# The effect of antisite disorder on magnetic and exchange bias properties of
Gd-substituted Y2CoMnO6 double perovskite.

Anasua Khan  Sarita Rajput  Department of Physics, Indian Institute of
Technology Roorkee, Roorkee-247667, India  M. Anas  Department of Physics,
Indian Institute of Technology Roorkee, Roorkee-247667, India  V. K. Malik
Department of Physics, Indian Institute of Technology Roorkee, Roorkee-247667,
India  T. Maitra  Department of Physics, Indian Institute of Technology
Roorkee, Roorkee-247667, India  T.K Nath  Department of Physics, Indian
Institute of Technology, Kharagpur-721302, India  A.Taraphder  Department of
Physics, Indian Institute of Technology, Kharagpur-721302, India

###### Abstract

Combining experimental investigations and first-principles DFT calculations,
we report physical and magnetic properties of Gd-substituted Y2CoMnO6 double
perovskite, which are strongly influenced by antisite-disorder-driven spin
configurations. On Gd doping, Co and Mn ions are present in mixed-valence
(Co3+, Co2+, Mn3+ and Mn4+) states. Multiple magnetic transitions have been
observed: i) paramagnetic to ferromagnetic transition is found to occur at
TC=95.5 K, ii) antiferromagnetic transition at TN=47 K is driven by $3d-4f$
polarisation and antisite disorder present in the sample, iii) change in
magnetization below T$\leq$20 K, primarily originating from Gd ordering, as
revealed from our DFT calculations. AC susceptibility measurement confirms the
absence of any spin-glass or cluster-glass phases in this material. A
significantly large exchange bias effect (HEB=1.07 kOe) is found to occur
below 47 K due to interfaces of FM and AFM clusters created by antisite-
disorder.

##  1 Introduction

Multifunctional insulators with strong magnetoelectric coupling, room-
temperature ferromagnetism and colossal magnetoresistance have sparked
substantial research interests during the last two decades [1]. In this
regard, double perovskite (DP) materials with the general formula R2BB′O6 (R=
Y, rare earth, B/B′ transition metal) show many promises: they exhibit
intriguing properties like magnetodielectric, magnetocapacitance, exchange
bias anisotropy, magnetocaloric effect[2, 3, 4], and others, which account for
their wide range of applications in spintronics, sensors, tunable microwave
filters, energy harvesting devices and transformers[5]. The strong interplay
between spin, charge, and lattice degree of freedom is responsible for such
interesting multifunctional characteristics[6, 7].

In the DP family, La2CoMnO6 (LCMO) and La2MnNiO6 (LNMO) have been widely
investigated. Several intriguing properties in their ordered and disordered
phases have been reported[8, 9]. There have been fewer investigations on
double perovskites that include rare earth having smaller cationic radii[10].
The rare earth cationic size in the DP system plays a vital role in their
physical and magnetic properties. The decrease in rare earth cationic size
significantly changes the B-O-B′s bond angle and bond length (B-O, B′-O). As a
result, frustration occurs in the structure associated with an octahedral tilt
which affects the magnetic and electronic properties[11]. For example, the
A-type AFM magnetic ground state of RMnO3 gets transformed into an E-type AFM
ground state depending upon the rare earth ion size[12, 13]. Furthermore, the
RCo0.5Mn0.5O3 (R=Eu, Tb, Y) system exhibits metastable behavior in the
presence of an external magnetic field, although the spontaneous magnetization
is lower than that of LCMO[14, 16]. On the other hand, the introduction of
Y/Yb/Lu at La site (R2CoMnO6) will induce
($\uparrow\uparrow\downarrow\downarrow$) E-type AFM ordering, which breaks the
inversion symmetry and gives rise to electric polarisation[17, 18, 19]. At the
same time, the other rare earth materials like Ho, Tm, and Er, having smaller
ionic radii, show usual ferromagnetism[20]. In particular, the Y-based DP
compounds have drawn significant interest due to their magnetic ground states.
The magnetic ground state of Y2CoMnO6 (YCMO) is still under debate. The first-
principle calculations reveal that the ground state comprises E-type AFM in
competition with FM and A-type magnetic ordering[21]. However, E-type order is
not observed experimentally[22].

Interestingly, the structural, magnetic and electronic properties of DPs can
be tuned when the A-site element is partially substituted by cations with
different ionic radii. For example, when the Eu3+ ion is partly replaced with
the Y3+ ion in EuMnO3, structural distortion affects the magnetic and
multiferroic properties[23, 24]. The mismatch in ionic radii at the A-site
induces quench disorder and local distortion in the structure. Therefore, the
frustration in the structure or the random Columb potential, due to different
valence states[25], works as a stimulating agent and suppresses ordering
parameters like magnetism, charge order and superconductivity[26, 27, 28].
However, interesting phenomena such as multiglass behavior, phase separation,
exchange bias and ferroelectricity[29, 30, 31] also appear out of such
frustration. Indeed, the properties become more interesting when the A site
dopant is a magnetic rare-earth. An interesting problem is to unravel such
possibilities in YCMO and to this end, we have performed experimental as well
as the first-principles study of partially Gd-substituted YCMO. Notably, we
focus on the case of YGdCoMnO6, where 50% Y3+ (r=1.075 Å) is replaced by Gd3+
(r=1.27 Å) ion. The rare earth Gd gains more attention because of its
significant magnetic moment and room temperature magnetocaloric
properties[32]. Also, the 3d-4f exchange interaction (originating from
interactions between the 3d orbital of TM and the complex, localized 4f
orbital of Gd) has a more significant impact on changing the ground-state
magnetic order. The magnetic nature of the A-site ion produces different
magnetic interactions in competition with the 3d magnetic ion and makes the
system highly frustrated, resulting in different magnetically ordered phases.

