text:
\section{Introduction}
Audio tagging (AT) aims at putting one or several tags on a sound clip. The tags are the sound events that occur in the audio clip, for example, ``speech", ``television", ``percussion", ``bird singing", and so on. Audio tagging has many applications in areas such as information retrieval \cite{wold1996content}, sound classification \cite{giannoulis2013detection} and recommendation system \cite{cano2005content}.

Many frequency domain audio features such as mel-frequency cepstrum coefficients (MFCCs) \cite{molau2001computing}, Mel filter banks feature (MFBs) \cite{nadeu2001time} and spectrogram \cite{kingsbury1998robust} have been used for speech recognition related tasks \cite{hinton2012deep} for many years. However, it is unclear how these features perform on the non-speech audio processing tasks. Recently MFCCs and the MFBs were compared on the audio tagging task \cite{xu2016fully} and the MFBs can get better performance in the framework of deep neural networks. The spectrogram has been suggested to be better than the MFBs in the sound event detection task \cite{espi2015exploiting}, but has not yet been investigated in the audio tagging task.

Besides the frequency domain audio features, processing sound from the raw time domain waveforms, has attracted a lot of attentions recently \cite{sainath2015learning, tuske2014acoustic, golik2015convolutional}. However, most of this works are for speech recognition related tasks; there are few works investigating raw waveforms for environmental audio analysis. For common signal processing steps, the short time Fourier transform (STFT) is always adopted to transform raw waveforms into frequency domain features using a set of Fourier basis. Recent research \cite{sainath2015learning} suggests that the Fourier basis sets may not be optimal and better basis sets can be learned from raw waveforms directly using a large set of audio data. To learn the basis automatically, convolutional neural network (CNN) is applied on the raw waveforms which is similar to CNN processing on the pixels of the image \cite{krizhevsky2012imagenet}. Processing raw waveforms has seen many promising results on speech recognition \cite{sainath2015learning} and generating speech and music \cite{oord2016wavenet}, with less research in non-speech sound processing.

Most audio tagging systems \cite{xu2016fully, lidy2016cqt, cakirdomestic, yundiscriminative} use mono channel recordings, or simply average the multi-channels as the input signal. However, using this kind of merging strategy disregards the spatial information of the stereo audio. This is likely to decrease recognition accuracy because the intensity and phase of the sound received from different channels are different. For example, kitchen sound and television sound from different directions will have different intensities on different channels, depending on the direction of the sources. Multi-channel signals contain spatial information which could be used to help to distinguish different sound sources. Spatial features have been demonstrated to improve results in scene classification \cite{eghbal2016cp} and sound event detection \cite{adavannesound}. However, there is little work using multi-channel information for the audio tagging task.

Our main contribution in this paper includes three parts. First, we show experimental results on different features including MFBs and spectrogram as well as the raw waveforms on the audio tagging task of the DCASE 2016 challenge. Second, we propose a convolutional gated recurrent neural network (CGRNN) which is the combination of the CNN and the gated recurrent unit (GRU) to process non-speech sounds. Third, the spatial features are incorporated in the hidden layer to utilize the location information. The work is organized as follows: in Section \ref{sec:cnn_gru}, the proposed CGRNN is presented for audio tagging. In section \ref{sec:spatial_fea}, the spatial features will be illustrated and incorporated into the proposed method. The experimental setup and results are shown in Section \ref{sec:exp_setup} and Section \ref{sec:results}. Section \ref{sec:conclusion} summarizes the work and foresees the future work.

\section{Convolutional Gated Recurrent Network for audio tagging}
\label{sec:cnn_gru}
Neural networks have several types of structures: the most common one is the deep feed-forward neural network. Another popular structure is the convolutional neural network (CNN), which is widely used in image classification \cite{ciresan2011flexible, krizhevsky2012imagenet}. CNNs can extract robust features from pixel-level values for images \cite{krizhevsky2012imagenet} or raw waveforms for speech signals \cite{sainath2015learning}. Recurrent neural network is the third structure which is often used for sequence modeling, such as language models \cite{mikolov2010recurrent} and speech recognition \cite{graves2013speech}. In this section, we will introduce the convolutional neural network and the recurrent neural network with gated recurrent units.

\begin{figure}[t]
	\centering
	\centerline{\includegraphics[width=\columnwidth]{cnn.pdf}}
	\caption{The structure of the one-dimension CNN which consists of one convolutional layer and one max-pooling layer. $N$ filters with a fixed size $F$ are convolved with the one dimensional signal to get outputs $p_t^i\{i=0,\cdots,(N-1)\}$. ${x}_t^i$ means the $i$-th dimension feature of the current frame.}
	\label{fig:cnn}
\end{figure}

\subsection{One dimension convolutional neural network}
Audio or speech signals are one dimensional. Fig. \ref{fig:cnn} shows the structure of a one-dimension CNN which consists of one convolutional layer and one max-pooling layer. $N$ filters with a fixed size $F$ are convolved with the one dimensional signal to get outputs $p_i^t\{i=0,\cdots,(N-1)\}$. Given that the dimension of the input features was $M$, the activation $\textit{h}$ of the convolutional layer would have $(M-F+1)$ values. The max-pooling size is also $(M-F+1)$ which means each filter will give one output value. This is similar to speech recognition work \cite{sainath2015learning} where CNN has been used to extract features from the raw waveform signal. The way of each filter producing one value can also be explained as a global pooling layer which is a structural regularizer that explicitly enforces feature maps to be confidence maps of meaningful feature channels \cite{lin2013network}. So $N$ activations are obtained as the robust features from the basic features. As for the input feature size $M$, a short time window, e.g., 32 ms, was fed into the CNN each time. The long-term pattern will be learned by the following recurrent neural network. As for the filter size or kernel size, a large receptive field is set considering that only one convolutional layer is designed in this work. For example, $F=400$ and $M=512$ are set in \cite{sainath2015learning}. If the input feature was raw waveforms, each filter of the CNN was actually learned as a finite impulse response (FIR) filter \cite{golik2015convolutional}. If the spectrograms or mel-filter banks were fed into the CNN, the filtering was operated on the frequency domain \cite{abdel2013exploring} to reduce the frequency variants, such as the same audio pattern but with different pitches.

\subsection{Gated recurrent unit based RNN}
Recurrent neural networks have recently shown promising results in speech recognition \cite{graves2013speech}. Fig. \ref{fig:rnn} shows the basic idea of the RNN. The current activation $\textbf{h}_t$ is determined by the current input $\textbf{x}_t$ and the previous activation $\textbf{h}_{t-1}$. RNN with the capability to learn the long-term pattern is superior to a feed-forward DNN, because a feed-forward DNN is designed that the input contextual features each time are independent. The hidden activations of RNN are formulated as:
\begin{equation}
	{\textbf{h}}_t=\varphi(\textbf{W}^h\textbf{x}_t+{\textbf{R}^h\textbf{h}_{t-1}}+\textbf{b}^h)
	\label{eq:simple_rnn}
\end{equation}
However, a simple recurrent neural network with the recurrent connection only on the hidden layer is difficult to train due to the well-known vanishing gradient or exploding gradient problems \cite{pascanu2013difficulty}. The long short-term memory (LSTM) structure \cite{hochreiter1997long} was proposed to overcome this problem by introducing input gate, forget gate, output gate and cell state to control the information stream through the time. The fundamental idea of the LSTM is memory cell which maintains its state through time \cite{wu2016investigating}.

