Is there a better way to initalize pointers in c++?

Below I have a bit of code for implementing Huffman compression. What I was curious about was if I could initialize the left and right pointers without including cstdlib, or rather, if I could initialize an empty memory location for storing the left and right without using malloc.

Also, in my combine function, I do not want to use "NULL" for the string parent node of my left and right, but would rather have an empty string. Will I have to make a new constructor for this? I get an error (basic_string::_M_construct null not valid) when I replace "NULL" with nullptr.

#include <string>
#include <cstdlib>

#ifndef PRIORITY_NODE
#define PRIORITY_NODE

namespace Huffman
{
  class PriorityNode
  {
    private:
      std::string key; // The character sequence to compress
      long frequency = 0;  // The frequency of the character sequence
      PriorityNode* left = (PriorityNode*)malloc(sizeof(PriorityNode));
      PriorityNode* right = (PriorityNode*)malloc(sizeof(PriorityNode));
    
    public:
      PriorityNode(std::string k, long f): frequency(f), key(k){};
      std::string getKey() const{ return key;}
      long getFrequency() const{ return frequency;}
      void setLeft(const PriorityNode& left){*this->left = left;}
      void setRight(const PriorityNode& right){*this->right = right;}
      PriorityNode& getLeft() const{ return *left;}
      PriorityNode& getRight() const{ return *right;}
      friend PriorityNode combine(const PriorityNode& lhs, const PriorityNode& rhs)
      {
        long ret_freq = lhs.getFrequency() + rhs.getFrequency();
        PriorityNode ret = PriorityNode("NULL", ret_freq);
        ret.setLeft(lhs);
        ret.setRight(rhs);
        return ret;
      };
  };
}

#endif