# Adversarial Training for Multi-domain Speaker Recognition

###### Abstract

In real-life applications, the performance of speaker recognition systems
always degrades when there is a mismatch between training and evaluation data.
Many domain adaptation methods have been successfully used for eliminating the
domain mismatches in speaker recognition. However, usually both training and
evaluation data themselves can be composed of several subsets. These inner
variances of each dataset can also be considered as different domains.
Different distributed subsets in source or target domain dataset can also
cause multi-domain mismatches, which are influential to speaker recognition
performance. In this study, we propose to use adversarial training for multi-
domain speaker recognition to solve the domain mismatch and the dataset
variance problems. By adopting the proposed method, we are able to obtain both
multi-domain-invariant and speaker-discriminative speech representations for
speaker recognition. Experimental results on DAC13 dataset indicate that the
proposed method is not only effective to solve the multi-domain mismatch
problem, but also outperforms the compared unsupervised domain adaptation
methods.

Index Terms: multi-domain adaptation, adversarial training, speaker
recognition

##  1 Introduction

In recent years, speaker recognition is becoming an important topic for
biometrics, and a lot of techniques have been studied to improve its
performance, such as i-vectors [1] and x-vectors [2]. However, like many
machine learning tasks, speaker recognition system can be susceptible to
performance degradation when substantial mismatch exists between the training
and evaluation data. The population of interest (the evaluation data), is
called target domain, for which the labels are usually not available, so it’s
impossible to train a classifier directly. At the same time, if data from
anther population (the training data), whose labels are available, it could be
used as source domain data. Thus, domain adaptation [3] is a common method to
overcome the differences between domains so that the classifier trained on the
source domain data generalizes well to the target domain data. When target
domain labels are not available for training or fine-tuning, unsupervised
domain adaptation becomes an alternative to improve the source domain trained
model.

In speaker recognition area, many domain adaptation approaches have been
successfully used to solve the domain mismatch problem [4, 5, 6, 7]. Most of
these domain adaptation methods assume that the examples inside source or
target domains are from the same distributions, however, usually the training
and evaluation data are composed of several different datasets. Considering
these data as a single domain will cause a sub-optimal solution, so
eliminating mismatches among the multiple domain is vital. Multiple domain
adaptation aims at obtaining a model with minimal average risk across multiple
domains. Several studies have addressed this problem. In inter-dataset
variability compensation (IDVC) [8], Aronowitz et al. found that the source
domain dataset and target domain dataset could be composed of several subsets
and there would be variances between the subsets. In [9], Pei et al. presented
a multi-adversarial domain adaptation approach, which captures multimode
structures to enable fine-grained alignment of different data distributions
based on multiple domain discriminators instead of just based on the single
discriminator. The adaptation can be achieved by stochastic gradient descent
with the gradients computed by back-propagation in linear-time. In [10], Lin
et al. proposed to use maximum mean discrepancy (MMD) to solve the problem of
multiple source domains in speaker recognition. They adopted MMD to measure
the discrepancies among multiple distributions and incorporated the
discrepancy term into the objective function for training auto-encoders.

Domain adversarial training (DAT) was proposed by Ganin et al. [11, 12] to
eliminate the domain mismatch in computer vision task, which inserted a
gradient reverse layer (GRL) to learn both class-discriminative and domian-
invariant intermediate representations in a multi-task framework. In recent
studies, adversarial learning has been widely applied in speech related tasks
[13, 14, 15, 16]. In speech recognition, Sun et al. [17] proposed to use DAT
in accented speech recognition. In [18], Guo et al. further refined the common
DAT method by introducing an adversarial dropout regularization term. Hou et
al. [19] applied DAT to improve keyword spotting performance of ESL speech. In
speaker recognition area, Wang et al. [20] firstly proposed to use DAT to
project source domain data and target domain data into a common space and
extract domain-invariant and speaker-discriminative speech representations.
Fang et al. [21] learned the channel-invariant and speaker-discriminative
representations via adversarial training. In [22, 23], Tu et al. proposed
variational domain adversarial neural network and information-maximized
variational domain adversarial neural network to reduce domain mismatch.

In this study, we propose to use adversarial training for multi-domain speaker
recognition. Due to the source and target domain data sets can be decomposed
into several different subsets, instead of just solving the mismatch problem
between source and target sets, we also take the inner variances of each
dataset into consideration. In other words, we regard each subset as an
independent domain and address this problem as a multi-domain mismatch in
speaker recognition. Our goal is to reduce the differences among all the
domains. In this multi-domain speaker recognition task, we mainly focus on
three conditions of domain adaptation: multiple source domains with one target
domain; one source domain with multiple target domains; as well as multiple
source domains with multiple target domains. In order to extract multi-domain-
invariant and speaker-discriminative speech representations, we use
adversarial training for multi-domain adaptation. During training, we use a
multi-task framework, while the first task is the speaker classifier and the
second task is the multi-domain discriminator. With gradient reversal layer
(GRL) added before the domain discriminator, the main network is not sensitive
to multiple domains and projects the data from different domains into a same
subspace. Experiments on 2013 domain adaptation challenge (DAC13) demonstrate
that our proposed method can eliminate the mismatches among all the domains.

##  2 Proposed method

###  2.1 Multi-domain adaptation by adversarial training

In unsupervised multi-domain adaptation task, we only have the access to a
source domain example $\mathbf{x}_{s_{n}}$ and its corresponding label
$y_{s_{n}}$ drawn from different labeled sub-source domain sets
$\\{\mathbf{X_{s}},\mathbf{Y_{s}}\\}=\\{(\mathbf{X}_{s_{1}},\mathbf{Y}_{s_{1}}),...,(\mathbf{X}_{s_{N}},\mathbf{Y}_{s_{N}})\\}$,
in which $N$ means the number of sub-source domains. And a target samples
$\mathbf{x}_{t_{m}}$ drawn from different unlabeled sub-target domain sets
$\\{\mathbf{X_{t}}\\}=\\{\mathbf{X}_{t_{1}},...,\mathbf{X}_{t_{M}}\\}$, in
which $M$ means the number of sub-target domains. The source domain and target
domain set themselves are decomposed into several subsets, which have
variances among each others. The mismatch problem is not only between the
distribution of source and target domains, but also among the subsets from the
source and target domains. In order to solve these mismatch problems, we try
to eliminate the mismatch between the source and target domain as well as to
reduce the variance among different subsets.

