Magnetic properties and their correlation with lattice dynamics in HoFe1-xCrxO3 (0 ≤ x ≤ 1) compounds

2.1(d) represents the particles of the compound after sintering. 2.2 Schematic diagram of X-ray diffraction (XRD) pattern. 3.6 (a) Intensity variation of Ag peak and (b) wavenumber shift of Ag. b) Variation of the band gap with respect to the Cr composition.

Perovskites

Crystal field effect

In general, the structure of perovskite compounds depends on the size ratio of the incorporated elements. The magnitude and nature of the crystal field effect depend critically on the symmetry of the local environment.

Figure 1.1: (a) Ideal perovskite ABO 3 with cubic structure (b) AO 12 cuboctahedra and (c) BO 6 octahedra.

Jahn-Teller distortion

For example, in the case of transition elements, due to the damping of the orbital momentum, there is a noticeable difference in the value of the theoretically calculated effective magnetic moment (eff g J J 1  B) and the experimentally measured values. Therefore, the 4f orbitals will not experience the crystal field effect of neighboring ions, making J = L + S in the case of rare earth elements.

Figure 1.3: Splitting of both e g and t 2g states in the octahedral environment due to Jahn- Jahn-Teller effect

Magnetism

• Diamagnetism
• Paramagnetism
• Ferromagnetism
• Anti-ferromagnetism
• Ferrimagnetism

Based on the interaction between the magnetic moments in the magnetic unit cell, different types of AFM arrangement are possible as shown in Fig. However, the magnitude of the magnetic moments in both sublattices will not be equal, leading to net magnetization.

Figure 1.4: Variation of reciprocal of magnetic susceptibility with temperature for para-, ferro- ferro-, and antiferromagnetic materials

Magnetic interactions

• Exchange interaction
• Direct exchange interaction
• Indirect exchange interaction
• Super exchange interaction
• Magnetic properties

Weak ferromagnetism in the orthoferrites has been attributed to the antisymmetric exchange interaction (DM interaction). In the figure, blue sphere is holmium (Ho), the sphere in the octahedron is iron (Fe) and red sphere indicates oxygen (drawn using VESTA Software).

Figure 1.6: Schematic representation of exchange interactions of (a) antiferromagnetic and ferromagnetic orientation in direct interaction, (b) the indirect interactions through conduction electrons, (c) antiferromagnetic and ferr

Magnetocaloric effect (MCE)

Basic theory of magnetocaloric effect

MCE can be realized through the thermodynamic process, which relates the magnetic variables (magnetization and magnetic field) to entropy and temperature. The change in magnetic entropy SMT H, for an adiabatic process can be calculated by integrating equation 1.20,.

Motivation and objectives

Band gap tuning and orbital mediated electron-phonon coupling

To our knowledge, the electron-phonon coupling has so far only been observed in the Jahn-Teller active compounds. However, it would be very interesting if we can observe the electron-phonon coupling in the inactive Jahn-Teller connection.

Magnetic and magnetocaloric properties

To achieve our goal, in the present work, Cr was chosen to apply the chemical pressure at Fe site of HoFeO3 compound. Therefore, in the present work, we have devoted our efforts to investigate the magnetic and local interactions in HoFe1-xCrxO3 (0 ≤ x ≤ 1) compounds by magnetization measurements and Mössbauer spectroscopy.

Spin – phonon coupling

Recently, the role of spin-phonon coupling in the stabilization of the ferroelectric order in rare earth chromites/ferrites/manganites (RMO3 with M = Cr, Fe, Mn) has been reported [134-136]. In yet another study, the crucial role of spin-phonon coupling in inducing FE order in GdCrO3 compound has been well manifested by Bhadram et. Therefore, there has been an intense debate about whether the spin-phonon coupling leads to structural change in the HoCrO3 compound.

Solid state reaction method

The driving force for sintering is the reduction of the surface free energy (interfacial free energy) of the consolidated particle mass. The total surface free energy of the compact powder is expressed as γA where γ represents the specific surface energy and A denotes the total surface area of ​​the compact powder. Basically, in the solid-state route, the replacement of the solid-vapor interface by the solid-solid interface gives the reduction of the interfacial energy.