Ferromagnetism in the DP systems is due to superexchange interaction between
an ordered arrangement of B2+ and B′4+ cations. In a pristine sample, however,
a perfectly ordered arrangement is impossible to accomplish. Antisite disorder
(ASD) (an imperfection caused by the misplacement of BO6 and B′O6 octahedra)
often occurs during sample synthesis. As a result, more B-O-B and B′-O-B′
couplings are formed, increasing the lattice strain and causing frustration in
the structure. Moreover, strong structural distortion indicates competitive
magnetic interactions between short-range FM next-nearest-neighbor interaction
and long-range AFM nearest-neighbor interaction[33]. Therefore, ASD breaks the
long-range ferromagnetic ordering and drives the system towards a magnetic
glassy order[34]. Murthy et al. show that the coupling between FM and AFM
phases increases with Sr doping at La site in LCMO[35]. Again, first-principle
calculations show that the ASD increases with Sr doping at La site in LCMO[5].
The present work deals with the occurrence of ASD with Gd doping at the Y site
and its effects on the magnetic properties of the system.

The Exchange bias (EB) phenomenon is generally observed in the magnetically
phase-separated system. The anisotropy arises due to exchange interaction at
the interface between the different magnetic ordered phases giving rise to EB
effect[42]. The interfaces can be ferromagnetic/antiferromagnetic,
ferromagnetic/ferrimagnetic, antiferromagnetic/spin glass[90], and so on.
Materials with large EB and coercivity are attracting a lot of attention these
days due to more significant impact on technology owing to its application in
spin-valves[36], read-heads in magnetic recording[37], permanent magnets[38],
giant magnetoresistive random access memory[39] and other devices. Moreover,
the EB effect is observed in many phase-segregated systems (where phase
segregation occurs spontaneously). Generally, in that case, the compounds
belong to a single phase at high temperature, and multiple magnetic phases are
originated with the lowering of temperature. Such kind of feature was observed
in Pr2/3Ca1/3MnO3[40] and Nd2/3Ca1/3MnO3[41]. We discuss here the correlation
between observed field-induced EB effect and complex magnetization in Gd-
substituted YCMO DP system.

##  2 Experimental and Computational Details

Using the standard Sol-gel method, polycrystalline, single-phase double
perovskite compound of Y2-xGdxCoMnO6 ($x$=1.0) has been synthesized. In
starting, the compounds Y2O3, Gd2O3, Co(No3)2, 6H2O and Mn(CH3COO)2,4H2O were
taken. A stoichiometric amount of rare earth oxides (Y2O3, Gd2O3) were
dissolved in dilute nitric acid to convert them into nitrate form and the rest
of the precursors were dissolved in deionized water. After that, two solutions
were mixed with the addition of citric acid as a chelating agent. The
resulting solution was first heated at 90 ∘C for 2 h then finally heated at
150 ∘C for 12 h to evaporate the solvents entirely. The obtained black fluffy
powder was calcined at 1100 ∘C for 10 h. To make a pellet of 10mm diameter for
measuring purpose, this powder was employed using hydraulic press and sintered
at 1200∘C for 12 h.

X-ray diffraction (XRD) measurement was carried out to investigate the crystal
structure of bulk YGdCMO sample using X’pert PRO from Philips Pananalytical
HRXRD-I PW 3040/60 of Cu-Kα radiation ($\lambda$= 1.5406 Å) at room
temperature. The Rietveld refinement[43] of the recorded XRD pattern was
executed using FULLPROF software[44]. The electronic charge state of Co, Mn,
and oxygen in the sample was determined using X-ray photoelectron spectroscopy
(XPS, PHI 5000 versa Probe II scanning) at room temperature. The field cool
(FC) and zero fields cool (ZFC) dc magnetization measurements have been
performed in the temperature ranging from 5 - 300K. This was performed under
the application of various dc magnetic fields by using a Quantum Design SQUID
magnetometer. AC susceptibility measurements have been carried out by using
PPMS (Physical property measurement system).

Density functional theory (DFT) calculations are performed to obtain
electronic structure of Gd-substituted Y2CoMnO6 using pseudo-potential and
plane-wave based method as implemented in the Vienna ab initio simulation
program (VASP)[45]. In our calculations we have used Perdew-Burke-Ernzerhof
generalized gradient approximation (PBE-GGA)[46] and included Coulomb
correlation within GGA+U approximation[47]. Structural parameters were
obtained from the experiment and relaxed keeping the Gd 4f states frozen as in
the core. Ionic positions were relaxed until the forces on the ions are less
than 0.1 meV. We have taken the supercell in c\- direction to implement the
calculation. To find out the magnetic ground structure of the system, we have
performed various magnetic calculations considering ferromagnetic and
antiferromagnetic arrangements among the spins of Gd, Mn and Co ions. For the
subsequent self-consistent calculations, the Gd 4f states were treated as
valence states. An energy cut-off of 500 eV was used for the plane waves in
the basis set, while a 6×6×6 Monkhorst-Pack k-mesh centered at $\Gamma$ was
used for performing the Brillouin zone integrations.

##  3 Results and discussion

###  3.1 Crystal structure

Figure 1: X-ray powder diffraction pattern along with Rietveld refinement of
YGdCMO. The inset represents a schematic of a unit cell of monoclinic YGdCMO,
where large golden spheres represent Y/Gd atoms sitting in the hollow formed
by CoO6(green) and MnO6(purple) octahedra. Small red spheres represent oxygen
atoms.

In the present experiment, the XRD technique was used to determine the phase
purity of crystal structure, lattice parameter, bond length, and bond angle of
powder YGdCMO. Figure 1 shows the recorded XRD data along with Reitveld
refinement at room temperature. The YGdCMO is found to crystallize in
monoclinic symmetry of space group $P2_{1}/n$ as a major phase and with
orthorhombic symmetry of space group Pnma as a minor phase. The major
reflection peaks are found to fit well with monoclinic symmetry rather than
orthorhombic symmetry. The concentration of the monoclinic phase is found to
be 99.42%, whereas 0.58% for the orthorhombic phase. As the dominatnt phase is
monoclinic, we continue our discussion based on this phase.

The monoclinic space group is commonly known as a distorted space group. A
schematic of the crystal structure of monoclinic YGdCMO has been shown in the
inset of Figure 1. Six oxygen atoms octahedrally surround Co and Mn atoms.
Here, every CoO6 octahedra share its corner with six MnO6 octahedra and vice-
versa. The Co and Mn ions are arranged alternately either at
2c($\frac{1}{2}$,0,0), or 2d(0,$\frac{1}{2}$,0) in the unit cell. The Co/Mn
ordering peak for double perovskite has commonly appeared around 2$\theta$
$\approx$ 20∘[48]. In the XRD data used in this experiment, this peak
intensity is too feeble compared to the most intense peak that arises at
2$\theta$ $\approx$ 33∘. So the background signal diminishes this feature.
Therefore, Co and Mn ions are not organized in an ordered arrangement in the
unit cell. Any other type of Co/Mn ions arrangement in the unit cell gives
rise to partial antisite disorder. It is tough to reveal the actual
distribution of Co/Mn atoms on both crystallographic sites by the X-ray
diffraction method, as both the cations have very similar scattering cross-
sections[49].

