#  Large magnetoresistance and first-order phase transition in
antiferromagnetic single-crystalline EuAg4Sb2

Sudip Malick<EMAIL_ADDRESS>Hanna Świątek  Faculty of Applied Physics
and Mathematics, Gdansk University of Technology, Narutowicza 11/12, 80-233
Gdańsk, Poland  Advanced Materials Center, Gdansk University of Technology,
Narutowicza 11/12, 80-233 Gdańsk, Poland  Joanna Bławat  John Singleton
National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los
Alamos, NM 87545, USA  Tomasz Klimczuk<EMAIL_ADDRESS>Faculty of
Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza
11/12, 80-233 Gdańsk, Poland  Advanced Materials Center, Gdansk University of
Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland

###### Abstract

We present the results of a thorough investigation of the physical properties
of EuAg4Sb2 single crystals using magnetization, heat capacity, and electrical
resistivity measurements. High-quality single crystals, which crystallize in a
trigonal structure with space group $R\bar{3}m$, were grown using a
conventional flux method. Temperature-dependent magnetization measurements
along different crystallographic orientations confirm two antiferromagnetic
phase transitions around $T_{N1}$ = 10.5 K and $T_{N2}$ = 7.5 K. Isothermal
magnetization data exhibit several metamagnetic transitions below these
transition temperatures. Antiferromagnetic phase transitions in EuAg4Sb2 are
further confirmed by two sharp peaks in the temperature-dependent heat
capacity data at $T_{N1}$ and $T_{N2}$, which shift to the lower temperature
in the presence of an external magnetic field. Our systematic heat capacity
measurements utilizing a long-pulse and single-slope analysis technique allow
us to detect a first-order phase transition in EuAg4Sb2 at 7.5 K. The
temperature-dependent electrical resistivity data also manifest two features
associated with magnetic order. The magnetoresistance exhibits a broad hump
due to the field-induced metamagnetic transition. Remarkably, the
magnetoresistance keeps increasing without showing any tendency to saturate as
the applied magnetic field increases, and it reaches $\sim$20000% at 1.6 K and
60 T. At high magnetic fields, several magnetic quantum oscillations are
observed, indicating a complex Fermi surface. A large negative
magnetoresistance of about -55% is also observed near $T_{N1}$. Moreover, the
$H$-$T$ phase diagram constructed using magnetization, heat capacity, and
magnetotransport data indicates complex magnetic behavior in EuAg4Sb2.

##  I INTRODUCTION

Even though there is a lack of single-ion anisotropy in divalent europium ($S$
= 7/2 and $L$ = 0), which results in negligible crystalline electric field
(CEF) effects, its compounds often manifest intriguing magnetic phase
transitions, leading to complex magnetic phase diagrams. Thus, Eu-based
intermetallics have always been fascinating candidates for exploring complex
magnetism Sengupta  _et al._ (2005); Jeevan  _et al._ (2008); Jin  _et al._
(2019); Paramanik  _et al._ (2014); Pöttgen and Johrendt (2000); Malick  _et
al._ (2022); Seiro and Geibel (2013); Bednarchuk and Kaczorowski (2015).
Meanwhile, the discovery of chiral magnetic anomalies, the anomalous Hall
effect, and the topological Hall effect in magnetic topological materials have
drawn significant attention to the Eu-based compounds as they offer an ideal
platform for studying the interplay between magnetism and band topology
Bernevig  _et al._ (2022); Tokura  _et al._ (2019); Yan and Felser (2017);
Chang  _et al._ (2018); Rout  _et al._ (2019). EuCd2As2, EuMg2Bi2, Eu$T$As
($T$ = Au and Ag), and EuB6 are the few examples of such magnetic topological
materials Ma  _et al._ (2020); Roychowdhury  _et al._ (2023); Marshall  _et
al._ (2021); Kondo  _et al._ (2023); Malick  _et al._ (2022); Laha  _et al._
(2021); Nie  _et al._ (2020); Gao  _et al._ (2021). Recently, the trigonal
CaCu4P2-type Eu-based ternary pnictide has received significant attention, as
this family of compounds reveals several interesting physical properties. For
instance, two successive antiferromagnetic transitions below 15 K and several
metamagnetic transitions under applied magnetic field are observed in EuAg4As2
Zhu  _et al._ (2021). Interestingly, the system goes to an incommensurate
noncollinear AFM state below 9 K, exhibiting an anomalous Hall effect. It also
shows unusual magnetoresistance ($MR$) with large positive as well as negative
values. The MR reaches 202% at 2 K and -78% around 10 K at 9 T. Similar
magnetotransport behavior is observed in ferromagnetic EuCu4As2 Li  _et al._
(2022). On the other hand, the non-magnetic members of this series, such as
Sr$T_{4}Pn_{2}$ ($T$ = Ag and Cu, $Pn$ = As and Sb), CaCu4As2, and SrCu4-xP2,
also feature several remarkable physical properties. For example, a phase
transition associated with a structural distortion is observed in SrAg4As2,
which also shows quantum oscillations associated with small Fermi pockets.
Intriguingly, some of the compounds, such as SrAg4Sb2, CaCu4As2 and SrCu4-xP2,
host nontrivial band topology, which results in the observation of large non-
saturating magnetoresistance, quantum oscillations, and multilayer quantum
Hall effect Shen  _et al._ (2018); Nie  _et al._ (2023a, 2024, b); Sasmal  _et
al._ (2022).

Here we explore another compound, EuAg4Sb2, from the same family, which is the
magnetic analogue of SrAg4Sb2 and has the potential to show complex magnetic
behavior and topological phenomena. Earlier investigation revealed that
EuAg4Sb2 crystallizes in CaCu4P2-type centrosymmetric trigonal structure with
space group $R\bar{3}m$ (No. 166); it orders antiferromagnetically below 11 K
and exhibits a metamagnetic transition at 0.24 T Gerke  _et al._ (2013).
However, there is no detailed investigation of the physical properties of
single crystals. This report thoroughly investigates the physical properties
of single crystals of EuAg4Sb2 along different crystallographic orientations
using magnetic, thermodynamic, and magnetotransport measurements. Magnetic
measurements reveal two antiferromagnetic phase transitions and multiple
metamagnetic phase transitions. Temperature-dependent heat capacity and
resistivity measurements further corroborate the magnetic phase transitions in
EuAg4Sb2. Careful heat capacity measurements allow us to detect a first-order
phase transition at 7.5 K. We have observed unusually large positive as well
as negative magnetoresistance in EuAg4Sb2. The constructed magnetic phase
diagram suggests a complex magnetic structure for EuAg4Sb2.