As an alternative structure to the LSTM, the gated recurrent unit (GRU) was proposed in \cite{cho2014learning}. The GRU was demonstrated to be better than LSTM in some tasks \cite{chung2014empirical}, and is formulated as follows \cite{wu2016investigating}:

\begin{equation}
\textbf{r}_t=\delta(\textbf{W}^r\textbf{x}_t+\textbf{R}^r\textbf{h}_{t-1}+\textbf{b}^r)
\end{equation}
\begin{equation}
\textbf{z}_t=\delta(\textbf{W}^z\textbf{x}_t+\textbf{R}^z\textbf{h}_{t-1}+\textbf{b}^z)
\end{equation}
\begin{equation}
\tilde{\textbf{h}}_t=\varphi(\textbf{W}^h\textbf{x}_t+\textbf{r}_t\odot{(\textbf{R}^h\textbf{h}_{t-1})}+\textbf{b}^h)
\label{eq:reset_gate}
\end{equation}
\begin{equation}
\textbf{h}_t=\textbf{z}_t\odot{\textbf{h}_{t-1}}+(1-\textbf{z}_t)\odot{\tilde{\textbf{h}}_t}
\label{eq:update_gate}
\end{equation}
where $\textbf{h}_t$, $\textbf{r}_t$ and $\textbf{z}_t$ are hidden activations, reset gate values and update gate values at frame $t$, respectively. The weights applied to the input and recurrent hidden units are denoted as $\textbf{W}^*$ and $\textbf{R}^*$, respectively. The biases are represented by $\textbf{b}^*$. The functions $\delta(\cdot)$ and $\varphi(\cdot)$ are the sigmoid and tangent activation functions. Compared to the LSTM, there is no separate memory cell in the GRU. The GRU also does not have an output gate, and combines the input and forget gates into an update gate $\textbf{z}_t$ to balance between the previous activation $\textbf{h}_{t-1}$ and the update activation $\tilde{\textbf{h}}_t$ shown in Eq. (\ref{eq:update_gate}). The reset gate $\textbf{r}_t$ can decide whether or not to forget the previous activation (shown in Eq. (\ref{eq:reset_gate})). $\odot$ in Eq. (\ref{eq:reset_gate}) and (\ref{eq:update_gate}) represents the element-wise multiplication.

\begin{figure}[t]
	\centering
	\centerline{\includegraphics[width=\columnwidth]{rnn.pdf}}
	\caption{The structure of the simple recurrent neural network and its unfolded version. The current activation $\textbf{h}_t$ is determined by the current input $\textbf{x}_t$ and the previous activation $\textbf{h}_{t-1}$.}
	\label{fig:rnn}
\end{figure}

\subsection{Convolutional Gated Recurrent Network for audio tagging}
Fig. \ref{fig:cnn_rnn_at} shows the framework of a convolutional gated recurrent neural network for audio tagging. The CNN is regarded as the feature extractor along the short window (e.g., 32ms) from the basic features, e.g., MFBs, spectrograms or raw waveforms. Then the robust features extracted are fed into the GRU-RNN to learn the long-term audio patterns. For the audio tagging task, there is a lot of background noise, and acoustic events may occur repeatedly and randomly along the whole chunk (without knowing the specific frame locations). The CNN can help to extract robust features against the background noise by the max-pooling operation, especially for the raw waveforms. Since the label of the audio tagging task is at the chunk-level rather than the frame-level, a large number of frames of the context were fed into the whole framework. The GRU-RNN can select related information from the long-term context for each audio event. To also utilize the future information, a bi-directional GRU-RNN is designed in this work. Finally the output of GRU-RNN is mapped to the posterior of the target audio events through one feed-forward neural layer, with sigmoid output activation function. This framework is flexible enough to be applied to any kinds of features, especially for raw waveforms. Raw waveforms have lots of values, which leads to a high dimension problem. However the proposed CNN can learn on short windows like the short-time Fourier transform (STFT) process, and the FFT-like basis sets or even mel-like filters can be learned for raw waveforms. Finally, one-layer feed-forward DNN gets the final sequence of GRUs to predict the posterior of tags.

Binary cross-entropy is used as the loss function in our work, since it was demonstrated to be better than the mean squared error in \cite{xu2016fully} for labels with zero or one values. The loss can be defined as:
\begin{equation}
E=-\sum_{n=1}^{N}\|\textbf{T}_{n}\text{log}\hat{\textbf{T}}_{n}+(1-\textbf{T}_{n})\text{log}(1-\hat{\textbf{T}}_n)\|
\label{eq:DNNerrors_bce}
\end{equation}
\begin{equation}
\hat{\textbf{T}}_{n}=(1+\text{exp}(-\textbf{O}))^{-1}
\label{eq:DNN_hidden_sigmoid}
\end{equation}
where $E$ is the binary cross-entropy, $\hat{\textbf{T}}_n$ and $\textbf{T}_{n}$ denote the estimated and reference tag vector at sample index $n$, respectively. The DNN linear output is defined as $\textbf{O}$ before the sigmoid activation function is applied. Adam \cite{kingma2014adam} is used as the stochastic optimization method.

\begin{figure}[t]
	\centering
	\centerline{\includegraphics[width=\columnwidth]{cnn_rnn_at.pdf}}
	\caption{The framework of convolutional gated recurrent neural network for audio tagging.}
	\label{fig:cnn_rnn_at}
\end{figure}

\section{Spatial features incorporated for audio tagging}
\label{sec:spatial_fea}
\begin{figure}[t]
	\centering
	\centerline{\includegraphics[width=2in]{cnn_imd.pdf}}
	\caption{The structure of incorporating the spatial features (IMD/ILD/IPD, etc.) using an additional CNN. Then the activations learned from the basic features and the activations learned from the spatial features are concatenated to be fed into the GRU-RNN shown in Fig. \ref{fig:cnn_rnn_at}.}
	\label{fig:cnn_imd}
\end{figure}
Spatial features can often offer additional cues to help to solve signal processing problems. Many spatial features can be used for audio tagging, such as interaural phase differences or interaural time differences (IPD or ITD) \cite{blauert1997spatial}, interaural level differences (ILD) \cite{blauert1997spatial}. The recordings of the audio tagging task of DCASE 2016 challenge are recorded in the home scenes. There are some TV, child speech, adult speech audio events. The spatial features potentially give additional information to analyze the content of the audio, e.g., recognizing the TV audio event by knowing the specific direction of the TV sound. The IPD and ILD are defined as:
\begin{equation}
ILD(t,k)=20\text{log}_{10}\left|\frac{X_{\text{left}}(t,k)}{X_{\text{right}}(t,k)}\right| \\
\end{equation}
\begin{equation}
IPD(t,k)=\angle\left(\frac{X_{\text{left}}(t,k)}{X_{\text{right}}(t,k)}\right)
\end{equation}
where $X_{left}(t,k)$ and ${X_{right}(t,k)}$ denote the left channel and right channel complex spectrum of the stereo audio. The operator $\left|\cdot\right|$ takes the absolute of the complex value, and $\angle(\cdot)$ finds the phase angle. In this work, we also define interaural magnitude differences (IMD) which is similar to the ILD. IMD is defined in linear domain while ILD is defined in logarithmic domain.
\begin{equation}
IMD(t,k)=\left|{X_{left}(t,k)}\right|-\left|{X_{right}(t,k)}\right|
\end{equation}
Fig. \ref{fig:cnn_imd} shows the structure of incorporating the spatial features (IMD/ILD/IPD, etc.) using an additional CNN. Then the activations learned from the basic features and the activations learned from the spatial features are concatenated to be fed into the GRU-RNN plotted in Fig. \ref{fig:cnn_rnn_at}.
\begin{figure}[t]
	\centering
	\centerline{\includegraphics[width=\columnwidth]{imd_ipd_ild_spec.pdf}}
	\caption{The spectrogram, IMD, ILD and IPD of ac recording from the audio tagging task of DCASE 2016 challenge. The labels of this audio are ``child speech" and ``TV sound".}
	\label{fig:imd_ipd_ild_v2}
\end{figure}
The audio files of the audio tagging task of the DCASE 2016 challenge are recorded in a domestic home environment. There are severe reverberation, high-level background noise and multiple acoustic sources. These factors might influence the effectiveness of IPD and ILD. Fig. \ref{fig:imd_ipd_ild_v2} shows the spectrogram, IMD, ILD and IMD of one recording from the audio tagging task of DCASE 2016 challenge. The IMD appears to have some meaningful patterns while the ILD and the IPD seem to be random which would lead to the training difficulties of the classifier. From our empirical experiments, IPD and ILD do not appear to help to improve the classifier performance while IMD is beneficial. Similar results were reported in \cite{adavannesound} where IPD was found not to be helpful for the sound event detection in home scenes but helpful for the event detection of residential areas. This may be because residential areas are open areas with less reverberation than indoor home environments. Hence we will use IMD as our spatial features in this work. The filter size of CNNs learned on the IMD is set the same with the related configuration for the spectrogram.

