Rare Earth Based Iron Garnet – A Survey on Its Magnetic Properties

Garnet is a well-known material for a long-time by the scientific community but still today scientists are focusing on it due to the rapid application-based development of this material. When rare earth iron garnets (REIG) are formed by substituting the rare-earth ions with unfilled 4fn orbitals, the magnetic properties of the iron garnets exhibit an interesting characteristic. For rare earth elements, the 4f electrons are shielded from the crystal field as these are surrounded by 5s, 5p, or 5d orbitals. That is why the exchange field between rare earth ions is much smaller than that between iron-iron and rare earth-iron. The magnetic moment of REIG will be both due to the orbital and spin moment. The magnetization of REIG at different temperatures (T) is due to the dominant contribution of different sublattices. At high and low T, the dominant sublattices are iron and rare earth sublattices respectively. The magnetic and non-magnetic ion substitution in REIG also play a very important role in deciding their magnetic property. In this review, we have tried to figure out the basic underlying physics behind the origin of remarkable magnetic behavior in REIG.


Introduction
Since the discovery of the fascinating properties of rare earth garnet by Forestier and Guiot-Guillain [1,2], it has become a potential candidate in various fields such as microwave applications, highquality filters, oscillators, spintronic devices, phase shifters, and many magneto-optical devices due to its unique electromagnetic, controllable magnetic, magneto-optical, magnetic compensation, mechanical, and thermal properties [3,4].The rare earth elements (REE) are a group of 15 elements that are located in the lanthanide series of the periodic table of elements.Scandium and yttrium are also a part of this categorization; although they are not true REEs.This is because they exhibit similar properties as that of the lanthanides and often found in the same mineral as the lanthanides [5].Garnets are a versatile and widely distributed mineral that can be found in wide range of rock types around the world.Their diverse occurrence and properties make them a valuable resource for a range of industrial and scientific applications.A mixture of REE and iron along with the silicate mineral garnet forms rare earth-iron garnet (REIG).This composition results in unique properties like high magnetic permeability and high electrical resistance [6] etc. that can be fine tuned by altering the composition of the material.In this article, we have discussed briefly about the basic understanding of magnetism in different types of REIGs.The cubic symmetry structure of garnet [9]; with copyright permission from the journal.
REIGs are ferrimagnetic in nature.This behaviour is a result of the exchange interaction between the Fe ions at the octahedral and tetrahedral sites mediated through oxygen anion.This interaction is crucial in deciding the magnetic properties of garnet materials, such as their magnetic ordering temperature and magnetic anisotropy.This interaction can be controlled through the use of various doping techniques, allowing for the manipulation of the crystal structure as well as the magnetic properties of the material.In the following section, we will discuss in detail about the magnetic exchange interaction of REIGs.