##  II EXPERIMENTAL DETAILS

Figure 1:  (a) Powder XRD pattern of the crushed single crystals with the
Rietveld refinement analysis. The red dots are the experimentally observed
data, and the black line is the calculated XRD pattern from the analysis. The
blue line represents the difference between the intensity of experimental and
calculated data. Green vertical lines are the Bragg positions. (b) Single
crystal XRD pattern. The inset shows an optical image of a single crystal. (c)
A schematic diagram of the crystal structure of EuAg4Sb2.

The single crystals of EuAg4Sb2 were grown using Ag-Sb binary flux as
described in Ref. Nie  _et al._ (2023a) for SrAg4Sb2. High purity elements Eu
(99.9%, Onyxmet), Ag (99.999%, Alfa Aesar), and Sb (99.999%, Alfa Aesar) were
taken in 1:7:4 molar ratio. All the elements were mixed thoroughly and put
into an alumina crucible. The crucible was sealed in a quartz ampule with
partial argon pressure. The ampule was then heated to 1000∘C for 10 h and
slowly cooled down to 600∘C at a rate of 1.5∘C/h. The ampule was taken out
from the furnace at 600∘C and the crystals were separated from the flux by
centrifuging. An optical image of a single crystal is displayed in the inset
in Fig 1(b). The crystal structure was confirmed by x-ray diffraction (XRD)
using a Bruker D2Phaser diffractometer with Cu Kα1 radiation. The chemical
composition was checked by energy dispersive x-ray spectroscopy (EDS)
employing a FEI Quanta FEG 250 electron microscope. All the physical
properties of the compound were measured in a Quantum Design EverCool-II
Physical Property Measurement System (PPMS). Electrical resistivity
measurements were performed using conventional four-probe techniques.
Measurements of heat capacity were carried out using the short as well as long
heat pulse method on the PPMS platform. Magnetic measurements were conducted
using a vibrating sample magnetometer (VSM) attached to the PPMS. The high
magnetic field data were taken at the pulsed-field facility of the National
High Magnetic Field Laboratory (NHMFL, Los Alamos). We performed Proximity
Detector Oscillator (PDO) measurements using a 10-turn pancake coil made of
50-gauge copper wire. The coil was connected to the PDO circuit with a
resonant frequency of 26 MHz. The technique is sensitive to the skin depth,
and therefore can be used to probe changes in conductivity, including magnetic
quantum oscillations Ghannadzadeh  _et al._ (2011); Götze  _et al._ (2020).
The magnetoresistivity measurements were performed using standard four-probe
technique. An AC current of 1 mA was applied at f = 100 kHz.

##  III Results and discussion

###  III.1 Crystal structure

The powder and single crystal XRD patterns collected at room temperature are
presented in Figs. 1 (a) and 1(b), respectively. The powder XRD pattern was
analyzed using the Rietveld refinement method in Fullprof software, which
suggests EuAg4Sb2 crystallizes in trigonal structure with space group
$R\bar{3}m$ (No. 166), which can be derived from the CaAl2Si2 Gladyshevskii
(1967) structure type by placing two additional silver atoms within the slab,
creating [Ag4Sb2]-2 layers. A schematic diagram of the crystal structure is
shown in Fig. 1(c). Within each layer, the Ag1 and Ag2 atoms form buckled
hexagons, which can be seen in the lower part of the figure. The estimated
lattice parameters from the refinement are $a$ = 4.7189(3) Å and $c$ =
24.661(3) Å , which agree well with the previous report Gerke  _et al._
(2013). Fig 1(b) shows the single-crystal XRD pattern of EuAg4Sb2, which has
extremely sharp reflections along (00$c$) directions, suggesting that the
crystallographic $c$ axis is perpendicular to the flat plane of the single
crystals. The sharp peaks indicate high crystalline quality of the grown
single crystals. Additionally, EDS data acquired from various points on the
single crystals confirms the expected stoichiometry.

###  III.2 Magnetic Properties

Figure 2:  Magnetic properties of single-crystal EuAg4Sb2: (a) and (b) $M/H$
data as a function of temperature for various fields applied along the
$H\parallel ab$ and $H\parallel c$ crystallographic orientations,
respectively. The inset of (a) shows the magnetic susceptibility in the 2–25 K
temperature range for $\mu_{0}H$ = 0.1 T along different crystallographic
directions. Inverse susceptibility and CW fits up to room temperature are
presented for both directions in the inset of (b). Isothermal magnetization
for magnetic fields of up to $\pm$4 T at 2 K applied along $H\parallel ab$ (c)
and $H\parallel c$ (d). Both the insets in (c) and (d) show the enlarged view
of the $M(H)$ data, revealing a hysteresis loop. The right panels of (c) and
(d) exhibit the first-order derivative of the $M(H)$ data, indicating the
critical fields. Magnetization data at various temperatures up to 4 T for
$H\parallel ab$ (e) and $H\parallel c$ (f). The inset of (e) indicates the
critical field $H_{C2}^{ab}$.

Magnetization ($M$) data at various applied fields (H) in the zero-field
cooled (ZFC) and field cooled (FC) configurations in the temperature range
2–30 K for $H\parallel ab$ and $H\parallel c$ crystallographic directions for
a EuAg4Sb2 single crystal are presented in Figs. 2(a) and 2(b), respectively.
The temperature-dependent $M/H$ data at 0.1 T along both crystallographic
directions show a cusp and a kink around $T_{N1}$ = 10.6 K and $T_{N2}$ = 7.5
K, respectively, indicating antiferromagnetic (AFM) phase transitions. A
similar temperature dependence of magnetic susceptibility ($\chi=M/H$) has
also been observed previously in polycrystalline EuAg4Sb2 Gerke  _et al._
(2013). As the applied field strength increases, the $T_{N1}$ and $T_{N2}$
shift to a lower temperature, a typical signature of an AFM Pakhira  _et al._
(2020). Both the anomalies are smeared out for fields $\mu_{0}H\geq 0.4$ T and
$\mu_{0}H\geq 3$ T along $H\parallel ab$ and $H\parallel c$, respectively.
Interestingly, a slight bifurcation is observed at low temperatures at
$\mu_{0}H=0.4$ T for $H\parallel ab$ in the ZFC and FC data, probably due to a
field-induced metamagnetic (MM) transition. However, in the $H\parallel c$
direction, no irreversible behavior is seen between the ZFC and FC data. The
magnetic susceptibility near the ordering increases significantly along
$H\parallel ab$ compared to the $H\parallel c$ direction, as illustrated in
the inset of Fig. 2(a). On the other hand, at low temperatures (below
$T_{N2}$), $\chi$ is larger along $H\parallel c$; it is nearly independent of
temperature and does not drop significantly below the magnetic ordering
temperature, as expected for a typical AFM. All these features suggest that
Eu2+ moments likely lie in the $ab$-plane and indicate a non-collinear
incommensurate magnetic structure, as observed in the isostructural Eu-based
compound EuAg4As2 Zhu  _et al._ (2021); Shen  _et al._ (2020). Moreover, at
temperatures above magnetic order, the $\chi(T)$ data can be described using
the Curie-Weiss (CW) law:

$\chi(T)=\dfrac{C}{T-\Theta_{P}}$ (1)

where $C$ is the Curie constant and $\Theta_{P}$ is the Curie temperature. The
inset of Fig. 2(b) shows a fit of the CW law to the $\chi^{-1}(T)$ data
measured at 0.1 T in the temperature range 20-300 K. The estimated values of
effective moment and Curie temperature are presented in Table 1. The effective
moment obtained is close to the theoretical value for the Eu2+ ion
($g\sqrt{S(S+1)}=7.94\mu_{B}$, $S=7/2$ and $g=2$). The fitted $\Theta_{P}$ is
positive for both crystallographic directions, as observed in the
polycrystalline sample, indicating a predominance of ferromagnetic exchange
interactions in the paramagnetic state of EuAg4Sb2 Gerke  _et al._ (2013).

Table 1: The estimated effective moment and Curie temperature along different crystallographic orientations are obtained from the CW fit. |  $H\parallel ab$ |  $H\parallel c$
---|---|---
$\mu_{eff}(\mu_{B})$ |  7.91(1) |  7.86(1)
$\Theta_{P}$(K) |  14.2(2) |  7.6(1)

Figs. 2(c) and 2(d) show the magnetization data acquired at 2 K for fields of
up to $\pm$4 T applied along the $H\parallel ab$ and $H\parallel c$
crystallographic orientations. As the magnetic field increases, the
magnetization initially increases linearly, consistent with expectations for
an AFM; but, around $H_{C1}^{ab}$ = 0.33 T ($H\parallel ab$) and $H_{C1}^{c}$
= 0.65 T ($H\parallel c$) there is a sudden jump in magnetization. For a field
larger than $H_{C1}$, $M$ increases linearly until $H_{C2}^{c}$ = 1.67 T for
$H\parallel c$, where it shows another jump in the magnetization. With further
increase of applied field strength, the magnetization saturates near
$H_{C3}^{ab}$ = 1.13 T and $H_{C3}^{c}$ = 3.16 T. The saturation values are
6.3 $\mu_{B}$ ($H\parallel ab$) and 6.9 $\mu_{B}$ ($H\parallel c$), close to
the theoretical value $gS\mu_{B}$ = 7 $\mu_{B}$ for the Eu2+ ion. The
derivative of $M$ as a function of $\mu_{0}H$, depicted in the right panel of
Fig. 2(c), reveals the critical fields where those magnetization jumps occur.
Such jumps in magnetization are due to field-induced metamagnetic transitions.
Interestingly, a hysteresis loop is seen in the metamagnetic transition
corresponding to $H_{C2}^{ab}$ and $H_{C1}^{c}$ for increasing and decreasing
fields, as illustrated in the inset of Figs. 2(c) and 2(d), respectively. The
observed hysteresis around the metamagnetic transitions indicates that these
phase transitions are likely first-order Cheng  _et al._ (2012). We have also
measured magnetization at various temperatures to get more insight into these
transitions, as shown in Figs. 2(e) and 2(f). As the temperature increases,
all the critical fields shift to lower values, and the observed anomalies
disappear. Surprisingly, along $H\parallel ab$, an additional metamagnetic
transition emerges at $H_{C2}^{ab}$ $\sim$ 0.3 T for $T\geq$ 4 K and persists
up to 10 K. For $T>$ 30 K, which is well above the magnetic ordering
temperature, the magnetization increases linearly as one anticipates for a
paramagnetic state at relatively low magnetic fields. Notably, the behavior of
$M(H)$ data closely resembles that of the isostructural compound EuAg4As2,
which reveals an incommensurate, non-collinear AFM state at low temperatures,
as confirmed by a neutron diffraction study Zhu  _et al._ (2021); Shen  _et
al._ (2020). Therefore, a thorough investigation using neutron diffraction
measurements is important to understand the complex magnetic structure of
EuAg4Sb2. Nevertheless, similar behavior of the magnetization isotherms is
also observed in Eu-based compounds like Eu3Ni4Ga4 Anupam  _et al._ (2012),
EuFe2As2 Jiang  _et al._ (2009), and EuCuAs Tong  _et al._ (2014).

###  III.3 Heat capacity

Figure 3: (a) The temperature dependence of heat capacity in the absence of
external magnetic field measured in the temperature range 2-160 K. The red
solid line represent the fitting of the data with the Eq. 2. Inset shows the
calculated magnetic entropy. (b) The evolution of the anomalies in the heat
capacity under the applied magnetic field ranging from 0 to 1.1 T with a step
of 0.1 T for the $H\parallel$ c. The inset depicts the zero-field $C_{P}$($T$)
data obtained from the warming and cooling cycles near $T_{N2}$. Figure 4: (a)
Zero-field electrical resistivity over the temperature range 2 - 300 K. The
inset shows an expanded view of $\rho$($T$) at low temperatures, highlighting
the features due to the AFM transitions at $T_{N1}$ and $T_{N2}$. The solid
green line represents the $T^{3/2}$ dependence of the electrical resistivity
in the AFM ground state. (b) Temperature-dependent electrical resistivity
under various applied fields 0 T $\leq\mu_{0}H\leq$ 9 T, where $H\parallel c$.
(c) Magnetoresistance as a function of magnetic field applied along
$H\parallel c$ at selected temperatures between 2 and 50 K. Inset shows the
first derivative of MR as a function of the field, indicating the critical
fields. (d) Field-dependent MR data up to 60 T at 1.6 K. The dashed red line
demonstrates that MR follows the $H^{1.6}$ field dependence in the high-field
region. The inset displays a clear quantum oscillation after a smooth
background subtraction.