Table 1: The room temperature lattice parameters, bond lengths and bond angles from Rietveld analysis of XRD data. Lattice parameters |
---|---
a (Å) | b (Å) | c (Å) |  $\alpha$(∘) |  $\beta$(∘) |  $\gamma$(∘) | Volume (Å3) | $\chi^{2}$
5.2672(3) | 5.5929(4) | 7.5075(5) | 90 | 89.889(10) | 90 | 221.16(3) | 1.08
Bond length and Bond angles
Y/Gd-O (Å) | Mn-O1 (Å) | Mn-O2 (Å) | Mn-O3(Å) | Co-O1 (Å) | Co-O2 (Å) | Co-O3(Å) |
2.4844 | 1.9915 | 1.8207 | 2.0200 | 1.9056 | 2.1327 | 1.9700 |
Co-O1-Mn |  |  | Co-O2-Mn |  |  | Co-O3-Mn |
148.665 |  |  | 152.563 |  |  | 148.0 |

The estimated lattice parameters from Rietveld refinement are tabulated in
Table 1. This is seen that the Co-O and Mn-O bond lengths are not similar,
suggesting that the CoO6 octahedra are larger in size in comparison to MnO6
octahedra. Again the ionic radii of A site rare-earth ions are different. As a
result, the CoO6 and MnO6 octahedra are rotated to balance the misfit of ionic
radii. So the bond angle value has strongly deviated from 180∘, a conventional
value of ideal double perovskite[50]. This can be understood by the tilting
angle $\phi$ between the CoO6 and MnO6 octahedra, which can be evaluated from
$\phi$=(180∘-$\theta$/2)[51]. $\theta$ is the average bond angle between Co
and Mn, and the value of $\phi$ comes out to be 17.6∘. These dissimilarities
in bond angle, bond length, and tilting angle $\phi$ indicate a significant
distortion present in the structure due to Gd doping.

###  3.2 X-ray photoelectron spectroscopy (XPS)

In the DP systems, B site cations are often present in mixed-valence states
due to several reasons, such as different synthesis conditions, charge
compensation, and different type of structures[52]. The physical and magnetic
properties of DP systems are strongly influenced by the oxidation states of
the B site cation. Therefore XPS was carried out to find out the oxidation
states of B site cations of the YGdCMO sample.

Figure 2: XPS spectra of (a) Co 2$p$, (b) Mn 2$p$ and (c) O 1$s$ powder YGdCMO. Data points are represented by black circles with overall fitted curve shown by the red line. De-convoluted spectral peaks and Shirley background are represented by solid lines of different colors. Table 2: Binding energy and the percentage of area obtained by deconvolution of XPS spectra for different oxidation state for Co and Mn ions. Oxidation | Binding | Area (%)
---|---|---
state | Energy (eV) |
Co2+2p3/2 (P1) | 779.38 | 39.9
Co2+2p1/2 (P3) | 795.22 |
Co3+2p3/2 (P2) | 780.98 | 60.11
Co3+2p1/2 (P4) | 796.20 |
Mn4+2p3/2 (P1) | 642.47 | 69.33
Mn4+2p1/2 (P3) | 654.90 |
Mn3+2p3/2 (P2) | 641.24 | 30.67
Mn3+2p1/2 (P4) | 652.09 |

Co-2p core-level spectra consists of two major peaks along with two satellite
peaks S1 and S2 illustrated in Figure 2(a). The two major peaks, namely,
Co-2P3/2 and Co-2P1/2 due to spin-orbit splitting are centered at 779.90 eV
and 795.15 eV, respectively with a separation of about 15.25 eV[53]. These
peaks are further deconvoluted into four peaks P1, P2, P3, and P4,
respectively. It signifies the existence of Co2+ in addition to Co3+ ion. The
obtained binding energy values and area under the peaks are presented in Table
2 and agree well with the literature value[54, 55]. The satellite peaks S1 and
S2 are at the high binding energy side (785.32 eV and 816.12 eV)[56]. This is
a clear indication of the existence of mixed oxidation states of Co ions. The
energy difference ($\Delta$E) between two-level, due to spin-orbit coupling
was found to be different for divalent ion and trivalent ion with $\Delta$E
$\sim$ 15.5 - 16 eV for Co2+ and 15.0 - 15.2 eV for Co3+ ion, respectively[58,
59]. In the present experiment, it is found to be 15.8 eV and 15.2 eV for Co2+
and Co3+, respectively. It confirms that the Co2+ and Co3+ ions are present in
our sample. The corresponding ratio of Co2+ and Co3+ ions is $\sim$ 4:6.

Mn-2p spectra associated with two major peaks are located at 641.80 eV and
653.37 eV, respectively. The energy difference between spin-orbit splitting
2p3/2 and 2p1/2 peaks is 11.57 eV[60, 61]. These peaks are deconvoluted into
four consecutive peaks, namely, P1, P2, P3, and P4, indicating the presence of
Mn4+ ion along with Mn3+ ion shown in Figure 2(b). The binding energy value
and area under the fitted peaks are summarized in Table 2. The observed
binding energy value for Mn4+ and Mn3+ are in good agreement with the reported
value[62, 63]. The full width at half maxima (FWHM) plays an important role in
the determination of the monovalent or multivalent oxidation states of the B
site cation. In our sample, the FWHM of Mn-2p3/2 peak is found to be 5.1 eV,
which is greater than that of the divalent and trivalent oxidation state of Mn
in MnO2 (3.2 eV), Mn2O3 (3.0 eV)[64]. This large value of FWHM signifies
coexistence of multivalent Mn ions in our sample. The ratio of the Mn4+ and
Mn3+ ions are equal to the ratio of the peak area and the obtained value is
$\sim$ 7:3.