Assume that we have the access to a set of labeled source domain sample comes
from $N$ sub-source domains and a set of unlabelled target domain samples from
$M$ sub-target domains as defined before. When the number of source domain $N$
and target domain $M$ are both equal to 1, the framework is the same as
conventional DAT in [20]. In order to eliminate the multi-domain mismatches
and dataset variances, we project the multiple domains into a common subspace
by multi-domain adversarial training, which aims to learn speaker-
discriminative and multi-domain-invariant feature representations. The details
of the proposed method are shown in the following context.

Figure 1: An overview of adversarial training for multi-domain speaker
recognition framework.

The model can be decomposed into three parts as shown in Figure 1: a feature
generation network $G$, which takes $\mathbf{x}_{s_{n}}$ or
$\mathbf{x}_{t_{m}}$ as the input; a speaker classifier $C$, which takes
source domain samples’ features from $G$ and classifies them into $K$ speaker
classes; as well as a domain discriminator $D$, which predicts the specific
domain label of the feature from $G$. For unsupervised domain adaptation task,
only the labeled source domain data are used to train the $C$ and both source
domain and target domain data are used to update the $D$. The mapping
functions can be formulated as: $G(\textbf{x};\Theta_{g})$,
$C(G(\textbf{x};\Theta_{g});\Theta_{c})$ and
$D(G(\textbf{x};\Theta_{g});\Theta_{d})$, where $\Theta_{g}$, $\Theta_{c}$ and
$\Theta_{d}$ are the parameters of the networks.

The following two requirements are satisfied in our method. First, $C$ and $D$
are estimated to ensure that they will perform accurate speaker and domain
classifications. Second, $G$ is used to extract speaker-discriminative and
multi-domain-invariant speech representations.

The objective function of the proposed model consists of two parts. In the
first part, $G$ and $C$ have to classify source samples into $K$ classes of
speakers correctly to obtain the speaker-discriminative features. Thus, we
update both networks’ parameters based on the following standard
classification loss. Given a source domain sample $\mathbf{x}_{s_{n}}$ and its
speaker labels $y_{s_{n}}$, the objective function is:

$\min_{G,C}L_{cls}=-\mathbb{E}_{(\mathbf{x}_{s_{n}},y_{s_{n}})\sim(\mathbf{X}_{s},\mathbf{Y}_{s})}\sum^{K}_{k=1}y_{k}\log
C(G(\mathbf{x}_{s_{n}}))_{k},$ (1)

where $C(G(\textbf{x}_{s_{n}}))_{k}$ returns the probability that the sample
$\textbf{x}_{s}$ is assigned to the class $k$.

In the second part, $D$ is trained as a discriminator to predict the domain
label of all the samples. The objective function of this part is:

$\min_{D}L_{adv}=-\mathbb{E}_{\textbf{x}\sim\\{\textbf{X}_{s},\textbf{X}_{t}\\}}\sum^{N+M}_{i}d_{i}\log
D(G(\textbf{x}))_{i},$ (2)

where $d_{i}$ refers to the domain label and $D(G(\textbf{x}))_{i}$ returns
the probability of the sample x belonging to the $i$-th domain.

We are supposed to jointly train the $G$, $C$ and $D$, and we need to seek a
$\Theta_{g}$ to minimize the speaker classification’s objective function and
to maximize the domain discriminator’s objective function at the same time.
Since $G$ should learn the speaker-discriminative features for source domain
samples as well as multi-domain-invariant features for the samples from all
the domains. There is a gradient reversal layer (GRL) [12] added between the
feature generator $G$ and the domain discriminator $D$ to search a saddle
point between $C$ and $D$. The GRL is multiplied by a certain $\lambda$ during
the back-propagation. $\lambda$ is a positive hyper-parameter used to trade
off the losses. Gradient reversal layer ensures the feature distributions over
different domains approaching similar so that we can get multi-domain-
invariant and speaker-discriminative speech embeddings. The final objective
function is defined as:

$\min_{G,C}\max_{D}L=L_{cls}-\lambda L_{adv}.$ (3)

We optimize with back-propagation using following formulas:

$\theta_{g}\longleftarrow\theta_{g}-\mu(\frac{\partial
L_{cls}}{\partial\theta_{g}}-\lambda\frac{\partial
L_{adv}}{\partial\theta_{g}}),$ (4)
$\theta_{c}\longleftarrow\theta_{c}-\mu(\frac{\partial
L_{cls}}{\partial\theta_{c}}),$ (5)
$\theta_{d}\longleftarrow\theta_{d}-\mu(\frac{\partial
L_{adv}}{\partial\theta_{d}}),$ (6)

where $\mu$ is the learning rate.

###  2.2 Adversarial training for multi-domain speaker recognition

In speaker recognition, the data we used to train the PLDA [24] are usually
supposed to share the same distribution with the evaluation data, which are
defined as target domain. However, in many scenarios, the target domain data
are insufficient or the speaker labels are unavailable. So we propose to
project multiple source and target domains into a common subspace, and we can
use the projected source domain data with speaker labels for the speaker
recognition.

First, we use multiple source and target data to train the multi-domain
adaptation neural network (MDANN). Since we don’t have speaker label of the
target domain data, only the multi-source domain data is used to train the
first task. The label of the first task is speaker ID. All the multi-source
and multi-target domain data are used to train the second task. The label of
the second task is subsets labels. After training the MDANN, we use multi-
source domain vectors ($\textbf{x}_{s_{n}}$), multi-target domain vectors
($\textbf{x}_{t_{m}}$), enroll vectors ($\textbf{i}_{e}$) and test vectors
($\textbf{i}_{t}$) as the inputs to the MDANN and we use the representation of
the hidden layer of the feature generation network as the new vectors
($\hat{\textbf{x}}_{s_{n}}$, $\hat{\textbf{x}}_{t_{m}}$,
$\hat{\textbf{i}}_{e}$ and $\hat{\textbf{i}}_{t}$) of all the data. The
extracted embeddings are therefore expected to be multi-domain-invariant and
speaker-discriminative speech representations which stand in the same
subspace. Then, we apply the pre-processing (whitening and length-
normalization [25]) to the $\hat{\textbf{x}}_{s_{n}}$,
$\hat{\textbf{x}}_{t_{m}}$, $\hat{\textbf{i}}_{e}$ and $\hat{\textbf{i}}_{t}$.
Finally, we use a scoring function to compute the scores between the speaker
model and the test sample. In this paper, we adopt PLDA as the scoring method.
Figure 2 shows how we use the proposed strategy in speaker recognition.