Fig. 3(a) shows the zero-field heat capacity ($C_{P}$) data at constant
pressure as a function of temperature. At low temperatures, $C_{P}$($T$)
exhibits two sharp anomalies at $T_{N1}$ = 10.5 K and $T_{N2}$ = 7.5 K as a
manifestation of AFM transitions, as observed in the magnetic susceptibility
data. The anomaly at $T_{N2}$ is extremely sharp, indicating a first-order
phase transition, whereas the AFM transition at $T_{N1}$ is likely a second-
order phase transition. A more detailed discussion about these transitions can
be found later. The behavior of the $C_{P}$($T$) above the magnetic ordering
temperature can be well replicated by considering the Debye ($C_{D}$) and
Einstein ($C_{E}$) models of specific heat, as combined in the equation
Pakhira  _et al._ (2020)

$C_{P}(T)=\gamma T+mC_{D}+(1-m)C_{E}~{}.$ (2)

The first term of the above equation is the electronic contribution to heat
capacity. The $\gamma$ is known as the Sommerfeld coefficient. The weight
factor $m$ establishes the proportionate contributions between $C_{D}$ and
$C_{E}$ to the total heat capacity. We use the semi-empirical method used in
Ref. Pakhira  _et al._ (2020) to treat the heat capacity of the related
material EuMg2Bi2. $C_{D}$ and $C_{E}$ are formulated as

$C_{D}=9nR\left(\frac{T}{\Theta_{D}}\right)^{3}\int_{0}^{\Theta_{D}/T}\frac{x^{4}e^{x}}{(e^{x}-1)^{2}}dx~{},$
(3)

$C_{E}=3nR\left(\frac{\Theta_{E}}{T}\right)^{2}\frac{e^{\Theta_{E}/T}}{(e^{\Theta_{E}/T}-1)^{2}}~{}.$
(4)

Fitting Eq. 2 to the heat capacity data yields $\gamma$ = 22.3 mJ/ mol K, $m$=
0.79, $\Theta_{D}$ = 208 K, and $\Theta_{E}$ = 50 K. The obtained fitting
parameters are comparable to the isostructural compound EuCu4As2 Li  _et al._
(2022). To get a rough estimation of magnetic entropy, we have extrapolated
the fitting to 2 K and subtracted it from the experimental data to obtain the
magnetic component ($C_{mag}$) of heat capacity. The inset of Fig. 3(a) shows
the magnetic entropy computed using the expression,
$S_{mag}=\int\frac{C_{mag}}{T}dT$. The magnetic entropy at $T_{N1}$ is about
14.5 J/mol K, and it increases further as temperature increases and saturates
around 16 K to an expected value of $S_{mag}=Rln(2S+1)$ = $Rln8$ for the Eu2+
ion.

All the low-temperature heat capacity data presented in Fig. 3 has been
measured using the long heat pulse technique, and the data extracted from the
single-slope analysis method in Quantum Design PPMS, which is one of the most
effective ways to identify a first-order phase transition Scheie (2018). The
observed peak at $T_{N2}$ is extremely sharp, having a full width at half
maximum (FWHM) of less than 0.1 K. In addition, a thermal hysteresis of around
0.16 K appears in the warming and cooling cycle of the $C_{P}$($T$) data, as
shown in the inset of Fig. 3(b). Remarkably, a discontinuity in temperature-
dependent magnetic entropy at $T_{N2}$ can be seen in the inset of Fig. 3(a).
All of these observations support the first-order nature of the AFM
transition, probably attributed to the reconstruction of the AFM structure
below $T_{N2}$ Kumar  _et al._ (2016); Guillou  _et al._ (2018). Fig. 3(b)
depicts the $C_{P}$($T$) at low temperatures for various applied fields. Both
features shifted to lower temperatures, with peaks broadening as the magnetic
field intensity increased, which is a typical characteristic of an AFM.

Figure 5:  (a) PDO data as a function of $1/\mu_{0}H$ after smooth background
subtraction measured at 12 T window along $H\parallel c$. (b) The frequency-
dependent FFT signals measured at various temperatures. The inset shows the
fitting of the FFT amplitude to Eq. 6.

###  III.4 Magnetotransport

Table 2: The parameters obtained from the quantum oscillation. |  $F_{\alpha}$ |  $F_{\beta}$ |  $F_{\gamma}$ |  $F_{\delta}$ |  $F_{\sigma}$ |  $F_{\eta}$
---|---|---|---|---|---|---
Frequency (T) |  22 |  160 |  193 |  1120 |  1273 |  1460
$m^{*}$ ($m_{e}$) |  – |  0.16 $\pm$ 0.01 |  0.19$\pm$ 0.01 |  0.67 $\pm$ 0.05 |  0.68 $\pm$ 0.05 |  0.64 $\pm$ 0.04
$A_{F}$ (nm-2) |  0.21 |  1.53 |  1.84 |  10.70 |  12.16 |  13.94
$k_{F}$ (nm-1) |  0.26 |  0.70 |  0.77 |  1.84 |  1.97 |  2.11
$v_{F}$ (106ms-1) |  – |  0.51 |  0.47 |  0.32 |  0.34 |  0.38

The electrical resistivity $\rho$($T$) as a function of temperature measured
in zero magnetic field for current along the $ab$-plane in the EuAg4Sb2 single
crystal is shown in Fig. 4 (a). $\rho$($T$) decreases monotonically with
decreasing temperature in a metallic fashion down to 25 K, then it starts to
increase and exhibits a peak at 10.7 K and a kink at 7.5 K as the system goes
through two antiferromagnetic phase transitions at these temperatures.
Remarkably, the behavior of electrical resistivity at low temperatures mimics
the magnetic susceptibility data seen in Fig. 2(a). The residual resistivity
ratio [RRR =$\rho$(300 K)/$\rho$(2 K) ] $\sim$ 50, is very high, suggesting
the very good quality of the as-grown single crystals. A similar RRR value is
also found in the nonmagnetic analogue compound SrAg4Sb2 Nie  _et al._
(2023a). The behavior of $\rho$($T$) above the magnetic ordering temperature
can be well explained by considering electron-phonon ($ep$) and electron-
electron ($ee$) scattering as described by the expression below v. Minnigerode
(1983)

$\small\rho_{xx}(T)=\rho_{0}+4R\left(\frac{T}{\Theta_{R}}\right)^{5}\int_{0}^{\Theta_{R}/T}\frac{x^{5}}{(e^{x}-1)(1-e^{-x})}dx+aT^{2},$
(5)

where the first term is the temperature-independent residual resistivity, the
second term is the Bloch-Gruneisen (BG) scattering model, which accounts for
$ep$ scattering, and the last term is the contribution from the $ee$
scattering. The fit parameters are $\rho_{0}$ = 34 $\mu\Omega$cm, $R$ = 404
$\mu\Omega$cm, $\Theta_{R}$ = 202 K, and $a$ = 4.7$\times$10-4 $\mu\Omega$cm
K-2. The Debye temperature obtained is close to that estimated from the heat
capacity data. Moreover, the temperature-dependent electrical resistivity
below the magnetic phase transition follows a $T^{3/2}$ dependence, as found
in several AFM Chattopadhyay  _et al._ (2012); Kamada  _et al._ (1977).