Figure 2(c) represents the XPS spectra of O 1s core level. The deconvoluted
peaks O1 and O2 are centered at 529.24 eV and 531.13 eV, respectively. The O1
peak comprises lattice oxygen bonding with metal (Co, Mn), whereas the O2 peak
is associated with absorbed oxygen on the surface[65, 66].

###  3.3 Magnetic measurements

####  3.3.1 Temperature dependent DC magnetization

Figure 3: (a) M(T) curve of YGdCMO measured at 500 Oe dc magnetic field Hdc
under ZFC and FC and its temperature derivative dMZFC/dT. (b) Modified CW law
fit to the experimental data of $\chi^{-1}$.

It was observed previously that the distortion and site disorder present in
the DP system have a significant impact on its magnetic properties[6]. To
elucidate the evolution of magnetic ground states with site disorder and
distortion, temperature-dependent FC and ZFC magnetization M(T) measurements
have been carried out.

Figure 3(a) shows the thermal variation (T) of ZFC and FC magnetization (M(T))
of Gd-substituted YCMO under the application of 500 Oe dc magnetic field.
Three magnetic transitions have been observed in the M-T curve, and
corresponding ordering temperatures are determined by the first-order
derivative of [dMZFC/dT] shown in Figure 3(a). i) A sharp change in
magnetization of FC and ZFC curves have been observed at Curie temperture
TC=95.5 K. This paramagnetic to ferromagnetic ordering is resulting from spin-
spin superexchange interaction[69] between Co2+ and Mn4+. The virtual electron
transfer between half-filled orbital (e${}_{g}^{2}\uparrow$) of Co2+(3d7:
t${}_{2g}^{3}\uparrow$ t${}_{2g}^{2}\downarrow$ e${}_{g}^{2}\uparrow$)to empty
orbital (e${}_{g}^{0}$) of Mn4+(3d3: t${}_{2g}^{3}\uparrow$ e${}_{g}^{0}$)
gives strong ferromagnetic coupling in this sample[67].

ii) A substantially significant bifurcation between FC and ZFC curves has been
observed below TC. This feature is common for cobaltite and dilute doped
manganite systems, indicating strong anisotropy and the existence of mixed
phases at a lower temperature[70]. Below TC, the MFC magnetization value
reaches a maximum at 50 K, then starts decreasing around TN= 47 K followed by
a broad peak, which indicates non-zero polarisation of magnetic ions with AFM-
like behavior. This AFM transition can be associated with strong 3d-4f
exchange interactions between FM sublattice of Co2+/Mn4+(3d7/3d3) and
Gd3+(4f7) ion[68] and due to ASD present in our sample.

iii) Below T$\leq$20 K, an up-turn anomaly in MZFC curve is visible, whereas
MFC curve shows a sharp downfall. This feature is more pronounced with an
increase in dc magnetic field shown in Figure. 4(a). This can be attributed to
the gradual development of Gd spins ordering along the ab plane below this
temperature which is initially in ac plane. This result is coherent with our
first-principles calculation. The short-range exchange interaction of
Gd3+-O-Gd3+ gives rise to an AFM ordering of Gd spin. Similar feature was
observed in Ho2NiMnO6[93].

Furthermore, in comparison with the parent compound YCMO[71], the substantial
increase of magnetization value of Gd-substituted YCMO is observed below TC
due to magnetic Gd3+ ion present in the sample. The Curie temperature TC is
one of the important parameter, which holds its potential application in real
devices. The higher value of TC makes it more applicable in the industry. The
larger size of Gd3+ ion would help to straighten the average bond angle of Co-
O-Mn and it contributes to large electron density at the Fermi level. This
will increase the electron hopping ability, consequently superexchange
interaction between Co2+ and Mn4+ ions via intervening oxygen. Hence the TC of
the Gd-substituted compound increases to 95.5 K whereas it is 75 K for parent
compound[71].

The temperature-dependent inverse of susceptibility has been displayed in Fig.
3(b) to delineate the nature of the magnetization in high-temperature regions
(i.e. in PM state). The non-linear nature of the curve above TC implies that
the conventional Curie-Weiss law deviates in the PM region. The bulging nature
of the curve signifies that the total magnetic contribution to the
susceptibility is the sum of the contribution of transition metal sublattices
and rare-earth sublattice site[93]. Here it is assumed that the rare earth and
transition metal paramagnetism are noninteracting in nature. It is possible
due to localize nature of heavy rare earth ion Gd. Therefore the modified
Curie-Weiss law with the following expression describes the magnetic behavior
in YGdCMO.

$\chi=\frac{C_{Co-Mn}}{T-\theta_{TM}}+\frac{C_{Gd}}{T-\theta_{Gd}}$ (1)

where CCo-Mn and CGd are the Curie constants of Co-O-Mn sublattice and Gd
sublattice, respectively, and $\theta_{TM}$ and $\theta_{Gd}$ are the Curie-
Weiss temperature for transition metal ions and rare earth (Gd) ion. The Curie
constant is related to $\mu_{eff}$ by the formula

$\mu_{eff}=\sqrt{\frac{3k_{B}C}{N\mu^{2}}}=2.827\sqrt{C}$ (2)