\section{Data set and experimental setup}
\label{sec:exp_setup}
\subsection{DCASE 2016 audio tagging challenge}
\label{ssec:data_set}
We conducted our experiments based on the DCASE 2016 audio tagging challenge \cite{dcase_t4}. This audio tagging task consists of the five-fold development set and the evaluation set, which are built based on the CHiME-home dataset \cite{foster2015}. The audio recordings were made in a domestic environment \cite{christensen2010}. The audio data are provided as 4-second chunks at 48kHz sampling rates in stereo mode. We downsampled them into 16kHz sampling rate.

For each chunk, three annotators gave three labels, namely multi-label annotations. Then the discrepancies among annotators are reduced by conducting a majority vote. The annotations are based on a set of seven audio events as presented in Table \ref{tab:annotations}.
A detailed description of the annotation procedure is provided in \cite{foster2015}.
\begin{table}[h]
	\centering
	\caption{Seven audio events used as the reference labels.}
	\begin{tabular}{|c|c|}
		\hline
		audio event & Event descriptions \\ \hline
		`b' & Broadband noise \\
		`c' & Child speech \\
		`f' & Adult female speech \\
		`m' & Adult male speech \\
		`o' & Other identifiable sounds \\
		`p' & Percussive sound events, \\
		& e.g. footsteps, knock, crash \\
		`v' & TV sounds or Video games \\
		\hline
	\end{tabular}
	\label{tab:annotations}
\end{table}

\begin{table}[h]
	\centering
	\caption{The configurations for the five-fold development set and the final evaluation set of the DCASE 2016 audio tagging task.}
	\begin{tabular}{|c|c|c|}
		\hline
		Fold index of development set & \#Training chunks& \#Test chunks\\ \hline
		0 & 4004 & 383 \\
		1 & 3945 & 442 \\
		2 & 3942 & 463 \\
		3 & 4116 & 271 \\
		4 & 4000 & 387 \\
		\hline
		\hline
		\hline
		Evaluation set & 4387 & 816 \\
		\hline
	\end{tabular}
	\label{tab:eval_data}
\end{table}

\subsection{Experimental setup}\label{ssec:exp_setup}

In the experiments below, we follow the standard specification of the DCASE 2016 audio tagging task \cite{dcase_t4},
On the development set, we use the official five folds for cross-validation.
Table \ref{tab:eval_data} shows
the number of chunks in the training and test set used for each fold. The number of final evaluation configuration is also listed.

The parameters of the networks are tuned based on the heuristic experience. All of the CNNs have 128 filters or feature maps. Following \cite{sainath2015learning}, the filter size for MFBs, spectrograms and raw waveforms are 30, 200, and 400, respectively. These parameters can form a large receptive field for each type of basic features considering that only one convolutional layer was designed. The CNN layer is followed by three RNN layers with 128 GRU blocks. One feed-forward layer with 500 ReLU units is finally connected to the 7 sigmoid output units. We pre-process each audio chunk by segmenting them using a $32$ms sliding window with a $16$ms hop size, and converting each segment into 40-dimension MFBs, 257-dimension spectrograms and 512-dimension raw waveforms. For performance evaluation, we use equal error rate (EER) as the main metric which is also suggested by the DCASE 2016 audio tagging challenge. EER is defined as the point of equal false negative ($FN$) rate and false positive ($FP$) rate \cite{murphy2012}. The source codes for this paper can be downloaded from Github\footnote{\url{https://github.com/yongxuUSTC/cnn_rnn_spatial_audio_tagging}}.

\subsection{Compared methods}
We compared our methods with the state-of-the-art systems. Lidy-CQT-CNN \cite{lidy2016cqt} and Cakir-MFCC-CNN \cite{cakirdomestic} won the first and the second prize of the DCASE2016 audio tagging challenge \cite{dcase_t4}. They both used convolutional neural networks (CNN) as the classifier. We also compare to our previous method \cite{xu2016fully} which demonstrated the state-of-the-art performance using de-noising auto-encoder (DAE) to learn robust features.

\section{Experimental results and analysis}
\label{sec:results}
In this section, the IMD effectiveness will be firstly evaluated on the development set of Task 4 of the DCASE 2016 challenge among the different features, i.e., spectrograms, MFBs and raw waveforms. Then the final evaluation will be presented by comparing with the state-of-the-art methods on the evaluation set of Task 4 of the DCASE 2016 challenge.
\subsection{The effectiveness of the IMD}
Table \ref{tab:imd_dev} shows the EER comparisons on seven labels among the spectrogram, the raw waveform and the MFB systems with or without the IMD information, which are evaluated on the development set of the DCASE 2016 audio tagging challenge. Firstly, we can compare the proposed convolutional gated recurrent neural networks on spectrograms, raw waveforms and MFBs. Spectrograms are better than the MFBs perhaps because the spectrogram has more detailed frequency information compared with the MFB. For example, spectrograms are much better than MFBs on child speech (denoted as `c') and female speech (denoted as `f') where a lot of high frequency information exists. The raw waveforms are worse than the spectrograms and the MFBs. One possible reason is that the learned FIR filters are not stable when the whole training set is small (about 3.5 hours of audio in this work). The same explanation was given in \cite{tuske2014acoustic} on the speech recognition task. \cite{sainath2015learning} shows that raw waveforms can get better recognition accuracy with the mel-spectra on 2000 hours Google voice search data.

With the help of the IMD spatial features, the EER are improved compared to all of the corresponding basic features alone. The raw waveforms with IMD can even get comparable results with the spectrograms and the MFBs. The MFB-IMD combination is slightly better than Spec-IMD, which may be because the IMD is calculated from the left and right spectrograms. The IMD has some common information with the spectrograms which can be seen from Fig. \ref{fig:imd_ipd_ild_v2}. However, the IMD is more complementary for the MFBs and the raw waveforms. The previous best performance on the development set of the DCASE 2016 audio tagging challenge was obtained in our recent work using denoising auto-encoder \cite{xu2016fully} with 0.126 EER, but here we get better performance with 0.10 EER.