In order to determine the effect of magnetic field on the electrical
resistivity, we conducted a systematic field-dependent measurement in the
temperature range 2–25 K with the field applied along $H\parallel c$, as
displayed in Fig. 4(b). As field strength increases, the ordering temperatures
shift to lower values, and both anomalies gradually disappear, in agreement
with magnetic susceptibility data. At $\mu_{0}H$ = 3 T, all resistivity peaks
disappear, suggesting metallic behavior. Interestingly, there is a large
positive magnetoresistance at low temperatures for $\mu_{0}H\geq$ 4 T; at 2 K
and 9 T, the resistivity reaches 40.6 $\mu\Omega$cm. Consequently, we measured
MR at several temperatures with the field applied along the $c$-axis, as shown
in Fig. 4(c). MR is calculated using the formula
$\textit{MR}=\dfrac{\rho(H)-\rho(0)}{\rho(0)}\times 100\%$, where $\rho(0)$
and $\rho(H)$ are the resistivity values in the absence and presence of the
external magnetic field. The MR measured at 2 K grows slowly with increasing
field, but at about 1.6 T, there is a significant jump in MR, resulting in a
broad hump which shifts to lower fields as the temperature increases, in
accordance with the $M(H)$ data. The abrupt increase in MR can be attributed
to increased magnetic scattering due to metamagnetic transitions. A
significant additional contribution to the resistivity on crossing the
boundary of the antiferromagnetic phase is likely to come from the
rearrangement of the Fermi surface as the magnetic unit cell changes,
resulting in an alteration of the density of states available for scattering
close to the Fermi energy Goodrich  _et al._ (2006). The dMR/d$H$ vs
$\mu_{0}H$ data, as presented in the inset of Fig. 4(c), exhibit three peaks,
which indicate three critical fields associated with the metamagnetic
transitions observed in the magnetization data. MR at low temperatures
continues to increase without showing any saturation. For $\mu_{0}H>$ 3, all
the spins are ferromagnetically aligned in the field direction, as indicated
by the magnetization; thus, one may anticipate saturation or a decrease in the
MR at high applied fields. Nevertheless, as the temperature increases, the MR
starts to decrease, and near the ordering temperature, it becomes negative due
to the suppression of magnetic scattering. At $T_{N1}$, it shows a maximum
negative MR of about -55%. Once the temperature increases beyond the ordering
temperature, the MR starts to increase again. However, at temperatures well
above magnetic order, MR is nearly independent of the external magnetic field.
Such behavior of MR near the ordering temperature is primarily due to the
response of magnetic scattering by the external field, as observed in similar
Eu-based compounds, EuAg4As2 and EuCu4As2 Zhu  _et al._ (2021); Li  _et al._
(2022). In order to investigate the high-field behavior of the sample,
additional measurements up to 60 T were performed at 1.6 K. The MR continues
to increase even at the highest field and reaches a very large value of $\sim$
20000%, as shown in Fig. 4(d). Moreover, MR follows a $H^{1.6}$ field
dependence, unlike the semi-classical $H^{2}$ dependence Niu and Zhu (2021). A
large MR is also observed in a similar compound, EuCu4As2, and its origin has
been attributed to a nontrivial band structure Li  _et al._ (2022). Likewise,
nonmagnetic SrAg4Sb2 exhibits unusually high MR due to its nontrivial
topological states Nie  _et al._ (2023a). Thus, the large non-saturating MR
and its deviation from the quadratic field dependence in EuAg4Sb2 may result
from a nontrivial band structure. The high-field MR data also indicates the
presence of quantum oscillations with multiple frequencies, suggesting a
complex Fermi surface.

Fig. 5(a) shows quantum oscillations after background subtraction using a
polynomial function in the contactless electrical resistivity data of EuAg4Sb2
measured using the proximity detector oscillator technique at high magnetic
fields (12 T $\leq\mu_{0}H\leq$ 60 T) and in the temperature range 0.68-60 K.
The PDO measurement detects Shubnikov-de Haas (SdH) oscillations in the
electrical resistivity, via the change in resonant frequencies ($f$) of the
oscillator circuit due to a change in the skin depth of the sample. The fast
Fourier transform (FFT), as shown in Fig. 5(b), reveals several fundamental
frequencies and their harmonics. The cyclotron effective mass can be
calculated by fitting the amplitude FFT signal to the temperature-dependent
part of the Lifshitz-Kosevich formula Shoenberg (2009)

$A(T,B_{m})\propto\dfrac{14.69m^{*}T/B_{m}}{sinh(14.69m^{*}T/B_{m})}$ (6)

where $B_{m}$ is the inverse-field midpoint of the field window used for the
FFT, defined as

$B_{m}=\left[\dfrac{1}{2}\left(\dfrac{1}{B_{1}}+\dfrac{1}{B_{u}}\right)\right]^{-1}$
(7)

Here, $B_{l}$ and $B_{u}$ are the lower and upper field limits of the window,
respectively. The estimated value of the effective mass and its corresponding
frequency are presented in Table 2. Frequency $F_{\alpha}$ exhibits unusual
temperature dependence, which limits the estimation of effective mass and is
subject to further study. Using the Onsager relation $F=(\hbar/2\pi e)A_{F}$,
we have calculated the cross-sectional areas of the Fermi surface ($A_{F}$)
perpendicular to the applied magnetic field. Further, under the assumption of
a circular Fermi-surface cross-section, we have estimated the Fermi wave
vectors ($k_{F}$) and the Fermi velocities ($v_{F}$) as presented in Table 2
using the expressions $k_{F}=\sqrt{2eF/\hbar}$ and $v_{F}=\hbar k_{F}/m^{*}$,
respectively, where $\hbar$ is the reduced Planck’s constant and $e$ is the
magnitude of electron charge.