Magnetic properties of REIGs
REIG is a type of magnetic material known for its high magnetic permeability, strong magnetic anisotropy, low magnetic loss, and high-frequency properties.These properties make it a potential candidate in the field of modern technologies like microwave application due to ferromagnetic resonance [10], spintronics applications [11], wide range of optical devices [12], Spin wave logic devices [13], magnetic data storage devices [14], etc.The magnetic properties of REIG depend on the composition of the material and the arrangement of the magnetic ions.Additionally, the magnetic properties of REIG can be easily controlled through external magnetic fields, making it a versatile material for magnetic applications.
In REIGs, the magnetic ions are typically rare earth elements with partially filled d or f electron shells, which give rise to the magnetic moments.The exchange interaction between them is responsible for their alignment, so as to minimize the total energy of the material [15].This quantum mechanical phenomenon was explained by Heisenberg in accordance with the Pauli exclusion principle.The exchange interaction between the two localized spins Si and Sj in terms of the Hamiltonian is given by, where Jij is the exchange coupling constant which is a measure of the strength of the interaction between neighbouring magnetic moments in a material.It determines the relative orientation of magnetic moments in a material.As a result, it affects the magnetic properties of the material such as its magnetic anisotropy and magnetization.The value of the exchange coupling constant is positive for ferromagnetic materials and negative for antiferromagnetic materials [16].The exchange field between different ions in REIG in ascending order are rare earth-rare earth, rare earthiron, and iron-iron [17].This is due to the shielding effect of the RE 4f electrons from the crystalline environment.But due to the strong spinorbit coupling in this case, these materials exhibit a strong magnetic anisotropy [18].The electrostatic interaction energy between 4f electrons and the crystal field results in the anisotropic energy per rare earth atom.Without the application of a magnetic field, the magnetization vector aligns itself along the magnetic easy axis to minimize the energy within the material [19].REIGs magnetic properties also depend on microstructural parameters like grain/particle size, porosity, defects and crystalline volume fraction, etc.With larger grain size, the density of the sample increases which leads to the presence of better magnetic domain movement (growth of the domain, domain walls movement, and domain spin rotation [20,21].This will result in the enhancement of magnetic permeability.Most of the garnet reveals magnetic reversal at compensation temperature (Tcomp) which occurs due to the equality of the magnetic moments in dodecahedral sublattice with that of octahedral and tetrahedral together.This behaviour is shown in Fig. 2. When the temperature is less than Tcomp, rare earth sub-lattice dominates over the other sublattices; whereas at a temperature greater than Tcomp iron sub-lattices are dominant.The schematic diagram for this magnetic moment dominance in the sublattice at different temperatures is explained in Fig. 3(a) and 3(b).The absence of Tcomp in some cases is due to the occupancy of dodecahedral sites by ions that are either nonmagnetic or RE with a small magnetic moment.In the REIG family, yttrium iron garnet (YIG), is the most explored and interesting garnet having applications as a magnetic insulator [23], magnonics [24], tunable magnetic qubit coupling [25], and many more.This extensive analysis is due to its ultralow Gilbert damping parameter [26,27] which makes it a perfect material for these applications.Apart from this, substituting Y with other RE elements like Gd [28,29], Dy [30], Tm, [31] Ho, Er, Yb [32], etc. have also attracted attention due to their complex magnetic structures that allow the alteration of the magnetic properties.In the subsequent section, we will provide a concise overview of the recent advancements made in the magnetic properties of these materials.

Magnetic properties of YIG
The magnetic properties of YIG are due to a combination of exchange interaction, magnetic anisotropy, magnetic moment, Curie temperature, magneto-optic effect, and spin wave excitations.Y 3+ ion does not have any magnetic moment because of its electronic configuration (4f 0 ).The ferrimagnetism in YIG is due to the superexchange interaction between the 3Fe 3+ ions at tetrahedral and 2Fe 3+ ions at octahedral sites mediated through oxygen ions.This interaction leads to collective excitations known as spin waves or magnons.These excitations have quantized energy and can propagate through the crystal lattice, making YIG a useful material for studying spin wave physics and for developing magnon-based devices.Due to the fascinating magnetic properties (high saturation magnetization, strong magnetic anisotropy, etc.) of YIG, many researchers have tried to fine-tune its properties by performing the cationic substitution at Fe and Y sites.YIG exhibits an excellent magneto-optical effect, which means that its optical properties (such as refractive index and polarization) can be altered a magnetic field.Mao et al. [33] have substituted Ce in YIG and have shown that lower doping (x ≤0.2) density can increase the saturation magnetization and remnant magnetization, while for higher doping concentration an extra phase is formed inside the sample which reduces these values.
When YIG is doped with erbium (Er), the magnetic moment is not influenced much over a wide temperature range except below 30K where the unpaired 4f electrons are coupled antiparallelly with the 3d electrons of iron cations [34].Thus Er:YIG exhibits antiferromagnet-like behaviour at this lower temperature whereas above this and at room temperature it exhibits ferromagnetic behaviour.Bsoul et al. [35] have substituted Ga in Er-doped iron garnets Er3Fe5-xGaxO12 (0.0 ≤ x ≤ 0.8) and obtained a significant change in the temperature-dependent behaviour of the rare earth and iron sub-lattices and a reduction of the overall magnetization above the Tcomp.Also, they observed the decrease in Curie temperature with the increase of x.This occurs because of the substitution of magnetic ion (Fe 3+ ) by the non-magnetic ion (Ga 3+ ) that leads to decrease in the strength of super exchange interactions.This means nonmagnetic ion substitution in this case significantly reduce the magnetization over Tcomp.
The doping of YIG with In [36] or Ni [37] or Ca [38,39] increases the magnetic moment of the octahedral sub-lattice.The substitution also makes it a charge-uncompensated material by either Fe 4+ or Fe 2+ formation or oxygen vacancies formation to ensure the charge neutrality of the lattice.This property makes them a potential material for device application.