where kB is the Boltzmann constant, $\mu_{B}$ is the Bohr magnetron, and N is
the number of magnetic atoms per unit volume. The $\chi^{-1}$ vs. T plot is
shown in Figure 3(b), and the curve is well fitted to Eq. (1), indicating by
the solid red line. The obtained values of fitting parameters $\theta_{TM}$ is
95.68 K which is positive and close to TC and CCo-Mn 3.93 emu K mol-1Oe-1.
Therefore the value of effective paramagnetic moment $(\mu_{eff})_{Co-Mn}$ is
estimated from Eq.(2), and it is found to be 5.60 $\mu_{B}$/f.u. The
theretical effective paramagnetic moment described as
$\mu_{theo}=\sqrt{\mu_{Co}^{2}+\mu_{Mn}^{2}}$ where $\mu_{Co}=g\sqrt{S(S+1)}$
and $\mu_{Mn}=g\sqrt{S(S+1)}$ with $g\approx$2.0. The effective moment value
for different spin configurations are given follows: 5.47 $\mu_{B}$ for
[Co${}_{HS}^{2+}$=3/2 and Mn${}_{HS}^{4+}$=3/2 (HS=High spin)]; 5.65 $\mu_{B}$
for [Co${}_{IM}^{3+}$ (Intermediate spin)=1 and Mn${}_{HS}^{3+}$=2]; 6.92
$\mu_{B}$ for [Co${}_{HS}^{3+}$=2 and Mn${}_{HS}^{3+}$=2]. Therefore, the
observed experimental moment value indicates that the existence spin
interaction mediated through mixed valence state. For Gd sublattice, the
extracted values of $\theta_{Gd}$ and CGd are 20 K and 9.06 emu K mol-1 Oe-1,
respectively. The positive value of $\theta_{Gd}$ indicates the FM ordering of
Gd sublattice at a lower temperature. The calculated value of
$(\mu_{eff})_{Gd}$ from Eq.(2) comes out to be 8.51 $\mu_{B}$/f.u.. This value
is higher than the effective paramagnetic moment for free Gd3+ ion (7.0
$\mu_{B}$/f.u.). The model of modified Curie-Weiss law is based on the non-
interacting Co/Mn and Gd sublattice. So, this higher value might be due to the
interaction between Co/Mn and Gd ions at lower temperature present in our
sample.

The effective paramagnetic moment for a perfectly ordered, well-known system
(LCMO) is 6 $\mu_{B}$[5], as reported earlier. In comparison with ordered LCMO
the effective moment of YCMO is a little bit lower. The 3d-4f exchange
interaction between Co/Mn sublattice and Gd spins plays a crucial role in
producing AFM interaction in the system. Moreover, the site disorder present
in the sample leads to the formation of mixed valences of Co and Mn ions. As a
result, different short-range AFM interactions such that Co3+-O-Co3+,
Mn3+-O-Mn3+ come into play along with FM interaction. So the overall magnetic
moment of the system decreases. However, in a perfectly ordered system, only
Co2+-O-Mn4+ superexchange interaction exists, which is responsible for FM
interaction and gives the higher value of the moment. Approximately we have
calculated the percentage of antisite disorder present in our sample by using
Eq. (3)[72], where MCo and MMn are the spin-only moment, and $x$ is the amount
of hole doping.

$M_{S}=(1-2ASD)[M_{Co}+M_{Mn}]+x(1-2ASD)$ (3)

The 1st term in the equation corresponds to the contribution of ASD to the MS
and the 2nd term is indicated the reduction of magnetization due to the doping
element. The value comes out to be 38%, which is quite considerable.

Figure 4: (a) Temperature dependent magnetization under the application of
various dc fields. (b) The H2/3 Vs T plot along with the fitting of Almeida
Thouless line.

To further study, temperature-dependent magnetizations have been measured
under the application of 100 Oe, 1 kOe and 10 kOe magnetic fields. All the ZFC
and FC curves follow the same pattern. It is seen that there is still a
bifurcation between the ZFC and FC curve under the application of even 10 kOe
field. It means that this field is not sufficient to align all the spin along
the field direction. This is a necessary condition (not sufficient) for spin-
glasses to be present in the system. There is irreversibility (at which
temperature the deviation between ZFC and FC curve takes place) observed below
100 K. Previously this type of feature was ascribed to spin-glass or SPM-like
behavior. But the AC susceptibility measurement rules out the possibility of
having spin-glass in the system. Figure 4(a) depicts the shifting of Tirr
towards the lower temperature with an application of a high field, indicating
that the frozen state is relaxed with the help of an external magnetic field.
The variation of Tirr with the external magnetic field can be mapped onto the
De-Almedia thoughtless (AT)-line[73, 74], which is given below

$H_{dc}(T_{irr})=\Delta J[1-\frac{T_{irr}(H_{dc})}{T_{SG}}]^{3/2}$ (4)

Here $\Delta J$ is associated with exchange interaction, TSG is the SG
freezing temperature at zero applied field. The experimental curve is nicely
fitted by Eq. 4 shown in Figure 4(b), and the slope of this straight line
gives the spin freezing temperature TSG=96.94 K. This indicates the volume
spin glass-like behavior[75, 76].

####  3.3.2 AC susceptibility

Figure 5: (a) Temperature dependent AC susceptibility for different
frequencies and (b) different dc fields superimposed.

The temperature dependent AC susceptibility measurements, with an AC field of
1 Oe and different frequencies, have been carried out to probe the presence of
glassy magnetic phase in the YGdCMO sample. The sharp peak corresponding to
ferromagnetic transition is observed nearly at 94.82 K, shown in Figure 5(a),
whereas no anomaly is noticed corresponding to AFM transition. All the peaks
are being frequency independent, which rules out the possibility of having
spin-glass phase in our sample. Moreover, the memory effect experiment was
performed (following the protocol[82]) below the transition temperature (plot
not shown here). No memory effect is observed near the waiting temperature,
which is in disfavor of the presence of SG/cluster glass. The AC
susceptibility with the variation of DC field is shown in Figure 5(b). The
curve depicts that the susceptibility maxima shifts towards higher temperature
with increase in DC magnetic field. This is ascribed to the presence of
critical fluctuations along with a continuous transition to a ferromagnetic
state.

Earlier it was reported that the $\chi^{\prime}$ remains constant down to low
temperature for a purely FM material. However, the $\chi^{\prime}$ decreases
below the transition temperature for many inhomogeneous magnetic oxide and
amorphous alloys, having a finite size of FM and AFM clusters. This is
associated to magnetic anisotropy[83]. The inhomogeneous FM clusters in many
FM systems, change their shape and size continuously below TC lead to magnetic
anisotropy. The sharpness of the susceptibility peak and decrease in amplitude
of susceptibility strongly depends upon the disorder present in the sample,
spin-spin correlation, and anisotropy energy. This anisotropy energy blocks
the spin and do not allow them to respond in a weak field below TC.

$\chi^{\prime}(T)\propto M_{S}^{\prime 2}(T)/K(T)$ (5)

From Eq. 5 it can be explained, where M${}^{\prime}_{S}$ is the spontaneous
magnetization and K(T) is the anisotropy energy at a particular
temperature[84]. The FM spin-spin correlation increases with the decrease in
temperature. Therefore, the spontaneous magnetization as well as anisotropy
energy increase below TC which results decrease in susceptibility.