Figure 2: Block diagram of adversarial training for multi-domain speaker
recognition.

##  3 Experimental setup

###  3.1 Dataset

We use the 2013 domain adaptation challenge (DAC2013) dataset [26] as the
evaluation data set. DAC2013 is designed based on LDC telephone corpora and
targeted the domain adaptation. It focuses on the effect of dataset mismatch
on hyper-parameters, such as the latent speaker and channel factors for PLDA.
Both the audio lists and i-vectors of NIST SRE data [27] and Switchboard data
[28] are provided. For fair comparison with other domain adaptation
techniques, DAC2013 i-vector dataset is used in this study. Table 1 shows the
details of DAC2013 i-vector dataset. The dimension of i-vectors is 600. Two
datasets are defined for hyper-parameter training: 1) the source domain SWB
set consists of all telephone calls from all speakers taken from the
Switchboard-I and Switchboard-II (all phases) corpora; 2) the target domain
SRE set consists of all the telephone calls without speaker labels are taken
from the NIST SRE 04, 05, 06, and 08 collections, while SRE-1phn is a reduced
set of SRE with only the i-vectors from 1 telephone number per speaker, which
makes it hard to estimate within-class variability because of the lack of
speaker and channel information. In this study, we selected the more
challenging SRE-1phn data for the domain adaptation task. The telephone data
of NIST SRE 2010 (SRE10) was selected as the evaluation set of DAC2013.

Table 1: i-vector statistic in DAC 13 i-vector dataset | SWB | SRE | SRE-1phn
---|---|---|---
#spks | 3114 | 3790 | 3787
#calls | 33039 | 36470 | 25640
#calls/spkrs | 10.6 | 9.6 | 6.77
#phone_num/spkrs | 3.8 | 2.8 | 1.0

###  3.2 Data partition for multi-domain

Data partition is performed in two kind of manners. Firstly, following the
work in [8], we divide the source domain data into 6 subsets based on the
different LDC codes (LDC97S62 Switchboard-1 Release2, LDC98S75 Switchboard-2
Phase I, LDC99S79 Switchboard-2 Phase II, LDC2002S06 Switchboard-2 Phase III
Audio, LDC2001S13 Switchboard Cellular Part 1 Audio and LDC2004S07 Switchboard
Cellular Part2 Audio). The second data parition manner is clustering. Because
some of the data are recorded in the same year, but released in different
subsets. We use k-means to cluster the source domain data into 3 subsets.

Because the target domain data is usually unlabeld, multi-target domain labels
may not be accessed. So if we don’t have the prior information of the target
domain, we did not partial the target domain data. When the prior information
is available, we adopt the same strategies as mentioned above to divide the
target domain data. The first one is based on the subset’s LDC codes (SRE2004,
SRE2005, SRE2006, SRE2008). As a result, the target domain data is divided
into 4 subsets according to the LDC distributions. Furthermore, k-means is
also used to cluster the target domain data into 2 subsets.

###  3.3 Experimental setup

In unsupervised adversarial training for multi-domain speaker recognition
experiments, the way we define the classes of multi-source and multi-target
domain is shown in Table 2, where $N$ and $M$ indicate the numbers of multi-
source domains and multi-target domains respectively. The conditions that with
the multiple source domains only or with the multiple target domains only are
denoted as MS-DAT and MT-DAT, respectively. In addition, MDAT is the condition
of both source and target domains have multiple subsets.

Table 2: Unsupervised multiple domain adaptation with adversarial training setup Adaptation Methods |  $N$ |  $M$
---|---|---
DAT [20] | 1 | 1
MS-DAT (based on LDC code) | 6 | 1
MT-DAT (based on LDC code) | 1 | 4
MDAT (based on LDC code) | 6 | 4
MS-DAT (based on k-means) | 3 | 1
MT-DAT (based on k-means) | 1 | 2
MDAT (based on k-means) | 3 | 2

For fair comparison, we use the same structure to all the DAT systems and we
follow the setup in [20]. In the multi-domain adversarial neural network,
there are two fully connected layers with 512 nodes for feature generation
network $G$, two fully connected layers with 300 hidden nodes for speaker
classification network $C$, and two fully connected layers with 512 hidden
nodes for domain discrimination network $D$.

In the training stage, we use SWB with speaker labels as multi-source domain
data and SRE-1phn with no speaker label as multi-target domain data for the
MDANN training, and use the subset domain labels as the supervised information
of the second task. During the test stage, we use SWB, SRE-1phn, enroll and
test data as the inputs of the network and extract the multi-domain-invariant
and speaker-discriminative speech representation from the first hidden layer
of the feature generation network $G$. After that the new SRE-1phn data is
used for the whitening and centering to all the new data, and the PLDA back-
end is trained using new SWB data with its speaker labels to obtain the
scores.

##  4 Experimental results and analysis

###  4.1 Result of baseline

Table 3 shows the performance of the SRE10 c2-extended test when the
parameters are trained with different datasets using the i-vector PLDA
framework. System 1 can be considered as the desired benchmark when the in-
domain dataset speaker label is known. System 2 is the baseline of the domain
mismatched condition when the in-domain database is unlabeled. Systems 3 and 4
are versions of systems 1 and 2, respectively on more challenging conditions.
System 3 is adapted using a matched in-domain labeled dataset SRE-1phn which
is subset of SRE. Note that, although system 3 is under domain matched
conditions and system 4 is under mismatched conditions, system 4 shows better
performance in EER than system 3. This is an interesting result and we believe
that performance was degraded by insufficient channel information. The dataset
‘SRE-1phn’ contains audio from only a single telephone number per speaker and
use of such a poor phone number diversity hinders the effective estimation of
within-speaker variability of in-domain.