\subsection{Overall evaluations}
Table \ref{tab:imd_eva} presents the EER comparisons on seven labels among Lidy-CQT-CNN \cite{lidy2016cqt}, Cakir-MFCC-CNN \cite{cakirdomestic}, our previous DAE-DNN \cite{xu2016fully}, and the proposed systems on the spectrogram, the raw waveform and the MFB systems with the IMD information, which are evaluated on the final evaluation set of the DCASE 2016 audio tagging challenge. The de-noising auto-encoder \cite{xu2016fully} was our recent work which can outperform the leading system in the DCASE 2016 audio tagging challenge, namely Lidy-CQT-CNN \cite{lidy2016cqt}. Our proposed convolutional gated recurrent neural network incorporating the IMD features in this work gives further improved performance. The MFB-IMD obtains the best performance with 0.123 EER which is the state-of-the-art performance on the evaluation set of the DCASE 2016 audio tagging challenge.

\begin{table}[t]
\scriptsize
	\centering
	\caption{EER comparisons on seven labels among the spectrogram, the raw waveform and the MFB systems with or without the IMD information, which are evaluated on the\textbf{ development set} of the DCASE 2016 audio tagging challenge.}
\begin{tabular}{l|cccccccc}
	\hline
	Dev set& c     & m     & f     & v     & p     & b     & o     & ave \\
	\hline
	Spec  & 0.121 & 0.085 & 0.155 & 0.025 & 0.138 & 0.017 & 0.231 & 0.110 \\
	RAW   & 0.157 & 0.085 & 0.156 & 0.028 & 0.139 & 0.059 & 0.263 & 0.127 \\
	MFB   & 0.145 & 0.086 & 0.167 & 0.024 & 0.133 & 0.037 & 0.239 & 0.119 \\
	Spec-IMD & \textbf{0.120} & \textbf{0.080} & 0.143 & \textbf{0.012} & 0.115 & 0.023 & 0.232 & 0.104 \\
	RAW-IMD & 0.135 & 0.085 & 0.164 & 0.014 & \textbf{0.108} & \textbf{0.006} & 0.231 & 0.106 \\
	MFB-IMD & 0.125 & 0.086 & \textbf{0.140} & \textbf{0.012} & 0.110 & 0.011 & \textbf{0.230} & \textbf{0.102} \\
	\hline
\end{tabular}%
	\label{tab:imd_dev}
\end{table}

\begin{table}[t]
\scriptsize
	\centering
	\caption{EER comparisons on seven labels among Lidy-CQT-CNN \cite{lidy2016cqt}, Cakir-MFCC-CNN \cite{cakirdomestic}, DAE-DNN \cite{xu2016fully}, and the proposed systems on the spectrogram, the raw waveform and the MFB systems with the IMD information, which are evaluated on the \textbf{final evaluation set} of the DCASE 2016 audio tagging challenge.}

\begin{tabular}{l|cccccccc}
	\hline
	Eval set& c     & m     & f     & v     & p     & b     & o     & ave \\
	\hline
	Cakir \cite{cakirdomestic} & 0.250 & 0.159 & 0.250 & 0.027 & 0.208 & 0.022 & 0.258 & 0.168 \\
	Lidy \cite{lidy2016cqt} & 0.210 & 0.182 & 0.214 & 0.035 & 0.168 & 0.032 & 0.320 & 0.166 \\
	DAE \cite{xu2016fully} & 0.210 & 0.149 & 0.207 & \textbf{0.022} & 0.175 & 0.014 & 0.256 & 0.148 \\
	RAW-IMD & 0.189 & 0.152 & 0.200 & 0.053 & 0.156 & \textbf{0.010} & \textbf{0.236} & 0.142 \\
	Spec-IMD & 0.166 & 0.165 & \textbf{0.143} & 0.024 & \textbf{0.123} & 0.034 & 0.250 & 0.129 \\
	MFB-IMD & \textbf{0.150} & \textbf{0.145} & \textbf{0.143} & 0.031 & 0.135 & 0.013 & 0.248 & \textbf{0.123} \\
	\hline
\end{tabular}%

	\label{tab:imd_eva}
\end{table}

\section{Conclusion}
\label{sec:conclusion}
In this paper, we propose a convolutional gated recurrent neural network (CGRNN) to learn on the mel-filter banks (MFBs), the spectrograms and even the raw waveforms. The spatial features, namely the interaural magnitude difference (IMDs), are incorporated into the framework and are demonstrated to be effective to further improve the performance. Spectrogram gives better performance than MFBs without the spatial features. However the MFBs with the IMDs can get the minimal EER, namely 0.102, on the development set of the DCASE 2016 audio tagging challenge. Raw waveforms give comparable performance on the development set. Finally, on the evaluation set of the DCASE 2016 audio tagging challenge, our proposed MFB-IMD system can get the state-of-the-art performance with 0.l23 EER. It is still interesting to further explore why the MFB-IMD system is better than the Spec-IMD system in our future work. In addition, we will also investigate the proposed framework to model raw waveforms on larger training datasets to learn more robust filters.

\section*{Acknowledgment}
This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under the grant EP/N014111/1. Qiuqiang Kong is partially supported by the China Scholarship Council (CSC).

\bibliographystyle{IEEEtran}


text:
\section{Introduction}

The continuous rotational symmetry of spins prevents any long-range magnetic ordering in the isotropic Heisenberg model in two-dimension, as described by the celebrated Hohenberg-Mermin-Wagner theorem.~\citep{PhysRev.158.383,PhysRevLett.17.1133} The long-wavelength excitations become gapless, and thus any tendency to magnetic order is destroyed at finite temperature.  However, spins in real materials are far from being isotropic, and the dipolar interaction or relativistic spin-orbit coupling produces magnetic anisotropy, which breaks the continuous rotational invariance of the spins. Therefore, the excitation becomes gapped, and a magnetic phase transition emerges in two-dimension.  Unfortunately, despite its immense importance , it is rare to find two-dimensional magnetic materials with strong spin-orbit coupling.~\citep{Gibertini2019,Gongeaav4450}

The recent discovery of antiferromagnetic ordering in FePS$_3$ together with the ferromagnetic ordering in CrGeTe$_3$ and CrI$_3$ are the first-ever demonstration of magnetic order in truly two-dimensional materials.~\citep{nanolett.6b03052,Gong,Huang} This breakthrough marks a new era in fundamental research along with enormous application possibilities in two dimensions, and extend functionalities beyond the already existing phases such as ferroelectricity, superconductivity, charge density waves, and various topological states. Apart from these materials, a few other ferromagnetic materials CrCl$_3$, CrBr$_3$, VI$_3$, VSe$_2$, Fe$_3$GeTe$_2$ and MnBi$_2$Te$_2$; and antiferromagnet like NiPS$_3$ have been discovered.~\citep{Kim11131,s41565-019-0565-0,s41567-019-0651-0, adma.201808074,s41565-018-0063-9,s41586-018-0626-9, s41467-018-08284-6} Further, electric manipulation of magnetism has been achieved in these two-dimensional materials, that opens up opportunities in spintronic applications.~\citep{s41565-018-0121-3,s41565-018-0135-x,s41586-018-0626-9} It is important to note here that all the materials that are discovered till date are derived from the van der Waals bulk materials and consists of 3$d$ transition-metals that have weak spin-orbit coupling strength.~\citep{Gibertini2019,Gongeaav4450} Since the anisotropic interactions originating from the spin-orbit coupling opens a gap in the spin-wave spectrum, the corresponding magnetic transition temperature is undesirably low in these materials.~\citep{Lado_2017} Therefore, it would be exciting to discover a new class of two-dimensional magnets with much stronger spin-orbit couplings that couple with strong electron correlation. The interplay between these competing interactions at the comparable energy scales along with the band topology is expected to trigger emergent physics and exciting functionalities in two-dimensional materials.