Therefore, the sharp peak in the susceptibility curve arises due to ASD
present in our sample as externally no disorder is added to the system. But
ASD is very common in DP system. So, ASD can not alone contribute to this
sharp peak. In our sample different interactions Co-O-Mn, Co-O-Co, Mn-O-Mn are
arise due to FM and AFM interaction, leading to magnetic frustration. Thus the
sharp peak could be result for both ASD and magnetic frustration.

####  3.3.3 Magnetization study using first principles DFT

Figure 6:  Schematic spin structure of room temperature (a) ordered YGdCMO (b)
disorder YGdCMO (right pannel).

In order to support experimental findings, we carried out first-principles DFT
calculations. We have considered supercells of size 1×1×2 containing 40 atoms.
The total-energy calculations were performed to obtain the ground-state of the
system using the relaxed structural parameters (starting from experimentally
obtained crystal structure) for various magnetic configurations within the
generalized gradient GGA+U and GGA+U+SO (which includes spin-orbit
interaction) approximations. The value of Ueff = U-J (where U is the Coulomb
correlation and J is Hund’s exchange) used for Gd, Mn, and Co are 6.1 eV, 3.1
eV, and 4.1 eV, respectively. Figure 6(a) shows an ordered arrangement of
YGdCMO where Co and Mn atoms are in alternate positions. Figure 6(b) Co and Mn
atoms are randomly distributed, known as a disordered structure.

For the collinear calculations with spin moments of Gd, Mn, and Co pointing
along the c direction, we have considered six different spin configurations to
determine the magnetic ground state of the system: a) AFM configuration Gd (↑
↑ ↑ ↑) Mn/Co (↑ ↓ ↑ ↓), b) FM configuration Gd, Mn/Co all pointing in same
direction c) Ferrimagnetic configuration – Gd (↑ ↑ ↑ ↑), Mn/Co (↓ ↓ ↓ ↓). In
the other three spin configurations, we have kept Mn/Co spin in the up
direction, while for Gd, we have taken G-type AFM, C-type AFM, and A-type AFM
spin configurations. The relative energy values are given in table 3. We
observe that the ground state magnetic order is ferromagnetic. The
corresponding moment values obtained from DFT calculations for Gd, Mn, and Co
are 7.05 $\mu_{B}$, 3.1 $\mu_{B}$ and 2.6 $\mu_{B}$, respectively. Therefore,
in an ordered structure Co and Mn ions are close to the nominal valence of +2
and +4, respectively, which corroborate the results of XPS analysis for
ordered structure.

Table 3: Relative energy per formula unit (in eV) of various spin configurations within GGA+U+SO approximation. Spin configurations | Energy values (eV)
---|---
AFM | 0.095
FM | 0.0
Ferrimagnetic | 0.10
G-type (Gd) | 0.03
C-type (Gd) | 0.055
A-type (Gd) | 1.18

We further computed total energies assuming noncollinear spin configurations
within the GGA +U + SO approximation to find out the preferred direction of
the Gd spin moments. We have chosen four different directions for Gd moments,
while keeping the Co and Mn spin moments fixed along c direction in FM spin
configuration: a) Gd spins along a direction b) Gd spins along b direction c)
Gd spins along c direction, and d) Gd spins moments confined in ab-plane
pointing along [110] direction. The relative energies are given in table 4. It
is found that Gd moments are lying in ab plane.

Table 4: Relative energy (in eV) of various spin configurations within GGA+U+SO approximation. Spin configurations of Gd | Energy values (eV)
---|---
(1, 0, 0) | 0.015
(0, 1, 0) | 0.04
(0, 0, 1) | 0.035
(1, 1, 0) | 0.0

We have also performed the non-collinear calculation with the anti-site
disordered structure of YGdCMO to investigate the ionic state of Mn/Co atoms.
The corresponding moment values obtained from DFT calculations for Mn and Co
are 3.8 $\mu_{B}$ and 1.9 $\mu_{B}$, respectively. It implies that the Mn, and
Co ions are in +3 oxidation state which is in good agreement with the XPS
result. We observed that the magnetic ground state of the system comprises of
Co and Mn moments being along c direction, while Gd moments residing in ab
plane, which is consistent with our experimental findings of DC magnetization.
Also, it is seen that the Co and Mn ions change their oxidation state due to
the effect of disordered. Both Co and Mn are in +3 state for disordered
structure, whereas Co and Mn are in +2 and +4 oxidation state, respectively
for the ordered structure. The moment of Co ion decreases which implies short-
range interaction with its neighbors in disordered state. In that case Co-3d
and O-2p hybridization increases. For Mn ion, the moment value increases due
to decrease in hybridization between Mn-3d and O-2p orbitals, indicating long-
range ordering. Therefore, there is a competition between long-range and
short-range interactions which is responsible for observed magnetic behavior
in our system.

####  3.3.4 Isothermal magnetization

To elucidate the magnetic properties of the Gd-substituted YCMO with the
variation of the external magnetic field, isothermal magnetization M(H)
measurements have been performed up to a field $\pm$7T at 5K, 10 K, 50 K and
100 K, respectively in ZFC mode. Figure. 7(a) shows the M(H) curve measured at
5 K. Inset of this Figure represents the virgin curve taken at 5 K from 0 to
7T of ZFC M(H). The Figure. 7(b) represents the M(H) curves measured at 10 K,
50 K, and 100 K, respectively. The M(H) loop at 5 K has a sizeable coercive
field Hcr 9.45 kOe and magnetic coercivity 0.73 $\mu_{B}$/f.u. shows FM-like
behavior. At 100 K, the M(H) loop is a perfect straight line with zero
coercive field and magnetic coercivity indicating that the sample behaves as a
perfect paramagnet and is free from any magnetic impurity. Figure. 7(b)
depicts that magnetization value increases with a decrease in temperature. The
localized Gd-4f moments would help to increase the magnetization value at a
lower temperature. It is clearly seen from the hysteresis loops, measured at
5K, 10K, 50K and 100K that the magnetization does not saturate even at H=7T
magnetic field. This feature is obvious for rare-earth sublattice present in
the compound. This incomplete saturation of magnetization corresponds to the
$3d$-$4f$ exchange interaction and ASD present in the sample. So the
incomplete saturation of magnetization at high field and low field hysteresis
loops (in the temperature range 5 K-50 K) indicate the existence of FM/AFM
phases.