Figure 2.1: Schematic representation of different stages of sintering process [141]. Fig

X-ray diffraction (XRD)

Rietveld refinement

Rietveld refinement was a most accurate method to accurately determine the structural parameters of the compound [144]. Here yi and yc,i represent the observed point (experimental) and the calculated point respectively, while a' indicates the number of data points. The total number of experimental points and the number of refined parameters are denoted by n and p, respectively.

Raman spectroscopy

Rayleigh scattering: the frequency of the emitted photon would be the same as the incident radiation. Stokes Raman scattering: the frequency of the emitted photon is lower than the frequency of the incident radiation. Anti-Stokes Raman scattering: the frequency of the emitted photon is higher than the frequency of the incident radiation.

Figure 2.3: Schematic of the energy level diagram of the Raman scattering.

UV-Vis-NIR spectrophotometer

In this thesis, the optical absorbance of the samples was measured at room temperature using a Perkin Elmer Lambda 1050 UV-Vis-NIR spectrophotometer in the wavelength range 200 - 800 nm.

Mӧssbauer spectroscopy

The detector measures the γ-ray transmission through the compound which can be used to deduce the absorption. This change in rate can be measured using the isomer shift that arises due to the slight change in the Coulomb interaction between the nuclear and electric charge distributions, which are associated with the change in the size of the 57Fe nucleus in the I = 3/2 state and I = 1/2 state. The first effect is due to the electric quadrupole moment of the excited 57Fe nucleus (the ground state with I = 1/2 of 57Fe has no electric quadrupole moment), when the nucleus is subjected to an electric field gradient, which leads to the splitting of I = 3/2 condition in a double.

Figure 2.4: Schematic illustration of the principles of Mӧssbauer technique. 57 Co decays slowly into an excited state of the 57 Fe nucleus

Magnetization measurement techniques

Vibrating sample magnetometer (VSM)

The sample is attached to the bottom of a sample container, which consists of three parts. A detachable quartz rod, which can be attached to the bottom of the copper tube, is the second part. The third part is the sample holder, which is attached to the bottom of the quartz rod.

Figure 2.6: Schematic diagram of vibrating sample magnetometer (VSM).

Magnetic property measurement system (MPMS)

This detection coil is connected to the input coil by the superconducting wires as shown in Fig. showed. When the sample moves through the pickup coil, an induced current will be produced in the coil that is proportional to the magnetization of the sample in the SQUID. Monitoring the output voltage of the SQUID as a function of the sample temperature makes it possible to detect changes in the sample magnetization with temperature.

Figure 2.7: Schematic diagram of DC SQUID (superconducting quantum interference device) [150]

Physical property measurement system (PPMS)

Heat capacity measurements were performed in the high vacuum so that the thermal conductivity between the sample platform and thermal bath is dominated by the conductivity of the metal wires. The heat capacity of the sample was determined by subtracting the heat capacity of the addenda from the total heat capacity. The characterization of HoFe1-xCrxO3 (0 ≤ x ≤ 1) compounds and the analysis of the results obtained are presented.

Figure 2.9: Thermal connections to sample and sample platform in PPMS Heat Capacity Option [152]

Experimental details

Structural properties

The increase in the intensity of the peak at about 670 cm-1 is observed only in the doped compounds as shown in Fig. The broadening of the peak around 670 cm-1 with increasing the amount of Cr3+ ions in the Fe3+ site can be related to structural disorder. 3.6 (b), this can be attributed to the compressive strain produced in the material by incorporating the Cr3+ ion into the iron site.

Figure 3.2: (a) Variation of lattice parameter with Cr composition. (b) Variation of tolerance factor (circle symbol) and FeO 6 average tilt angle (square symbol) with Cr composition

Optical properties

The direct band gap value for HoFeO3 and HoCrO3 is calculated as 2.07 eV and 3.26 eV respectively. 3.8 (b) and for compounds with a combination of Fe3+ and Cr3+, it is evident that the band gap decreases with Cr3+. Further increase in Cr3+ content results in increased band gap value and a maximum value of 3.26 eV at x = 1.

Figure 3.7: Absorption spectra of HoFe 1-x Cr x O 3 (0 ≤ x ≤ 1) compounds.