Transition metal oxides with the 4$d$ and 5$d$ elements are the prime examples of such competing interactions with comparable electron correlation and spin-orbit coupling.~\citep{Khomskii, Cox} Consequently, many exotic physics have been discovered in these oxides in their bulk phases. For example, spin-triplet superconductivity~\citep{JPSJ.81.011009} and emergent Higgs mode oscillations have been discovered in the ruthenium-based materials.~\citep{nphys4077,PhysRevLett.119.067201}
In the context of two-dimensional magnetism, the difficulty in exfoliation of these non-vdW materials is the main obstacle. While the magnetism in many of these oxides appears in layers, these magnetic layers are chemically bonded with one another, which makes exfoliation a challenging task.

Another bottleneck that prevents the use of these 4$d$ and 5$d$ transition metal oxides in multifunctional devices is that the magnetic transition temperatures of most of these oxides are far below room temperature. Only a very few 4$d$ and 5$d$ oxides, such as CaTcO$_3$,~\citep{10.1021/ja109431t} SrTcO$_3$,~\citep{PhysRevLett.106.067201} NaOsO$_3$~\citep{PhysRevB.80.161104,PhysRevLett.108.257209} and Sr$_3$OsO$_6$,~\citep{s41467-019-08440-6} have been discovered to have very high magnetic ordering temperatures but none of these materials displays layered magnetic structure.
Hence, the realization of strongly correlated oxides with high transition temperatures is an area of intense theoretical and experimental investigations.  In this context, the recent discovery of SrRu$_2$O$_6$ with high Neel temperature $T_{\rm N}$ of 560 K is of great importance,~\citep{Nan1,Hiley2} which also holds some exotic electronic properties owing to both localized and itinerant character of electrons.~\citep{Nan3, mazin} Bulk SrRu$_2$O$_6$ is a layered antiferromagnetic insulator with honeycomb magnetic lattice of Ru$^{5+}$ ions and the properties could be further tailored by inducing strain in the lattice to host topological states.~\citep{Nan1,Nan2, Hiley1, Hiley2}  Therefore, the layered SrRu$_2$O$_6$ is a  potential candidate for exfoliation,  and consequently  for experimental realization of two-dimensional magnetism in strongly correlated oxides.

Here, we report the synthesis of ultra-thin sheets of SrRu$_2$O$_6$ using the scalable technique of liquid exfoliation. These nano-sheets are formed and preserved in the liquid medium of ethanol, which enables easy drop-casting on a suitable substrate for further characterization and device patterning. The ultra-thin sheets are characterized by a wide range of complementary experimental and theoretical techniques. Experimental results indicate stable nano-sheets with the thickness between three to five monolayers. The theoretical calculations suggest the survival of antiferromagnetism in these nano-sheets.  Therefore, these few-layer oxide sheets serve as the new platform beyond the current family of two-dimensional magnetic materials, which additionally host electron correlation and spin-orbit coupling at competing scales.  Moreover, the strongly correlated electrons on the hexagonal lattice with antiferromagnetic interactions provide a fertile playground for emergent phenomena.~\citep{Kane,Haldane,Zhang1}  In this context, SrRu$_2$O$_6$ is also quite similar to the celebrated RuCl$_3$~\citep{Kitaev4,PhysRevB.91.144420} and Na$_2$IrO$_3$ systems,~\citep{Yogesh3} in which Ru or Ir ions form a magnetic hexagon with antiferromagnetic correlations. Both these systems are extensively explored for the possibility of hosting fractionalized Kitaev physics with unconventional excitations.~\citep{Khaliullin, Yogesh1, Yogesh2, Yogesh3,Knolle,Streltsov}

\begin{figure*}[!t]
\includegraphics[width=1\textwidth]{Figure1}
\caption{(a) Schematic of a honeycomb lattice of Ru ions (gray balls) in the $ab$ plane. The Ru layers are separated by Sr layers (green balls) along the $c$ axis. (b) depicts room temperature powder XRD data for  SrRu$_2$O$_6$ synthesized using the hydrothermal method. Here the intensity has been normalized with the most intense peak of SrRu$_2$O$_6$. A  tiny impurity of RuO$_2$ is marked by stars. (c) shows the Raman data, obtained on a crystallite of SrRu$_2$O$_6$, with the optical image for the crystallite being shown in the inset. The morphology of the sample is depicted in the SEM image of bulk SrRu$_2$O$_6$ as shown in (d), which depicts an overall view of micron-size crystallites forming in regular morphology. (e) and (f) are images of isolated hexagonal crystallites and regular polyhedra.The liquid exfoliation technique has been employed to obtain ultra-thin sheets of SrRu$_2$O$_6$, using these regular shaped  crystallites shown in (d) to (f).}
\label{Figure1}
\end{figure*}

\section{Experimental Techniques}
SrRu$_2$O$_6$ crystallites  are synthesized via the hydrothermal route, using an autoclave from Parr instruments. The morphology and size of as-synthesized bulk  crystallites as well as the nano-sheets of the same, are recorded using a Zeiss Ultra plus FESEM.  Powder X-ray diffraction (XRD) on the crystallites have been conducted using Bruker D8 Advance with Cu $K_\alpha$ radiation ($\lambda$ = 1.54056 \AA). Raman spectroscopy has been done using Horiba instruments equipped with a blue laser ($\lambda$ = 488 nm) and a confocal microscope. The nano-sheets are characterized by Transmission Electron Microscopy  (FEI/TFS Tecnai 20, equipped with LaB6 electron gun, operated at 200 kV). TEM specimens are prepared by drop casting a few $\mu$L  of solution of SrRu$_2$O$_6$ nano-sheets, dispersed and preserved in ethanol, onto Cu TEM grids coated with amorphous carbon support film. The Selected Area Electron Diffraction patterns (SAED) and Fast Fourier Transform (FFT) diffractograms are analyzed by ELDISCA software.~\citep{Gemming} The nano-sheets are further characterized using Atomic Force Microscopy (AFM) using JPK Nanowizard II.  For the synthesis of SrRu$_2$O$_6$ nano-sheets, sonicator (Model Bandelin Sonorex RK 100 H) and Hettich centrifuge (Model MIKRO 200-R) has been used.

The process of liquid exfoliation is routinely employed to form ultra-thin sheets of graphene-like  van der Waals materials, including a wide variety of chalcogenides  such as MoS$_2$.~\citep{Nicolosi1, Griffin, Sean,Backes} This process involves finding a suitable liquid medium in which the bulk sample is sonicated and centrifuged. Here  important synthesis parameters include  (i) sonication  which enables separation of layers which are weakly bonded (ii) centrifugation which enables isolation of thin sheets. The suitable choice of liquid medium  is important, as it prevents the isolated nano-sheets from coagulating again. Time of sonication and centrifugation are also crucial parameters that can be tuned to further refine the thickness distribution as well as size of the nano sheets.~\citep{Nicolosi1, Griffin, Sean,Backes} While a large number of  layered van der Waals materials have been successfully exfoliated using this technique, there are relatively  few reports~\citep{Balan,Sasaki,Sun, Robinson} of exfoliation of magnetic oxides, especially layered ones, with high spin-orbit coupling. Oxides such as SrRu$_2$O$_6$ are quasi two dimensional in the sense of weak inter-layer bonding as compared to in-plane bonding, though both inter-plane and intra-layer bonding are covalent in nature. This anisotropy in bonding strength can thus be exploited to exfoliate ultra-thin sheets of non van der Waals but layered systems,  using the technique of liquid exfoliation.