###  III.5 $H$-$T$ phase diagram

To get an overall picture of the magnetic behavior of EuAg4Sb2 at low
temperatures, we have constructed an $H$-$T$ phase diagram based on the
magnetic, heat capacity, and magnetotransport measurements for the field
orientations $H\parallel ab$ and $H\parallel c$, as presented in Figs. 6(a)
and 6(b), respectively. The overall $H$-$T$ phase diagram can be divided into
six domains. As the temperature decreases from room temperature, the system
enters the first antiferromagnetic (AFM1) state from the paramagnetic (PM)
state around 10.5 K. With a further decrease in temperature, the system
exhibits a first-order AFM phase transition, as confirmed by the heat capacity
data. The region below this transition is labeled as AFM2. Both ordering
temperatures shift to lower temperatures with increasing magnetic field,
forming a distinct phase diagram boundary in accordance with the molecular
field theory expression $H=H_{0}[1-T_{N}(H)/T_{N}(H=0)]^{1/2}$, where $H_{0}$
is the critical field that destroys the antiferromagnetic transitions at 0 K
Sangeetha  _et al._ (2016). The estimated values of $\mu_{0}H_{0}$ for
$H\parallel ab$ are 0.39 T ($T_{N2}$), whereas for $H\parallel c$,
$\mu_{0}H_{0}$ = 3.5 T ($T_{N1}$) and 1.98 T ($T_{N2}$). When a magnetic field
of $H_{C1}$ is applied to the system within the AFM2 regime, the system
undergoes a metamagnetic transition (MM1). For $H\parallel ab$, the phase
boundaries MM1 and AFM2 overlap with each other. However, for $H\parallel c$,
MM1 and AFM2 create two separate regions. Another metamagnetic transition
(MM2) occurs when the magnetic field hits $H_{C2}$. These MM transitions are
most likely the results of spin-flop transitions Cheng  _et al._ (2012). At
low temperatures (below 6 K), the AFM2 and MM2 phase boundaries overlap in the
case of $H\parallel c$. As the applied magnetic field increases further, the
system undergoes another transition at $H_{C3}$, at which point all spins
align along the field direction; it behaves like a ferromagnet (FM).
Interestingly, for $H\parallel c$, the phase boundary for $H_{C3}$ at higher
fields almost overlaps with the first AFM transition. However, we could not
clearly distinguish between PM and FM states based on the available data.

Figure 6:  Magnetic phase diagram of EuAg4Sb2 single crystal for (a)
$H\parallel ab$ and (b) $H\parallel c$ orientations, constructed using
magnetization, heat capacity, and magnetotransport data. Black dot lines are
the hand drawing for visual guides. Orange dash lines originate from the
molecular field theory expression given in the text.

##  IV Conclusion

We have studied the magnetic, thermodynamic, and electrical transport
properties of high-quality single-crystal EuAg4Sb2 grown using Ag-Sb binary
flux. The XRD data confirm that EuAg4Sb2 crystallizes in a trigonal structure.
Our comprehensive analysis of temperature-dependent magnetization, electrical
resistivity, and heat capacity data reveals that EuAg4Sb2 orders
antiferromagnetically at 10.5 K and 7.5 K. The transition at 7.5 K is
identified as a first-order phase transition using systematic heat capacity
measurements performed with the long heat pulse technique. Several
metamagnetic transitions are observed in the isothermal magnetization data.
Further investigation using neutron diffraction measurements is required to
fully understand the complex magnetic structure of EuAg4Sb2. Interestingly, MR
displays non-saturation behavior at low temperatures, which reaches a very
large value of $\sim$20000% at 1.6 K and 60 T. Moreover, as the temperature
rises, the MR decreases and becomes negative. Near the first AFM phase
transition, a large negative value of about 55% is observed. In addition, the
field-dependent magnetoresistance shows a hump as a characteristic of
metamagnetic transitions. At high magnetic fields, several magnetic quantum
oscillations are observed, indicating a complex Fermi surface. Our findings on
EuAg4Sb2 indicate that it is an antiferromagnetic system with a complex
magnetic structure and a potential topological material.

##  V ACKNOWLEDGMENTS

The work at Gdansk University of Technology was supported by the National
Science Center (Poland), Grant No. 2022/45/B/ST5/03916. A portion of this work
was performed at the National High Magnetic Field Laboratory, which is
supported by National Science Foundation Cooperative Agreement No.
DMR-2128556, the US Department of Energy (DoE) and the State of Florida. JB
and JS acknowledge support from the DoE BES FWP “Science of 100 T”, which
permitted development of some of the high-field techniques used in the paper

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# Speaker recognition with two-step multi-modal deep cleansing

###### Abstract

Neural network-based speaker recognition has achieved significant improvement
in recent years. A robust speaker representation learns meaningful knowledge
from both hard and easy samples in the training set to achieve good
performance. However, noisy samples (i.e., with wrong labels) in the training
set induce confusion and cause the network to learn the incorrect
representation. In this paper, we propose a two-step audio-visual deep
cleansing framework to eliminate the effect of noisy labels in speaker
representation learning. This framework contains a coarse-grained cleansing
step to search for the peculiar samples, followed by a fine-grained cleansing
step to filter out the noisy labels. Our study starts from an efficient audio-
visual speaker recognition system, which achieves a close to perfect equal-
error-rate (EER) of 0.01%, 0.07% and 0.13% on the Vox-O, E and H test sets.
With the proposed multi-modal cleansing mechanism, four different speaker
recognition networks achieve an average improvement of 5.9%. Code has been
made available at: https://github.com/TaoRuijie/AVCleanse.

Index Terms—  speaker recognition, noisy label, audio-visual, deep cleansing

##  1 Introduction

Fig. 1: The proposed two-step audio-visual deep cleansing framework. The lock
represents that the network is frozen.

Automatic speaker recognition aims to distinguish a legitimate user from
imposters based on their voices [1, 2]. Over the last decade, deep learning-
based speaker representation, such as x-vector [3], xi-vector [4], and network
architectures, such as ResNet [5] and ECAPA-TDNN [6], have achieved remarkable
performance by training on the large-scale speech dataset. To further enhance
the performance, previous works usually focus on the network structure [7],
loss function [8] and back-end score calibration [9]. However, the existence
of noisy labels in the training set has not been taken care of.

Large-scale dataset for speaker recognition typically consists of thousands of
speakers and over millions of samples, whereby utterances from the same person
share the same speaker labels. These datasets are typically collected from the
Internet within automatic pipeline [10, 11]. However, it is not surprising to
find that utterances assigned with the same label might actually come from
different speakers, i.e., the noisy labels problem. From the study of noisy-
label learning, training data can be divided into three categories according
to the learning difficulty [12, 13]: easy, hard and noisy samples. Note that
we use the term noisy samples referring to samples with wrong labels following
the terminology in [10]. Due to the memorization effects [14], neural networks
tend to fit the easy samples and converge rapidly in the early stage of
training. In the later stage of training, the network has to distil correct
but difficult knowledge from the peculiar samples. However, these peculiar
samples contain hard and noisy samples, which deters the learning process.

Prior works dealing with noisy labels in speaker recognition include: training
the speaker network and manually setting the threshold to filter out the
unusual utterances [15]; dropping out the samples with large training loss as
the noisy data in self-supervised learning [16]. However, there are two major
problems with the existing approach. In terms of quality, it is challenging
for the speaker network to recognize the difficult utterances [17]. In terms
of logic, the speaker network has been trained on the entire dataset
(including noisy ones) and push them to their class centre. Using the same
network to decide the noisy ones is not a good choice.