Conclusions

When x > 0.5, the width of the available unoccupied d orbitals of Fe3+ in the conduction band decreases, which can lead to a shift of the minimum conduction band to higher energies (as shown in Fig. From the results above, it is indeed possible to tune the band gap in rare earth orthoferrites and other compounds with similar structure by controlling the Fe3+/Cr3+ ratio.In this chapter we demonstrate our efforts in realizing the magnetic, hyperfine and magnetocaloric properties of compounds HoFe1-xCrxO3 (0 ≤ x ≤ 1) .

Experimental details

Physically, J denotes the strength of the exchange interaction between a pair of the closest magnetic ions in the orthoferrites. 183] observed a decrease in TN in Pr1-xSrxFeO3 compounds due to an increase in the oxidation state of Fe from Fe3+ to Fe4+. With an increase in the concentration of Cr3+, the strength of AFM interaction decreases, resulting in a decrease in the internal magnetic field experienced by the Fe3+ ion at 300 K.

Figure 4.2: Variation of Néel temperature T N of HoFe 1-x Cr x O 3 (0 ≤ x ≤ 1) compounds with Cr 3+ concentration

Magnetocaloric properties and nature of magnetic phase transition

The QS value increases with an increase in the Cr composition and is quite sensitive to compounds x ≥ 0.5. From the above equation 4.3, it can be observed that the value of –ΔSM depends on both the values ​​of magnetization (M) and. The large values ​​of –ΔSM in all compounds can be attributed to the evident metamagnetic transition and Ho3+.

Figure 4.6: First quadrant magnetization isotherms around (a – b) SR transition related to

Significant change in the value of Cp (H, T) is not evident up to the maximum magnetic field of 70 kOe. It is well known that magnetic materials with large value of –ΔSM and ΔTad are needed for refrigeration application [101]. It is clear that the value of ΔTad increases with the increase of the applied magnetic field and reaches a maximum value of 0.41 K around TN.

Figure 4.11: (a) Variation of specific heat C p with temperature (T) at different magnetic fields (b) subtraction of phonon and electron contribution using third order polynomial from the specific heat data

Conclusions

According to Equation 4.6, a large value of ΔTad can be expected to occur around the PM - AFM transition since the rate of change of the magnetization is large as the temperature increases. The variation of ΔTad with respect to the magnetic field (H) around the AFM ordering (TN) is shown in the graph of Figure H. It shows that the metamagnetic transitions prevail in the low field regime of M vs.

Experimental details

Room temperature Raman spectroscopic studies

In the case of the HoCrO3 compound, twelve phonon modes have been observed, as shown in Fig. On the other hand, the intensity of most Raman modes appears to be suppressed in the case of the HoCr0.5Fe0.5O3 compound, as shown in Fig. However, we exclude the possibility of the above origin for the presence of Raman mode around 670 cm-1 in the HoCr0.5Fe0.5O3.

Table 5.1: The symmetry analysis of the Raman modes in HoCr 1-x Fe x O 3 (x = 0 and 0.5) compounds recorded at room temperature

Magnetic properties

In this thesis, we essentially investigated the correlation between the structural and magnetic properties of HoFe1-xCrxO3 (0 ≤ x ≤ 1) compounds. White, Review of recent work on the magnetic and spectroscopic properties of the rare-earth orthoferrites, J. Auluck, Electronic and magneto-optical properties of rare-earth orthoferrites RFeO3 (R= Y, Sm, Eu, Gd and Lu), J .

Simon, High-throughput screening of the propylene and ethanol sensing properties of rare-earth orthoferrites and orthochromites, sensors and actuators B. Sampathkumaran, Effect of rare-earth (Er and Gd) substitution on the magnetic and multiferroic properties of DyFe0.5Cr0 .5O3 , J .

Figure 5.3: (a – e) variation of peak position pertinent to Raman modes of B 2g (2), A g (4), A g (5), B 2g (3) and B 3g (3) respectively

Temperature dependent Raman scattering studies

Conclusions

Suib, Narayan Poudel, Bernd Lorenz and Menka Jain, Magnetic and Magnetocaloric Properties of HoCrO3 Tuned by Selective Rare Earth Doping, Phys. Garg, Compositional dependence of structural parameters, polyhedral distortion and magnetic properties of gallium ferrite, Sol. Poster presentation entitled "Magnetic and magnetocaloric properties of HoFe1-xCrxO3 (0≤x≤1) joints" at the 62nd Annual Conference on Magnetism and Magnetic Materials (MMM2017) held November 6-10, 2017 at The David L.