\section{Results and Discussions}

The compound SrRu$_2$O$_6$, crystallizes in a quasi-2D structure with space group  $P\bar{3}1m$ and lattice parameters $a$ = 0.520573 nm,  $c$ = 0.523454 nm.~\citep{Hiley1} As shown in Figure~\ref{Figure1}(a), the structure of SrRu$_2$O$_6$ comprises of edge-sharing RuO$_6$ layers separated by Sr$^{2+}$ ions. Within the $ab$ plane, the Ru ions are arranged in a honeycomb structure  and Ru moments couple antiferromagnetically both in-plane and out-of-plane. The magnetic moment is 1.30 $\mu_B$/Ru at room temperature and the system possesses the G-type magnetic structure.~\citep{Hiley1, Hiley2}

\begin{figure}[!t]
\includegraphics[width=0.49\textwidth]{Figure2}
\caption {(a)--(c) are SEM images of thin flakes of SrRu$_2$O$_6$, post the process of liquid exfoliation, indicating that sheets of various thickness and shapes have been formed. These images are recorded after drop casting the exfoliated sample on Si substrates. }
\label{Figure2}
\end{figure}

For obtaining the nano-sheets, we first synthesize bulk SrRu$_2$O$_6$ employing the hydrothermal technique described earlier.~\cite{Hiley1} For this purpose, KRuO$_4$ and SrO$_2$ (in stoichiometric ratios) are added in distilled water and stirred, prior to heating the mixture at 200 C for 24 hours in an  autoclave. The precipitate was recovered using a vacuum filtration assembly and washed with diluted HCl, distilled water and acetone. The sample thus obtained was characterized by XRD and Raman, as is shown in Figure~\ref{Figure1}(b) and Figure~\ref{Figure1}(c), respectively.  The  XRD pattern matches well with, JCPDS (04-021-3995) entry assigned for SrRu$_2$O$_6$.~\cite{Hiley1} The lattice parameters derived from XRD data  are  $a$ = 0.5205(7) nm,  $c$ = 0.5219(5) nm. A  tiny amount of  RuO$_2$ phase, JCPDS (65-2824), is also observed as marked by stars in Figure~\ref{Figure1}(b). This impurity  could be systematically reduced by repeated washing the \textit{as-prepared} compound and does not interfere in the exfoliation of SrRu$_2$O$_6$. A characteristic Raman spectra  acquired using blue laser  is shown in the main panel of Figure~\ref{Figure1}(c). The inset shows the optical  image of the crystallite, on which the Raman data has been recorded. The Raman data shown in Figure~\ref{Figure1}(c) are consistent with the previous reports.~\cite{Ponosov} .  Magnetic Characterization on SrRu$_2$O$_6$ crystallites is conducted using SQUID magnetometry ( Quantum Design MPMS) and magnetization as function of temperature from 5K to 600 K  is presented in Supp.Info Figure S1. The magnetization data are in agreement with previous reports~\cite{Hiley1, Hiley2} and further confirm the phase purity of the parent compound used for the process of liquid exfoliation. The morphology of the SrRu$_2$O$_6$ depicting micron-size  crystallites observed  with regular facets, vertices and edges is shown in Figure~\ref{Figure1}(d)-(f). It is to be noted that a large number of crystallites are formed in regular hexagonal shape as is highlighted in Figure~\ref{Figure1}(e).

\begin{figure*}[!t]
\includegraphics[width=1\textwidth]{Figure3}
\caption {(a) - (d) are AFM images of the SrRu$_2$O$_6$ nano sheets of different shape and thickness drop-cast on a mica substrate. (a) cover a broad area, depicting a large number of nano flakes. Both isolated and agglomerated nano-sheets can be clearly seen here. (b) shows a hexagonal shaped nano flake, depicting the morphology of the as-prepared bulk SrRu$_2$O$_6$ shown in Figure~\ref{Figure1}. The  average thickness of the individual  nano-sheet is in the range of 1.5 to 2.2 nm, as is evident from the corresponding line profile shown at the bottom of (a) to (d).}
\label{Figure3}
\end{figure*}

To obtain nano-sheets of SrRu$_2$O$_6$, the first task is to determine a suitable  liquid medium, in which the bulk crystallites can be dispersed. This solution , containing the bulk crystallites (in an optimized liquid-medium and crystallite ratio) is then subjected to sonication for  mechanically isolating the weakly bonded layers. After trying a number of solvents, we found that ethanol is most suitable  for obtaining ultra-thin sheets of SrRu$_2$O$_6$. For this purpose, as-prepared  SrRu$_2$O$_6$  crystallites  were dispersed in ethanol. Usage of ethanol as a solvant for the process of liquid exfoliation has certain advantages. For instance, nano-sheets preserved in ethanol are easy to drop-cast on a suitable substrate. As ethanol evaporates, this provides an opportunity for easy device patterning.  In order to synthesize ultra-thin sheets, we first make a solution of SrRu$_2$O$_6$ crystallites in ethanol, typically in a 1:10 ratio. This solution is subjected to 4 hours of bath and probe sonication, following which the solution is kept undisturbed for 24 hours. The top portion of the solution is collected and centrifuged at 2000 rpm for 30 minutes. These experimental parameters ( such and time of sonication or centrifugation etc.) can be further refined to obtain thinner nano-sheets. For instance, multiple rounds of sonication and centrifuge usually leads to the collection of relatively thinner sheets in the top portion of the centrifuge vial. The centrifuge vial is also kept undisturbed for a few hours  prior to retrieving a few $\mu$L from the top layer using a micro pippet. This refined solution is then drop-cast onto the various suitable substrates for further characterization.

The Figures~\ref{Figure2}(a)-(c) displays SEM images of the nano-sheets thus formed. The images are recorded by drop-casting a few $\mu$L of the solution, that contains dispersed nano sheets,  on a Si substrate. As evident from Figure~\ref{Figure2}, the sheets are formed in various shapes and size, for which a few representatives are shown here. Most importantly, we observe a significant fraction of sheets  retain the shape of regular polyhedra of \textit{as-formed} micro-crystals shown in Figure~\ref{Figure1}(d). Both isolated as well as a bunch of nano-sheets (which lie on top of each other) can be found. The lateral length of such nano-sheets varied from few tens of nano meters to a few 100 nm and again appears to correlate with dimensions of the bulk SrRu$_2$O$_6$ crystallites, from which these sheets have been exfoliated.

While the presence of sheets with different thicknesses can be gauged from the contrast in the SEM images, we performed AFM measurements for determining the average thickness of the nano sheets. For this purpose,  solution containing dispersed nano -sheets is drop-casted on a freshly cleaved mica substrate. The Figures~\ref{Figure3}(a)-(d) show some representative AFM images on the nano-sheets of SrRu$_2$O$_6$. The Figure~\ref{Figure3}(a) shows a broad area AFM image, displaying a large number of sheets  of various shape and size on the substrate - also demonstrating the scalability which the technique of liquid exfoliation provides. This also grants us  means to pick the sheets with desired thickness for future magnetotransport measurements. Many of the individual nano-sheets, such as shown in Figure~\ref{Figure3}(a), retain the shape of the bulk crystallites, used in the exfoliation.  This is evident from  AFM images shown in Figure~\ref{Figure3}(b)-(c), which show some neatly formed hexagonal sheets, and a rather distorted hexagon.  A fairly arbitrary shape sheet is shown in Figure~\ref{Figure3}(d) which bears striking  similarities in SEM images shown for arbitrary shaped sheets in Figure~\ref{Figure3}(c).