Figure 7: (a) ZFC M(H) isotherms in the range ±70 kOe at 5 K. Inset shows the
virgin curve isotherm taken at 5 K. (b) Isothermal hysteresis loops are
measured at different temperatures 10 K, 50 K and 100 K.

So from the virgin M(H) curve shown in the inset of Figure. 7(a) taken at 5K,
we have estimated saturation magnetization value by fitting the high magnetic
field part (H$\geq$20 kOe) using the Eq.6[77] where c is the high field
differential susceptibility, a comprised with the structural defect and
nonmagnetic inclusion of local magnetic moments and b is associated to
magnetocrystalline anisotropy of the system.

$M(H)=M_{S}[1-\frac{a}{H}-\frac{b}{H^{2}}]+cH$ (6)

From the fitting, the obtained value of MS is 9.14 $\mu_{B}$/f.u., which is
deviated from the sum of the theoretically estimated value of fully polarised
Co2+-O-Mn4+ (6.0 $\mu_{B}$/f.u.) and Gd spin (7.0 $\mu_{B}$/f.u.) system. So
it is seen that the obtained saturation magnetization value is much lower than
the theoretically obtained value. This decrease in the moment is a clear
impact of ASD present in our sample[80] because ASD creates ABPs, which are
also responsible for reducing the saturation magnetization value[51, 93, 79].
The presence of a strong magnetic pinning force with disorder restricts the
moments to align along the field direction[78]. Thus the magnetization value
decreases. This disordered structure generates several types of AFM
interaction such as Co2+-O-Co2+, Co3+-O-Co3+, Co2+-O-Co3+, Mn3+-O-Mn3+,
Mn4+-O-Mn4+ and Mn3+-O-Mn4+ along with the Co2+-O-Mn4+ FM interaction. This
AFM interaction helps to reduce the overall magnetization value. However,
there is a direct dependence between the ASD and reduction of the magnetic
moment[80]. Fig. 7(b) depicts that at low temperatures, our sample exhibits
large coercivity. This is ascribed to the pinning of the FM domain wall due to
ASD defects and magnetocrystalline anisotropy of the sublattices[79]. Again at
high temperatures the thermal energy suppresses the magnetocrystalline
anisotropy energy, and the domain wall starts moving, as a result, the
coercivity decreases[79]. As the YGdCMO compound contains mixed magnetic
phases due to ASD, metamagnetic-like transitions are expected which reflects
in the nature of the hysteresis curves. Previously this type of phenomenon is
observed in RCo1-xMnxO3 (R=Eu, Y, Nd)[81]. Therefore it is seen that ASD has a
more significant influence on saturation magnetization and also some other
magnetic properties.

###  3.4 Exchange bias effect

The competition between different magnetic interactions and uncompensated
moment at pinning boundary of FM/AFM phases in oxide sample plays a
significant role in engendering the exchange bias (EB) phenomena[85]. The
coexistence of mixed valences of Co and Mn ions, $3d-4f$ exchange interaction,
and site disorder in the YGdCMO compound are responsible for producing FM and
AFM exchange interactions at low temperature, resulting a significant amount
of frustration, and anisotropy at the FM/AFM interface in the system. These
are the adequate conditions to observe EB in oxide samples. So we could expect
similar kinds of phenomena in the YGdCMO compound. To understand this feature
properly ZFC and FC hysteresis loops are measured at 5 K, after cooling the
system from PM region to measure temperature with the different cooling
fields.

Figure 8: (a) M(H) isotherms measured at different cooling fields at 5 K. (b)
Variation of HEB and HC with temperature. (c) HEB and HC dependence with
cooling field at 5 K. (d) Variation of MEB and MC with cooling field at 5 K.

The minimum anisotropy field required to flip the spin should be known to get
the conventional exchange bias effect is approximately estimated by using the
fitting parameter b in Eq. 6. The value becomes 500 Oe[86]. Figure. 8(a)
depicts the zoomed view of three hysteresis loops, measured at 5 K after
cooling the sample with three different external magnetic fields (0 kOe, 10
kOe and 20 kOe). A considerable amount of shift in hysteresis loops is seen
along the negative field and positive magnetization direction. This is the
manifestation of conventional exchange bias[85]. Zero field cooled loop shift
is not noticeable in this compound which excludes the possibility of
occurrence of spontaneous EB effect. In terms of loop shift along the field
direction as well as the magnetization direction, the EB field is defined by
the average of the zero magnetization intercept
[HEB=$\frac{H_{C1}+H_{C2}}{2}$] and coercive field is defined by half of the
width of the hysteresis loop at the average of zero field intercepts
[HC=$\frac{\mid{H_{C1}}\mid+\mid{H_{C2}}\mid}{2}$], EB magnetization is given
by [MEB=$\frac{M_{r1}+M_{r2}}{2}$] and magnetization coercivity is defined by
[MC=$\frac{\mid{M_{r1}\mid}+\mid{M_{r2}}\mid}{2}$] where HC1 and HC2 are the
left and right coercive field[79]. Similarly, Mr1 and Mr2 are the positive and
negative remanent magnetization. Fig. 8(c) shows the variation of HEB and HC
with cooling field. HEB increases rapidly with the cooling field and reaches
saturation at 20 kOe, whereas HC tends to decrease. The maximum shifts
observed in EB and coercivity are 1.07 kOe and 8.85 kOe at 20 kOe and 0 Oe
fields, respectively. The dependence of MEB and MC with a cooling field is
shown in Figure 8 (d). The MEB increases with the cooling field and attains
saturation at 20 kOe, while MC decreases with the cooling field.