Table 3: Results of DAC 2013 i-vector dataset without domain adaptation Systems# | PLDA | EER (%) | DCF10 | DCF08
---|---|---|---|---
1 | SRE | 2.33 | 0.402 | 0.235
2 | SWB | 5.65 | 0.632 | 0.427
3 | SRE-1phn | 9.35 | 0.724 | 0.520
4 | SWB | 5.66 | 0.633 | 0.427

###  4.2 Result of proposed method

The experimental results are given in Table 4. As a comparison, the first five
systems are other domain adaptation methods [7] in speaker recognition. The
system DAT is when the number of sub-source and sub-target domain are both
equal to 1, which is the conventional domain adversarial neural network in
[20]. The last six systems are multi-domain adversarial training experiments.
The configurations of them are shown in Table 2. The experimental results
demonstrate that, by projecting the multi-source domain data and multi-target
domain data to a common space with the proposed approach, we can achieve the
lowest EER, DCF10 and DCF08 compared to the conventional DAT [20] and other
adaptation methods [7]. And almost all the systems of our method outperform
the conventional DAT.

When the inner variances of both source and target domain are considered, we
can get the best performance in system MS-DAT (based on LDC code or k-means).
With the adversarial training for multi-domain speaker recognition, the EER is
improved from 5.66% to 3.58%, with +36.7% relative error reduction compared to
the baseline system, and also outperforms other compared domain adaptation
techniques. Especially, comparing to the the traditional DAT in [20], +4.0%
relative error reduction on EER, and a +11.6% relative improvement on DCF10,
as well as a +10.7% relative improvement on DCF08 are achieved by this
solution. The experimental results indicate that when both of multi-source and
multi-target domain information is taken into consideration, domain mismatches
and data variability can be largely alleviated. Considering the inner
variances of each datasets makes the domain adaptation more efficient and can
help to project the samples of all the domains into a more common space.

Table 4: Proposed method vs. other unsupervised domain adaptation methods Adaptation Methods | EER (%) | DCF10 | DCF08
---|---|---|---
Interpolated [29] [7] | 6.55 | 0.652 | 0.454
IDV [30] [7] | 6.15 | 0.676 | 0.476
DICN [31] [7] | 4.99 | 0.623 | 0.416
DAE [32] [7] | 4.81 | 0.610 | 0.398
AEDA [7] | 4.50 | 0.589 | 0.362
DAT [20] | 3.73 | 0.541 | 0.335
| MS-DAT
---
(based on LDC code)
3.62 | 0.516 | 0.319
| MT-DAT
---
(based on LDC code)
3.78 | 0.489 | 0.300
| MDAT
---
(based on LDC code)
3.59 | 0.478 | 0.299
| MS-DAT
---
(based on k-means)
3.65 | 0.543 | 0.321
| MT-DAT
---
(based on k-means)
3.69 | 0.538 | 0.319
| MDAT
---
(based on k-means)
3.58 | 0.525 | 0.301

##  5 Conclusions

In this study, we proposed adversarial training for multi-domain speaker
recognition to eliminate multi-domain mismatches among different subsets in
speaker recognition. Compared to previous domain adaptation studies, we take
inner dataset variance into consideration and extract multi-domain-invariant
and speaker-discriminative representations for the speaker recognition. With
the proposed methods, we obtained +36.7% and +4.0% relative EER improvement
compared to baseline system and conventional DAT method respectively.
Moreover, our approach improved DCF10 and DCF08 yields up to +11.6% and +10.7%
compared to DAT. These results suggest the effectiveness of the multi-domain-
invariant and speaker-discriminative speech representations in speaker
recognition. In our future work, we will combine our method with teacher-
student learning and conduct experiments on more complex scenarios.

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# Tailoring the magnetic landscape in Al-doped LaMnO3: An experimental and
computational perspective

Tushar Kanti Bhowmik<EMAIL_ADDRESS>Saswata Halder  Tripurari
Prasad Sinha  Bose Institute, Department of Physics, 93/1, APC Road, Kolkata-
700009, India

###### Abstract

We have presented the synthesis, structural and the magnetic properties from
the experimental point of view. Then we verified our experimental observation
by studying the electronic and the magnetic properties of Al-doped LaMnO3 from
the first principle density functional theory (DFT) and Monte-Carlo
simulation. We have synthesized the LaAlxMn1-xO3 (x= 0.05, 0.15, 0.25) and
performed the Rietveld refinement of XRD data to determine the lattice
parameters. To see the mixed valance of Mn-ion, we have performed the XPS of
25% Al doped material. The magnetic study shows the ferromagnetic transition
of these materials. Using xrd refinement values, we have performed the DFT
calculations. The Monte Carlo simulation has been done through the anisotropic
Ising model to analyze the origin of magnetic transition. We have determined
the anisotropy and the interaction constants from the DFT calculations.

###### keywords:

Magnetic properties , Ferromagnetic insulator , DFT , Monte Carlo simulation ,
Rietveld refinement , Double exchange

††journal: Journal Name

##  1 Introduction

Rare-earth based perovskite manganates have been in the centre of research
intrigue due to their rich inter-related structural[1], electronic[2] and
magnetic properties[3, 4], which account for their giant magnetoresistance[5],
colossal magnetoresistance[6], magnetocapacinatce[7] and high
magnetocaloric[8, 9] and magnetodielectric effects[10] to name a few. The
underlying physics which drives the unusual but rich physical properties of
the manganites results from the array of different complex interactions like
double exchange (DE)[11], super exchange (SE)[12], electron-phonon
interaction[13], electron-electron interaction[14] etc. The manganates have
the empirical formula of ABO3, where A and B mainly belong to large rare-earth
and transition metal cations respectively. The structure of these perovskites
are mostly deviated from high symmetry with the tilting and the distortion of
the BO6 octahedra being the main structural characteristics which affect their
physical properties. The tunable cation-cation ordering (long-range and short-
range) at the transition metal site actively modulated by chemical doping at
these active sites. Thus the combination of structural deviations and cation-
cation ordering modulate the observed exotic properties in these perovskites
which range from structural phase transitions[15], magnetic phase
transitions[16] and electronic metal insulator transitions[17] which have
direct implications on their magneto-dielectric[10], magneto-caloric effect[9]
and magneto-resistive effects[18] which are useful for switchable spintronics
applications[19]. The hexagonal perovskite manganites belong to multiferroic
group of materials which show the electric ($\sim$ 900 K) and magnetic (
$\sim$ 100 K) ordering simultaneously[20, 21].