\begin{figure*}[!t]
\includegraphics[width=0.95\textwidth]{Figure4}
\caption{TEM, SAED and HRTEM characterization of the exfoliated SrRu${_2}$O${_6}$ flakes. (a) and (b) show an overview TEM image and corresponding SAED pattern of an exfoliated flake respectively. The diffraction pattern is indexed in agreement with [102] zone axis of SrRu${_2}$O${_6}$. (c) and (d) show a HRTEM image and corresponding  FFT of an area at the edge of a few-layer flake respectively. The hexagonal symmetry of the spots in the FFT, marked by circles, is indexed in agreement with [001] zone axis of SrRu${_2}$O${_6}$. (e) and (f)  show HRTEM image and corresponding FFT respectively of an area at the edge of another few-layer flake. In this FFT, multiple spots with 0.26 nm and 0.31 nm d-spacing are marked with outer and inner partial circle respectively. The spot corresponding to 0.30 nm d-spacing (bulk Ru-Ru spacing in [001] projection) is marked by an arrow.  The spots in FFT marked by numbered circles originate from four different regions at the edges of the flake in the corresponding HRTEM image, where (110) planes are rotated with respect to each other. The inner skewed hexagonal spots close to center of FFT, marked by white circle markers are indexed with [001] zone axis SAED of SrRu${_2}$O${_6}$ crystal structure. The (1-10) and (010) spots in the FFT are observed to deviate away from bulk crystal SAED pattern positions. This may be due to shrinking of the d-spacing of these planes in the real space after exfoliation.}
\label{Figure4}
\end{figure*}

From the AFM images presented in Figure~\ref{Figure3}(a), we estimated average thickness of sheets $\sim$ 1.31 nm ($\pm$ 0.12 nm), taking into account about 30  different sheets.  The  thickness of the hexagonal shaped sheets shown in Figure~\ref{Figure3}(b)-(c) is $\sim$ 1.5 nm, whereas it is $\sim$ 2.2 nm for the sheet shown in Figure 3d. Considering that the process of liquid exfoliation enables termination of sheets from Sr layer, the number of layers in perfectly stacked sheets can be gauged by looking into the lattice parameter $c$ = 0.523 nm, corresponding to bulk SrRu$_2$O$_6$.  This approach  suggests  three to five monolayers, considering a significant reduction in lattice parameter $c$ from  its bulk value. This is especially interesting, as  prior density functional theory (DFT) calculations have suggested that strain mediated topological properties could be observed in  samples with certain thickness.~\citep{Nan2}

We also observed that repeating the entire process of sonication and centrifugation (after leaving the dispersed nano-sheets for months in the vial) resulted in narrower distribution of thickness. The dispersed nano sheets in the solution, even after prolonged time-periods, retained the morphology, such as shown in  Figure~\ref{Figure2}. Furthermore,  repeated process of sonication and centriguation performed using  the solution preserved in the same vial led to the observation of relatively thinner sheets. In all these samples, many regions with partially stacked sheets, such as shown in Figure~\ref{Figure2}(b), could also be found.  Thus it is evident that the each step involved in the process of liquid exfoliation, including the time of sonication and centrifugation  can be further refined to obtain either monolayers or fully/partially stacked  stacked nano-sheets.

Exploring novel electronic states in van der Waals driven 2D materials, especially graphene  is an area of extensive research~\citep{Kim3,Kim4,Kim5}.  However, antiferromagnetic interactions in a system with magnetic honeycomb and large spin orbit coupling  is a testbed for exploring topological states. This is especially so in the case of SrRu${_2}$O${_6}$, where DFT predicts strain mediated topological state and band inversion when the crystallographic $c$ axis could be significantly tailored, leaving the $a$ and $b$ lattice parameters relatively unchanged \cite{Nan2}. It is evident here that the nano-sheets of SrRu$_2$O$_6$ produced using the technique of liquid exfoliation possibly provides a means to obtain ultra-thin 2D sheets, of various thickness and lateral lengths. From SEM and AFM images shown in Figure~\ref{Figure2} and Figure~\ref{Figure3}, it is evident that these 2D sheets can range from a few 100 nm to a few microns. Thus, depending on the size and the thickness of the nano-sheet, both $a$ as well as $c$ lattice parameters can be strained anisotropically. For instance, a monolayer  which extends to a few microns in length, the $c$  parameter is likely to be more strained than  $a$  lattice parameter.  Experimental realization  of such nano-sheets with varying thickness and lateral length  also enables a possibility in which a particular lattice parameter (perpendicular to the weakly bonded layers) can be tuned, without significantly disturbing the  (in-plane) lattice parameters.  Such  2D sheets of SrRu${_2}$O${_6}$ can provide an opportunity to  test the theoretical predictions, such as discussed in reference 32.

A representative overview TEM image of an individual flake is shown in Figure~\ref{Figure4}(a). It shows portion of a typical folded sheet of SrRu$_2$O$_6$, which is about 100 nm wide and a few 100 nm long. The corresponding SAED pattern obtained from this sheet, as shown in Figure~\ref{Figure4}(b), could be indexed in agreement with the [102] zone axis diffraction pattern of SrRu$_2$O$_6$. Figure~\ref{Figure4}(c) shows HRTEM image from an edge of the exfoliated nano-flake. In this image, atleast three different nano sheets edges can be seen. The FFT of this image in Figure~\ref{Figure4}(d) shows the spots in agreement with the
hexagonal spot pattern of [001] zone axis Selected Area Electron diffraction (SAED) pattern of SrRu$_2$O$_6$. The measured d-spacing from these spots, 0.26 nm, is in good agreement with the (110), (2-10) and (1-20) planes spacing of d= 0.2603 nm (from JCPDS card entry  04-021-3995 for SrRu$_2$O$_6$). This  observation  not only confirms that these crystalline  nano -sheets have retained the bulk phase but also suggests that the nano-sheets may have been exfoliated from planes perpendicular to the $c$-axis of this system.

Figure~\ref{Figure4}(e) shows HRTEM image from a region of another flake, where some regions with moire pattern like contrast are observed. The corresponding FFT, Figure~\ref{Figure4}(f), shows FFT multiple spots with 0.26 nm d-spacing (supplementary figure TEM-S2), i.e. (110) planes as marked with outer partial circle. The spots that lie on this ring, as marked by numbered circles, originate from four different regions at the edges of the flake in the corresponding HRTEM image where (110) planes are rotated with respect to each other. Presence of multiple spots along a ring with constant d-spacings is typical of SAED/FFT pattern from a polycrystalline sample with randomly oriented grains. However, this does not appear to be the case here and is reminiscent of prior observations in few layer 2D materials like graphene, where similar FFT patterns were observed due to rotational stacking faults.~\citep{Warner} To satisfy this condition each spot in the marked numbered circle should clearly show a set of corresponding hexagonal spots which are not clearly observed in Figure~\ref{Figure4}(f). Thus, we can speculate that the  pattern observed here may point towards the presence of stacked exfoliated sheets with different azimuthal rotation between them. However, it is worth noting that such a possibility of rotationally stacked nano-sheets is highly likely in this sample, as this tendency is also observed seen in SEM images, Figure~\ref{Figure2}(b).