Thus it is seen that the EB effect generally occurs in a spin-glass type
system or a frustrated DP system[85]. In our sample spin-glass phase is ruled
out. The long-range FM ordering is getting affected by the AFM phases
originating from the site disorder and 3d-4f exchange interaction due to Gd
doping in the compound[87]. It would contribute a net unidirectional
anisotropy at the FM/AFM interface. Therefore the uncompensated AFM moments
with different anisotropies get pinned into the FM matrix, resulting in
exchange bias phenomena[88, 89]. However, the net value of unidirectional
anisotropy is zero in the absence of any applied cooling field, ensuing no
loop shift. Now we try to explain the variation of HEB with the cooling field
with the help of the magnetic ground state. Below $\leq$10 kOe field, a rapid
increment of HEB is due to large unidirectional anisotropy at the pinning
boundary in comparison with the size of the FM domain as well as total FM
magnetization. The HEB value is found to be saturated above 10 kOe indicating
that strong interfacial magnetic unidirectional anisotropy exists at the
interface. Generally HEB and MEB decrease with high cooling field where the EB
is driven by SG/FM interface[89]. Also, the decrements of MC and HC with the
cooling field support our statement.

To further investigate the origin of EB, the temperature dependence of EB is a
vital tool. Hysteresis loops were measured at different temperatures with a
fixed cooling field of 10 kOe. The variation of HEB and HC with temperature is
presented in Figure 8(b). HEB and HC both are decreased with increase in
temperature and the value of HEB and HC almost reaches zero near TN[89]. So
the EB arises only below TN $\leq$47 K, which indicates that the existence of
AFM phases are the reason to observe EB in this compound.

Figure 9: (a) Zoomed-in view of the hysteresis loops showing the TE effect of
EB. (b) The variation of HEB as a function of loop number ($\lambda$)
evaluated from hysteresis loops measured at 5 K. The solid and dashed lines
represent the best fit for two different models mentioned in the text.

The training effect (TE)[89] is another important feature to unravel the
origin of intrinsic EB. The variation of the EB switching field with
consecutive hysteresis loops cycled across a particular cooling field is known
as the training effect. The EB value decreases with successive field cycling
due to rearrangement of spin towards equilibrium[89, 90]. The smaller the
value of TE is better for application. So ten successive cycles have been
measured repeatedly at 5 K, after cooling the sample with a 10 kOe field.
Figure 9(a). represents the enlarged view of the hysteresis loops in the
negative field regime (only a few hysteresis loops are shown for a better
view). Figure 9(b) reveals that the EB value decreases with an increase in the
loop no. $\lambda$, indicating the presence of TE in the YGdCMO compound. In
our sample, the decrements between the 1st and 2nd hysteresis loop are small,
indicating that the interfacial spins are more stable against the applied
external magnetic field. The dependence of HEB with loop number can be
described by following power law[91].

$H_{EB}(\lambda)-H_{EB}(\infty)\propto\frac{1}{\sqrt{\lambda}}$ (7)

where HEB($\infty$) is the EB field at $\lambda\rightarrow$ $\infty$. The
fitted curve for $\lambda$=2 to $\lambda$=10 is represented by the solid red
line shown in Figure 9(b). The approximate value of obtained fitting parameter
HEB($\infty$) is 979 Oe. The power-law explains only the evolution of free
energy due to the deviation of interfacial AFM magnetization[91]. So this
power law is not able to describe the steep relaxation between $\lambda$=1 and
$\lambda$=2 loop accurately. Microscopically the monotonic decrease of EB
field with different field cycling can be explained with the help of two
different uncompensated spins (frozen and rotatable) present at a magnetically
disordered interface, affected by the magnetization reversals. These spins
will contribute distinctively to the TE through different relaxation rates.
Therefore we have used the following model proposed by Mishra et al. to
describe the TE completely[92].

$H_{EB}(\lambda)=H_{EB}(\infty)+A_{f}exp(\frac{-\lambda}{P_{f}})+A_{i}exp(\frac{-\lambda}{P_{i}})$
(8)

where Af and Pf are related to the frozen spin configuration. Ai and Pi are
associated with flipping of rotatable spin. The A parameters have the
dimension of magnetic field whereas the P parameters are dimensionless and
resemble a relaxation time. It is seen that the Eq. (8) is fitted well to the
experimental data including first two points than Eq. (7), dashed blue line
represents the fitted curve shown in Figure 9(b). The estimated value of the
fitted parameters are HEB ($\infty$) = 1007 Oe $\pm$10 Oe which is close to
the obtained value from Eq. (7), Af= 148 Oe $\pm$3 Oe, Pf= 0.32 $\pm$0.15, Ai=
802 Oe $\pm$ 30 Oe, Pi = 8.5 $\pm$ 0.28. The obtained value of $P_{i}$ is much
larger than the value of $P_{f}$ and their ratio indicates the relative rate
of their relaxation. It indicates that frustrated or rotatable uncompensated
interfacial spins are contributing more to the TE and the frozen one relaxes
slowly to the first one.

##  4 Conclusion

In summary, the influence of ASD on the physical and magnetic properties of
Gd-substituted YCMO has been investigated. Structural refinement confirms that
the dominant phase of YGdCMO compound is monoclinic symmetry with space group
P21/n. XPS analysis reveals that Co and Mn ions are present in mixed-valence
states with Gd doping. Various experimental evidences confirmed that the
multi-magnetic phases appear in the YGdCMO system. Multimagnetic orderings are
achieved by Gd doping. This result is corroborated by our DFT calculations. AC
susceptibility and memory effect measurements depict that the clusters do not
form electronic-phase separation or spin-glass states. Although the FM
transition temperature is observed at 95.5 K, the EB is visible only below
TN=47 K, indicating that there is a connection between ASD and EB. The pinning
of the magnetic moments at the interface of FM clusters separated by the AFM
antiphase boundary is responsible for the observed EB effect with a large HEB=
1.07 kOe and HC= 8.85 kOe. Due to various magnetic ordering and large EB
fields, the sample can be considered as a potential candidate in spintronics
applications. Therefore, it could be concluded that the EB effect and all the
interesting properties originated from ASD present in the frustrated YGdCMO
sample.

##  5 Acknowledgment

The authors acknowledge Central Research Facility (CRF) and use of XPS under
the DST-FIST facility in department of physics, IIT Kharagpur for this work.
The authors also acknowledge use of SQUID in UGC-DAE, Indore for measurement.
AK would like to acknowledge University Grants Commission (UGC) and Ministry
of Education (MoE) for their financial support. VKM would like to acknowledge
SMIL-13 grant from IIT Roorkee.

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