Figure 1: The magnetic spin structure of LAM95 unit cell (a) For R-3c and (b)
Pnma space group

Among the rare-earth manganites, LaMnO3 is highly studied material, which
takes part as a parent compound due to its highly enriched and intense
properties. Previous studies shows that it belongs to the orthorhombic
centrosymmetric space group[22, 23]. The MnO6 octahedra becomes tilted and
distorted due to orthorhombic distortion of this material[24]. This leads to
the cooperative John-Teller effect of this material which lifts the degeneracy
of d-orbital of Mn3+-ion [t${}_{2g}^{3}(d_{XY}^{1},d_{YZ}^{1},d_{XZ}^{1})$ and
e${}_{g}^{1}(d_{Z^{2}}^{1},d_{X^{2}+Y^{2}}^{0})$]. The spins (S=2) of the
magnetic Mn3+-ions are ferromagnetically aligned through the O2- due the Hund
rule and the orbital ordering in the Basal plane. Now, the perpendicular
planes show the antiferromagnetic alignment with this plane due to cooperative
John-Teller distortion[25], which forms the A-type anti-ferromagnetism of this
material[26]. A study shows that the system becomes ferromagnetic instead of
antiferromagnetic if the cooperative JT distortion is absent[27, 28]. Later,
it is studied that the doping of divalent atom in the La-site removes the JT
distortion and the system shows the ferromagnetic behaviour at low
temperatures[29]. The doping of this cations generates the Mn4+-ion in the
material due to the charge neutrality. Now the eg electron of Mn3+ is hopped
towards the empty eg-orbital of Mn4+ through the O2- induces the
ferromagnetism in the system; this whole process is called the double exchange
(DE) mechanism[30]. So, the Mn4+ is mainly responsible for FM transition in
LaMnO3.

During the synthesis of LaMnO3, the uncontrolled sintering and annealing
create some vacancy of the cationic sites which produces some extra amount of
non-stoichiometric oxygen (3+$\delta$) to balance the charge neutrality[31].
As a result of this procedure, the system creates some Mn4+-ion, which is
called the self-doping[32]. This generates the DE ferromagnetic interaction in
the materials. If the system crosses the certain limit of self doping, it
becomes fully ferromagnetic. So, the lower value of $\delta$ enhances the
super-exchange (SE) which creates the canted A-AFM magnetic structure. The DE
interaction (FM) wins the competition for higher $\delta$ values. If the
$\delta\geq 0.1$, the crystal structure changes from orthorhombic to
rhombohedral[32].

In case of magnetic cations (M = Fe, Ni, Co) doping in the Mn site lead to the
Orthorhombic crystal structure with ferromagnetic transition[33, 34, 35]. The
exchange interactions between Mn3+ and M3+ are responsible for the
ferromagnetic behaviour of these materials. But doping of the non-magnetic
tetravalent Ti4+-ion shows the Rhombohedral R-3c structure and the material
creates Mn2+-ion for the charge neutrality[36]. The DE interaction between
Mn3+ and Mn2+ generates the ferromagnetism in this material. In this context,
we have studied the effect of non-magnetic trivalent Al-doping in Mn-site of
LaMnO3. The detailed structural properties have studied through X-ray
diffraction and X-ray Photo-electron Spectroscopy (XPS) method, which supports
the presence of Mn4+ state in this sample. The detailed magnetic analysis have
performed through the M-T and M-H curves and the DFT calculations with the
magnetic Monte-Carlo simulations.

##  2 Experimental Details

Figure 2: The XRD data and the Rietveld refinement of LaAlxMn1-xO3 [x= (a)
0.05, (b) 0.15, (c) 0.25]. (d) The zoomed view of main perovskite peaks of
these materials and the 4th one is for the LaAl0.5Mn0.5O3, taken from our
previous study.

Al doped LaMnO3 is prepared through sol-gel citrate method. Firstly all the
nitrates La(NO3)3.$6$H2O, Mn(NO3)3.$9$H2O, and Al(NO3)2.$6$H2O were taken with
calculated stoichiometric ratio in a de-ionised water medium with appropriate
molar ratio of citric acid and ethylene glycol. Then, the solution is stirred
and heated to achieve a gel and and fluffy ash-like powder. The obtained
powder is calcined and sintered at 1173 K and 1223 K to get the final
material. LaAlxMn1-xO3 (x= 0.05, 0.15, 0.25) are prepared with the help of
above described method. The room temperature X-ray diffraction (XRD) pattern
of these materials are obtained from X-ray powder diffractometer (Rigaku
Miniflex II, Cu-K$\alpha:\lambda$=1.54 Å), where the range of 2$\theta$ is 10°
to 80° at a scanning rate of 0.02° per step. We get the crystal structure and
the lattice parameters from the Rietveld refinement analysis of the XRD data
using the Fullprof suite program [37]. The X-ray photoemission spectra of
LaAl0.25Mn0.75O3 are taken by X-ray photoelectron spectroscopy (XPS). The
magnetic properties are taken from the vibrating sample magnetometer
(VSM;Lakeshore).

Table 1: Atomic coordinates and lattice parameters of LaAlxMn1-xO3 (x= 0.05, 0.15, 0.25) determined from Rietveld Refinement method. Sample | Atom | x | y | z | lattice | Reliability | Occu- | Wickoff
---|---|---|---|---|---|---|---|---
|  |  |  |  | parameters (Å) | factors | pancy | site
LAM95 | La | 0.000 | 0.000 | 0.250 | a = 5.505 |  $\chi^{2}$=1.23 | 1.00 | 6a
| Mn | 0.000 | 0.000 | 0.000 | b = 5.505 | Rp=7.90 | 0.991 | 6b
| Al | 0.0000 | 0.0000 | 0.000 | c = 13.311 | Rwp=10.3 | 0.021 | 6b
| O | 0.456 | 0.000 | 0.250 |  $\gamma$=120° | Rexp=8.67 | 1.128 | 18e
LAM85 | La | 0.000 | 0.000 | 0.250 | a = 5.486 |  $\chi^{2}$=1.18 | 1.00 | 6a
| Mn | 0.000 | 0.000 | 0.000 | b = 5.486 | Rp=7.53 | 0.933 | 6b
| Al | 0.0000 | 0.0000 | 0.000 | c = 13.288 | Rwp=9.74 | 0.054 | 6b
| O | 0.451 | 0.000 | 0.250 |  $\gamma$=120° | Rexp=8.44 | 1.161 | 18e
LAM75 | La | 0.000 | 0.000 | 0.250 | a = 5.471 |  $\chi^{2}$=1.16 | 1.00 | 6a
| Mn | 0.000 | 0.000 | 0.000 | b = 5.471 | Rp=7.46 | 0.891 | 6b
| Al | 0.0000 | 0.0000 | 0.000 | c = 13.275 | Rwp=9.67 | 0.055 | 6b
| O | 0.452 | 0.000 | 0.250 |  $\gamma$=120° | Rexp=8.97 | 1.184 | 18e