In Figure~\ref{Figure4}(f), the spot corresponding to 0.30 nm d-spacing (bulk Ru-Ru spacing in [001] projection of SrRu$_2$O$_6$) is marked by an arrow, below which  the multiple spots with constant d-spacing are marked with inner partial circles. The average spacing of the spots on this ring is measured to be 0.31 nm (supplementary figure TEM-S3). This observation indicate slight in plane shrinking of Ru-Ru interatomic spacing in the exfoliated nanosheets. Finally, in Figure~\ref{Figure4}(f), the six spots close to the center of FFT (as marked by white circle markers) show a distorted hexagonal arrangement. They are indexed with [001] zone axis SAED of SrRu$_2$O$_6$ crystal structure. The (1-10) and (010) spots in the FFT are observed to deviate away from their expected positions in simulated [001] zone axis SAED pattern positions. The measured d-spacing of these planes show an average spacing of 0.365 nm as compared to the bulk value of 0.45 nm. This indicates shrinking of the d-spacing of these planes after exfoliation. Also the measured d-spacing of 100 planes in the FFT (0.43 nm) indicate slight decrease of the inter planar spacing between them (supplementary Figure S4). We believe that strain effects in lattice parameters upon exfoliating a non van der Waals but layered system such as SrRu$_2$O$_6$, are likely to be larger. TEM data presented here is indicative of large strain effects as observed in these nano sheets. We also recorded EDX in TEM on a number of  2D nano-sheets, a representative of which is shown as Figure S5 in the supplementary information.

\begin{figure}[!t]
\includegraphics[width=0.49\textwidth]{Figure5}
\caption {(a) Top and side views of the optimized lattice of 3L SrRu$_2$O$_6$ ultrathin film. The surface Sr-layer relaxes toward the RuO$_6$ octahedra, and the O-positions indicate distortion in the RuO$_6$ octahedra at the surface. (b) Band dispersion of the 3L SrRu$_2$O$_6$ in the G-type antiferromagnetic magnetic structure exhibit metallic character. The Fermi energy is set to $E=0$. The metallic solution remains invariant in the non-magnetic state, and also when the spin-orbit coupling is incorporated in the calculation. }
\label{Figure5}
\end{figure}

To gain further insights,  about the electronic structure, we characterize the SrRu$_2$O$_6$ nano-sheets within the first-principles density functional theory (DFT) calculations as implemented in the Vienna Ab Initio Simulation Package.~\cite{Kresse1, Kresse2} The wave function is described within the projector augmented wave formalism with 500 eV kinetic energy cut-off.~\cite{Blochl} The exchange-correlation is treated with the Perdew-Burke-Ernzerhof functional,~\cite{Perdew} and the spin-orbit coupling is treated self-consistently. A large vacuum of 17 \AA\ is maintained perpendicular to the surface of the few-layer SrRu$_2$O$_6$ nano-sheet to minimize the spurious interaction between the periodic images. The structure is completely relaxed until the forces reduce below $\pm$0.01 eV/\AA\ threshold. The Brillouin zone is sampled using a 9$\times$9$\times$9 and 9$\times$9$\times$1  $k$-mesh for the bulk and few-layered samples, respectively.

Before we discuss the structural, electronic and magnetic properties of the ultrathin SrRu$_2$O$_6$ nano-sheet, we revisit the intriguing bulk phase within the same theoretical hierarchy. The calculated lattice parameters ($a$ = 5.29 and $c$ = 5.26 \AA) are in good agreement with the experimental values calculated from the neutron diffraction data~\cite{Hiley1}. The Ru$^{5+}$-ions in the hexagonal $P\bar{3}1m$ lattice of  SrRu$_2$O$_6$ are octahedrally coordinated with the oxygen ions, which supports the half-filled $t_{2g}$-manifold with 3 $\mu_B$ expected moment. However, due to the strong hybridization between Ru-$t_{2g}$ and O-2$p$ orbitals, the Ru-moment is substantially reduced to 1.38 $\mu_B$, in agreement with prior experimental and theoretical results.~\cite{Tian, Hiley2, Suzuki1, David, Streltsov, Hariki, Nan3} The two-dimensional Ru-spins exhibit G-type antiferromagnetic with semiconducting electronic structure. The corresponding non-magnetic solution indicates a small bandgap of 68 meV in the present calculation, while the gap increases with the Ru-moment~\cite{Streltsov}. We find the G-type antiferromagnetic SrRu$_2$O$_6$ to have a higher 0.44 eV gap, and the inclusion of spin-orbit coupling does not further influence the gap (0.41 eV).

The structure of the Sr-terminated 3L SrRu$_2$O$_6$ sheet is fully relaxed [Figure~\ref{Figure5}(a)],  and the in-plane lattice parameter $a$ is slightly stretched (5.38 \AA), in comparison to the corresponding bulk value. In contrast, the perpendicular lattice parameter $c$ is critically contracted in 3L SrRu$_2$O$_6$ (4.27 \AA~ compared to 5.26 \AA ~in bulk) due to the relaxation of surface Sr-layer toward the RuO-octahedra, which is in remarkable agreement with the experimental observations, particularly  the AFM  and TEM measurements presented in Figure~\ref{Figure3}, Figure~\ref{Figure4} and supplementary Figure S3. These data bring out significant strain effects in the interlayer spacing,  which leads to associated compression or expansion in the lattice parameters of SrRu$_2$O$_6$ nano-sheets.

Similar to the bulk, the ultra-thin SrRu$_2$O$_6$ sheet exhibits G-type antiferromagnetic ordering, which is 30 meV/Ru lower in energy compared to the corresponding ferromagnetic state. The individual Ru-moments decreases to 1.32 $\mu_B$ at the middle RuO-layer, which further reduces at the surface due to RuO$_6$ distortion. Surprisingly, an insulator to metal transition is observed while the thickness is reduced to few-layer [Figure~\ref{Figure5}(b)]. The 3L SrRu$_2$O$_6$ sheet is found to be metallic, which is mostly contributed by the $p-d$ hybridization at the distorted surface RuO$_6$ octahedra. The predicted (antiferro) magnetism in the ultrathin SrRu$_2$O$_6$ nano-sheets will have implications in the search for magnetism in the two-dimension, that is typically observed in the van der Waals systems.~\citep{nanolett.6b03052,Gong,Huang,Gibertini2019,Gongeaav4450}

\section{Conclusions}
In conclusion, we demonstrate a new platform to realize two-dimensional magnetism in non-van der Waals and magnetically layered 4$d$ oxide with strong electron correlation and competing spin-orbit coupling. We exfoliate the ultra-thin nano-sheets of SrRu$_2$O$_6$ using the scalable technique of liquid exfoliation.  While the method of liquid exfoliation was primarily meant for van der Waals materials like graphene, we show that the same technique can be successfully employed to obtain nano-sheets of inherently layered magnetic oxides such as SrRu$_2$O$_6$, with anisotropic in-plane and out-of-plane bond strengths. These nano-sheets could be obtained and preserved using ethanol as a medium. This enables one to easily drop-cast them on a suitable substrate for characterization as well as on patterned substrates for magneto-transport measurements. Scanning and Transmission electron microscopy, as well as Atomic force microscopy, have been used to characterize these nano-sheets. Within the complementary first-principles calculations, we show that antiferromagnetism survives in these ultra-thin nano-sheets. Experimental realization of  two-dimensional sheets of SrRu$_2$O$_6$  which has a graphene-like  magnetic honeycomb,  along with competing electronic correlations and spin-orbit coupling offers tremendous potential to investigate emergent phenomena in this particular type of two-dimensional magnets. The present study will incite further attention in this regard.

\section{Acknowledgments}
Authors acknowledge Prof. A.K.Nigam for useful discussions,  Mr. Rudheer Bapat and Mr. J. Parmar  for TEM measurements and Mr. A. Shetty for SEM measurements. A.B. acknowledges Department of Science and Technology (DST), India for funding support through a Ramanujan Grant. A.B., S.N., M.K., and S.P. acknowledge DST Nanomission Thematic Unit Program for financial support. R.K., S.N. and A.B. acknowledge funding support through Joint DST-DFG projects INT/FRG/DFG/P-06/2017 and KL1824/11-1. M.K. acknowledges funding from the Science and Engineering Research Board through EMR/2016/006458 grant.

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