneto-Transport Study on Topological Chiral Semimetal CoSi

Heusler alloys are materials with the composition X2YZ, where X and Y are transition metals and Z is the p-element. By the change of an element in the composition, new properties, e. g. the magnetocaloric effect, spin-polarization, or coexistence of ferromagnetism and superconductivity can be achieved. Those properties can be combined to achieve multifunctional Heusler alloys. Nowadays, new superconducting materials are being explored, such as HTC superconductors, superconducting magnets, and also as mentioned, ferromagnetic superconductors. Heusler alloy Ni2NbSn represents the superconductor with the ferromagnetic behaviour under the critical temperature of superconductivity. It would be difficult for the alloy Ni2NbSn to find practical usage since the critical temperature is 3.4 K at zero external magnetic field. One of the possibilities to increase the critical temperature can be the doping with various p-elements, to modify the lattice constant. In this topic, we decided to study the doped series of alloys Ni50Nb25Sn25-xZx, where Z is Ga, Ge, or Sb and x = 1, 2. Their structural, magnetic, and electric properties were analyzed to show the effect of modifying the lattice constant on the critical temperature of the Ni2NbSn Heusler alloy. This research was supported by the projects APVV-16-0079 and Slovak VEGA grant. No. 1/0053/19.

**References:**

T. Graf, C. Felser and S. S.P. Parkin, Progress in Solid State Chemistry, Vol. 39, p.1-50 (2011) T. Klimczuk, C. H. Wang and K. Gofryk, PHYSICAL REVIEW B, Vol. 85, p.174505 (2012)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9aa3b7f404eada4a41ac7bf2a0b0b864.jpg)
Hysteresis loops of alloys with 1% doping.

 Effect of doping on ferromagnetic and superconducting properties of Ni2NbSnZ (Z = Ga, Ge, and Sb) Heusler alloy

The study of quantum critical effects and more generally of the physical properties of “strange metals” is currently of high interest in condensed-matter physics [1]. In rare-earth based intermetallics, heavy-fermion behaviors and quantum criticality are mainly investigated in materials where Ce or Yb are alloyed with non-magnetic elements [2]. Quantum critical effects are then generally perceived at low temperature near the magnetic instability of almost trivalent 4f element. Recently, we showed that the situation is somewhat different in YbMn6Ge6-xSnx where intermediate valent Yb is alloyed with a ferromagnetic Mn sublattice. In this series of compounds, several very unusual phenomena have been evidenced using magnetic measurements, neutron diffraction and electronic spectroscopies [3-6]. That includes an abnormal thermal variation of the Yb valence [3,4], a record value for the Yb magnetic ordering temperature (up to TYb = 125 K [4,5]), a Yb magnetic instability occurring for far from trivalent Yb (υ ~ 2.73) and signatures of quantum criticality up to room temperature [6]. These unusual phenomena have been tentatively ascribed to the strong Mn-Yb exchange interactions. For a further understanding of the YbMn6Ge6-xSnx series of compounds (x ≥ 4.0), we have performed specific heat (Cp) measurements. Our results indicate that these alloys are heavy-fermion materials (γ &gt; 50 mJ.mol-1.K-2) and that the electronic specific heat coefficient reaches a maximum value γ ~ 280 mJ.mol-1.K-2 for compositions close to the Yb magnetic instability near x ~ 5.20 (Figure 1). Details about the analysis of the data will be presented on the poster together with a discussion of the results.

**References:**

[1] H. Zhao, et al., Nat. Phys. 15, 1261-1266 (2019). [2] H. V. Löhneysen, et al., Rev. Mod. Phys. 79, 1015 (2007). [3] T. Mazet, et al., Phys. Rev. Lett. 11, 096402 (2013). [4] T. Mazet, et al., Phys. Rev. B. 92, 075105 (2015). [5] L. Eichenberger, et al., Phys. Rev. B. 96, 155129 (2017). [6] L. Eichenberger, et al., Phys. Rev. B. 101, 020408 (R) (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f438e8a96f89b2fa974fad75794646cb.jpg)
Fig. 1: Composition dependence of the electronic specific heat 
coefficient γ in YbMn6Ge6-xSnx (x ≥ 4.0)

Phase States and Critical Properties of a Dilute Magnet with Frustration

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