##  3 Computational details

###  3.1 Ab-initio Calculations

The electronic and magnetic properties of Al doped LaMnO3 have been thoroughly
investigated through full-potential linearized augmented plane wave (FPLAPW)
method as implemented in WIEN2K[38, 39]. The crystal structure of LaMnO3 is
being optimized through spin-polarized general gradient approximation (GGA)
with Coulomb repulsion U (GGA+U) method. We have taken five magnetic spin
configurations for the optimization process such as ferromagnetic (FM), non-
magnetic (NM) and three antiferromagnetic (AFM) [A-AFM, C-AFM, G-AFM]. Now we
have made the supercell for the other three Al-doped systems. In the
supercell, we have replaced the Mn through the Al atoms in appropriate
percentage. The all the structures is being optimized through the above
described process. The Hubbard parameter $U_{eff}$ for Mn-d orbital are fixed
to 3 eV for all structures. The self consistent criteria for energy and charge
convergence have been set to $10^{-4}$ Ry and $10^{-3}$ e, respectively.

Figure 3: (a)The whole XPS spectra of LaAl0.25Mn0.75O3 and fitted data are
shown for (b) La and (c) Mn atom

###  3.2 Monte Carlo Simulations

Monte-Carlo simulation is a very useful technique to study the magnetic
properties theoretically[40, 41, 42, 43]. We have used the anisotropic Ising
model for this simulation[44]. The anisotropy comes from the two types of Mn
ions, Mn3+ and Mn4+, which is verified by XPS spectra, discussed later. So,
the Hamiltonian, we have taken for the computation of the magnetic properties,
is described in the following.

$H=-J_{1}\sum_{<i,j>}{S_{i}S_{j}}-J_{2}\sum_{<i,k>}{S_{i}S_{k}}-\Delta\sum_{i}{S_{i}^{2}}-h\sum_{i}{S_{i}}$
(1)

Where h and $\Delta$ are the external field and the anisotropic constant,
respectively. $J{{}_{1}}$ and $J{{}_{2}}$ are the interaction constants for
the nearest neighbour (NN) and next nearest neighbour (NNN) interaction,
respectively. Due to the two type of Mn-ions, we have used two spins value S =
2 and 1.5 for Mn3+ and Mn4+, respectively. The value of these constants are
determined from the first principle calculations described in later part of
this article.

The single flip standard sampling method with periodic boundary condition is
applied to the whole lattice size (L=30) in all three Cartesian directions.
106 MCS steps are used for the lattice equilibrium and the next 107 steps for
the average of the magnetization and other observable. The physical
quantities, which have been measured using MCS, are described as follows [45].

##  4 Results and Discussions

###  4.1 Crystallographic Information

Figure 4: (a) The M vs T curve for LaAlxMn1-xO3 (x= 0.05, 0.15, 0.25). (inset)
The inverse susceptibility and its linear fitted curve with respect to the
temperature in the paramagnetic region. (b) The magnetic hysteresis for these
materials and its zoomed view at origin (inset).

The crystal structure of these materials are determined from XRD, described in
Figure 2 (a-d). The main peak near 32° as well as next to this splitted into
two parts, which indicates that it might be fitted with the Rhombohedral
symmetry. However, we have performed the Rietveld refinement of these
diffraction pattern with the pseudo-voigt function in Fullprof suite
programme. The refinement suggests that these three samples crystallizing with
the R$\bar{3}$c (space group 167) symmetry. The lattice parameter, atomic
coordinates and the goodness of fit ($\chi^{2}$) are given in table 1. Figure
2(d) represents the zoomed view of main peaks and next two other peaks of
LaAlxMn1-xO3 (x= 0.05, 0.15, 0.25). The splitting of main peaks are going to
abolish with higher Al concentration. For 75% Mn, the 32° peak almost marges
into one peak. From our previous study of LaAl0.5Mn0.5O3, there is no sign of
splitting of peaks (Figure 2(d-d))[46]. This 50% Al-doped material’s symmetry
also completely changes to Monoclinic P21/n. So, this material have a
structural phase transition from R$\bar{3}$c to P21/n with increasing Al-
concentration.

The surface elemental composition and oxidation states of LaAl0.25Mn0.75O3 are
investigated using X-ray photoelectron spectroscopy (XPS) in a wide energy
window of 0-1200 eV. The survey spectrum of LaAl0.25Mn0.75O3 in figure 3(a)
shows the presence of La(3d), Al(2p), Mn(2p) and O(1s). The high resolution
core level XPS spectra for La 3d and Mn 2p in are presented in figure 3(b),
and figure 3(c), respectively showing their formal oxidation valence states.
The XPS spectra of La-3d in figure 3(b) shows two sets of spin-orbit split
peaks (834.6 eV; 838.1 eV) corresponding to La 3d5/2 and (851.4 eV; 855.0 eV)
corresponding to La 3d3/2 respectively, which are known-markers for the +3
oxidation state for La. The core-level XPS spectra of Mn-2p, shown in figure
3(c) demonstrates a mixed or variable oxidation state for Mn. The double
splitting of individual peaks corresponding to Mn 2p${{}_{3}/2}$ at $\sim$643
ev and Mn 2p1/2 at $\sim$653 eV marks the presence of two oxidation states for
Mn, namely Mn3+ and Mn4+. The lower binding energies corresponding to 642.2 eV
and 652.6 eV mark the presence of the Mn3+ state whereas the higher binding
energies at 644.8 eV and 654.8 eV correspond to the Mn4+ oxidation state. In
addition, satellite peaks for 2p3/2 and 2p1/2 occur at 529.7 eV, and 531.2 eV,
respectively. The system has 30% of Mn4+ state in the Mn-site, which means the
excess of non-stoichiometric oxygen ($\delta$) is 0.3. The presence of
heterogeneous oxidation states of Mn is important to gain insights into the
intriguing magnetic landscape of the materials which will be discussed in the
subsequent sections.

Figure 5: The energy with respect to the volume for different spin
configurations of LaAlxMn1-xO3 [x= (a) 0.0, (b) 0.05, (c) 0.15, (d) 0.25].