In this paper, we propose a two-step multi-modal deep cleansing framework to
solve the above mentioned problems. Firstly, we do a coarse-grained cleansing
based on the speech modality only, which divides the training data into easy
and peculiar samples. Secondly, we train a new speaker recognition network
based on easy samples to do a fine-grained cleansing, which divides the
peculiar samples into hard and noisy ones. Since the network does not train on
the noisy samples, using it to do the cleansing is more reliable. On the other
hand, from the biometric recognition study [18, 19], face image and speech
utterance can provide complementary identity information. Motivated by this,
we use the face recognition network in the second step to boost the system.

Our contribution can be summarized as follows. Firstly, we propose a robust
audio-visual speaker recognition system which can achieve close-to-perfect
verification. Secondly, a two-step audio-visual cleansing framework is
designed to filter out the noisy data in the training set. Thirdly, four
speaker recognition networks are trained on the original and cleansed dataset
to show the impact of our method.

##  2 Audio-visual speaker recognition

In this section, we propose an efficient audio-visual speaker recognition
system containing both speaker and face modalities since a reliable identity
recognition system is the foundation of noisy sample cleansing.

For training, the speaker network is used to extract the speaker embedding
from the input utterance. This embedding contains the characteristics of the
speaker’s voice. Then it follows a speaker classifier to distinguish the
utterances from different speakers with an AAM-softmax loss [20]. Similarly,
the face network takes one face image as the input and outputs the face
embedding. This embedding is trained with a face classifier [21]. For testing,
speaker and face embeddings are used together to enhance the verification
performance.

Compared with previous works [22, 23], we take two strategies to simplify the
system and improve the stability. Firstly, we align all the faces with the
detected landmarks during preprocessing [24] since the unaligned faces in the
training set make recognition harder [25]. Secondly, existing approaches
usually attempt to combine the speaker and face modality by the attention
mechanism [18, 26]. However, we argue that training two modalities separately
and directly concatenating two embeddings for testing is an effective and
convenient solution. [23, 19]

##  3 Audio-visual deep cleansing

For audio-visual deep cleansing, we consider a training set with $N$ video
clips. Each video clip consists of synchronized speech utterance and face
frames. And, there exists a few video clips with wrong labels, i.e., noisy
samples. Our proposed audio-visual two-step deep cleansing framework is shown
in Fig 1 to discover these noisy samples.

###  3.1 Step 1: Coarse-grained cleansing

Firstly, we design coarse-grained cleansing to divide the training set into
easy and peculiar samples to narrow down the selection of noisy data. The main
concern of this step is successfully dividing all the noisy samples into the
peculiar class. It is noted that this step uses speech modality only since
face modality can only assist in deciding the correctness of samples.

Firstly, we train a speaker network with all the utterances in the training
set. Then we fix this network’s parameters and extract the speaker embeddings
from the entire training set. These embeddings are represented as
$s_{1},\cdots,s_{N}$. The corresponding speaker labels are annotated as
$c_{1},\cdots,c_{N},c_{i}\in\\{1,2,\cdots,K\\}$, where $K$ is the number of
speakers in the training set. Then we compute the average cosine similarity
between the speaker embedding of each sample and the other samples from the
same speaker. The score $x_{i}$ of the embedding $s_{i}$ can be represented
as:

$x_{i}=\frac{1}{M_{k}}\sum_{j=1}^{N}\mathbbm{1}_{\begin{subarray}{c}c_{i}=c_{j}\end{subarray}}{cos(s_{i},s_{j})}$
(1)

Here $M_{k}$ is the number of samples in the $k^{th}$ class. $\mathbbm{1}$ is
an indicator function evaluating 1 when $c_{i}=c_{j}$. For the computed
scores, we set a threshold $\tau$. Samples with scores smaller than $\tau$ are
the peculiar samples; otherwise, they are deemed to be easy samples.

###  3.2 Step 2: Fine-grained cleansing

As mentioned earlier, the network without training on the noisy samples can
provide an objective and accurate representation. Motivated by that, we train
the network without noisy samples in fine-grained cleansing to filter out
noisy samples.

####  3.2.1 Speaker and face network

Firstly, we train a new speaker network with the easy samples found from the
coarse-grained cleansing. Then considering sufficient annotated face datasets,
the pre-trained face recognition network is applied to our multi-modal
cleansing proposal. It is noted that training a face network with the images
of the found easy samples is also a reasonable solution.

####  3.2.2 Decision boundary

Then we train a classifier in the two-dimensional score space to separate
noisy samples from the hard samples. The binary classifier is trained on a
validation set consisting of target trials [10, 11], i.e., two video clips
from the same speakers, and the imposter trials, i.e., two video clips are
from different speakers. We can compute the speaker and face cosine similarity
for each trial using our multi-modal system. Then an SVM [27] is learnt on
these two-dimensional scores and using the ground-truth labels in the
validation. The SVM decision boundary can efficiently distinguish trials into
the target and the imposter ones. Target and imposter trials are associated
with the clean and noisy samples, respectively.

####  3.2.3 Deep cleansing

In this stage, we freeze the networks to extract the speaker and face
embeddings of all the samples in the training set. Speaker and face embeddings
are represented as $s_{1},\cdots,s_{N}$ and $f_{1},\cdots,f_{N}$,
respectively. We compute the average cosine similarity between the embedding
of each sample and the other samples from the same class. The speaker scores
$x_{i}$ of the embedding $s_{i}$ is similar to that in (1). The face score
$y_{i}$ of the embedding $f_{i}$ is computed as:

$y_{i}=\frac{1}{M_{k}}\sum_{j=1}^{N}\mathbbm{1}_{\begin{subarray}{c}c_{i}=c_{j}\end{subarray}}{cos(f_{i},f_{j})}$
(2)

Finally, we apply the learnt SVM to predict the correctness of each training
sample using $x_{i}$ and $y_{i}$. The samples predicted as the target trials
are defined as clean data; otherwise, they are noisy data.

##  4 Experimental setup

Our training set is the VoxCeleb2 [11], an audio-visual dataset derived from
YouTube interviews. It contains 1,091,724 video clips from 5,994 speakers, and
each video clip has one synchronized and visible talking face.

For audio-visual speaker recognition, the original VoxCeleb2 is used for
training. Here we also report the performance of the face network trained on
the large face dataset Glint360K [28] to show the effectiveness of face
modality. The speaker network is the ECAPA-TDNN with a large channel size
equal to 1024 (refer to ECAPA-L) [6]. The face network is the ResNet18
(training on VoxCeleb2) and ResNet50 (training on Glint360K) [20, 29]. We
select Vox1-O set for validation, Vox1-E and Vox1-H for testing [10].