Magnetic properties of Gadolinium iron garnet (GdIG)
GdIG is a ferrimagnetic insulator that exhibits a large magneto-optical activity and has low magnetic damping which means that spin waves can propagate over long distances without significant energy loss.In GdIG, the Gd 3+ ions are in the S state with J = 7/2 and are magnetized parallel to the Fe 3+ ions present in octahedral sites.Thus, when the crystalline electric field is compared with the exchange field, it can be neglected [40].The exchange field in the lattice in ascending order is between the Gd ions, the Fe and Gd sublattice, and the two iron sublattices.The material exhibit temperature-dependent magnetization as shown in Fig. 2 and at Tcomp, the magnetic moment of the Fe and Gd sublattices cancel each other.The compensation temperature for this material is close to room temperature (286−295 K) [41][42][43][44][45]. Above Tcomp, how spontaneous magnetization may be increased, Nguyet et al. [46] suggested a mechanism for that.In this mechanism at high temperatures, Gd and Fe ions that are present on the surface layer, their spins are largely decoupled and the spins of Fe ions at the surface align themselves along the magnetic moments of the core.The magnetic anisotropy which is largely influenced by the presence of a magnetic compensation point can be fine-tuned in GdIG samples by preparing it on a different substrate and thereby varying the film strain [47].The magnetic behaviour is also influenced by inter-particle interactions.GdIG has been extensively studied for its properties related to the Spin Seebeck effect (SSE) [48,49].This is a phenomenon where a temperature gradient applied to a magnetic material generates a gradient in the magnon chemical potential, which in turn drives a magnon spin current.High-energy exchange magnons, which have a large energy compared to the thermal energy, can overcome the damping in the material and travel long distances, leading to a strong SSE signal [29].The Spin Seebeck effect in GdIG has several unique features that make it attractive for spintronics applications, energy harvesting, and thermal management.Doping GdIG with a non-S-state ion like erbium (Er 3+ ) ion, the orbital angular momentum is quenched by the crystalline electric field.The exchange field along with the crystal electric field play a significant role in making double conical arrangement of Er 3+ moments relative to the easy direction of the magnetization [40].Thus, Er doping can enhance the magnetic anisotropy and saturation magnetization thereby making it an interesting material for magneto-optical and microwave devices [50].Bismuth (Bi) substitution for gadolinium (Gd) in the GdIG crystal can lead to an increase in the Curie temperature which is attributed due to the fact that Bi 3+ ions are larger than that of Gd 3+ , thereby leading to the distortion of the dodecahedral site.This distortion may influence the Fe-O-Fe super exchange interactions in the structure [51].Y 3+ has a similar ionic radius as Gd 3+ but a higher magnetic moment, and when it substitutes Gd 3+ in the lattice, it affects the magnetic interactions between the Fe 3+ ions in the structure.This can lead to changes in the magnetic anisotropy, saturation magnetization, and other magnetic properties of the material [52].In addition to these doping, other dopants have been studied in GdIG, including cobalt (Co), calcium(Ca), cerium (Ce), Ruthenium(Ru) and manganese (Mn) etc. [53][54][55][56][57][58][59].These dopants can affect the magnetic properties of GdIG in various ways, including changes in magnetic ordering, magnetic anisotropy, and magnetization.

Magnetic properties of dysprosium iron garnet (DyIG)
The main advantage of Dysprosium iron garnet (DyIG) over other magnetic materials is its high saturation magnetization, which makes it ideal for use in high-field magnets.It also has a very high Curie temperature, making it suitable for use in high-temperature applications.It is a type of ferrimagnetic material that exhibits a large Faraday rotation effect, which is a phenomenon where the polarization plane of linearly polarized light is rotated in the presence of a magnetic field.This garnet has a particularly large Faraday rotation compared to other magnetic materials due to its high magnetic anisotropy (due to strong spin-orbit coupling) and high magnetic susceptibility.This property makes it useful in a number of applications, including in the field of magneto optics as a Faraday rotator, circulator, isolator, data storage, and magnetic field sensors [60] etc.In these devices, DyIG is used to selectively transmit or reflect light based on its polarization state, which can be controlled by an applied magnetic field.The reason of its large Faraday rotation is due to the strong interaction between the magnetic moments of the dysprosium ions and the applied magnetic field.Doping Dysprosium iron garnet (DyIG) with other elements can modify its magnetic properties.Doping DyIG by Ga, further can enhance the magnetic anisotropy resulting in a larger Faraday rotation angle [61].Ga-doped DyIG has been used in magneto-optic devices such as optical isolators and circulators.Co doping can increase the magnetic moment of DyIG and enhance its magnetization dynamics.Co-doped DyIG has been studied for its potential use in microwave devices and magnetic sensors [60].Al doping can reduce the magnetic anisotropy of DyIG, which can reduce its Faraday rotation angle [62].It was shown by Rekha et al. [63] that magnetic property of DyIG (doped with Mn) can be controlled with respect to cationic distribution at different sites, the crystallite size and surface morphology of grains, porosity (that affects the magnetization process), spin-orbital interaction between the cations.Thus Mn-doped DyIG or doping DyIG with other elements can lead to interesting modifications of its magnetic properties, which can make it useful for a variety of applications in magnetics, spintronics, and magneto-optics.
Depending on the sample preparation technique and chemical composition, different garnet materials may have different values of the magnetic parameters like permeability, magnetic loss, magnetic anisotropy, saturation magnetization, Curie temperature, frequency etc.These properties are compared and tabulated in Table 1.