###  4.2 Magnetic Properties

The temperature dependency of magnetization is plotted in Figure 4(a). The
value of magnetization decreases gradually with increasing temperature for all
three materials. The magnetic moment should be decreased with the decreasing
Mn concentration. But we have seen that the value of magnetization for x=0.15
is greater than the x=0.05. This happens due the increasing percentage of Mn4+
ion in the x=0.15 sample. The magnetization vs Temperature plot clearly
indicates the ferromagnetic transition of these materials. The transition
temperatures are T${}^{0.05}_{C}$ = 135 K, T${}^{0.15}_{C}$ = 110 K and
T${}^{0.25}_{C}$ = 85 K which are determined from the minimum point of 1st
derivative of M-T curve.

Figure 6: The energy with respect to the volume for different spin
configurations of LaAlxMn1-xO3 [x= (a) 0.0, (b) 0.05, (c) 0.15, (d) 0.25].

The inverse of the dc susceptibility is plotted in the inset of Figure 4(a).
The linear part (paramagnetic region) of this curve is fitted through Curie-
Weiss law, $\chi=C/(T-\Theta_{CW})$. The positive value of $\Theta_{CW}$
indicates the ferromagnetic ordering of these materials at lower temperatures.
The effective magnetic moments are 3.76 $\mu_{B}$/FU, 3.51 $\mu_{B}$/FU and
3.32 $\mu_{B}$/FU, calculated from the Curie constant C. The spin only moment
value of Mn3+ is 4.9 $\mu_{B}$. So, the theoretical magnetic moments for
x=0.05, 0.15 and 0.25 are 4.66 $\mu_{B}$/FU, 4.17 $\mu_{B}$/FU and 3.68
$\mu_{B}$/FU, respectively. It is clearly seen that there is a difference
between experimental and theoretical moment value. In the octahedral
environment the d-orbital of Mn3+ ion is separated to eg and t2g due to the
crystal field effect. This discrepancy of the moment arises due to the much
stronger crystal field interaction than the spin-orbit interaction. But with
lower Mn-concentration this difference in the moment is small due to the
presence of extra Mn4+ in the system, which is proved from the XPS data
previously. In this case, the crystal field interaction creates less impact
because there is no eg electron in Mn4+-ion. The origin of ferromagnetic
character of these material are mainly due to the double exchange interaction
(DE) between Mn3+ and Mn4+ through the O2--ion. One t2g electron of Mn3+
transfers through O2--ion to Mn4+, creates the ferromagnetism in these
materials.

Table 2: Calculated magnetic moments of each atoms, interstitial and cell for Al doped LaMnO3 in $\mu_{B}$ unit Symmetry | Materials | $\mu_{La}$ | $\mu_{Al}$ | $\mu_{Mn^{1}}$ | $\mu_{Mn^{2}}$ | $\mu_{O}$ | $\mu_{int}$ | $\mu_{cell}$
---|---|---|---|---|---|---|---|---
Pnma | LAM95 | 0.01 | 0.007 | 3.23 | -3.24 | -0.06 | -0.51 | 3.99
| LAM85 | 0.01 | 0.006 | 3.37 | 3.40 | 0.02 | 3.23 | 27.98
| LAM75 | 0.02 | 0.003 | 2.86 | 3.01 | 0.04 | 2.44 | 11.99
R-3c | LAM95 | 0.01 | 0.008 | 2.96 | 2.58 | 0.05 | 2.51 | 30.00
| LAM85 | 0.01 | 0.009 | 3.76 | 3.68 | -0.02 | 1.83 | 28.00
| LAM75 | 0.01 | 0.015 | 3.70 | 3.69 | -0.01 | 0.76 | 12.00

Figure 4(b) and its inset figure represent the magnetic hysteresis loop and
its zoomed view of these three materials at 80 K. For x=0.05, the loop behaves
like ferromagnet as magnetization saturates in high 10 kG magnetic field. The
value of coercivity HC = 333 Oe and the remanent magnetization Mr = 0.25
$\mu_{B}$/f.u. suggest the ferromagnetic behaviour of this material. In case
of x=0.15, the curve also saturates at high field and coercivity HC = 78.15 Oe
and the remanent magnetization Mr = 0.11 $\mu_{B}$/f.u., which indicates the
ferromagnetic character of this material. But for x=0.25 sample, we have seen
the paramagnetic type behaviour at 80 K.

###  4.3 Electronic and Magnetic Structure: DFT

The electronic and magnetic structure of the material play a crucial role for
different transport properties of the materials. To know the better physics of
the material, the first principle density functional theory is most accurate
tool in this regards. The crystal structure should be optimized to get
accurate results. The minimization of the energy with respect to the volume is
a best way to achieve a optimized structure. However, we have taken the atomic
coordinates and lattice parameters of the Rhombohedral R-3c LaMnO3 and
optimized this structure through the WIEN2K structure optimization. We have
used four different spin configurations (FM, A-AFM, C-AFM and G-AFM). Among
these we have seen that FM has the lowest energy, so the LaMnO3 is
ferromagnetic (Figure 5). Then we have introduced the Al-atom by replacing
some Mn-ion with appropriate proportion 5%, 15% and 25% in the B-site of the
perovskites. All the structures have shown the ferromagnetic in the ground
state.

But, in literature, we have seen that the Orthorhombic Pnma LaMnO3 shows the
A-type antiferromagnetic spin configuration in the ground state. So, we have
taken this structure and optimized for four different spin configurations. The
result of this study shows that the A-AFM has the lowest energy among them.
So, the structural symmetry has responsible for the magnetic structure in this
case. The superexchange interaction through Mn+3-O-Mn+3 causes the
antiferromagnetic interaction of this material. In the orthorhombic structure,
there is very less amount of Mn4+. So, the superexchange interaction has
dominated over the ferromagnetic DE interaction (Mn+3-O-Mn+4). Now, for the 5%
Al-doped LaMnO3 (Pnma), shows the A-AFM magnetic structure in the ground
state. But the other two materials have shown the FM ground state. The doping
of non magnetic Al-atom (above 5%) breaks the superexchange AFM interaction
between NN Mn+3-ions.

Figure 7: The DOS and PDOS curve for (a,b) Pnma LaAlxMn1-xO3 [x= 0.05, 0.25]
and (c,d) R-3c LaAlxMn1-xO3 (x= 0.05, 0.25). The Fermi energy (EF) is set to
zero, shown with the vertical dotted line.