Table 1: The EER (%) of audio-visual speaker recognition. ‘-Vox2’ denotes training on VoxCeleb2 dataset, ’-Glint’ denotes training on Glint360K dataset. Modality | System | Vox1-O | Vox1-E | Vox1-H
---|---|---|---|---
Speech | Sari et al. [23] | 2.20 | - | -
Qian et al. [18] | 1.62 | 1.75 | 3.16
Chen et al. [26] | 2.31 | 2.23 | 3.78
(1) Ours-Vox2 | 1.02 | 1.23 | 2.36
Face | Sari et al. [23] | 3.90 | - | -
Qian et al. [18] | 3.04 | 2.18 | 4.23
Chen et al. [26] | 2.26 | 1.54 | 2.37
(2) Ours-Vox2 | 0.97 | 0.81 | 1.16
(3) Ours-Glint | 0.03 | 0.07 | 0.09
Fusion | Sari et al. [23] | 0.90 | - | -
Qian et.al. [18] | 0.71 | 0.48 | 0.85
Chen et al. [26] | 0.59 | 0.43 | 0.74
(1) + (2) | 0.16 | 0.23 | 0.42
(1) + (3) | 0.01 | 0.07 | 0.13

For audio-visual deep cleansing, the speaker network is an ECAPA-L, and the
face network is a ResNet50 network. In fine-grained cleansing, we set the
threshold $\tau$ to divide 92% of training data as the easy samples. Here we
only need to ensure that no noisy samples are involved [15]. In coarse-grained
cleansing, the face network is trained on Glint360K [28]. Here only the
cleansed samples are used to decide the class centre, so we repeat five rounds
to compute each sample’s similarity score and find clean samples.

To show the impact of our audio-visual deep cleansing framework, we train four
speaker networks with and without cleansing and compare their performances.
The networks include x-vector [3], ResNet34 [5], ECAPA-TDNN [6] with a small
channel size equal to 512 (refer to ECAPA-S) and the ECAPA-L. All the
experiments are repeated three times with the same setting. Vox1-O, E and H
are used for in-domain evaluation and CnCeleb-VoxSRC22
[30]111https://www.robots.ox.ac.uk/~vgg/data/voxceleb/data_workshop_2022/Track3_validation_trials.txt
is used for cross-domain evaluation.

During training, we apply data augmentation for speaker and face networks to
boost performance [31, 32]. During the evaluation, all test sets provide a set
number of trials, each containing two samples. For single modality, the cosine
similarity between the speaker embedding (from the entire utterance) or the
face embedding (from five face frames) of the given trial is calculated. For
multi-modal, the combined speaker and face embedding is applied. The
performance metric is the equal error rate (EER).

##  5 Results and Analysis

###  5.1 Audio-visual speaker recognition

Table 2: In-domain evaluation EER(%) of the speaker networks trained on the original and cleansed VoxCeleb2. Network | Method | Vox1-O | Vox1-E | Vox1-H
---|---|---|---|---
X-vector | w/o cleanse | 2.20 | 2.32 | 4.06
with cleanse | 2.09 | 2.13 | 3.76
$\Delta$ | 5.0% | 8.2% | 7.4%
ResNet34 | w/o cleanse | 1.31 | 1.41 | 2.58
with cleanse | 1.24 | 1.28 | 2.52
$\Delta$ | 5.3% | 9.2% | 2.3%
ECAPA-S | w/o cleanse | 1.24 | 1.34 | 2.49
with cleanse | 1.17 | 1.28 | 2.37
$\Delta$ | 5.6% | 4.5% | 4.8%
ECAPA-L | w/o cleanse | 1.02 | 1.23 | 2.36
with cleanse | 0.93 | 1.18 | 2.22
$\Delta$ | 8.8% | 4.1% | 5.9%

First, we report the performance of our audio-visual speaker recognition
system in Tab 1. Both speaker and face networks perform better than existing
approaches when trained on the VoxCeleb2 dataset. Here the face recognition
network can achieve even 0.03% EER when trained on Glint360K. For multi-modal
verification, we obtain 0.16% and 0.01% EER on Vox1-O when the face network is
trained on VoxCeleb2 and Glint360K, respectively. So our audio-visual system
can accurately define the person’s identity to guarantee the cleansing
process.

###  5.2 Audio-visual deep cleansing

Then we compare the performance of the speaker network trained on the original
VoxCeleb2 and the VoxCeleb2 with our deep cleansing. In Tab 2, for in-domain
evaluation on VoxCeleb1, our audio-visual deep cleansing can remove the side-
effect of the noisy data and boost the speaker recognition system with an
average improvement of 5.9%. In Tab 3, for cross-domain evaluation on CnCeleb-
VoxSRC22, our approach achieve an average improvement of 3.2%, which proves
the network obtains a stronger generality.

Table 3: Cross-domain evaluation EER(%) of the speaker networks trained on the original and cleansed VoxCeleb2. Method | X-vector | ResNet34 | ECAPA-S | ECAPA-L
---|---|---|---|---
w/o cleanse | 17.00 | 14.90 | 18.15 | 19.86
with cleanse | 16.34 | 14.64 | 17.39 | 19.26
$\mathbf{\Delta}$ | 3.9% | 1.7% | 4.2% | 3.0%

###  5.3 Visualization of results

Fig. 2: Visualization of (a) audio-visual speaker recognition on Vox1-O; (b)
audio-visual deep cleansing on VoxCeleb2.

We visualize our results in Fig 2. The left panel (a) represents audio-visual
speaker recognition on Vox1-O. Each point denotes a test trial. The X-axis and
Y-axis represent the speaker and face similarity score between the two samples
in each trial, respectively. Target trials have high audio-visual scores, and
imposter trials are the opposite, so the decision boundary is clear and
reliable. The right panel (b) represents audio-visual deep cleansing on
VoxCeleb2 with the same boundary. Each point represents a training sample. The
similarity score is between this point and the cleansed samples from the same
speaker. Here most of the noisy samples have a very different representation
to the mainstream samples in their class since they have a low audio-visual
score. Our method finds 1.9% noisy samples on VoxCeleb2.

Fig. 3: Visualization of the clean and noisy samples with the speaker and face
similarity score.

In Fig 3, each row contains four face images from the samples with the same
speaker label, the left three are from the clean samples, and the right one is
from the noisy sample. Both speaker and face similarity score has been marked
below. Visual modality can assist speech modality in finding noisy samples.

##  6 Conclusion

In this paper, we design an audio-visual speaker recognition system that
achieves close-to-perfect verification on the VoxCeleb1 test sets. A two-step
audio-visual deep cleansing framework is proposed to automatically pick up
noisy training sounds and strengthen the speaker recognition network. We
observe that noisy samples (i.e., with wrong labels) are commonplace in large-
scale datasets, and 5.9% of performance improvement could be achieved by
simply removing a considerable percentage of noisy samples from the training
set. In future work, we will study an end-to-end approach to combine the
training and cleansing steps.

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