Table 1.
Comparison of magnetic properties of different garnet materials.

Magnetic properties of other iron garnets
There are many other REIGs with their fascinating magnetic properties.In the small scope of the article, it is not possible to cover them all.So, here in this section we will discuss in brief about the magnetic properties of other REIGs where the rare earth elements are Ho, Sm, Er etc. Holmium iron garnet (HoIG) [74], Erbium iron garnet (ErIG) [75], Terbium iron garnet (TbIG) [76] exhibits high magnetic anisotropy, magnetic ordering, low magnetic damping making it useful in research on magnetism and magnetic materials.At the compensation temperature, they exhibit an umbrella-like magnetic structure as shown in Fig. 2. Compared to other REIGs, HoIG has large room temperature magneto-electric coupling, which is the coupling between magnetic and electric orders [77].The magnetic domain wall pinning in HoIG leads to a complex magnetic behavior that is highly dependent on the temperature and the strength of the external magnetic field [78].Samarium iron garnet (SmIG) exhibits a relatively weak magnetic anisotropy and does not exhibit magnetic domain wall pinning.Rather, SmIG exhibits a phenomenon called spin-reorientation, where the magnetic orientation of the material changes with changing temperature or applied magnetic field.This property makes it an interesting candidate for magnetic field sensors with high sensitivity and accuracy, magnetic storage etc [79,80].Thulium iron garnet (TmIG) has recently been found to exhibit spin orbit torque (SOT) effects [81].The SOT effect is due to the strong spin-orbit coupling of the thulium ions in the material.This coupling allows the thulium ions to transfer angular momentum to the magnetic moments in the material.SOT can be used to manipulate the magnetic state of a material without the need for an external magnetic field, which could lead to more efficient and compact devices.The discovery of SOT in TmIG has potential implications for the development of spintronic devices such as magnetic memory and logic devices.
Thus from the above discussion, it is understood that this class of ferrites exhibit interesting magnetic properties that make them promising materials for various technological applications such as magnonics, quantum information processing, high entropy ceramics, biomedical applications [82][83][84] etc.Their magnetic properties depend on their specific composition, cationic distribution with variety of dopants, magnetocrystalline anisotropy, domain formation, spin orbit coupling etc. [85] having different magnetic and optical properties.Apart from this, the magnetic properties can also vary depending on the synthesis method, crystal structure, and sample quality.

Conclusion
REIGs are considered to be the important technological magnetic materials which find multiple applications in major industries like electrical, optical, magnetic, magneto-optical, microwave integrated circuits and biomedical etc.Though they are having unique magnetic properties, yet there is no unified theory which can explain their magnetic properties with different dopant and host combination.The purpose of this article is to give an outline about the basic physics behind the origin of the magnetic properties of these systems.In the limited scope of the article, it is difficult to discuss all iron garnet substituted with different rare earth elements, so we have discussed in brief about the magnetic properties of different REIGs on one platform.
Fig.1: The cubic symmetry structure of garnet[9]; with copyright permission from the journal.

Fig. 3 :
Fig. 3: The schematic diagram of magnetic moment dominance in the sublattice for the temperature (a) T< Tcomp (b) T> Tcomp.The sublattices a, d, and c refer to octahedral, tetrahedral and dodecahedron respectively.[22, p-181].