The bond lengths of Mn-O in MnO6 octahedra derived from DFT are 1.69 Å, 2.09
Å, and 2.24 Åfor Pnma LAM95 structure. Whereas these bond lengths become 1.91
Å, 1.96 Å, and 2.18 Åfor Pnma LAM85. So, clearly the John-Teller effect is
dominated in the 1st case which leads to the antiferromagnetic ground state of
0.05% Al doped LaMnO3. The John-Teller effect lifting the degeneracy of eg
orbital and the system shows the orbital ordering, which is responsible for
long range AFM ordering of Mn-ions here. This is called the cooperative John-
Teller effect. In the second case, the cooperative JT effect disappears which
means the system is no longer antiferromagnetic. For, LaGa1-xMnxO3, the
antiferromagnetic state is progressively destroyed above the 30% of Ga-doped
LaMnO3 and the compound becomes ferromagnetic just like our case[47].

The Total DOS and the partial DOS of Al-doped LaMnO3 (x=0.05 and 0.25) are
shown in figure 6(a-d). Figure 6(a) represents the DOS of Pnma LAM95. In the
TDOS, we see a symmetric states for up and down spin configuration, which
proves the antiferromagnetic character present here. But for 25% Al-doped
compound, we clearly a asymmetric Total DOS, which confirms the ferromagnetic
ground state. For Pnma space group, it shows some gap in the Fermi level for
both spins, which indicate the semiconducting behaviour of these compounds.
But for R-3c space group, there is no gap in the up-spin states whereas in
down-spin it creates some gap for all compounds, which support the half-
metallic behaviour of these materials. It also shows the asymmetric DOS in the
TDOS for up and down spins because of the ferromagnetic ground state of these
compounds. The U-value for Mn is taken to 4 eV for all calculations.

Figure 8: The magnetic properties are shown for LaAlxMn1-xO3 (x= 0.05, 0.15,
0.25) from the Monte-Carlo simulation (a) The Magnetization vs Temperature
curve, (b) The magnetic susceptibility (c) The specific heat curve and (d) The
magnetic hysteresis curve with respect to external magnetic field.

###  4.4 Magnetic properties: Monte-Carlo Simulation

Now, we have studied the magnetic properties of Al-doped LaMnO3 from the
Monte-Carlo simulation. The magnetic properties of these materials arise from
the Mn-atom, which is situated at the corner-site of the unit cell. The
interaction between two nearest neighbour Mn-ion must be ferromagnetic for
these case. So, the interaction constant is a very important parameter to
determine the magnetic state. We have calculated the nn and nnn interaction
constants $J_{1}$ and $J_{2}$ from our DFT data. The constants are calculated
from the following equation[48, 49, 50],

$J_{1}=\frac{E_{A-AFM}-E_{FM}}{2*Z*(S_{1}.S_{2})}$ (2)
$J_{2}=\frac{E_{C-AFM}-E_{G-AFM}}{2*Z*(S_{1}.S_{2})}$ (3)

And the magnetic anisotropic constants are determined from this equation,

$\Delta=\frac{E_{a}}{\sum_{i}(S_{i})^{2}}$ (4)

Where, $E_{FM,AFM}$ stands for the minimum energy of different spin
configuration. The Z, $S_{1}$ and $S_{2}$ are co-ordination number and the
spin of two types of Mn ions. $E_{a}$ is the magnetic an-isotropic energy,
calculated from this literature[51]. The value of nn interaction constants
($J_{1}$) are 0.69 meV, 0.52 meV, and 0.56 meV respectively for x=0.05, 0.15,
and 0.25 samples. Whereas the nnn interaction constants ($J_{2}$) are 0.008
meV, 0.08 meV, and 0.01 meV respectively. The anisotropic constants are 0.017
meV, 0.013 meV, and 0.01 meV rexpectively. The experimental magnetic data
shows a long range ferromagnetism for all three cases. From the DFT
calculations, we have seen that the ferromagnetic configuration has the
minimum energy for the Rhombohedral R-3c space group.

Figure 8(a-c) and 8(d) represent the temperature-dependent magnetic properties
and magnetic hysteresis loop, derived with the help of these interaction
constants from the Monte-Carlo simulation. The value of magnetization
decreases sharply with increasing temperature for all three materials. The
magnetization curves follow the experimental DC-magnetization. The
magnetization for x=0.05 is lesser than the x=0.15 curve as the experimental
one. The presence of higher percentage of Mn4+-ion in x=0.15 material means
the more amount of double exchange interaction, which increases the
magnetization. Now the transition temperature of this ferromagnetism are
determined from the magnetic susceptibility and specific heat curve, displayed
in figure 8(b) and 8(c). The critical temperatures are 140 K, 110 K and 87 K
for x=0.05, 0.15 and 0.25 respectively. From the hysteresis curve, we have
seen that the saturation magnetization (MS) of x=0.15 is larger than the
x=0.05 material.

##  5 Conclusions

We have synthesized the LaAlxMn1-xO3 (x= 0.05, 0.15, 0.25) in sol-gel
procedure. The XRD data confirm the R-3c symmetry of the all compounds. The
mixed valance of Mn-ions (Mn3+ and Mn4+) are present of 25% Al doped material.
For balancing the extra oxygen (3+$\delta$), the system introduces the
Mn4+-ion which is responsible for the ferromagnetic DE interaction. As a
result, the experimental magnetic study shows the ferromagnetic transition of
these materials. We have performed the DFT calculations to see the magnetic
ground state. We have seen the cooperative John-Teller effect for Pnma space
group is responsible for antiferromagnetic state of 5% Al-doped compound. For
higher Al-concentrations, the JT-effect is vanishes and the systems shows the
ferromagnetic behaviour. We have performed the Monte Carlo simulation through
the anisotropic Ising model to analyze the origin of magnetic transition. The
interaction constants are calculated from the DFT calculations. It shows the
ferromagnetic behaviour for all the compounds and the critical temperatures
are 140 K, 110 K and 87 K for x=0.05, 0.15 and 0.25 respectively.

##  6 Acknowledgement

T.K Bhowmik would like to thank Department of Science and Technology (DST),
Government of India for providing the financial support in the form of DST-
INSPIRE fellowship (IF160418).

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